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2145163 | 10.1007/s00021-011-0075-9 | We study the global existence of solutions to a two-component generalized
Hunter-Saxton system in the periodic setting. We first prove a persistence
result of the solutions. Then for some particular choices of parameters
$(\alpha, \kappa)$, we show the precise blow-up scenarios and the existence of
global solutions to the generalized Hunter-Saxton system under proper
assumptions on the initial data. This significantly improves recent results
obtained in [M. Wunsch, DCDS Ser. B 12 (2009), 647-656] and [M. Wunsch, SIAM J.
Math. Anal. 42 (2010), 1286-1304].Comment: 22 pages; submitted in modified form on August 7, 201 | Global existence for the generalized two-component Hunter-Saxton system | global existence for the generalized two-component hunter-saxton system | hunter saxton setting. persistence solutions. choices alpha kappa precise blow scenarios hunter saxton proper assumptions data. improves wunsch dcds ser. wunsch siam math. anal. .comment pages submitted august | non_dup | [] |
2256998 | 10.1007/s00021-012-0102-5 | In order to obtain quite precise information about the shape of the particle
paths below small-amplitude gravity waves travelling on irrotational deep
water, analytic solutions of the nonlinear differential equation system
describing the particle motion are provided. All these solutions are not closed
curves. Some particle trajectories are peakon-like, others can be expressed
with the aid of the Jacobi elliptic functions or with the aid of the
hyperelliptic functions. Remarks on the stagnation points of the
small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with
arXiv:1106.382 | On the particle paths and the stagnation points in small-amplitude
deep-water waves | on the particle paths and the stagnation points in small-amplitude deep-water waves | precise paths travelling irrotational analytic describing provided. curves. trajectories peakon jacobi elliptic hyperelliptic functions. remarks stagnation irrotational math. mech. admin overlap | non_dup | [] |
24765735 | 10.1007/s00021-012-0115-0 | For inviscid fluid flow in any n-dimensional Riemannian manifold, new
conserved vorticity integrals generalizing helicity, enstrophy, and entropy
circulation are derived for lower-dimensional surfaces that move along fluid
streamlines. Conditions are determined for which the integrals yield constants
of motion for the fluid. In the case when an inviscid fluid is isentropic,
these new constants of motion generalize Kelvin's circulation theorem from
closed loops to closed surfaces of any dimension.Comment: 14 pages; typos correcte | New conserved vorticity integrals for moving surfaces in
multi-dimensional fluid flow | new conserved vorticity integrals for moving surfaces in multi-dimensional fluid flow | inviscid riemannian manifold conserved vorticity integrals generalizing helicity enstrophy circulation move streamlines. integrals fluid. inviscid isentropic generalize kelvin circulation loops pages typos correcte | non_dup | [] |
5237496 | 10.1007/s00021-013-0145-2 | In this paper we investigate the issue of the inviscid limit for the
compressible Navier-Stokes system in an impermeable fixed bounded domain. We
consider two kinds of boundary conditions. The first one is the no-slip
condition. In this case we extend the famous conditional result obtained by
Kato in the homogeneous incompressible case. Kato proved that if the energy
dissipation rate of the viscous flow in a boundary layer of width proportional
to the viscosity vanishes then the solutions of the incompressible
Navier-Stokes equations converge to some solutions of the incompressible Euler
equations in the energy space. We provide here a natural extension of this
result to the compressible case. The other case is the Navier condition which
encodes that the fluid slips with some friction on the boundary. In this case
we show that the convergence to the Euler equations holds true in the energy
space, as least when the friction is not too large. In both cases we use in a
crucial way some relative energy estimates proved recently by Feireisl, Ja Jin
and Novotn{\'y} | On the inviscid limit for the compressible Navier-Stokes system in an
impermeable bounded domain | on the inviscid limit for the compressible navier-stokes system in an impermeable bounded domain | inviscid compressible navier stokes impermeable domain. kinds conditions. slip condition. extend famous conditional kato homogeneous incompressible case. kato proved dissipation viscous viscosity vanishes incompressible navier stokes converge incompressible euler space. compressible case. navier encodes slips friction boundary. euler friction large. crucial proved feireisl novotn | non_dup | [] |
25010138 | 10.1007/s00021-013-0152-3 | This paper is to study global-in-time existence of weak solutions to zero
Mach number system which derives from the full Navier-Stokes system, under a
special relationship between the viscosity coefficient and the heat
conductivity coefficient such that, roughly speaking, the source term in the
equation for the newly introduced divergence-free velocity vector field
vanishes. In dimension two, thanks to a local-in-time existence result of a
unique strong solution in critical Besov spaces given in \cite{Danchin-Liao},
for arbitrary large initial data, we will show that this unique strong solution
exists globally in time, by a weak-strong uniqueness argument | A global existence result for a zero Mach number system | a global existence result for a zero mach number system | mach derives navier stokes viscosity conductivity roughly speaking newly divergence vanishes. thanks besov cite danchin liao globally uniqueness argument | non_dup | [] |
24938985 | 10.1007/s00021-013-0158-x | We investigate the influence of the topography on the lake equations which
describe the two-dimensional horizontal velocity of a three-dimensional
incompressible flow. We show that the lake equations are structurally stable
under Hausdorff approximations of the fluid domain and $L^p$ perturbations of
the depth. As a byproduct, we obtain the existence of a weak solution to the
lake equations in the case of singular domains and rough bottoms. Our result
thus extends earlier works by Bresch and M\'etivier treating the lake equations
with a fixed topography and by G\'erard-Varet and Lacave treating the Euler
equations in singular domains | Topography influence on the Lake equations in bounded domains | topography influence on the lake equations in bounded domains | topography lake incompressible flow. lake structurally hausdorff approximations perturbations depth. byproduct lake singular rough bottoms. extends bresch etivier treating lake topography erard varet lacave treating euler singular | non_dup | [] |
80910310 | 10.1007/s00021-013-0159-9 | We consider the boundary-value problem for the steady isothermal flow of an incompressible viscoelastic liquid of
Oldroyd type in a bounded domain with a Navier type slip boundary condition. We prove that under some restrictions on
the material constants and the data, there exists a strong solution which is locally unique. The proof is based on a fixed
point argument in which the boundary-value problem is decomposed into a transport equation and a Stokes system.http://link.springer.com/journal/21hb201 | On flows of viscoelastic fluids of oldroyd type with wall slip | on flows of viscoelastic fluids of oldroyd type with wall slip | steady isothermal incompressible viscoelastic oldroyd navier slip condition. restrictions locally unique. argument decomposed stokes system. | non_dup | [] |
24961257 | 10.1007/s00021-014-0163-8 | We discuss the problem of well-posedness of the compressible (barotropic)
Euler system in the framework of weak solutions. The principle of maximal
dissipation introduced by C.M. Dafermos is adapted and combined with the
concept of admissible weak solutions. We use the method of convex integration
in the spirit of the recent work of C.DeLellis and L.Szekelyhidi to show
various counterexamples to well-posedness. On the other hand, we conjecture
that the principle of maximal dissipation should be retained as a possible
criterion of uniqueness as it is violated by the oscillatory solutions obtained
in the process of convex integration | Maximal dissipation and well-posedness for the compressible Euler system | maximal dissipation and well-posedness for the compressible euler system | posedness compressible barotropic euler solutions. maximal dissipation c.m. dafermos adapted admissible solutions. convex spirit lellis l.szekelyhidi counterexamples posedness. conjecture maximal dissipation retained criterion uniqueness violated oscillatory convex | non_dup | [] |
24998933 | 10.1007/s00021-014-0166-5 | We give an example of a well posed, finite energy, 2D incompressible active
scalar equation with the same scaling as the surface quasi-geostrophic equation
and prove that it can produce finite time singularities. In spite of its
simplicity, this seems to be the first such example. Further, we construct
explicit solutions of the 2D Boussinesq equations whose gradients grow
exponentially in time for all time. In addition, we introduce a variant of the
2D Boussinesq equations which is perhaps a more faithful companion of the 3D
axisymmetric Euler equations than the usual 2D Boussinesq equations.Comment: 9 pages; simplified a solution formula in section 4 and added a
sentence on the time growth rate in the solutio | An incompressible 2D didactic model with singularity and explicit
solutions of the 2D Boussinesq equations | an incompressible 2d didactic model with singularity and explicit solutions of the 2d boussinesq equations | posed incompressible quasi geostrophic singularities. spite simplicity example. boussinesq gradients grow exponentially time. variant boussinesq perhaps faithful companion axisymmetric euler usual boussinesq pages simplified sentence solutio | non_dup | [] |
24957897 | 10.1007/s00021-014-0169-2 | Time-periodic solutions to the linearized Navier-Stokes system in the
$n$-dimensional whole-space are investigated. For time-periodic data in
$L^q$-spaces, maximal regularity and corresponding a priori estimates for the
associated time-periodic solutions are established. More specifically, a Banach
space of time-periodic vector fields is identified with the property that the
linearized Navier-Stokes operator maps this space homeomorphically onto the
$L^q$-space of time-periodic data.Comment: 19 page | Maximal regularity of the time-periodic Navier-Stokes system | maximal regularity of the time-periodic navier-stokes system | linearized navier stokes investigated. maximal regularity priori established. banach linearized navier stokes homeomorphically | non_dup | [] |
25007006 | 10.1007/s00021-014-0187-0 | A linear stochastic vector advection equation is considered; the equation may
model a passive magnetic field in a random fluid. When the driving velocity
field is rough but deterministic, in particular just H\"{o}lder continuous and
bounded, one can construct examples of infinite stretching of the passive
field, arising from smooth initial conditions. The purpose of the paper is to
prove that infinite stretching is prevented if the driving velocity field
contains in addition a white noise component.Comment: 23 pages, 4 figure | Noise prevents infinite stretching of the passive field in a stochastic
vector advection equation | noise prevents infinite stretching of the passive field in a stochastic vector advection equation | stochastic advection passive fluid. driving rough deterministic lder infinite stretching passive arising conditions. infinite stretching prevented driving pages | non_dup | [] |
25050886 | 10.1007/s00021-015-0201-1 | We investigate the long-term behavior, as a certain regularization parameter
vanishes, of the three-dimensional Navier-Stokes-Voigt model of a viscoelastic
incompressible fluid. We prove the existence of global and exponential
attractors of optimal regularity. We then derive explicit upper bounds for the
dimension of these attractors in terms of the three-dimensional Grashof number
and the regularization parameter. Finally, we also prove convergence of the
(strong) global attractor of the 3D Navier-Stokes-Voigt model to the (weak)
global attractor of the 3D Navier-Stokes equation. Our analysis improves and
extends recent results obtained by Kalantarov and Titi in [31].Comment: v2: the statement and proof of Theorem 5.2 have changed. In the
previous version, the proof was based on Theorem 4.9 in a book of
Ladyzhenskaya, which turns out to be based on a faulty assumption. See Remark
5.5 for detail | Singular limits of Voigt models in fluid dynamics | singular limits of voigt models in fluid dynamics | regularization vanishes navier stokes voigt viscoelastic incompressible fluid. exponential attractors regularity. derive bounds attractors grashof regularization parameter. attractor navier stokes voigt attractor navier stokes equation. improves extends kalantarov titi .comment statement changed. book ladyzhenskaya turns faulty assumption. remark | non_dup | [] |
24985820 | 10.1007/s00021-015-0203-z | We consider the equations of motion for an incompressible Non-Newtonian fluid
in a bounded Lipschitz domain $G\subset\mathbb R^d$ during the time intervall
$(0,T)$ together with a stochastic perturbation driven by a Brownian motion
$W$. The balance of momentum reads as $$dv=\mathrm{div}\, S\,dt-(\nabla
v)v\,dt+\nabla\pi \,dt+f\,dt+\Phi(v)\,dW_t,$$ where $v$ is the velocity, $\pi$
the pressure and $f$ an external volume force. We assume the common power law
model $S(\varepsilon(v))=\big(1+|\varepsilon(v)|\big)^{p-2} \varepsilon(v)$ and
show the existence of weak (martingale) solutions provided
$p>\tfrac{2d+2}{d+2}$. Our approach is based on the $L^\infty$-truncation and a
harmonic pressure decomposition which are adapted to the stochastic setting | Existence theory for stochastic power law fluids | existence theory for stochastic power law fluids | incompressible newtonian lipschitz mathbb intervall stochastic perturbation brownian balance reads mathrm nabla nabla force. varepsilon varepsilon varepsilon martingale tfrac infty truncation harmonic decomposition adapted stochastic | non_dup | [] |
29499669 | 10.1007/s00021-015-0213-x | We study the Euler equations with the so-called Ekman damping in the whole 2D
space. The global well-posedness and dissipativity for the weak infinite energy
solutions of this problem in the uniformly local spaces is verified based on
the further development of the weighted energy theory for the Navier-Stokes and
Euler type problems. In addition, the existence of weak locally compact global
attractor is proved and some extra compactness of this attractor is obtained.Comment: arXiv admin note: text overlap with arXiv:1203.573 | Infinite energy solutions for Dissipative Euler equations in R^2 | infinite energy solutions for dissipative euler equations in r^2 | euler ekman damping space. posedness dissipativity infinite uniformly verified weighted navier stokes euler problems. locally attractor proved extra compactness attractor admin overlap | non_dup | [] |
25013184 | 10.1007/s00021-015-0214-9 | As in our previous paper, the 3D Navier-Stokes equations with a
translationally bounded force contain pullback attractors in a weak sense.
