This paper presents a distributed position synchronization strategy that also preserves the initial communication links for single-integrator multi-agent systems with time-varying delays. The strategy employs a coordinating proportional control derived from a specific type of potential energy, augmented with damping injected through a dynamic filter. The injected damping maintains all agents wi...

In this paper we find explicit formulas for: (1) Green’s function for a system of one-dimensional bosons interacting via a delta-function potential with particles confined to the positive half-line; and (2) the transition probability for the one-dimensional asymmetric simple exclusion process (ASEP) with particles confined to the nonnegative integers. These are both for systems with a finite nu...

We derive the exact rate of pair production of oppositely charged scalar particles by a smooth potential step φ(x) ∝ tanh kz in three dimensions. As a check we recover from this the known results for an infinitely sharp step as well as for a uniform electric field.

Variational methods have a long and remarkable role in theoretical physics. Few of our students when first exposed to them fail to admire their elegance and efficacy in the formulation and solution of physical problems. In this paper we apply the variational approach that leads to the Euler-Lagrange equations to the determination of the shape of the surface of a mass of water that partially fil...

Abstract This paper is concerned with the existence of normalized solutions to a class Schrödinger equations driven by fractional operator parametric potential term. We obtain minimization energy functional associated that assuming basic conditions for potential. Our work offers partial extension previous results non-local case.