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Triangulated categories of periodic complexes and orbit categories

Jian Liu — 2023

Czechoslovak Mathematical Journal

We investigate the triangulated hull of orbit categories of the perfect derived category and the bounded derived category of a ring concerning the power of the suspension functor. It turns out that the triangulated hull corresponds to the full subcategory of compact objects of certain triangulated categories of periodic complexes. This specializes to Stai and Zhao’s result on the finite dimensional algebra of finite global dimension. As the first application, if A , B are flat algebras over a commutative...

Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis

Claire Chainais-HillairetJian-Guo LiuYue-Jun Peng — 2003

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We introduce a finite volume scheme for multi-dimensional drift-diffusion equations. Such equations arise from the theory of semiconductors and are composed of two continuity equations coupled with a Poisson equation. In the case that the continuity equations are non degenerate, we prove the convergence of the scheme and then the existence of solutions to the problem. The key point of the proof relies on the construction of an approximate gradient of the electric potential which allows us to deal...

Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis

Claire Chainais-HillairetJian-Guo LiuYue-Jun Peng — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce a finite volume scheme for multi-dimensional drift-diffusion equations. Such equations arise from the theory of semiconductors and are composed of two continuity equations coupled with a Poisson equation. In the case that the continuity equations are non degenerate, we prove the convergence of the scheme and then the existence of solutions to the problem. The key point of the proof relies on the construction of an approximate gradient of the electric potential which allows us to deal...

Macroscopic models of collective motion and self-organization

Pierre DegondAmic FrouvelleJian-Guo LiuSebastien MotschLaurent Navoret

Séminaire Laurent Schwartz — EDP et applications

In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view...

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