Moreover, those attractors consist of complete bounded trajectories. In this
paper, we present a sufficient condition under which the pullback attractors
are degenerate. That is, if the Grashof constant is small enough, the pullback
attractor will be a single point on a unique, complete, bounded, strong
solution. We then apply our results to provide a new proof of the existence of
a unique, strong, periodic solution to the 3D Navier-Stokes with a small,
periodic forcing term | Degenerate pullback attractors for the 3D Navier-Stokes equations | degenerate pullback attractors for the 3d navier-stokes equations | navier stokes translationally pullback attractors sense. attractors consist trajectories. pullback attractors degenerate. grashof pullback attractor solution. navier stokes forcing | non_dup | [] |
77019802 | 10.1007/s00021-015-0218-5 | The purpose of this work is to analyze the mathematical model governing motion of n-component, heat conducting reactive mixture of compressible gases. We prove sequential stability of weak variational entropy solutions when the state equation essentially depends on the species concentration and the species diffusion fluxes depend on gradients of partial pressures. Of crucial importance for our analysis is the fact that viscosity coefficients vanish on vacuum and the source terms enjoy the admissibility condition dictated by the second law of thermodynamics | Mixtures: Sequential Stability of Variational Entropy Solutions | mixtures: sequential stability of variational entropy solutions | analyze mathematical governing conducting reactive mixture compressible gases. sequential variational essentially fluxes gradients pressures. crucial viscosity vanish enjoy admissibility dictated thermodynamics | non_dup | [] |
29531053 | 10.1007/s00021-015-0221-x | We investigate the stabilizing effects of the magnetic fields in the
linearized magnetic Rayleigh-Taylor (RT) problem of a nonhomogeneous
incompressible viscous magnetohydrodynamic fluid of zero resistivity in the
presence of a uniform gravitational field in a three-dimensional bounded
domain, in which the velocity of the fluid is non-slip on the boundary. By
adapting a modified variational method and careful deriving \emph{a priori}
estimates, we establish a criterion for the instability/stability of the
linearized problem around a magnetic RT equilibrium state. In the criterion, we
find a new phenomenon that a sufficiently strong horizontal magnetic field has
the same stabilizing effect as that of the vertical magnetic field on growth of
the magnetic RT instability. In addition, we further study the corresponding
compressible case, i.e., the Parker (or magnetic buoyancy) problem, for which
the strength of a horizontal magnetic field decreases with height, and also
show the stabilizing effect of a sufficiently large magnetic field.Comment: 33 page | On Linear Instability and Stability of the Rayleigh-Taylor Problem in
Magnetohydrodynamics | on linear instability and stability of the rayleigh-taylor problem in magnetohydrodynamics | stabilizing linearized rayleigh taylor nonhomogeneous incompressible viscous magnetohydrodynamic resistivity gravitational slip boundary. adapting variational careful deriving emph priori establish criterion instability linearized state. criterion phenomenon sufficiently stabilizing instability. compressible i.e. parker buoyancy stabilizing sufficiently | non_dup | [] |
25015624 | 10.1007/s00021-015-0222-9 | The Hall-magnetohydrodynamics (Hall-MHD) equations, rigorously derived from
kinetic models, are useful in describing many physical phenomena in geophysics
and astrophysics. This paper studies the local well-posedness of classical
solutions to the Hall-MHD equations with the magnetic diffusion given by a
fractional Laplacian operator, $(-\Delta)^\alpha$. Due to the presence of the
Hall term in the Hall-MHD equations, standard energy estimates appear to
indicate that we need $\alpha\ge 1$ in order to obtain the local
well-posedness. This paper breaks the barrier and shows that the fractional
Hall-MHD equations are locally well-posed for any $\alpha>\frac12$. The
approach here fully exploits the smoothing effects of the dissipation and
establishes the local bounds for the Sobolev norms through the Besov space
techniques. The method presented here may be applicable to similar situations
involving other partial differential equations.Comment: 13 pages, this version improves the previous on | Local well-posedness for the Hall-MHD equations with fractional magnetic
diffusion | local well-posedness for the hall-mhd equations with fractional magnetic diffusion | hall magnetohydrodynamics hall rigorously describing phenomena geophysics astrophysics. posedness hall fractional laplacian delta alpha hall hall alpha posedness. breaks barrier fractional hall locally posed alpha frac exploits smoothing dissipation establishes bounds sobolev norms besov techniques. applicable situations involving pages improves | non_dup | [] |
29530119 | 10.1007/s00021-015-0225-6 | We introduce a continuous data assimilation (downscaling) algorithm for the
two-dimensional Navier-Stokes equations employing coarse mesh measurements of
only one component of the velocity field. This algorithm can be implemented
with a variety of finitely many observables: low Fourier modes, nodal values,
finite volume averages, or finite elements. We provide conditions on the
spatial resolution of the observed data, under the assumption that the observed
data is free of noise, which are sufficient to show that the solution of the
algorithm approaches, at an exponential rate asymptotically in time, to the
unique exact unknown reference solution, of the 2D Navier-Stokes equations,
associated with the observed (finite dimensional projection of) velocity | Abridged continuous data assimilation for the 2D Navier-Stokes equations
utilizing measurements of only one component of the velocity field | abridged continuous data assimilation for the 2d navier-stokes equations utilizing measurements of only one component of the velocity field | assimilation downscaling navier stokes employing coarse mesh field. implemented finitely observables fourier nodal averages elements. exponential asymptotically unknown navier stokes projection | non_dup | [] |
29541150 | 10.1007/s00021-015-0245-2 | As a continuation of the previous work [40], in this paper we focus on the
Cauchy problem of the two-dimensional (2D) incompressible Boussinesq equations
with fractional Laplacian dissipation. We give an elementary proof of the
global regularity of the smooth solutions of the 2D Boussinesq equations with a
new range of fractional powers of the Laplacian. The argument is based on the
nonlinear lower bounds for the fractional Laplacian established in [12].
Consequently, this result significantly improves the recent works [12, 38, 40].Comment: This version fix several typos of the previous one. 25 page | Global well-posedness of the 2D Boussinesq equations with fractional
Laplacian dissipation | global well-posedness of the 2d boussinesq equations with fractional laplacian dissipation | continuation cauchy incompressible boussinesq fractional laplacian dissipation. elementary regularity boussinesq fractional powers laplacian. argument bounds fractional laplacian improves .comment typos one. | non_dup | [] |
29565710 | 10.1007/s00021-016-0249-6 | In this paper we investigate the qualitative behaviour of the pressure
function beneath an extreme Stokes wave over infinite depth. The presence of a
stagnation point at the wave-crest of an extreme Stokes wave introduces a
number of mathematical difficulties resulting in the irregularity of the free
surface profile. It will be proven that the pressure decreases in the
horizontal direction between a crest-line and subsequent trough-line, except
along these lines themselves where the pressure is stationary with respect to
the horizontal coordinate. In addition we will prove that the pressure strictly
increases with depth throughout the fluid body.Comment: 12 pages, 2 figures. To appear in Journal of Mathematical Fluid
Mechanic | The pressure in a deep-water Stokes wave of greatest height | the pressure in a deep-water stokes wave of greatest height | qualitative beneath extreme stokes infinite depth. stagnation crest extreme stokes introduces mathematical difficulties irregularity profile. proven crest trough stationary coordinate. strictly pages figures. mathematical mechanic | non_dup | [] |
80912935 | 10.1007/s00021-016-0254-9 | This work is concerned with the time discrete analysis of the Oseen system of equations driven by nonlinear slip
boundary conditions of friction type. We study the existence of solutions of the time discrete model and derive several a priori
estimates needed to recover the solution of the continuous problem by means of weak compactness. Moreover, for the
difference between the exact and approximate solutions, we obtainhttp://link.springer.com/journal/212017-12-31hb2016Mathematics and Applied Mathematic | Analysis of a time implicit scheme for the Oseen model driven by nonlinear slip boundary conditions | analysis of a time implicit scheme for the oseen model driven by nonlinear slip boundary conditions | concerned oseen slip friction type. derive priori recover compactness. approximate obtainhttp mathematics mathematic | non_dup | [] |
29527044 | 10.1007/s00021-016-0256-7 | In the present paper we study a singular perturbation problem for a
Navier-Stokes-Korteweg model with Coriolis force. Namely, we perform the
incompressible and fast rotation asymptotics simultaneously, while we keep the
capillarity coefficient constant in order to capture surface tension effects in
the limit. We consider here the case of variable rotation axis: we prove the
convergence to a linear parabolic-type equation with variable coefficients. The
proof of the result relies on compensated compactness arguments. Besides, we
look for minimal regularity assumptions on the variations of the axis.Comment: Section 5 of the previous version was remove | A singular limit problem for rotating capillary fluids with variable
rotation axis | a singular limit problem for rotating capillary fluids with variable rotation axis | singular perturbation navier stokes korteweg coriolis force. incompressible asymptotics simultaneously keep capillarity capture tension limit. parabolic coefficients. relies compensated compactness arguments. besides look regularity assumptions remove | non_dup | [] |
42655925 | 10.1007/s00021-016-0265-6 | We make a consistent derivation, from the governing equations, of the
pressure transfer function in the small-amplitude Stokes wave regime and the
hydrostatic approximation in the small-amplitude solitary water wave regime, in
the presence of a background shear flow. The results agree with the well-known
formulae in the zero vorticity case,but they incorporate the effects of
vorticity through solutions to the Rayleigh equation. We extend the results to
permit continuous density stratification and to internal waves between two
constant-density fluids. Several examples are discussed.Comment: 20 page | Pressure transfer functions for interfacial fluid problems | pressure transfer functions for interfacial fluid problems | derivation governing stokes hydrostatic solitary flow. agree formulae vorticity incorporate vorticity rayleigh equation. extend permit stratification fluids. | non_dup | [] |
29555463 | 10.1007/s00021-016-0268-3 | Because pressure is determined globally for the incompressible Euler
equations, a localized change to the initial velocity will have an immediate
effect throughout space. For solutions to be physically meaningful, one would
expect such effects to decrease with distance from the localized change, giving
the solutions a type of stability. Indeed, this is the case for solutions
having spatial decay, as can be easily shown. We consider the more difficult
case of solutions lacking spatial decay, and show that such stability still
holds, albeit in a somewhat weaker form.Comment: Revised statement of Theorem 1 to include a missing definitio | Incompressible Euler Equations and the Effect of Changes at a Distance | incompressible euler equations and the effect of changes at a distance | globally incompressible euler localized immediate space. physically meaningful localized giving stability. shown. lacking albeit somewhat weaker revised statement missing definitio | non_dup | [] |
25014055 | 10.1007/s00021-016-0271-8 | In 2000 Constantin showed that the incompressible Euler equations can be
written in an "Eulerian-Lagrangian" form which involves the back-to-labels map
(the inverse of the trajectory map for each fixed time). In the same paper a
local existence result is proved in certain H\"older spaces $C^{1,\mu}$.
We review the Eulerian-Lagrangian formulation of the equations and prove that
given initial data in $H^s$ for $n\geq2$ and $s>\frac{n}{2}+1$, a unique
local-in-time solution exists on the $n$-torus that is continuous into $H^s$
and $C^1$ into $H^{s-1}$. These solutions automatically have $C^1$
trajectories.
The proof here is direct and does not appeal to results already known about
the classical formulation. Moreover, these solutions are regular enough that
the classical and Eulerian-Lagrangian formulations are equivalent, therefore
what we present amounts to an alternative approach to some of the standard
theory.Comment: 17 pages, to appear in J. Math. Fluid Mech. Lemmas 4 and 6 revised,
several minor change | An Eulerian-Lagrangian Form for the Euler Equations in Sobolev Spaces | an eulerian-lagrangian form for the euler equations in sobolev spaces | constantin incompressible euler eulerian lagrangian involves labels trajectory proved older eulerian lagrangian formulation frac torus automatically trajectories. appeal formulation. eulerian lagrangian formulations amounts pages math. mech. lemmas revised minor | non_dup | [] |
29565067 | 10.1007/s00021-016-0277-2 | New results are obtained for global regularity and long-time behavior of the
solutions to the 2D Boussinesq equations for the flow of an incompressible
fluid with positive viscosity and zero diffusivity in a smooth bounded domain.
Our first result for global boundedness of the solution $(u, \theta) \in
D(A)\times H^1$ improves considerably the main result of the recent article
[7]. Our second result on global regularity of the solution $(u, \theta) \in V
\times H^1$ for both bounded domain and the whole space ${\mathbb R}^2$ is a
new one. It has been open and also seems much more challenging than the first
result. Global regularity of the solution $(u, \theta) \in D(A) \times H^2$ is
also proved | Global Regularity and Long-time Behavior of the Solutions to the 2D
Boussinesq Equations without Diffusivity in a Bounded Domain | global regularity and long-time behavior of the solutions to the 2d boussinesq equations without diffusivity in a bounded domain | regularity boussinesq incompressible viscosity diffusivity domain. boundedness theta improves considerably regularity theta mathbb one. challenging result. regularity theta proved | non_dup | [] |
73418350 | 10.1007/s00021-016-0283-4 | A two-dimensional water wave system is examined consisting of two discrete
incompressible fluid domains separated by a free common interface. In a
geophysical context this is a model of an internal wave, formed at a pycnocline
or thermocline in the ocean. The system is considered as being bounded at the
bottom and top by a flatbed and wave-free surface respectively. A current
profile with depth-dependent currents in each domain is considered. The
Hamiltonian of the system is determined and expressed in terms of canonical
wave-related variables. Limiting behaviour is examined and compared to that of
other known models. The linearised equations as well as long-wave
approximations are presented.Comment: LaTeX, 21 pages, 1 figure, available online in J. Math. Fluid Mech.
(2016 | The Dynamics of Flat Surface Internal Geophysical Waves with Currents | the dynamics of flat surface internal geophysical waves with currents | consisting incompressible separated interface. geophysical pycnocline thermocline ocean. flatbed respectively. currents considered. canonical variables. limiting models. linearised approximations latex pages math. mech. | non_dup | [] |
73351970 | 10.1007/s00021-016-0301-6 | It is well known that the full Navier-Stokes-Fourier system does not possess
a strong solution in three dimensions which causes problems in applications.
