Scaling limit for a second-order particle system with local annihilation

The Second Order Particle System

In this paper we present an extension to the classical particle system. We unify particles, particle sources, and force generators into a second order particle system. In the second order particle system the particle sources and force generators are subject to the forces as well as visual particles. This fundamental change, along with suitable set of force classes, enables us to create better r...

On the property of for a second-order system with zero diagonal coefficient

Abstract: This paper investigates the problem of whether all trajectories of the system and cross the vertical isocline, which is very important for the existence of periodic solutions and oscillation theory. Sufficient conditions are given for all trajectories to cross the vertical isocline.  

Design of a Model Reference Adaptive Controller Using Modified MIT Rule for a Second Order System

Sometimes conventional feedback controllers may not perform well online because of the variation in process dynamics due to nonlinear actuators, changes in environmental conditions and variation in the character of the disturbances. To overcome the above problem, this paper deals with the designing of a controller for a second order system with Model Reference Adaptive Control (MRAC) scheme usi...

Limit Circle/Limit Point Criteria for Second-Order Superlinear Differential Equations with a Damping Term

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...