Related papers: On Lieb-Robinson Bounds for the Double Bracket Flo…
Consider the Boltzmann equation in a general non-convex domain with the diffuse boundary condition. We establish optimal BV estimates for such solutions. Our method consists of a new $W^{1,1}-$trace estimate for the diffuse boundary…
So far fluid mechanical Nambu brackets have mainly been given on an intuitive basis. Alternatively an algorithmic construction of such a bracket for the two-dimensional vorticity equation is presented here. Starting from the Lie--Poisson…
We consider a general formalism for treating a Hamiltonian (canonical) field theory with a spatial boundary. In this formalism essentially all functionals are differentiable from the very beginning and hence no improvement terms are needed.…
We revisit the problem of the overdamped (large friction) limit of the Brownian dynamics in an inhomogeneous medium characterized by a position-dependent friction coefficient and a multiplicative noise (local temperature) in one space…
We study the modular Hamiltonian of an interval for the ground state of a massive free scalar field on the half line with Robin boundary conditions, by employing a numerical method. When the interval is adjacent to the boundary, we find…
In this article, we calculate the friction between two counter-flowing bosonic and fermionic super-fluids. In the limit where the boson-boson and boson-fermion interactions can be treated within the mean-field approximation, we show that…
We consider an extension of the well-known Hamilton-Jacobi-Bellman (HJB) equation for fractional order dynamical systems in which a generalized performance index is considered for the related optimal control problem. Owing to the…
The flow equation approach investigated by Wegner et al. is applied to an unbounded Hamiltonian system with a generalization. We show that a well-known quantized complex energy eigenvalues which is related to decay widths can be given with…
We review the first and second boundary value problems for the Stokes system posed in a bounded Lipschitz domain in $\mathbb{R}^n.$ Particular attention is given to the mixed boundary condition: a Dirichlet condition is imposed for the…
We will give self-contained and detailed proofs of the (multidimensional) Hastings factorization as well as a (1-dimensional) area law in a wider setup than previous works. Especially, they are applicable to both quantum spin and fermion…
The goal of this paper is to supplement the large deviation principle of the Freidlin--Wentzell theory on exit problems for diffusion processes with results of classical central limit theorem kind. We describe a class of situations where…
The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…
We study the nonhomogeneous boundary value problem for Navier--Stokes equations of steady motion of a viscous incompressible fluid in a two--dimensional bounded multiply connected domain $\Omega=\Omega_1\setminus\bar{\Omega}_2,…
We consider parabolic Bellman equations with Lipschitz coefficients. Error bounds of order $h^{1/2}$ for certain types of finite-difference schemes are obtained.
Variation of coupling constants of integrable system can be considered as canonical transformation or, infinitesimally, a Hamiltonian flow in the space of such systems. Any function $T(\vec p, \vec q)$ generates a one-parametric family of…
We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region $D=(0, L)\times \mathbb{R}^2$. We are concerned with flows that are periodic in the second and third variables and that have…
We study the regularity properties of the Hamilton-Jacobi flow equation and infimal convolution in the case where initial datum function is continuous and lies in given Sobolev-space $W^{1,p}(\rn)$. We prove that under suitable assumptions…
We develop the notion of Brakke flow with free-boundary in a barrier surface. Unlike the classical free-boundary mean curvature flow, the free-boundary Brakke flow must "pop" upon tangential contact with the barrier. We prove a compactness…
In this paper, a lattice Boltzmann (LB) model with double distribution functions is proposed for two-phase flow in porous media where one distribution function is used for pressure governed by the Poisson equation, and the other is applied…
A floating hemisphere under forced harmonic oscillation at very high and very low frequencies is considered. The problem is reduced to an elliptic one, that is, the Laplace operator in the exterior domain with standard Dirichlet and Neumann…