However, when modeling the flow of a fluid in a thin long pipe, the influence
of the cross section can be neglected and the flow is basically
one-dimensional. This allows us to deal with strong solutions which are more
convenient for numerical computations. The goal of this paper is to provide a
rigorous justification of this approach. Namely, we prove that any suitable
weak solution to the three-dimensional NSF system tends to a strong solution to
the one-dimensional system as the thickness of the pipe tends to zero.Comment: arXiv admin note: text overlap with arXiv:1111.4256 by other author | Dimension reduction for the full Navier-Stokes-Fourier system | dimension reduction for the full navier-stokes-fourier system | navier stokes fourier possess applications. pipe neglected basically dimensional. deal convenient computations. goal rigorous justification approach. tends pipe tends admin overlap | non_dup | [] |
73401751 | 10.1007/s00021-017-0315-8 | The main subject of this paper concerns the establishment of certain classes
of initial data, which grant short time uniqueness of the associated weak
Leray-Hopf solutions of the three dimensional Navier-Stokes equations. In
particular, our main theorem that this holds for any solenodial initial data,
with finite $L_2(\mathbb{R}^3)$ norm, that also belongs to to certain subsets
of $VMO^{-1}(\mathbb{R}^3)$. As a corollary of this, we obtain the same
conclusion for any solenodial $u_{0}$ belonging to $L_{2}(\mathbb{R}^3)\cap
\mathbb{\dot{B}}^{-1+\frac{3}{p}}_{p,\infty}(\mathbb{R}^3)$, for any
$3<p<\infty$. Here,
$\mathbb{\dot{B}}^{-1+\frac{3}{p}}_{p,\infty}(\mathbb{R}^3)$ denotes the
closure of test functions in the critical Besov space
${\dot{B}}^{-1+\frac{3}{p}}_{p,\infty}(\mathbb{R}^3)$. Our results rely on the
establishment of certain continuity properties near the initial time, for weak
Leray-Hopf solutions of the Navier-Stokes equations, with these classes of
initial data. Such properties seem to be of independent interest. Consequently,
we are also able to show if a weak Leray-Hopf solution $u$ satisfies certain
extensions of the Prodi-Serrin condition on $\mathbb{R}^3 \times ]0,T[$, then
it is unique on $\mathbb{R}^3 \times ]0,T[$ amongst all other weak Leray-Hopf
solutions with the same initial value. In particular, we show this is the case
if $u\in L^{q,s}(0,T; L^{p,s}(\mathbb{R}^3))$ or if it's $L^{q,\infty}(0,T;
L^{p,\infty}(\mathbb{R}^3))$ norm is sufficiently small, where $3<p< \infty$,
$1\leq s<\infty$ and $3/p+2/q=1$.Comment: 44 pages. Submitted. Corollary 1.4, Proposition 1.6 and Section 5
have been added. Additional remarks included in the introduction and at the
end of section 4. Another subsection has been added to the 'Preliminaries'.
Minor typos have also been correcte | Uniqueness Results for Weak Leray-Hopf Solutions of the Navier-Stokes
System with Initial Values in Critical Spaces | uniqueness results for weak leray-hopf solutions of the navier-stokes system with initial values in critical spaces | concerns establishment uniqueness leray hopf navier stokes equations. solenodial mathbb norm belongs subsets mathbb corollary solenodial belonging mathbb mathbb frac infty mathbb infty mathbb frac infty mathbb closure besov frac infty mathbb rely establishment continuity leray hopf navier stokes data. seem interest. leray hopf satisfies extensions prodi serrin mathbb mathbb amongst leray hopf value. mathbb infty infty mathbb norm sufficiently infty infty .comment pages. submitted. corollary added. remarks subsection preliminaries minor typos correcte | non_dup | [] |
73402954 | 10.1007/s00021-017-0328-3 | We study the inviscid damping of Couette flow with an exponentially
stratified density. The optimal decay rates of the velocity field and the
density are obtained for general perturbations with minimal regularity. For
Boussinesq approximation model, the decay rates we get are consistent with the
previous results in the literature. We also study the decay rates for the full
Euler equations of stratified fluids, which were not studied before. For both
models, the decay rates depend on the Richardson number in a very similar way.
Besides, we also study the dispersive decay due to the exponential
stratification when there is no shear | Linear Inviscid Damping for Couette Flow in Stratified Fluid | linear inviscid damping for couette flow in stratified fluid | inviscid damping couette exponentially stratified density. perturbations regularity. boussinesq literature. euler stratified fluids before. richardson way. besides dispersive exponential stratification | non_dup | [] |
73359555 | 10.1007/s00021-017-0329-2 | We present a new linearly stable solution of the Euler fluid flow on a torus.
On a two-dimensional rectangular periodic domain $[0,2\pi)\times[0,2\pi /
\kappa)$ for $\kappa\in\mathbb{R}^+$, the Euler equations admit a family of
stationary solutions given by the vorticity profiles $\Omega^*(\mathbf{x})=
\Gamma \cos(p_1x_1+ \kappa p_2x_2)$. We show linear stability for such flows
when $p_2=0$ and $\kappa \geq |p_1|$ (equivalently $p_1=0$ and
$\kappa{|p_2|}\leq{1}$). The classical result due to Arnold is that for $p_1 =
1, p_2 = 0$ and $\kappa \ge 1$ the stationary flow is {nonlinearly} stable via
the energy-Casimir method. We show that for $\kappa \ge |p_1| \ge 2, p_2 = 0$
the flow is linearly stable, but one cannot expect a similar nonlinear
stability result. Finally we prove nonlinear instability for all equilibria
satisfying $p_1^2+\kappa^2{p_2^2}>\frac{{3(\kappa^2+1)}}{4(7-4\sqrt{3})}$. The
modification and application of a structure-preserving Hamiltonian truncation
is discussed for the $\kappa\neq 1$ case. This leads to an explicit Lie-Poisson
integrator for the truncated system | Stability Results for Idealised Shear Flows on a Rectangular Periodic
Domain | stability results for idealised shear flows on a rectangular periodic domain | linearly euler torus. rectangular kappa kappa mathbb euler admit stationary vorticity omega mathbf gamma kappa flows kappa equivalently kappa arnold kappa stationary nonlinearly casimir method. kappa linearly result. instability equilibria satisfying kappa frac kappa sqrt modification preserving truncation kappa case. poisson integrator truncated | non_dup | [] |
83867307 | 10.1007/s00021-017-0331-8 | The main aim of the paper is to investigate the transitions of the
thermohaline circulation in a spherical shell in a parameter regime which only
allows transitions to multiple equilibria. We find that the first transition is
either continuous (Type-I) or drastic (Type-II) depending on the sign of the
transition number. The transition number depends on the system parameters and
$l_c$, which is the common degree of spherical harmonics of the first critical
eigenmodes, and it can be written as a sum of terms describing the nonlinear
interactions of various modes with the critical modes. We obtain the exact
formulas of this transition number for $l_c=1$ and $l_c=2$ cases. Numerically,
we find that the main contribution to the transition number is due to nonlinear
interactions with modes having zero wave number and the contribution from the
nonlinear interactions with higher frequency modes is negligible. In our
numerical experiments we encountered both types of transition for $Le<1$ but
only continuous transition for $Le>1$. In the continuous transition scenario,
we rigorously prove that an attractor in the phase space bifurcates which is
homeomorphic to the 2$l_c$ dimensional sphere and consists entirely of
degenerate steady state solutions | Transitions of Spherical Thermohaline Circulation to Multiple Equilibria | transitions of spherical thermohaline circulation to multiple equilibria | thermohaline circulation spherical equilibria. drastic number. spherical harmonics eigenmodes describing modes. formulas cases. numerically negligible. encountered rigorously attractor bifurcates homeomorphic sphere entirely degenerate steady | non_dup | [] |
73991451 | 10.1007/s00021-017-0334-5 | Topology changes in multi-phase fluid flows are difficult to model within a
traditional sharp interface theory. Diffuse interface models turn out to be an
attractive alternative to model two-phase flows. Based on a
Cahn-Hilliard-Navier-Stokes model introduced by Abels, Garcke and Gr\"{u}n
(Math. Models Methods Appl. Sci. 2012), which uses a volume averaged velocity,
we derive a diffuse interface model in a Hele-Shaw geometry, which in the case
of non-matched densities, simplifies an earlier model of Lee, Lowengrub and
Goodman (Phys. Fluids 2002). We recover the classical Hele-Shaw model as a
sharp interface limit of the diffuse interface model. Furthermore, we show the
existence of weak solutions and present several numerical computations
including situations with rising bubbles and fingering instabilities.Comment: 41 pages, 75 figure | A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with
different densities | a hele-shaw-cahn-hilliard model for incompressible two-phase flows with different densities | topology flows traditional sharp theory. diffuse attractive flows. cahn hilliard navier stokes abels garcke math. sci. averaged derive diffuse hele shaw matched densities simplifies lowengrub goodman phys. fluids recover hele shaw sharp diffuse model. computations situations rising bubbles fingering pages | non_dup | [] |
73353372 | 10.1007/s00021-017-0337-2 | This paper concerns the instability and stability of the trivial steady
states of the incompressible Navier-Stokes equations with Navier-slip boundary
conditions in a slab domain in dimension two. The main results show that the
stability (or instability) of this constant equilibrium depends crucially on
whether the boundaries dissipate energy and the strengthen of the viscosity and
slip length. It is shown that in the case that when all the boundaries are
dissipative, then nonlinear asymptotic stability holds true, otherwise, there
is a sharp critical viscosity, which distinguishes the nonlinear stability from
instability.Comment: 34 page | Stability analysis for the incompressible Navier-Stokes equations with
Navier boundary conditions | stability analysis for the incompressible navier-stokes equations with navier boundary conditions | concerns instability trivial steady incompressible navier stokes navier slip slab two. instability crucially boundaries dissipate strengthen viscosity slip length. boundaries dissipative asymptotic sharp viscosity distinguishes | non_dup | [] |
83862870 | 10.1007/s00021-017-0338-1 | We consider the initial value problem to the Isobe-Kakinuma model for water
waves and the structure of the model. The Isobe-Kakinuma model is the
Euler-Lagrange equations for an approximate Lagrangian which is derived from
Luke's Lagrangian for water waves by approximating the velocity potential in
the Lagrangian. The Isobe-Kakinuma model is a system of second order partial
differential equations and is classified into a system of nonlinear dispersive
equations. Since the hypersurface $t=0$ is characteristic for the
Isobe-Kakinuma model, the initial data have to be restricted in an infinite
dimensional manifold for the existence of the solution. Under this necessary
condition and a sign condition, which corresponds to a generalized
Rayleigh-Taylor sign condition for water waves, on the initial data, we show
that the initial value problem is solvable locally in time in Sobolev spaces.
We also discuss the linear dispersion relation to the model | Solvability of the initial value problem to the Isobe-Kakinuma model for
water waves | solvability of the initial value problem to the isobe-kakinuma model for water waves | isobe kakinuma model. isobe kakinuma euler lagrange approximate lagrangian luke lagrangian approximating lagrangian. isobe kakinuma classified dispersive equations. hypersurface isobe kakinuma restricted infinite manifold solution. rayleigh taylor solvable locally sobolev spaces. | non_dup | [] |
83841591 | 10.1007/s00021-017-0342-5 | The abstract theory of critical spaces developed in [22] and [20] is applied
to the Navier-Stokes equations in bounded domains with Navier boundary
conditions as well as no-slip conditions. Our approach unifies, simplifies and
extends existing work in the $L_p$-$L_q$ setting, considerably. As an essential
step, it is shown that the strong and weak Stokes operators with Navier
conditions admit an $\mathcal{H}^\infty$-calculus with
$\mathcal{H}^\infty$-angle 0, and the real and complex interpolation spaces of
these operators are identified.Comment: 21 page | On critical spaces for the Navier-Stokes equations | on critical spaces for the navier-stokes equations | navier stokes navier slip conditions. unifies simplifies extends considerably. stokes navier admit mathcal infty calculus mathcal infty interpolation | non_dup | [] |
83845241 | 10.1007/s00021-017-0344-3 | Consider the Navier-Stokes flow in 3-dimensional exterior domains, where a
rigid body is translating with prescribed translational velocity
$-h(t)u_\infty$ with constant vector $u_\infty\in \mathbb R^3\setminus\{0\}$.
Finn raised the question whether his steady slutions are attainable as limits
for $t\to\infty$ of unsteady solutions starting from motionless state when
$h(t)=1$ after some finite time and $h(0)=0$ (starting problem). This was
affirmatively solved by Galdi, Heywood and Shibata for small $u_\infty$. We
study some generalized situation in which unsteady solutions start from large
motions being in $L^3$. We then conclude that the steady solutions for small
$u_\infty$ are still attainable as limits of evolution of those fluid motions
which are found as a sort of weak solutions. The opposite situation, in which
$h(t)=0$ after some finite time and $h(0)=1$ (landing problem), is also
discussed. In this latter case, the rest state is attainable no matter how
large $u_\infty$ is | Navier-Stokes flow past a rigid body: attainability of steady solutions
as limits of unsteady weak solutions, starting and landing cases | navier-stokes flow past a rigid body: attainability of steady solutions as limits of unsteady weak solutions, starting and landing cases | navier stokes exterior rigid translating prescribed translational infty infty mathbb setminus finn raised steady slutions attainable infty unsteady motionless affirmatively solved galdi heywood shibata infty unsteady motions steady infty attainable motions sort solutions. opposite landing discussed. attainable infty | non_dup | [] |
83858312 | 10.1007/s00021-017-0352-3 | We study the compressible and incompressible two-phase flows separated by a
sharp interface with a phase transition and a surface tension. In particular,
we consider the problem in $\mathbb{R}^N$, and the Navier-Stokes-Korteweg
equations is used in the upper domain and the Navier-Stokes equations is used
in the lower domain. We prove the existence of $\mathcal{R}$-bounded solution
operator families for a resolvent problem arising from its model problem.
