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We focus on numerical study of the dynamical Ginzburg-Landau equations under the temporal gauge, and propose a decoupled numerical scheme based on the finite element method. For the variable A, the se...
An implicit asymptotic-preserving and energy-charge conserving (APECC) Particle-In-Cell method is proposed to solve the Vlasov-Maxwell (VM) equations in the quasi-neutral limit. Charge conservation is...
In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow,surface diffusion flow, Willmore flow, etc., which arise from materials science...
In this talk, we discuss Y. Wei, B. Yang and T. Zhou’s preprint arXiv:2210.06035, in which they consider volume preserving curvature flows of smooth, closed and convex hypersurfaces in hyperbolic spac...
We propose a novel kind of energy/dissipation-preserving split Birkhoffian multi-symplectic (S-BMS) methods for Maxwell's equations with dissipation terms. After investigating the non-autonomous and a...
It's been more than a year since the first cases were identified in China, yet the exact origins of the COVID-19 pandemic remain a mystery. Though strong evidence suggests that the responsible coronav...
We study deterministic and stochastic perturbations of incompressible flows on a two-dimensional torus. Even in the case of purely deterministic perturbations, the long-time behavior of such &...
We study deterministic and stochastic perturbations of incompressible flows on a two-dimensional torus. Even in the case of purely deterministic perturbations, the long-time behavior of such ...
This paper focuses on methods of constructing of reduced-order models of mechanical systems which preserve the Lagrangian structure of the original system. These methods may be used in combination wit...
This paper describes newly invented multiscale transforms known under the name of the ridgelet [6] and the curvelet transforms [9, 8]. These systems combine ideas of multiscale analysis and geometry. ...
We investigate the discretization of of an electron-optical phonon scattering using a nite volume method. The discretization is conservative in mass and is essentially based on an energy point of v...
We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. We claim that the evolution of a statistical Ehrenfe...
Center manifold analysis can be used in order to investigate the stability of the stationary solutions of various PDEs. This can be done by considering the PDE as an ODE between certain Banach spaces ...
Abstract: Motivated by positivity-, monotonicity-, and convexity preserving differential equations, we introduce a definition of shape preserving operator semigroups and analyze their fundamental prop...

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