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The logistic regression model is known to converge to a Poisson point process model if the binary response tends to infinitely imbalanced. In this paper, it is shown that this phenomenon is universal in a wide class of link functions on…
The key to understanding the universal behaviour of systems driven away from equilibrium lies in the common description obtained when particular microscopic models are reduced to order parameter equations. Universal order parameter…
We study the quasineutral limit of the isothermal Euler-Poisson system describing a plasma made of ions and massless electrons. The analysis is achieved in a domain of $\R^3$ and thus extends former results by Cordier and Grenier [Comm.…
In this paper, we consider the quasi-neutral limit of a three dimensional Euler-Poisson system of compressible fluids coupled to a magnetic field. We prove that, as Debye length tends to zero, periodic initial-value problems of the model…
The Vlasov-Poisson-BGK (VPBGK) model is a kinetic model for describing the dynamics of collisional plasmas. Although various numerical schemes have been developed for it, a corresponding convergence theory has been absent. This paper fills…
We construct global dissipative solutions on the torus of dimension at most three of the defocusing isothermal Euler-Langevin-Korteweg system, which corresponds to the Euler-Korteweg system of compressible quantum fluids with an isothermal…
Recently developed concept of dissipative measure-valued solution for compressible flows is a suitable tool to describe oscillations and singularities possibly developed in solutions of multidimensional Euler equations. In this paper we…
Exceptional points (EPs) are non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to unusual physical effects across scientific disciplines. The concept of EPs has recently been extended to nonlinear physical…
We consider a class of general SDEs with a jump integral term driven by a time-inhomogeneous Poisson random measure. We propose a two-parameters Euler-type scheme for this SDE class and prove an optimal rate for the strong convergence with…
We consider the asymptotic behavior of the soltion to the wave equation with time-dependent damping and analytic nonlinearity. Our main goal is to prove the convergence of a global solution to an equilibrium as time goes to infinity by…
We show that, conditioned on the (empirical) particle density exceeding the critical value, the finite volume Bose loop soup converges to the superposition of the Bosonic loop soup (on the whole space) and the Poisson point process of…
In this work, we study the behavior of blow-up solutions to the multidimensional restricted Euler--Poisson equations which are the localized version of the full Euler--Poisson system. We provide necessary conditions for the existence of…
We investigate the relaxation problem for the one-dimensional pressureless Euler--Poisson equations with the initial density being a finite Radon measure. The entropy solution of this linearly degenerate hyperbolic system converges to the…
A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional…
The Euler-Poisson (EP) system describes the dynamic behavior of many important physical flows. In this work, a Riccati system that governs two-dimensional EP equations is studied. The evolution of divergence is governed by the Riccati type…
This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations…
In this paper, the design and analysis of high order accurate IMEX finite volume schemes for the compressible Euler-Poisson (EP) equations in the quasineutral limit is presented. As the quasineutral limit is singular for the governing…
In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model. To better describe the processes of deformation and diffusion, we firstly reformulate the nonlinear fluid-solid coupling problem into a…
We consider a three-dimensional kinetic model for a two species plasma consisting of electrons and ions confined by an external nonconstant magnetic field. Then we derive a kinetic-fluid model when the mass ratio $m_e/m_i$ tends to zero.…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…