According to Shibata \cite{GS2014}, the regularity of $\rho_+$ is $W^1_q$ in
space, but to solve the kinetic equation: $\mathbf{u}_\Gamma\cdot\mathbf{n}_t =
[[\rho\mathbf{u}]]\cdot\mathbf{n}_t /[[\rho]]$ on $\Gamma_t$ we need
$W^{2-1/q}_q$ regularity of $\rho_+$ on $\Gamma_t$, which means the regularity
loss. Since the regularity of $\rho_+$ dominated by the Navier-Stokes-Korteweg
equations is $W^3_q$ in space, we eliminate the problem by using the
Navier-Stokes-Korteweg equations instead of the compressible Navier-Stokes
equations.Comment: Typos correcte | Compressible-incompressible two-phase flows with phase transition: model
problem | compressible-incompressible two-phase flows with phase transition: model problem | compressible incompressible flows separated sharp tension. mathbb navier stokes korteweg navier stokes domain. mathcal families resolvent arising problem. shibata cite regularity solve mathbf gamma cdot mathbf mathbf cdot mathbf gamma regularity gamma regularity loss. regularity dominated navier stokes korteweg eliminate navier stokes korteweg compressible navier stokes typos correcte | non_dup | [] |
84094266 | 10.1007/s00021-017-0355-0 | We provide the existence and asymptotic description of solitary wave
solutions to a class of modified Green-Naghdi systems, modeling the propagation
of long surface or internal waves. This class was recently proposed by
Duch{\^e}ne, Israwi and Talhouk (Stud. Appl. Math.,137 (2016)) in order to
improve the frequency dispersion of the original Green-Naghdi system while
maintaining the same precision. The solitary waves are constructed from the
solutions of a constrained minimization problem. The main difficulties stem
from the fact that the functional at stake involves low order non-local
operators, intertwining multiplications and convolutions through Fourier
multipliers | Solitary wave solutions to a class of modified Green-Naghdi systems | solitary wave solutions to a class of modified green-naghdi systems | asymptotic solitary naghdi propagation waves. duch israwi talhouk stud. appl. math. naghdi maintaining precision. solitary constrained minimization problem. difficulties stake involves intertwining multiplications convolutions fourier multipliers | non_dup | [] |
83859903 | 10.1007/s00021-017-0358-x | We study the 3-D compressible barotropic radiation fluid dynamics system
describing the motion of the compressible rotating viscous fluid with
gravitation and radiation confined to a straight layer. We show that weak
solutions in the 3-D domain converge to the strong solution of the rotating 2-D
Navier-Stokes-Poisson system with radiation for all times less than the maximal
life time of the strong solution of the 2-D system when the Froude number is
small or to the strong solution of the rotating pure 2-D Navier- Stokes system
with radiation | Derivation of the Navier - Stokes - Poisson system with radiation for an
accretion disk | derivation of the navier - stokes - poisson system with radiation for an accretion disk | compressible barotropic describing compressible rotating viscous gravitation confined straight layer. converge rotating navier stokes poisson maximal froude rotating navier stokes | non_dup | [] |
83863068 | 10.1007/s00021-018-0361-x | The main objective of this article is to study the nonlinear stability and
dynamic transitions of the basic (zonal) shear flows for the three-dimensional
continuously stratified rotating Boussinesq model. The model equations are
fundamental equations in geophysical fluid dynamics, and dynamics associated
with their basic zonal shear flows play a crucial role in understanding many
important geophysical fluid dynamical processes, such as the meridional
overturning oceanic circulation and the geophysical baroclinic instability. In
this paper, first we derive a threshold for the energy stability of the basic
shear flow, and obtain a criteria for nonlinear stability in terms of the
critical horizontal wavenumbers and the system parameters such as the Froude
number, the Rossby number, the Prandtl number and the strength of the shear
flow. Next we demonstrate that the system always undergoes a dynamic transition
from the basic shear flow to either a spatiotemporal oscillatory pattern or
circle of steady states, as the shear strength $\Lambda$ of the basic flow
crosses a critical threshold $\Lambda_c$. Also we show that the dynamic
transition can be either continuous or catastrophic, and is dictated by the
sign of a transition parameter $A$, fully characterizing the nonlinear
interactions of different modes. A systematic numerical method is carried out
to explore transition in different flow parameter regimes. We find that the
system admits only critical eigenmodes with horizontal wave indices $(0,m_y)$.
Such modes, horizontally have the pattern consisting of $m_y$-rolls aligned
with the x-axis. Furthermore, numerically we encountered continuous transitions
to multiple steady states, continuous and catastrophic transitions to
spatiotemporal oscillations.Comment: 20 pages, 7 figure | Dynamic Transitions and Baroclinic Instability for 3D Continuously
Stratified Boussinesq Flows | dynamic transitions and baroclinic instability for 3d continuously stratified boussinesq flows | zonal flows continuously stratified rotating boussinesq model. geophysical zonal flows crucial geophysical meridional overturning oceanic circulation geophysical baroclinic instability. derive wavenumbers froude rossby prandtl flow. undergoes spatiotemporal oscillatory circle steady lambda crosses lambda catastrophic dictated characterizing modes. explore regimes. admits eigenmodes indices horizontally consisting rolls aligned axis. numerically encountered steady catastrophic spatiotemporal pages | non_dup | [] |
161229574 | 10.1007/s00021-018-0367-4 | The paper deals with the non-stationary Oseen system of equations for the generalized Newtonian incompressible fluid with multivalued and nonmonotone frictional slip boundary conditions. First, we provide a result on existence of a unique solution to an abstract evolutionary inclusion involving the Clarke subdifferential term for a nonconvex function. We employ a method based on a surjectivity theorem for multivalued L-pseudomonotone operators. Then, we exploit the abstract result to prove the weak unique solvability of the Oseen system | Evolutionary Oseen model for generalized Newtonian fluid with Multivalued Nonmonotone Friction Law | evolutionary oseen model for generalized newtonian fluid with multivalued nonmonotone friction law | deals stationary oseen newtonian incompressible multivalued nonmonotone frictional slip conditions. evolutionary inclusion involving clarke subdifferential nonconvex function. employ surjectivity multivalued pseudomonotone operators. exploit solvability oseen | non_dup | [] |
83865645 | 10.1007/s00021-018-0370-9 | This paper presents existence theories for several families of axisymmetric
solitary waves on the surface of an otherwise cylindrical ferrofluid jet
surrounding a stationary metal rod. The ferrofluid, which is governed by a
general (nonlinear) magnetisation law, is subject to an azimuthal magnetic
field generated by an electric current flowing along the rod.
The ferrohydrodynamic problem for axisymmetric travelling waves is formulated
as an infinite-dimensional Hamiltonian system in which the axial direction is
the time-like variable. A centre-manifold reduction technique is employed to
reduce the system to a locally equivalent Hamiltonian system with a finite
number of degrees of freedom, and homoclinic solutions to the reduced system,
which correspond to solitary waves, are detected by dynamical-systems methods | Spatial dynamics methods for solitary waves on a ferrofluid jet | spatial dynamics methods for solitary waves on a ferrofluid jet | presents families axisymmetric solitary cylindrical ferrofluid surrounding stationary rod. ferrofluid governed magnetisation azimuthal flowing rod. ferrohydrodynamic axisymmetric travelling formulated infinite axial variable. manifold locally freedom homoclinic solitary | non_dup | [] |
93940553 | 10.1007/s00021-018-0372-7 | In this paper, we reconsider a circular cylinder horizontally floating on an
unbounded reservoir in a gravitational field directed downwards, which was
studied by Bhatnargar and Finn in 2006. We follow their approach but with some
modifications. We establish the relation between the total energy relative to
the undisturbed state and the total force. There is a monotone relation between
the height of the centre and the wetting angle. We study the number of
equilibria, the floating configurations and their stability for all parameter
values. We find that the system admits at most two equilibrium points for
arbitrary contact angle, the one with smaller wetting angle is stable and the
one with larger wetting angle is unstable. The initial model has a limitation
that the fluid interfaces may intersect. We show that the stable equilibrium
point never lies in the intersection region, while the unstable equilibrium
point may lie in the intersection region.Comment: 40 pages, 27 figure | A Floating Cylinder on An Unbounded Bath | a floating cylinder on an unbounded bath | reconsider circular cylinder horizontally floating unbounded reservoir gravitational directed downwards bhatnargar finn modifications. establish undisturbed force. monotone wetting angle. equilibria floating configurations values. admits wetting wetting unstable. limitation interfaces intersect. never lies intersection unstable intersection pages | non_dup | [] |
2064916 | 10.1007/s00022-012-0139-x | Almost hypercomplex manifolds with Hermitian and Norden metrics and more
specially the corresponding quaternionic Kaehler manifolds are considered. Some
necessary and sufficient conditions the investigated manifolds be isotropic
hyper-Kaehlerian and flat are found. It is proved that the quaternionic Kaehler
manifolds with the considered metric structure are Einstein for dimension at
least 8. The class of the non-hyper-Kaehler quaternionic Kaehler manifold of
the considered type is determined.Comment: 10 page | Quaternionic Kaehler manifolds with Hermitian and Norden metrics | quaternionic kaehler manifolds with hermitian and norden metrics | hypercomplex manifolds hermitian norden metrics specially quaternionic kaehler manifolds considered. manifolds isotropic hyper kaehlerian found. proved quaternionic kaehler manifolds einstein hyper kaehler quaternionic kaehler manifold | non_dup | [] |
10186076 | 10.1007/s00022-013-0189-8 | Codes from Hall planes of even order, J. D. Key, T. P. McDonough and V. C. Mavron, Journal of Geometry, volume 105, issue 1, April 2014, pages 33?41.We show that the binary code C of the projective Hall plane Hq2 of even order q 2 where q = 2 t , for t?2 has words of weight 2q 2 in its hull that are not the difference of the incidence vectors of two lines of Hq2 ; together with an earlier result for the dual Hall planes of even order, this shows that for all t?2 the Hall plane and its dual are not tame. We also deduce that dim(C)>32t+1, the dimension of the binary code of the desarguesian projective plane of order 22t , thus supporting the Hamada?Sachar conjecture for this infinite class of planes.authorsversionPeer reviewe | Codes from Hall planes of even order | codes from hall planes of even order | codes hall planes mcdonough mavron april pages projective hall hull incidence hall planes hall tame. deduce desarguesian projective supporting hamada sachar conjecture infinite thorsversionpeer reviewe | non_dup | [] |
25015663 | 10.1007/s00022-014-0257-8 | We derive several results in classical Euclidean elementary geometry using
the steering ellipsoid formalism from quantum mechanics. This gives a
physically motivated derivation of very non-trivial geometric results, some of
which are entirely new. We consider a sphere of radius $r$ contained inside
another sphere of radius $R$, with the sphere centres separated by distance
$d$. When does there exist a nested tetrahedron circumscribed about the smaller
sphere and inscribed in the larger? We derive the Grace-Danielsson inequality
$d^2 \leq (R+r)(R-3r)$ as the sole necessary and sufficient condition for the
existence of a nested tetrahedron. Our method also gives the condition $d^2
\leq R(R-2r)$ for the existence of a nested triangle in the analogous
2-dimensional scenario. These results imply the Euler inequality in 2 and 3
dimensions. Furthermore, we formulate a new inequality that applies to the more
general case of ellipses and ellipsoids.Comment: 8 pages, 1 figure. Published versio | The Euler and Grace-Danielsson inequalities for nested triangles and
tetrahedra: a derivation and generalisation using quantum information theory | the euler and grace-danielsson inequalities for nested triangles and tetrahedra: a derivation and generalisation using quantum information theory | derive euclidean elementary steering ellipsoid formalism mechanics. physically motivated derivation trivial geometric entirely new. sphere sphere sphere centres separated nested tetrahedron circumscribed sphere inscribed derive grace danielsson inequality sole nested tetrahedron. nested triangle analogous scenario. imply euler inequality dimensions. formulate inequality applies ellipses pages figure. versio | non_dup | [] |
29519229 | 10.1007/s00022-015-0268-0 | We study geodesics in generalized Wallach spaces which are expressed as
orbits of products of three exponential terms. These are homogeneous spaces
$M=G/K$ whose isotropy representation decomposes into a direct sum of three
submodules $\frak{m}=\frak{m}_1\oplus\frak{m}_2\oplus\frak{m}_3$, satisfying
the relations $[\frak{m}_i,\frak{m}_i]\subset \frak{k}$. Assuming that the
submodules $\frak{m}_i$ are pairwise non isomorphic, we study geodesics on such
spaces of the form $\gamma (t)=\exp (tX)\exp (tY)\exp (tZ)\cdot o$, where
$X\in\fr{m}_1, Y\in\fr{m}_2, Z\in\fr{m}_3$ ($o=eK$), with respect to a
$G$-invariant metric. Our investigation imposes certain restrictions on the
$G$-invariant metric, so the geodesics turn out to be orbits of two exponential
terms.
We give a point of view using Riemannian submersions.
As an application, we describe geodesics in generalized flag manifolds with
three isotropy summands and with second Betti number $b_2(M)=2$, and in the
Stiefel manifolds $SO(n+2)/S(n)$. We relate our results to geodesic orbit
spaces (g.o. spaces).Comment: Journal of Geometry (2015 | Geodesics in generalized Wallach spaces | geodesics in generalized wallach spaces | geodesics wallach orbits exponential terms. homogeneous isotropy decomposes submodules frak frak oplus frak oplus frak satisfying frak frak frak submodules frak pairwise isomorphic geodesics gamma cdot metric. imposes restrictions geodesics orbits exponential terms. riemannian submersions. geodesics flag manifolds isotropy summands betti stiefel manifolds relate geodesic orbit g.o. .comment | non_dup | [] |
29547290 | 10.1007/s00022-015-0291-1 | Applications of harmonic analysis on finite groups were recently introduced
to measure partition problems, with a variety of equipartition types by convex
fundamental domains obtained as the vanishing of prescribed Fourier transforms.
