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21.
Sorin Bastea Raffaele Esposito Joel L. Lebowitz Rossana Marra 《Journal of statistical physics》2006,124(2-4):445-483
We derive hydrodynamic equations describing the evolution of a binary fluid segregated into two regions, each rich in one species,which are separated (on the macroscopic scale) by a sharp interface. Our starting point is a Vlasov-Boltzmann (VB) equation describing the evolution of the one particle position and velocity distributions, fi (x, v, t), i = 1, 2. The solution of the VB equation is developed in a Hilbert expansion appropriate for this system. This yields incompressible Navier-Stokes equations for the velocity field u and a jump boundary condition for the pressure across the interface. The interface, in turn, moves with a velocity given by the normal component of u. 相似文献
22.
23.
Joel Kamnitzer 《Advances in Mathematics》2007,215(1):66-93
In an earlier work, we proved that MV polytopes parameterize both Lusztig's canonical basis and the Mirkovi?-Vilonen cycles on the affine Grassmannian. Each of these sets has a crystal structure (due to Kashiwara-Lusztig on the canonical basis side and due to Braverman-Finkelberg-Gaitsgory on the MV cycles side). We show that these two crystal structures agree. As an application, we consider a conjecture of Anderson-Mirkovi? which describes the BFG crystal structure on the level of MV polytopes. We prove their conjecture for sln and give a counterexample for sp6. Finally we explain how Kashiwara data can be recovered from MV polytopes. 相似文献
24.
Joel David Hamkins 《Proceedings of the American Mathematical Society》1998,126(11):3223-3226
Iteratively taking the automorphism group of any group leads, transfinitely, to a fixed point.
25.
26.
Alexandre Joel Chorin 《Communications in Mathematical Physics》1990,132(3):519-536
We consider a simplified model of vorticity configurations in the inertial range of turbulent flow, in which vortex filaments are viewed as random walks in thermal equilibrium subjected to the constraints of helicity and energy conservation. The model is simple enough so that its properties can be investigated by a relatively straightforward Monte-Carlo method: a pivot algorithm with Metropolis weighting. Reasonable values are obtained for the intermittency dimensionD, a Kolmogorov-like exponent , and higher moments of the velocity derivatives. Qualitative conclusions are drawn regarding the origin of non-gaussian velocity statistics and regarding analogies with polymers and with systems near a critical point.This work was supported in part by the Applied Mathematical Sciences Subprogram of the Office of Energy Research, US Department of Energy, under Contract Number DE-AC03-76SF000098 相似文献
27.
Joel L. Lebowitz Christian Maes Eugene R. Speer 《Journal of statistical physics》1990,59(1-2):117-170
We investigate the behavior of discrete-time probabilistic cellular automata (PCA), which are Markov processes on spin configurations on ad-dimensional lattice, from a rigorous statistical mechanics point of view. In particular, we exploit, whenever possible, the correspondence between stationary measures on the space-time histories of PCAs on
d
and translation-invariant Gibbs states for a related Hamiltonian on (
d+1). This leads to a simple large-deviation formula for the space-time histories of the PCA and a proof that in a high-temperature regime the stationary states of the PCA are Gibbsian. We also obtain results about entropy, fluctuations, and correlation inequalities, and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high-noise regime. We discuss phase transitions in the low-noise (or low-temperature) regime and review Toom's proof of nonergodicity of a certain class of PCAs. 相似文献
28.
Joel L. Lebowitz Harvey A. Rose Eugene R. Speer 《Journal of statistical physics》1988,50(3-4):657-687
We investigate the statistical mechanics of a complex fieldø whose dynamics is governed by the nonlinear Schrödinger equation. Such fields describe, in suitable idealizations, Langmuir waves in a plasma, a propagating laser field in a nonlinear medium, and other phenomena. Their Hamiltonian $$H(\phi ) = \int_\Omega {[\frac{1}{2}|\nabla \phi |^2 - (1/p) |\phi |^p ] dx}$$ is unbounded below and the system will, under certain conditions, develop (self-focusing) singularities in a finite time. We show that, whenΩ is the circle and theL 2 norm of the field (which is conserved by the dynamics) is bounded byN, the Gibbs measureυ obtained is absolutely continuous with respect to Wiener measure and normalizable if and only ifp andN are such that classical solutions exist for all time—no collapse of the solitons. This measure is essentially the same as that of a one-dimensional version of the more realisitc Zakharov model of coupled Langmuir and ion acoustic waves in a plasma. We also obtain some properties of the Gibbs state, by both analytic and numerical methods, asN and the temperature are varied. 相似文献
29.
We investigate the existence of nontranslation invariant (periodic) density profiles, for systems interacting via translation invariant long-range potentials, as minimizers of local mean field free energy functionals. The existence of a second-order transition from a uniform to a nonuniform density at a specified temperature is proven for a class of model systems. 相似文献
30.
Detlef Dürr Sheldon Goldstein Joel L. Lebowitz 《Probability Theory and Related Fields》1987,75(2):279-290
Summary We generalize the results of Spitzer, Jepsen and others [1–4] on the motion of a tagged particle in a uniform one dimensional system of point particles undergoing elastic collisions to the case where there is also an external potential U(x). When U(x) is periodic or random (bounded and statistically translation invariant) then the scaled trajectory of a tagged particle
converges, as A , to a Brownian motion W
D
(t) with diffusion constant
, where
is the average density,
is the mean absolute velocity and –1 the temperature of the system. When U(x) is itself changing on a macroscopic scale, i.e.
, then the limiting process is a spatially dependent diffusion. The stochastic differential equation describing this process is now non-linear, and is particularly simple in Stratonovich form. This lends weight to the belief that heuristics are best done in that form.Dedicated to Frank Spitzer on the occasion of his 60th birthdayWork supported in part by NSF Grants No. PHY 8201708 and No. DMR 81-14726Heisenberg-fellowAlso Department of Physics 相似文献