Confinement in nonlocal interaction equations
نویسنده
چکیده
We investigate some dynamical properties of nonlocal interaction equations. We consider sets of particles interacting pairwise via a potential W , as well as continuum descriptions of such systems. The typical potentials we consider are repulsive at short distances, but attractive at long distances. The main question we consider is whether an initially localized configuration remains localized for all times, regardless of the number of particles or their arrangement. In particular we find sufficient conditions on the potential W for the above “confinement” property to hold. We use the framework of weak measure solutions developed in [8] to provide unified treatment of both particle and continuum systems.
منابع مشابه
Nonlocal Bending Analysis of Bilayer Annular/Circular Nano Plates Based on First Order Shear Deformation Theory
In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) whic...
متن کاملNonlinear Vibration Analysis of the Fluid-Filled Single Walled Carbon Nanotube with the Shell Model Based on the Nonlocal Elacticity Theory
Nonlinear vibration of a fluid-filled single walled carbon nanotube (SWCNT) with simply supported ends is investigated in this paper based on Von-Karman’s geometric nonlinearity and the simplified Donnell’s shell theory. The effects of the small scales are considered by using the nonlocal theory and the Galerkin's procedure is used to discretize partial differential equations of the governing i...
متن کاملNonperturbative QCD Vacuum Effects in Nonlocal Quark Dynamics
A straightforward calculation reveals the essentially nonlocal character of the leading heavy QQ̄ interaction arising from nonperturbative gluon field correlations in the model of a fluctuating QCD vacuum. In light of this quarkonium spin splitting ratio predictions which have supported the scalar confinement ansatz are reconsidered as a specific example of possible consequences for spectroscopy.
متن کاملGlobal-in-time Weak Measure Solutions, Finite-time Aggregation and Confinement for Nonlocal Interaction Equations
In this paper, we provide a well-posedness theory for weak measure solutions of the Cauchy problem for a family of nonlocal interaction equations. These equations are continuum models for interacting particle systems with attractive/repulsive pairwise interaction potentials. The main phenomenon of interest is that, even with smooth initial data, the solutions can concentrate mass in finite time...
متن کاملNonlocal Interaction Equations in Environments with Heterogeneities and Boundaries
We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets M of Rd endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqu...
متن کامل