Considering the circle group, we extend this approach to the compact Lie group
setting, in which case the annihilation of transforms in the classical Fourier
series produces measure transversality similar in spirit to the classical
centerpoint theorem of Rado: for any $q\geq 2$, the existence of a complex
hyperplane whose surrounding regular $q$-fans are close -- in an $L^2$-sense --
to equipartitioning a given set of measures. The proofs of these results
represent the first application of continuous as opposed to finite group
actions in the usual equivariant topological reductions prevalent in
combinatorial geometry.Comment: 7 page | Measure Partitions via Fourier Analysis II: Center Transversality in the
$L^2$-norm for Complex Hyperplanes | measure partitions via fourier analysis ii: center transversality in the $l^2$-norm for complex hyperplanes | harmonic partition equipartition convex vanishing prescribed fourier transforms. circle extend annihilation transforms fourier produces transversality spirit centerpoint rado hyperplane surrounding fans equipartitioning measures. proofs opposed usual equivariant topological reductions prevalent combinatorial | non_dup | [] |
42647794 | 10.1007/s00022-016-0325-3 | The purpose of this paper is to study $\mathcal{P}\mathcal{R}$-semi-invariant
warped product submanifolds of a paracosymplectic manifold $\widetilde{M}$. We
prove that the distributions associated with the definition of
$\mathcal{P}\mathcal{R}$-semi-invariant warped product submanifold $M$ are
always integrable. A necessary and sufficient condition for an isometrically
immersed $\mathcal{P}\mathcal{R}$-semi-invariant submanifold of $\widetilde{M}$
to be a $\mathcal{P}\mathcal{R}$-semi-invariant warped product submanifold is
obtained in terms of the shape operator.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1510.0204 | Geometry of $\mathcal{P}\mathcal{R}$-semi-invariant warped product
submanifolds in paracosymplectic manifold | geometry of $\mathcal{p}\mathcal{r}$-semi-invariant warped product submanifolds in paracosymplectic manifold | mathcal mathcal warped submanifolds paracosymplectic manifold widetilde mathcal mathcal warped submanifold integrable. isometrically immersed mathcal mathcal submanifold widetilde mathcal mathcal warped submanifold pages. admin overlap | non_dup | [] |
129362656 | 10.1007/s00022-016-0333-3 | In this paper, we consider the CPE conjecture in the frame-work of
$K$-contact and $(\kappa, \mu)$-contact manifolds. First, we prove that if a
complete $K$-contact metric satisfies the CPE is Einstein and is isometric to a
unit sphere $S^{2n+1}$. Next, we prove that if a non-Sasakian $ (\kappa, \mu)
$-contact metric satisfies the CPE, then $ M^{3} $ is flat and for $ n > 1 $, $
M^{2n+1} $ is locally isometric to $ E^{n+1}\times S^{n}(4)$.Comment: In the published version there was a sign error in Eq. (1.3). We have
fixed it her | The Critical Point Equation And Contact Geometry | the critical point equation and contact geometry | conjecture kappa manifolds. satisfies einstein isometric sphere sasakian kappa satisfies locally isometric .comment | non_dup | [] |
29546933 | 10.1007/s00022-016-0350-2 | In this paper, the third in the series, we define the generalized orthocenter
$H$ corresponding to a point $P$, with respect to triangle $ABC$, as the unique
point for which the lines $HA, HB, HC$ are parallel, respectively, to $QD, QE,
QF$, where $DEF$ is the cevian triangle of $P$ and $Q=K \circ \iota(P)$ is the
$isotomcomplement$ of $P$, both with respect to $ABC$. We prove a generalized
Feuerbach Theorem, and characterize the center $Z$ of the cevian conic
$\mathcal{C}_P$, defined in Part II, as the center of the affine map $\Phi_P =
T_P \circ K^{-1} \circ T_{P'} \circ K^{-1}$, where $T_P$ is the unique affine
map for which $T_P(ABC)=DEF$; $T_{P'}$ is defined similarly for the isotomic
conjugate $P'=\iota(P)$ of $P$; and $K$ is the complement map. The affine map
$\Phi_P$ fixes $Z$ and takes the nine-point conic $\mathcal{N}_H$ for the
quadrangle $ABCH$ (with respect to the line at infinity) to the inconic
$\mathcal{I}$, defined to be the unique conic which is tangent to the sides of
$ABC$ at the points $D, E, F$. The point $Z$ is therefore the point where the
nine-point conic $\mathcal{N}_H$ and the inconic $\mathcal{I}$ touch. This
theorem generalizes the usual Feuerbach theorem and holds in all cases where
the point $P$ is not on a median, whether the conics involved are ellipses,
parabolas, or hyperbolas, and also holds when $Z$ is an infinite point. We also
determine the locus of points $P$ for which the generalized orthocenter $H$
coincides with a vertex of $ABC$; this locus turns out to be the union of three
conics minus six points. All our proofs are synthetic, and combine affine and
projective arguments.Comment: 34 pages, 7 figure | Synthetic foundations of cevian geometry, III: The generalized
orthocenter | synthetic foundations of cevian geometry, iii: the generalized orthocenter | orthocenter triangle cevian triangle circ iota isotomcomplement feuerbach characterize cevian conic mathcal affine circ circ circ affine isotomic conjugate iota complement map. affine fixes nine conic mathcal quadrangle abch infinity inconic mathcal conic tangent sides nine conic mathcal inconic mathcal touch. generalizes usual feuerbach conics ellipses parabolas hyperbolas infinite point. locus orthocenter coincides locus turns union conics minus points. proofs synthetic combine affine projective pages | non_dup | [] |
42736951 | 10.1007/s00022-016-0352-0 | Minimal surfaces with planar curvature lines are classical geometric objects,
having been studied since the late 19th century. In this paper, we revisit the
subject from a different point of view. After calculating their metric
functions using an analytical method, we recover the Weierstrass data, and give
clean parametrizations for these surfaces. Then, using these parametrizations,
we show that there exists a single continuous deformation between all minimal
surfaces with planar curvature lines. In the process, we establish the
existence of axial directions for these surfaces | Deformation of minimal surfaces with planar curvature lines | deformation of minimal surfaces with planar curvature lines | planar curvature geometric century. revisit view. calculating recover weierstrass clean parametrizations surfaces. parametrizations deformation planar curvature lines. establish axial directions | non_dup | [] |
73956286 | 10.1007/s00022-017-0391-1 | An $n$-arc in a projective plane is a collection of $n$ distinct points in
the plane, no three of which lie on a line. Formulas counting the number of
$n$-arcs in any finite projective plane of order $q$ are known for $n \le 8$.
In 1995, Iampolskaia, Skorobogatov, and Sorokin counted $9$-arcs in the
projective plane over a finite field of order $q$ and showed that this count is
a quasipolynomial function of $q$. We present a formula for the number of
$9$-arcs in any projective plane of order $q$, even those that are
non-Desarguesian, deriving Iampolskaia, Skorobogatov, and Sorokin's formula as
a special case. We obtain our formula from a new implementation of an algorithm
due to Glynn; we give details of our implementation and discuss its
consequences for larger arcs.Comment: 19 pages, to appear in Journal of Geometr | Counting Arcs in Projective Planes via Glynn's Algorithm | counting arcs in projective planes via glynn's algorithm | projective line. formulas counting arcs projective iampolskaia skorobogatov sorokin counted arcs projective count quasipolynomial arcs projective desarguesian deriving iampolskaia skorobogatov sorokin case. glynn consequences pages geometr | non_dup | [] |
42750500 | 10.1007/s00022-017-0398-7 | In this work we are interested in the characterization of curves that belong
to a given surface. To the best of our knowledge, there is no known general
solution to this problem. Indeed, a solution is only available for a few
examples: planes, spheres, or cylinders. Generally, the characterization of
such curves, both in Euclidean ($E^3$) and in Lorentz-Minkowski ($E_1^3$)
spaces, involves an ODE relating curvature and torsion. However, by equipping a
curve with a relatively parallel moving frame, Bishop was able to characterize
spherical curves in $E^3$ through a linear equation relating the coefficients
which dictate the frame motion. Here we apply these ideas to surfaces that are
implicitly defined by a smooth function, $\Sigma=F^{-1}(c)$, by reinterpreting
the problem in the context of the metric given by the Hessian of $F$, which is
not always positive definite. So, we are naturally led to the study of curves
in $E_1^3$. We develop a systematic approach to the construction of Bishop
frames by exploiting the structure of the normal planes induced by the casual
character of the curve, present a complete characterization of spherical curves
in $E_1^3$, and apply it to characterize curves that belong to a non-degenerate
Euclidean quadric. We also interpret the casual character that a curve may
assume when we pass from $E^3$ to $E_1^3$ and finally establish a criterion for
a curve to lie on a level surface of a smooth function, which reduces to a
linear equation when the Hessian is constant.Comment: 22 pages (23 in the published version), 3 figures; this version is
essentially the same as the published on | Moving frames and the characterization of curves that lie on a surface | moving frames and the characterization of curves that lie on a surface | interested belong surface. problem. planes spheres cylinders. euclidean lorentz minkowski involves relating curvature torsion. equipping moving bishop characterize spherical relating dictate motion. ideas implicitly sigma reinterpreting hessian definite. naturally bishop frames exploiting planes casual character spherical characterize belong degenerate euclidean quadric. interpret casual character pass establish criterion reduces hessian pages essentially | non_dup | [] |
73360194 | 10.1007/s00022-017-0400-4 | A Hopf hypersurface in a (para-)Kaehler manifold is a real hypersurface for
which one of the principal directions of the second fundamental form is the
(para-)complex dual of the normal vector.
We consider particular Hopf hypersurfaces in the space of oriented geodesics
of a non-flat space form of dimension greater than 2. For spherical and
hyperbolic space forms, the oriented geodesic space admits a canonical
Kaehler-Einstein and para-Kaehler-Einstein structure, respectively, so that a
natural notion of a Hopf hypersurface exists.
The particular hypersurfaces considered are formed by the oriented geodesics
that are tangent to a given convex hypersurface in the underlying space form.
We prove that a tangent hypersurface is Hopf in the space of oriented geodesics
with respect to this canonical (para-)Kaehler structure iff the underlying
convex hypersurface is totally umbilic and non-flat.
In the case of 3 dimensional space forms, however, there exists a second
canonical complex structure which can also be used to define Hopf
hypersurfaces. We prove that in this dimension, the tangent hypersurface of a
convex hypersurface in the space form is always Hopf with respect to this
second complex structure.Comment: 10 pages AMS-TE | Hopf hypersurfaces in spaces of oriented geodesics | hopf hypersurfaces in spaces of oriented geodesics | hopf hypersurface para kaehler manifold hypersurface principal directions para vector. hopf hypersurfaces oriented geodesics spherical hyperbolic oriented geodesic admits canonical kaehler einstein para kaehler einstein notion hopf hypersurface exists. hypersurfaces oriented geodesics tangent convex hypersurface form. tangent hypersurface hopf oriented geodesics canonical para kaehler convex hypersurface totally umbilic flat. canonical hopf hypersurfaces. tangent hypersurface convex hypersurface hopf pages | non_dup | [] |
2343826 | 10.1007/s00023-001-8594-1 | In this paper we complete the first step, namely the uniform bound on
completely convergent contributions, towards proving that a three dimensional
interacting system of Fermions is a Fermi liquid in the sense of Salmhofer. The
analysis relies on a direct space decomposition of the propagator, on a bosonic
multiscale cluster expansion and on the Hadamard inequality, rather than on a
Fermionic expansion and an angular analysis in momentum space, as was used in
the recent proof by two of us of Salmhofer's criterion in two dimensions.Comment: 85 pages, 13 figure | Interacting Fermi liquid in three dimensions at finite temperature: Part
I: Convergent Contributions | interacting fermi liquid in three dimensions at finite temperature: part i: convergent contributions | convergent proving interacting fermions fermi salmhofer. relies decomposition propagator bosonic multiscale hadamard inequality fermionic salmhofer criterion pages | non_dup | [] |
2553660 | 10.1007/s00023-001-8596-z | We set up and analyze a model of radiation damping within the framework of
continuum mechanics, inspired by a model of post-Newtonian hydrodynamics due to
Blanchet, Damour and Schaefer. In order to simplify the problem as much as
possible we replace the gravitational field by the electromagnetic field and
the fluid by kinetic theory. We prove that the resulting system has a
well-posed Cauchy problem globally in time for general initial data and in all
solutions the fields decay to zero at late times. In particular, this means
that the model is free from the runaway solutions which frequently occur in
descriptions of radiation reaction | The Vlasov-Poisson system with radiation damping | the vlasov-poisson system with radiation damping | analyze damping continuum mechanics inspired newtonian hydrodynamics blanchet damour schaefer. simplify replace gravitational electromagnetic theory. posed cauchy globally times. runaway frequently descriptions | non_dup | [] |
2557211 | 10.1007/s00023-002-8621-x | We prove a localization theorem for continuous ergodic Schr\"odinger
operators $ H_\omega := H_0 + V_\omega $, where the random potential $ V_\omega
$ is a nonnegative Anderson-type perturbation of the periodic operator $ H_0$.
We consider a lower spectral band edge of $ \sigma (H_0) $, say $ E= 0 $, at a
gap which is preserved by the perturbation $ V_\omega $. Assuming that all
Floquet eigenvalues of $ H_0$, which reach the spectral edge 0 as a minimum,
have there a positive definite Hessian, we conclude that there exists an
interval $ I $ containing 0 such that $ H_\omega $ has only pure point spectrum
in $ I $ for almost all $ \omega $.Comment: 21 page | Localization for random perturbations of periodic Schroedinger operators
with regular Floquet eigenvalues | localization for random perturbations of periodic schroedinger operators with regular floquet eigenvalues | localization ergodic schr odinger omega omega omega nonnegative anderson perturbation sigma preserved perturbation omega floquet eigenvalues definite hessian omega omega .comment | non_dup | [] |
2350464 | 10.1007/s00023-002-8635-4 | Bose-Einstein condensation is usually modeled by nonlinear Schroedinger
equations with harmonic potential. We study the Cauchy problem for these
equations. We show that the local problem can be treated as in the case with no
potential. For the global problem, we establish an evolution law, which is the
analogue of the pseudo-conformal conservation law for the nonlinear
Schroedinger equation. With this evolution law, we give wave collapse criteria,
as well as an upper bound for the blow up time. Taking the physical scales into
account, we finally give a lower bound for the blow up time.Comment: 16 pages, no figur | Remarks on nonlinear Schroedinger equations with harmonic potential | remarks on nonlinear schroedinger equations with harmonic potential | bose einstein condensation modeled schroedinger harmonic potential. cauchy equations. potential. establish analogue pseudo conformal conservation schroedinger equation. collapse blow time. blow pages figur | non_dup | [] |
2554236 | 10.1007/s00023-003-0122-z | We present a proof of the central limit theorem for a pair of mutually
non-commuting operators in mixing quantum spin chains. The operators are not
necessarily strictly local but quasi-local. As a corollary we obtain a direct
construction of the time evolution of the algebra of normal fluctuation for
Gibbs states of finite range interactions on a one-dimensional lattice. We show
that the state of the algebra of normal fluctuation satisfies the $\beta$-KMS
condition if the microscopic state is a $\beta$-KMS state | On the Algebra of Fluctuation in Quantum Spin Chains | on the algebra of fluctuation in quantum spin chains | mutually commuting chains. necessarily strictly quasi local. corollary fluctuation gibbs lattice. fluctuation satisfies beta microscopic beta | non_dup | [] |
2554226 | 10.1007/s00023-003-0128-6 | We investigate the ground state energy of an electron coupled to a photon
field. First, we regard the self-energy of a free electron, which we describe
by the Pauli-Fierz Hamiltonian. We show that, in the case of small values of
the coupling constant $\alpha$, the leading order term is represented by
$2\pi^{-1} \alpha (\Lambda - \ln[1 + \Lambda])$.
