Related papers: Uniform regularity for linear kinetic equations wi…
A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal…
The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an…
The entropic lattice Boltzmann framework proposed the construction of the discrete equilibrium by taking into consideration minimization of a discrete entropy functional. The effect of this form of the discrete equilibrium on properties of…
For nearly a century the universal logarithmic behaviour of the mean velocity profile in a parallel flow was a mainstay of turbulent fluid mechanics and its teaching. Yet many experiments and numerical simulations are not fit exceedingly…
For non-uniformly hyperbolic dynamical systems we consider the time series of maxima along typical orbits. Using ideas based upon quantitative recurrence time statistics we prove convergence of the maxima (under suitable normalization) to…
Learning an appropriate (dis)similarity function from the available data is a central problem in machine learning, since the success of many machine learning algorithms critically depends on the choice of a similarity function to compare…
We study the convergence of a random iterative sequence of a family of operators on infinite dimensional Hilbert spaces, inspired by the Stochastic Gradient Descent (SGD) algorithm in the case of the noiseless regression, as studied in [1].…
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which…
This paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a…
We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs), possibly ill-posed), subject to very strong damping and quasi-periodic external forcing. We study…
We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous…
Probabilistic dynamics model ensemble is widely used in existing model-based reinforcement learning methods as it outperforms a single dynamics model in both asymptotic performance and sample efficiency. In this paper, we provide both…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
In this article, we propose a finite volume discretization of a one dimensional nonlinear reaction kinetic model proposed in [Neumann, Schmeiser, Kint. Rel. Mod. 2016], which describes a 2-species recombination-generation process.…
In this paper, we study parabolic equations in divergence form with coefficients that are singular degenerate as some Muckenhoupt weight functions in one spatial variable. Under certain conditions, weighted reverse H\"{o}lder's inequalities…
We propose a new macroscopic model derived from the classical nonlinear Boltzmann equation. A set of partial differential equations is obtained easily. The unknowns depend on the time and space coordinates, and are related to the…
In this paper we study the global regularity for the solution to the Dirichlet problem of the equation of minimal graphs over a convex domain in hyperbolic spaces. We find that the global regularity depends only on the convexity of the…
We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation…
Dynamical low-rank algorithms are a class of numerical methods that compute low-rank approximations of dynamical systems. This is accomplished by projecting the dynamics onto a low-dimensional manifold and writing the solution directly in…