Graph‐to‐local limit for a multi‐species nonlocal cross‐interaction system

On massless electron limit for a multispecies kinetic system with external magnetic field

Hypocoercivity for a Linearized Multispecies Boltzmann System

A new coercivity estimate on the spectral gap of the linearized Boltzmann collision operator for multiple species is proved. The assumptions on the collision kernels include hard and Maxwellian potentials under Grad’s angular cut-off condition. Two proofs are given: a non-constructive one, based on the decomposition of the collision operator into a compact and a coercive part, and a constructiv...

Design and Implementation of a Control System for a DC Servomechanism with an Internal Dither Created by a Limit Cycle

Purpose of this paper is designing of a positional angle control system for a DC servomechanism. The servomechanism system consists of a direct current (DC) motor, a motor driver, a measuring sensor, and a control board to adjust angular position. The motor in the servomechanism has a non-linear element called dead-zone. Presence of dead-zone causes the nonlinear behavior of system. Injecting a...

THE LIMIT AS p →∞ IN A NONLOCAL p−LAPLACIAN EVOLUTION EQUATION. A NONLOCAL APPROXIMATION OF A MODEL FOR SANDPILES

In this paper we study the nonlocal ∞−Laplacian type diffusion equation obtained as the limit as p →∞ to the nonlocal analogous to the p−Laplacian evolution, ut(t, x) = ∫ RN J(x− y)|u(t, y)− u(t, x)|p−2(u(t, y)− u(t, x)) dy. We prove existence and uniqueness of a limit solution that verifies an equation governed by the subdifferetial of a convex energy functional associated to the indicator fun...

Nonlocal rheological properties of granular flows near a jamming limit.

We study the rheology of sheared granular flows close to a jamming transition. We use the approach of partially fluidized theory (PFT) with a full set of equations extending the thin layer approximation derived previously for the description of the granular avalanches phenomenology. This theory provides a picture compatible with a local rheology at large shear rates [G. D. R. Midi, Eur. Phys. J...