Next we put the electron in the field of an arbitrary external potential $V$,
such that the corresponding Schr\"odinger operator $p^2 + V$ has at least one
eigenvalue, and show that by coupling to the radiation field the binding energy
increases, at least for small enough values of the coupling constant $\alpha$.
Moreover, we provide concrete numbers for $\alpha$, the ultraviolet cut-off
$\Lambda$, and the radiative correction for which our procedure works.Comment: final version, to appear in Ann. Henri Poincar | One non-relativistic particle coupled to a photon field | one non-relativistic particle coupled to a photon field | field. regard pauli fierz hamiltonian. alpha alpha lambda lambda schr odinger eigenvalue alpha concrete alpha ultraviolet lambda radiative ann. henri poincar | non_dup | [] |
2428359 | 10.1007/s00023-003-0133-9 | We prove that there are no restrictions on the spatial topology of
asymptotically flat solutions of the vacuum Einstein equations in
(n+1)-dimensions. We do this by gluing a solution of the vacuum constraint
equations on an arbitrary compact manifold to an asymptotically Euclidean
solution of the constraints on R^n. For any compact manifold which does not
admit a metric of positive scalar curvature, this provides for the existence of
asymptotically flat vacuum spacetimes with no maximal slices. Our main theorem
is a special case of a more general gluing construction for nondegenerate
solutions of the vacuum constraint equations which have some restrictions on
the mean curvature, but for which the mean curvature is not necessarily
constant. This generalizes the construction [IMP] (gr-qc/0109045), which is
restricted to constant mean curvature data.Comment: 14 pages, v2 is a substantial revision of the previous version:
superfluous condition removed from main theorem and applications to the
existence of spacetimes with no maximal Cauchy surfaces adde | On the topology of vacuum spacetimes | on the topology of vacuum spacetimes | restrictions topology asymptotically einstein dimensions. gluing manifold asymptotically euclidean manifold admit curvature asymptotically spacetimes maximal slices. gluing nondegenerate restrictions curvature curvature necessarily constant. generalizes restricted curvature pages substantial revision superfluous removed spacetimes maximal cauchy adde | non_dup | [] |
2554610 | 10.1007/s00023-003-0141-9 | Motivated by structural issues in the AdS-CFT correspondence, the theory of
generalized free fields is reconsidered. A stress-energy tensor for the
generalized free field is constructed as a limit of Wightman fields. Although
this limit is singular, it fulfils the requirements of a conserved local
density for the Poincar'e generators. An explicit "holographic" formula
relating the Klein-Gordon field on AdS to generalized free fields on Minkowski
space-time is provided, and contrasted with the "algebraic" notion of
holography. A simple relation between the singular stress-energy tensor and the
canonical AdS stress-energy tensor is exhibited.Comment: 25 page | Generalized free fields and the AdS-CFT correspondence | generalized free fields and the ads-cft correspondence | motivated correspondence reconsidered. wightman fields. singular fulfils conserved poincar generators. holographic relating klein gordon minkowski contrasted algebraic notion holography. singular canonical | non_dup | [] |
2556141 | 10.1007/s00023-003-0142-8 | We consider a relativistic Ansatz for the vacuum expectation values (VEVs) of
a quantum field on a globally hyperbolic space-time which is motivated by
certain Euclidean field theories. The Yang-Feldman asymptotic condition w.r.t.
a "in"-field in a quasi-free representation of the canonic commutation
relations (CCR) leads to a solution of this Ansatz for the VEVs. A GNS-like
construction on a non-degenerate inner product space then gives local,
covariant quantum fields with indefinite metric on a globally hyperbolic
space-time. The non-trivial scattering behavior of quantum fields is analyzed
by construction of the "out"-fields and calculation of the scattering matrix. A
new combined effect of non-trivial quantum scattering and non-stationary
gravitational forces is described for this model, as quasi-free "in"- fields
are scattered to "out"-fields which form a non quasi-free representations of
the CCR. The asymptotic condition, on which the construction is based, is
verified for the concrete example of de Sitter space-time | An indefinite metric model for interacting quantum fields with
non-stationary background gravitation | an indefinite metric model for interacting quantum fields with non-stationary background gravitation | relativistic ansatz expectation vevs globally hyperbolic motivated euclidean theories. feldman asymptotic w.r.t. quasi canonic commutation ansatz vevs. degenerate covariant indefinite globally hyperbolic time. trivial matrix. trivial stationary gravitational forces quasi scattered quasi representations ccr. asymptotic verified concrete sitter | non_dup | [] |
2554845 | 10.1007/s00023-003-0150-8 | The general theory of simple transport processes between quantum mechanical
reservoirs is reviewed and extended. We focus on thermoelectric phenomena,
involving exchange of energy and particles. Entropy production and Onsager
relations are relevant thermodynamic notions which are shown to emerge from the
microscopic description. The theory is illustrated on the example of two
reservoirs of free fermions coupled through a local interaction. We construct a
stationary state and determine energy- and particle currents with the help of a
convergent perturbation series.
We explicitly calculate several interesting quantities to lowest order, such
as the entropy production, the resistance, and the heat conductivity.
Convergence of the perturbation series allows us to prove that they are
strictly positive under suitable assumptions on the interaction between the
reservoirs.Comment: 55 pages; 2 figure | Dissipative Transport: Thermal Contacts and Tunnelling Junctions | dissipative transport: thermal contacts and tunnelling junctions | reservoirs reviewed extended. thermoelectric phenomena involving particles. onsager thermodynamic notions emerge microscopic description. illustrated reservoirs fermions interaction. stationary currents convergent perturbation series. explicitly quantities conductivity. perturbation strictly assumptions pages | non_dup | [] |
25334563 | 10.1007/s00023-003-0158-0 | The lattice model of scalar quantum electrodynamics (Maxwell field coupled to a complex scalar field) in the Hamiltonian framework is discussed. It is shown that the algebra of observables ${\cal O}({\Lambda})$ of this model is a $C^*$-algebra, generated by a set of gauge-invariant elements satisfying the Gauss law and some additional relations. Next, the faithful, irreducible and non-degenerate representations of ${\cal O}({\Lambda})$ are found. They are labeled by the value of the total electric charge, leading to a decomposition of the physical Hilbert space into charge superselection sectors. In the Appendices we give a unified description of spinorial and scalar quantum electrodynamics and, as a byproduct, we present an interesting example of weakly commuting operators, which do not commute strongly | Charge Superselection Sectors for Scalar QED on the Lattice | charge superselection sectors for scalar qed on the lattice | electrodynamics maxwell discussed. observables lambda satisfying gauss relations. faithful irreducible degenerate representations lambda found. labeled decomposition hilbert superselection sectors. appendices unified spinorial electrodynamics byproduct weakly commuting commute | non_dup | [] |
2469699 | 10.1007/s00023-003-0916-z | According to the present understanding, the observed diversity of the strong
interaction phenomena is described by Quantum Chromodynamics, a gauge field
theory with only very few parameters. One of the fundamental questions in this
context is how precisely the world of mesons and nucleons is related to the
properties of the theory at high energies, where quarks and gluons are the
important degrees of freedom. The lattice formulation of QCD combined with
numerical simulations and standard perturbation theory are the tools that allow
one to address this issue at a quantitative level.Comment: Plenary talk, International Conference on Theoretical Physics, Paris,
UNESCO, 22--27 July 2002; TeX source, 15 pages, figures include | Lattice QCD -- from quark confinement to asymptotic freedom | lattice qcd -- from quark confinement to asymptotic freedom | diversity phenomena chromodynamics parameters. precisely mesons nucleons quarks gluons freedom. formulation perturbation plenary talk paris unesco pages | non_dup | [] |
25364710 | 10.1007/s00023-003-0926-x | Inflation has been the driving idea in cosmology for two decades and is a pillar of the New Cosmology. The inflationary paradigm has now passed its first round of significant tests, with two of its three basics predictions confirmed at about the 10% level. The Inflationary Paradigm has some of the truth. Over the next decade the precision of these tests, most of which involve measurements of CMB anisotropy and polarization, will improve 30 fold or more(!), testing inflation more sharply and possibly elucidating the underlying cause. Especially important in this regard is detecting the inflation-produced gravitational waves, either directly or through their CMB polarization signature. While inflation has by no means been verified, its successes have raised the bar for competitor theories: Any alternative must feature the two hallmarks of inflation: superluminal expansion and entropy production | The New Cosmology: Mid-term Report Card for Inflation | the new cosmology: mid-term report card for inflation | inflation driving cosmology decades pillar cosmology. inflationary paradigm passed round basics confirmed level. inflationary paradigm truth. decade precision involve anisotropy inflation sharply possibly elucidating cause. regard detecting inflation gravitational signature. inflation verified successes raised competitor hallmarks inflation superluminal | non_dup | [] |
2356737 | 10.1007/s00023-003-0928-8 | Over the years, problems like percolation and self-avoiding walks have
provided important testing grounds for our understanding of the nature of the
critical state. I describe some very recent ideas, as well as some older ones,
which cast light both on these problems themselves and on the quantum field
theories to which they correspond. These ideas come from conformal field
theory, Coulomb gas mappings, and stochastic Loewner evolution.Comment: Plenary talk given at TH-2002, Paris. 21 pages, 9 figure | Conformal Invariance in Percolation, Self-Avoiding Walks and Related
Problems | conformal invariance in percolation, self-avoiding walks and related problems | percolation avoiding walks grounds state. ideas older cast correspond. ideas come conformal coulomb mappings stochastic loewner plenary talk paris. pages | non_dup | [] |
2554990 | 10.1007/s00023-003-0935-9 | This article will review recent results on dimensional reduction for branched
polymers, and discuss implications for critical phenomena. Parisi and Sourlas
argued in 1981 that branched polymers fall into the universality class of the
Yang-Lee edge in two fewer dimensions. Brydges and I have proven in
[math-ph/0107005] that the generating function for self-avoiding branched
polymers in D+2 continuum dimensions is proportional to the pressure of the
hard-core continuum gas at negative activity in D dimensions (which is in the
Yang-Lee or $i \phi^3$ class). I will describe how this equivalence arises from
an underlying supersymmetry of the branched polymer model.
-
I will also use dimensional reduction to analyze the crossover of
two-dimensional branched polymers to their mean-field limit, and to show that
the scaling is given by an Airy function (the same as in [cond-mat/0107223]).Comment: 15 pages, 1 eps figur | Dimensional Reduction and Crossover to Mean-Field Behavior for Branched
Polymers | dimensional reduction and crossover to mean-field behavior for branched polymers | branched polymers phenomena. parisi sourlas argued branched polymers fall universality fewer dimensions. brydges proven math generating avoiding branched polymers continuum continuum equivalence arises supersymmetry branched polymer model. analyze crossover branched polymers airy cond .comment pages figur | non_dup | [] |
2362943 | 10.1007/s00023-003-0943-9 | The study of many body physics has provided a scientific playground of
surprise and continuing revolution over the past half century. The
serendipitous discovery of new states and properties of matter, phenomena such
as superfluidity, the Meissner, the Kondo and the fractional quantum hall
effect, have driven the development of new conceptual frameworks for our
understanding about collective behavior, the ramifications of which have spread
far beyond the confines of terrestrial condensed matter physics- to cosmology,
nuclear and particle physics. Here I shall selectively review some of the
developments in this field, from the cold-war period, until the present day. I
describe how, with the discovery of new classes of collective order, the
unfolding puzzles of high temperature superconductivity and quantum
criticality, the prospects for major conceptual discoveries remain as bright
today as they were more than half a century ago.Comment: Write up of talk presented at TH-2002, July 2002, Paris. Various
corrections adde | Many Body Physics: Unfinished Revolution | many body physics: unfinished revolution | playground surprise continuing revolution century. serendipitous discovery phenomena superfluidity meissner kondo fractional hall conceptual frameworks collective ramifications spread confines terrestrial condensed cosmology physics. selectively developments cold day. discovery collective unfolding puzzles superconductivity criticality prospects conceptual discoveries bright today century talk paris. adde | non_dup | [] |
2356234 | 10.1007/s00023-003-0961-7 | There exist methods to reformulate in an exact way the many-body problem of
interacting bosons in terms of the stochastic evolution of single particle wave
functions. For one such reformulation, the so-called simple Fock scheme, we
present an elementary derivation, much simpler than the original one.
