相关论文: A recursive algorithm and a series expansion relat…
We present numerical investigations into the question of the validity of the Boltzmann prescription in Statistical Mechanics for large systems, addressing the issue of whether extensivity of energy implies the extensivity of the Boltzmann…
We consider systems of stochastic differential equations of the form \[ \d X_t^i = \sum_{j=1}^d A_{ij}(X_{t-}) \d Z_t^j\] for $i=1,\dots,d$ with continuous, bounded and non-degenerate coefficients. Here $Z_t^1,\dots,Z_t^d$ are independent…
A numerical algorithm to solve the spectral problem for arbitrary self-adjoint extensions of 1D regular Schroedinger operators is presented. It is shown that the set of all self-adjoint extensions of 1D regular Schroedinger operators is in…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
We address the problem of finding the zeros of the sum of a maximally monotone operator and a cocoercive operator. Our approach introduces a modification to the forward-backward method by integrating an inertial/momentum term alongside a…
Intractable distributions present a common difficulty in inference within the probabilistic knowledge representation framework and variational methods have recently been popular in providing an approximate solution. In this article, we…
Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…
We consider the rate of convergence of solutions of spatially inhomogenous Boltzmann equations, with hard sphere potentials, to some equilibriums, called Maxwellians. Maxwellians are spatially homogenous static Maxwell velocity…
This article deals with the weak and strong unique continuation principle for fractional Schr\"odinger equations with scaling-critical and rough potentials via Carleman estimates. Our methods allow to apply the results to variable…
This paper studies the quantum Boltzmann Nordheim equation from a Boltzmann equation for Haldane statistics. Strong solutions are obtained for the Cauchy problem with initial data in L1 and uniformly bounded on a one (resp. two or…
In this paper, we will introduce a precise classification of characteristic functions in the Fourier space according to the moment constraint in the physical space of any order. Based on this, we construct measure valued solutions to the…
In this paper, we derive a Fast Reflected Forward-Backward (Fast RFB) algorithm to solve the problem of finding a zero of the sum of a maximally monotone operator and a monotone and Lipschitz continuous operator in a real Hilbert space. Our…
We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equation in a bounded domain with any of the usual physical boundary conditions: in-flow, bounce-back, specular-reflection and diffuse-reflection. When the mass, energy…
With applications in astroparticle physics in mind, we generalize a method for the solution of the nonlinear, space homogeneous Boltzmann equation with isotropic distribution function to arbitrary matrix elements. The method is based on the…
This article studies some numerical approximations of the homogenized matrix for stochastic linear elliptic partial differential equations in divergence form. We focus on the case when the underlying random field is a small perturbation of…
In this paper, we prove some a priori stability estimates (in weighted Sobolev spaces) for the spatially homogeneous Boltzmann equation without angular cutoff (covering every physical collision kernels). These estimates are conditioned to…
We solve the probability continuity equation within the Madelung-Bohm framework, assuming a separable phase expressed as $S(x,t) = Q(x)\dot{\nu}(t) + \mu(t)$. Using operator methods, we reformulate the wave function's amplitude into a form…
This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the…
We develop a new formalism for the treatment of gravitational backreaction in the cosmological setting. The approach is inspired by projective techniques in non-equilibrium statistical mechanics. We employ group-averaging with respect to…
In this paper, we get the quantitative space-time behavior of the full Boltzmann equation with soft potentials ($-2<\gamma <0$) in the close to equilibrium setting, under some velocity decay assumption, but without any Sobolev regularity…