Furthermore, we show that two other schemes, based on coherent states of the
matter field rather than on Fock states, lead to an infinite statistical
uncertainty in the continuous time limit. The simple Fock scheme is therefore,
up to now, the only one that was proved to lead to a convergent Monte Carlo
simulation scheme at all times.Comment: Proceedings of the Laser Physics Workshop held in Bratislava, July
2002. Submitted to Laser Physic | Exact reformulation of the bosonic many-body problem in terms of
stochastic wave functions: convergence issues | exact reformulation of the bosonic many-body problem in terms of stochastic wave functions: convergence issues | reformulate interacting bosons stochastic functions. reformulation fock elementary derivation simpler one. schemes coherent fock infinite limit. fock proved convergent monte carlo workshop held bratislava submitted physic | non_dup | [] |
2362536 | 10.1007/s00023-003-0964-4 | Arising as a fluctuation phenomenon, the equilibrium distribution of
meandering steps with mean separation $<\ell>$ on a "tilted" surface can be
fruitfully analyzed using results from RMT. The set of step configurations in
2D can be mapped onto the world lines of spinless fermions in 1+1D using the
Calogero-Sutherland model. The strength of the ("instantaneous",
inverse-square) elastic repulsion between steps, in dimensionless form, is
$\beta(\beta-2)/4$. The distribution of spacings $s< \ell>$ between neighboring
steps (analogous to the normalized spacings of energy levels) is well described
by a {\it "generalized" Wigner surmise}: $p_{\beta}(0,s) \approx a
s^{\beta}\exp(-b s^2)$. The value of $\beta$ is taken to best fit the data;
typically $2 \le \beta \le 10$. The procedure is superior to conventional
Gaussian and mean-field approaches, and progress is being made on formal
justification. Furthermore, the theoretically simpler step-step distribution
function can be measured and analyzed based on exact results. Formal results
and applications to experiments on metals and semiconductors are summarized,
along with open questions. (conference abstract)Comment: 7 pages, 2 figures; based on talk presented at TH-2002, UNESCO,
Paris, July 2002; to be published in Ann. Henri Poincare | Applications of Ideas from Random Matrix Theory to Step Distributions on
"Misoriented" Surfaces | applications of ideas from random matrix theory to step distributions on "misoriented" surfaces | arising fluctuation phenomenon meandering tilted fruitfully rmt. configurations mapped spinless fermions calogero sutherland model. instantaneous elastic repulsion dimensionless beta beta spacings neighboring analogous spacings wigner surmise beta approx beta beta beta superior progress formal justification. theoretically simpler results. formal metals semiconductors summarized questions. comment pages talk unesco paris ann. henri poincare | non_dup | [] |
2357119 | 10.1007/s00023-003-0966-2 | We discuss recently discovered links of the statistical models of normal
random matrices to some important physical problems of pattern formation and to
the quantum Hall effect. Specifically, the large $N$ limit of the normal matrix
model with a general statistical weight describes dynamics of the interface
between two incompressible fluids with different viscousities in a thin plane
cell (the Saffman-Taylor problem). The latter appears to be mathematically
equivalent to the growth of semiclassical 2D electronic droplets in a strong
uniform magnetic field with localized magnetic impurities (fluxes), as the
number of electrons increases. The equivalence is most easily seen by relating
the both problems to the matrix model.Comment: 10 pages, 3 figures, Talk given at TH-2002, Paris, UNESCO, July 200 | New applications of non-hermitian random matrices | new applications of non-hermitian random matrices | discovered links hall effect. describes incompressible fluids viscousities saffman taylor mathematically semiclassical droplets localized impurities fluxes increases. equivalence relating pages talk paris unesco | non_dup | [] |
2355057 | 10.1007/s00023-003-0975-1 | We show for a model of scale-free graphs with biased partner choice that
knowing the exponent for the degree distribution is in general not sufficient
to decide epidemic threshold properties for exponents less than three.We show
that the connectivity between the high degree vertices and therefore the
diameter is the relevant geometric quantity for epidemic threshold
estimations.Absence of epidemic threshold happens precisely when a positive
fraction of the nodes form a cluster of bounded diameter.Comment: 10 page | Epidemic thresholds on scale-free graphs: the interplay between exponent
and preferential choice | epidemic thresholds on scale-free graphs: the interplay between exponent and preferential choice | biased partner knowing exponent decide epidemic exponents three.we connectivity geometric quantity epidemic estimations.absence epidemic happens precisely | non_dup | [] |
2570528 | 10.1007/s00023-004-0160-1 | This is the first in a series of works devoted to small non-selfadjoint
perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2.
In the present work we treat the case when the classical flow of the
unperturbed part is periodic and the strength $\epsilon$ of the perturbation is
$\gg h$ (or sometimes only $\gg h^2$) and bounded from above by $h^{\delta}$
for some $\delta>0$. We get a complete asymptotic description of all
eigenvalues in certain rectangles $[-1/C, 1/C]+ i\epsilon [F_0-1/C,F_0+1/C]$.Comment: 81 page | Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions I | non-selfadjoint perturbations of selfadjoint operators in 2 dimensions i | devoted selfadjoint perturbations selfadjoint pseudodifferential treat unperturbed epsilon perturbation sometimes delta delta asymptotic eigenvalues rectangles epsilon .comment | non_dup | [] |
2555149 | 10.1007/s00023-004-0165-9 | The asymptotic properties at future null infinity of the solutions of the
relativistic Vlasov-Maxwell system whose global existence for small data has
been established by the author in a previous work are investigated. These
solutions describe a collisionless plasma isolated from incoming radiation. It
is shown that a non-negative quantity associated to the plasma decreases as a
consequence of the dissipation of energy in form of outgoing radiation. This
quantity represents the analogue of the Bondi mass in general relativity.Comment: 13 pages; version in press. This paper continues the analysis started
in math-ph/021101 | Outgoing radiation from an isolated collisionless plasma | outgoing radiation from an isolated collisionless plasma | asymptotic infinity relativistic vlasov maxwell investigated. collisionless incoming radiation. quantity dissipation outgoing radiation. quantity analogue bondi pages press. continues started math | non_dup | [] |
2568752 | 10.1007/s00023-004-0166-8 | We consider the system of $N$ ($\ge2$) hard balls with masses $m_1,...,m_N$
and radius $r$ in the flat torus $\Bbb T_L^\nu=\Bbb R^\nu/L\cdot\Bbb Z^\nu$ of
size $L$, $\nu\ge3$. We prove the ergodicity (actually, the Bernoulli mixing
property) of such systems for almost every selection $(m_1,...,m_N; L)$ of the
outer geometric parameters. This theorem complements my earlier result that
proved the same, almost sure ergodicity for the case $\nu=2$. The method of
that proof was primarily dynamical-geometric, whereas the present approach is
inherently algebraic.Comment: 31 pages, no figure | Proof of the Ergodic Hypothesis for Typical Hard Ball Systems | proof of the ergodic hypothesis for typical hard ball systems | balls torus cdot ergodicity bernoulli outer geometric parameters. complements proved sure ergodicity primarily geometric inherently pages | non_dup | [] |
2555158 | 10.1007/s00023-004-0170-z | We present an implementation in conformal field theory (CFT) of local finite
conformal transformations fixing a point. We give explicit constructions when
the fixed point is either the origin or the point at infinity. Both cases
involve the exponentiation of a Borel subalgebra of the Virasoro algebra. We
use this to build coherent state representations and to derive a close analog
of Wick's theorem for the Virasoro algebra. This allows to compute the
conformal partition function in non trivial geometries obtained by removal of
hulls from the upper half plane. This is then applied to stochastic Loewner
evolutions (SLE). We give a rigorous derivation of the equations, obtained
previously by the authors, that connect the stochastic Loewner equation to the
representation theory of the Virasoro algebra. We give a new proof that this
construction enumerates all polynomial SLE martingales. When one of the hulls
removed from the upper half plane is the SLE hull, we show that the partition
function is a famous local martingale known to probabilists, thereby
unravelling its CFT origin.Comment: 41 pages, 4 figure | Conformal transformations and the SLE partition function martingale | conformal transformations and the sle partition function martingale | conformal conformal transformations fixing point. constructions infinity. involve exponentiation borel subalgebra virasoro algebra. build coherent representations derive analog wick virasoro algebra. conformal partition trivial geometries removal hulls plane. stochastic loewner evolutions rigorous derivation connect stochastic loewner virasoro algebra. enumerates martingales. hulls removed hull partition famous martingale probabilists thereby unravelling pages | non_dup | [] |
2555065 | 10.1007/s00023-004-0180-x | The Pauli operator describes the energy of a nonrelativistic quantum particle
with spin 1/2 in a magnetic field and an external potential. A new
Lieb-Thirring type inequality on the sum of the negative eigenvalues is
presented. The main feature compared to earlier results is that in the large
field regime the present estimate grows with the optimal (first) power of the
strength of the magnetic field. As a byproduct of the method, we also obtain an
optimal upper bound on the pointwise density of zero energy eigenfunctions of
the Dirac operator. The main technical tools are:
(i) a new localization scheme for the square of the resolvent of a general
class of second order elliptic operators;
(ii) a geometric construction of a Dirac operator with a constant magnetic
field that approximates the original Dirac operator in a tubular neighborhood
of a fixed field line. The errors may depend on the regularity of the magnetic
field but they are uniform in the field strength.Comment: latex file. Revised final version: typos corrected, the definition of
the lengthscale simplified, references added/update | Uniform Lieb-Thirring inequality for the three dimensional Pauli
operator with a strong non-homogeneous magnetic field | uniform lieb-thirring inequality for the three dimensional pauli operator with a strong non-homogeneous magnetic field | pauli describes nonrelativistic potential. lieb thirring inequality eigenvalues presented. grows field. byproduct pointwise eigenfunctions dirac operator. localization resolvent elliptic geometric dirac approximates dirac tubular neighborhood line. regularity latex file. revised typos corrected lengthscale simplified update | non_dup | [] |
2555292 | 10.1007/s00023-004-0182-8 | We study a system of a quantum particle interacting with a singular
time-dependent uniformly rotating potential in 2 and 3 dimensions: in
particular we consider an interaction with support on a point (rotating point
interaction) and on a set of codimension 1 (rotating blade). We prove the
existence of the Hamiltonians of such systems as suitable self-adjoint
operators and we give an explicit expression for their unitary semigroups.
Moreover we analyze the asymptotic limit of large angular velocity and we prove
strong convergence of the time-dependent propagator to some one-parameter
unitary group as (\omega \to \infty).Comment: Minor changes, to appear in Ann. H. Poincare', 35 pages, LaTe | Rotating Singular Perturbations of the Laplacian | rotating singular perturbations of the laplacian | interacting singular uniformly rotating rotating codimension rotating blade hamiltonians adjoint unitary semigroups. analyze asymptotic propagator unitary omega infty .comment minor ann. poincare pages | non_dup | [] |
2555284 | 10.1007/s00023-004-0183-7 | The method of scaling algebras, which has been introduced earlier as a means
for analyzing the short-distance behaviour of quantum field theories in the
setting of the model-independent, operator-algebraic approach, is extended to
the case of fields carrying superselection charges. In doing so, consideration
will be given to strictly localizable charges ("DHR-type" superselection
charges) as well as to charges which can only be localized in regions extending
to spacelike infinity ("BF-type" superselection charges). A criterion for the
preservance of superselection charges in the short-distance scaling limit is
proposed. Consequences of this preservance of superselection charges are
studied. The conjugate charge of a preserved charge is also preserved, and for
charges of DHR-type, the preservance of all charges of a quantum field theory
in the scaling limit leads to equivalence of local and global intertwiners
between superselection sectors.Comment: Latex 2e, 57 pages. Supersedes hep-th/030114 | Scaling algebras for charged fields and short-distance analysis for
localizable and topological charges | scaling algebras for charged fields and short-distance analysis for localizable and topological charges | algebras analyzing algebraic carrying superselection charges. consideration strictly localizable charges superselection charges charges localized extending spacelike infinity superselection charges criterion preservance superselection charges proposed. consequences preservance superselection charges studied. conjugate preserved preserved charges preservance charges equivalence intertwiners superselection latex pages. supersedes | non_dup | [] |
2430409 | 10.1007/s00023-004-0189-1 | A positive cosmological constant simplifies the asymptotics of forever
expanding cosmological solutions of the Einstein equations. In this paper a
general mathematical analysis on the level of formal power series is carried
out for vacuum spacetimes of any dimension and perfect fluid spacetimes with
linear equation of state in spacetime dimension four. For equations of state
stiffer than radiation evidence for development of large gradients, analogous
to spikes in Gowdy spacetimes, is found. It is shown that any vacuum solution
satisfying minimal asymptotic conditions has a full asymptotic expansion given
by the formal series. In four spacetime dimensions, and for spatially
homogeneous spacetimes of any dimension, these minimal conditions can be
derived for appropriate initial data. Using Fuchsian methods the existence of
vacuum spacetimes with the given formal asymptotics depending on the maximal
number of free functions is shown without symmetry assumptions.Comment: 23 page | Asymptotics of solutions of the Einstein equations with positive
cosmological constant | asymptotics of solutions of the einstein equations with positive cosmological constant | cosmological simplifies asymptotics forever expanding cosmological einstein equations. mathematical formal spacetimes perfect spacetimes spacetime four. stiffer gradients analogous spikes gowdy spacetimes found. satisfying asymptotic asymptotic formal series. spacetime spatially homogeneous spacetimes data. fuchsian spacetimes formal asymptotics maximal | non_dup | [] |
2555738 | 10.1007/s00023-004-0190-8 | Within the algebraic setting of quantum field theory, a condition is given
which implies that the intersection of algebras generated by field operators
localized in wedge--shaped regions of two--dimensional Minkowski space is
non--trivial; in particular, there exist compactly localized operators in such
theories which can be interpreted as local observables. The condition is based
on spectral (nuclearity) properties of the modular operators affiliated with
wedge algebras and the vacuum state and is of interest in the algebraic
approach to the formfactor program, initiated by Schroer. It is illustrated
here in a simple class of examples.Comment: 14 pages, no figure | Modular Nuclearity and Localization | modular nuclearity and localization | algebraic intersection algebras localized wedge shaped minkowski trivial compactly localized interpreted observables. nuclearity modular affiliated wedge algebras algebraic formfactor initiated schroer. illustrated pages | non_dup | [] |
2555238 | 10.1007/s00023-004-0194-4 | We consider an external potential, $-\lambda \phi$, due to one or more
nuclei. Following the Dirac picture such a potential polarizes the vacuum. The
polarization density as derived in physics literature, after a well known
renormalization procedure, depends decisively on the strength of $\lambda$. For
small $\lambda$, more precisely as long as the lowest eigenvalue,
$e_1(\lambda)$, of the corresponding Dirac operator stays in the gap of the
essential spectrum, the integral over the density vanishes. In other words the
vacuum stays neutral. But as soon as $e_1(\lambda)$ dives into the lower
continuum the vacuum gets spontaneously charged with charge $ 2e$. Global
charge conservation implies that two positrons were emitted out of the vacuum,
this is, a large enough external potential can produce electron-positron pairs.
We give a rigorous proof of that phenomenon.Comment: proofs correcte | On the Vacuum Polarization Density Caused by an External Field | on the vacuum polarization density caused by an external field | lambda nuclei. dirac picture polarizes vacuum. renormalization decisively lambda lambda precisely eigenvalue lambda dirac stays vanishes. stays neutral. soon lambda dives continuum gets spontaneously conservation positrons emitted positron pairs. rigorous proofs correcte | non_dup | [] |
2555901 | 10.1007/s00023-004-0195-3 | Products of random matrices associated to one-dimensional random media
satisfy a central limit theorem assuring convergence to a gaussian centered at
the Lyapunov exponent. The hypothesis of single parameter scaling states that
its variance is equal to the Lyapunov exponent. We settle discussions about its
validity for a wide class of models by proving that, away from anomalies,
single parameter scaling holds to lowest order perturbation theory in the
disorder strength. However, it is generically violated at higher order. This is
explicitely exhibited for the Anderson model.Comment: minor corrections to previous version, to appear in Annales H.
Poincar | Perturbative test of single parameter scaling for 1D random media | perturbative test of single parameter scaling for 1d random media | satisfy assuring centered lyapunov exponent. lyapunov exponent. settle discussions validity proving away anomalies perturbation disorder strength. generically violated order. explicitely exhibited anderson minor annales poincar | non_dup | [] |
2555414 | 10.1007/s00023-004-0196-2 | We present a rigorous proof of an ordering transition for a two-component
two-dimensional antiferromagnet with nearest and next-nearest neighbor
interactions. The low-temperature phase contains two states distinguished by
local order among columns or, respectively, rows. Overall, there is no magnetic
order in accord with the classic Mermin-Wagner theorem. The method of proof
employs a rigorous version of "order by disorder," whereby a high degeneracy
among the ground states is lifted according to the differences in their
associated spin-wave spectra.Comment: 22 pages, 1 eps fi | Order by disorder, without order, in a two-dimensional spin system with
O(2) symmetry | order by disorder, without order, in a two-dimensional spin system with o(2) symmetry | rigorous ordering antiferromagnet nearest nearest neighbor interactions. distinguished columns rows. accord classic mermin wagner theorem. employs rigorous disorder whereby degeneracy lifted pages | non_dup | [] |
2555724 | 10.1007/s00023-005-0199-7 | We study the ground state solutions of the Dirac-Fock model in the case of
weak electronic repulsion, using bifurcation theory. They are solutions of a
min-max problem. Then we investigate a max-min problem coming from the
electron-positron field theory of Bach-Barbaroux-Helffer-Siedentop. We show
that given a radially symmetric nuclear charge, the ground state of Dirac-Fock
solves this max-min problem for certain numbers of electrons. But we also
exhibit a situation in which the max-min level does not correspond to a
solution of the Dirac-Fock equations together with its associated
self-consistent projector | Some connections between Dirac-Fock and Electron-Positron Hartree-Fock | some connections between dirac-fock and electron-positron hartree-fock | dirac fock repulsion bifurcation theory. problem. coming positron bach barbaroux helffer siedentop. radially dirac fock solves electrons. exhibit dirac fock projector | non_dup | [] |
2430810 | 10.1007/s00023-005-0202-3 | We prove that generic solutions of the vacuum constraint Einstein equations
do not possess any global or local space-time Killing vectors, on an
asymptotically flat Cauchy surface, or on a compact Cauchy surface with mean
curvature close to a constant, or for CMC asymptotically hyperbolic initial
data sets. More generally, we show that non-existence of global symmetries
implies, generically, non-existence of local ones. As part of the argument, we
prove that generic metrics do not possess any local or global conformal Killing
vectors.Comment: latex2e, 38 pages in A4 now, minor corrections throughou | KIDs are non-generic | kids are non-generic | generic einstein possess killing asymptotically cauchy cauchy curvature asymptotically hyperbolic sets. symmetries generically ones. argument generic metrics possess conformal killing latex pages minor throughou | non_dup | [] |
2554968 | 10.1007/s00023-005-0203-2 | We prove a product formula which involves the unitary group generated by a
semibounded self-adjoint operator and an orthogonal projection $P$ on a
separable Hilbert space $\HH$, with the convergence in
$L^2_\mathrm{loc}(\mathbb{R};\HH)$. It gives a partial answer to the question
about existence of the limit which describes quantum Zeno dynamics in the
subspace \hbox{$\mathrm{Ran} P$}. The convergence in $\HH$ is demonstrated in
the case of a finite-dimensional $P$. The main result is illustrated in the
example where the projection corresponds to a domain in $\mathbb{R}^d$ and the
unitary group is the free Schr\"odinger evolution.Comment: LaTeX 2e, 24 pages, with substantial modifications, to appear in Ann.
H. Poincar | Product formula related to quantum Zeno dynamics | product formula related to quantum zeno dynamics | involves unitary semibounded adjoint orthogonal projection separable hilbert mathrm mathbb answer describes zeno subspace hbox mathrm illustrated projection mathbb unitary schr odinger latex pages substantial modifications ann. poincar | non_dup | [] |
2555825 | 10.1007/s00023-005-0204-1 | It is known that for multi-level time-dependent quantum systems one can
construct superadiabatic representations in which the coupling between
separated levels is exponentially small in the adiabatic limit. For a family of
two-state systems with real-symmetric Hamiltonian we construct such a
superadiabatic representation and explicitly determine the asymptotic behavior
of the exponentially small coupling term. First order perturbation theory in
the superadiabatic representation then allows us to describe the
time-development of exponentially small adiabatic transitions. The latter
result rigorously confirms the predictions of Sir Michael Berry for our family
of Hamiltonians and slightly generalizes a recent mathematical result of George
Hagedorn and Alain Joye.Comment: 24 page | Precise coupling terms in adiabatic quantum evolution | precise coupling terms in adiabatic quantum evolution | superadiabatic representations separated exponentially adiabatic limit. superadiabatic explicitly asymptotic exponentially term. perturbation superadiabatic exponentially adiabatic transitions. rigorously confirms michael berry hamiltonians generalizes mathematical george hagedorn alain | non_dup | [] |
2555876 | 10.1007/s00023-005-0208-x | We consider continuum random Schr\"odinger operators of the type $H_{\omega}
= -\Delta + V_0 + V_{\omega}$ with a deterministic background potential $V_0$.
We establish criteria for the absence of continuous and absolutely continuous
spectrum, respectively, outside the spectrum of $-\Delta +V_0$. The models we
treat include random surface potentials as well as sparse or slowly decaying
random potentials. In particular, we establish absence of absolutely continuous
surface spectrum for random potentials supported near a one-dimensional surface
(``random tube'') in arbitrary dimension.Comment: 14 pages, 2 figure | Absence of continuous spectral types for certain nonstationary random
models | absence of continuous spectral types for certain nonstationary random models | continuum schr odinger omega delta omega deterministic establish absolutely delta treat potentials sparse slowly decaying potentials. establish absolutely potentials tube pages | non_dup | [] |
2555916 | 10.1007/s00023-005-0209-9 | We consider the magnetic Schrodinger operator in a two-dimensional strip. On
the boundary of the strip the Dirichlet boundary condition is imposed except
for a fixed segment (window), where it switches to magnetic Neumann boundary
condition (see Section 2, Eq. (2.2) for the definition of this boundary
condition}. We deal with a smooth compactly supported field as well as with the
Aharonov-Bohm field. We give an estimate on the maximal length of the window,
for which the discrete spectrum of the considered operator will be empty. In
the case of a compactly supported field we also give a sufficient condition for
the presence of eigenvalues below the essential spectrum | Spectrum of the Magnetic Schrodinger Operator in a Waveguide with
Combined Boundary Conditions | spectrum of the magnetic schrodinger operator in a waveguide with combined boundary conditions | schrodinger strip. strip dirichlet imposed segment window switches neumann deal compactly aharonov bohm field. maximal window empty. compactly eigenvalues | non_dup | [] |
2523650 | 10.1007/s00023-005-0210-3 | We show how the Hopf algebra of rooted trees encodes the combinatorics of
Epstein-Glaser renormalization and coordinate space renormalization in general.
In particular we prove that the Epstein-Glaser time-ordered products can be
obtained from the Hopf algebra by suitable Feynman rules, mapping trees to
operator-valued distributions. Twisting the antipode with a renormalization map
formally solves the Epstein-Glaser recursion and provides local counterterms
due to the Hochschild 1-closedness of the grafting operator $B_+$.Comment: 19p, minor corrections and improvements. To appear in AH | The Hopf algebra of rooted trees in Epstein-Glaser renormalization | the hopf algebra of rooted trees in epstein-glaser renormalization | hopf rooted trees encodes combinatorics epstein glaser renormalization coordinate renormalization general. epstein glaser ordered hopf feynman trees valued distributions. twisting antipode renormalization formally solves epstein glaser recursion counterterms hochschild closedness grafting .comment minor improvements. | non_dup | [] |
2373314 | 10.1007/s00023-005-0213-0 | We prove that the two dimensional Hubbard model at finite temperature T and
half-filling is analytic in the coupling constant in a radius at least $c/(\log
T)^2$. We also study the self-energy through a new two-particle irreducible
expansion and prove that this model is not a Fermi liquid, but a Luttinger
liquid with logarithmic corrections. The techniques used are borrowed from
constructive field theory so the result is mathematically rigorous and
completely non-perturbative.
Together with earlier results on the existence of two dimensional Fermi
liquids, this new result proves that the nature of interacting Fermi systems in
two dimensions depends on the shape of the Fermi surface.Comment: 45 pages, 28 figure | Renormalization of the 2-point function of the Hubbard model at
half-filling | renormalization of the 2-point function of the hubbard model at half-filling | hubbard filling analytic irreducible fermi luttinger logarithmic corrections. borrowed constructive mathematically rigorous perturbative. fermi liquids proves interacting fermi fermi pages | non_dup | [] |
2576264 | 10.1007/s00023-005-0215-y | In this paper we construct star products on Marsden-Weinstein reduced spaces
in case both the original phase space and the reduced phase space are
(symplectomorphic to) cotangent bundles. Under the assumption that the original
cotangent bundle $T^*Q$ carries a symplectique structure of form
$\omega_{B_0}=\omega_0 + \pi^*B_0$ with $B_0$ a closed two-form on $Q$, is
equipped by the cotangent lift of a proper and free Lie group action on $Q$ and
by an invariant star product that admits a $G$-equivariant quantum momentum
map, we show that the reduced phase space inherits from $T^*Q$ a star product.
Moreover, we provide a concrete description of the resulting star product in
terms of the initial star product on $T^*Q$ and prove that our reduction scheme
is independent of the characteristic class of the initial star product. Unlike
other existing reduction schemes we are thus able to reduce not only strongly
invariant star products. Furthermore in this article, we establish a relation
between the characteristic class of the original star product and the
characteristic class of the reduced star product and provide a classification
up to $G$-equivalence of those star products on $(T^*Q,\omega_{B_0})$, which
are invariant with respect to a lifted Lie group action. Finally, we
investigate the question under which circumstances `quantization commutes with
reduction' and show that in our examples non-trivial restrictions arise | Phase Space Reduction of Star Products on Cotangent Bundles | phase space reduction of star products on cotangent bundles | marsden weinstein symplectomorphic cotangent bundles. cotangent bundle carries symplectique omega omega equipped cotangent lift proper admits equivariant inherits product. concrete product. unlike schemes products. establish equivalence omega lifted action. circumstances quantization commutes trivial restrictions arise | non_dup | [] |
2555940 | 10.1007/s00023-005-0217-9 | We study spontaneous symmetry breaking for field algebras on Minkowski space
in the presence of a condition of geometric modular action (CGMA) proposed
earlier as a selection criterion for vacuum states on general space-times. We
show that any internal symmetry group must commute with the representation of
the Poincare group (whose existence is assured by the CGMA) and each
translation-invariant vector is also Poincare invariant. The subspace of these
vectors can be centrally decomposed into pure invariant states and the CGMA
holds in the resulting sectors. As positivity of the energy is not assumed,
similar results may be expected to hold for other space--times.Comment: Dedicated to the memory of Siegfried Schlieder. 17 pages, no figures.
Revised version: simplified arguments and improved results; as to appear in
Annales H. Poincar | Geometric modular action and spontaneous symmetry breaking | geometric modular action and spontaneous symmetry breaking | spontaneous breaking algebras minkowski geometric modular cgma criterion times. commute poincare assured cgma translation poincare invariant. subspace centrally decomposed cgma sectors. positivity hold dedicated siegfried schlieder. pages figures. revised simplified arguments annales poincar | non_dup | [] |
2555771 | 10.1007/s00023-005-0218-8 | We study semiclassical approximations to the time evolution of coherent
states for general spin-orbit coupling problems in two different semiclassical
scenarios: The limit \hbar to zero is first taken with fixed spin quantum
number s and then with \hbar*s held constant. In these two cases different
classical spin-orbit dynamics emerge. We prove that a coherent state propagated
with a suitable classical dynamics approximates the quantum time evolution up
to an error of size \sqrt{\hbar} and identify an Ehrenfest time scale.
Subsequently an improvement of the semiclassical error to an arbitray order
\hbar^{N/2} is achieved by a suitable deformation of the state that is
propagated classically | Semiclassical propagation of coherent states with spin-orbit interaction | semiclassical propagation of coherent states with spin-orbit interaction | semiclassical approximations coherent orbit semiclassical scenarios hbar hbar held constant. orbit emerge. coherent propagated approximates sqrt hbar ehrenfest scale. subsequently semiclassical arbitray hbar deformation propagated classically | non_dup | [] |