Origin and manifestation of the anharmonic potential felt by an ion-cloud in an actual Paul trap

The anharmonic potential felt by a single-species ions confined in a rf quadrupole trap which results from a non-ideal trap configuration and the charge distribution of the ion cloud is studied. The rf resonance-absorption spectra are explained by a Duffing oscillator and a representation of the line-shape parameter is derived. For > 0.77, the electric signals will exhibit hysteresis. The relation with the anharmonic potential is discussed.     

Exact solutions for Belousov-Zhabotinskii reaction-diffusion system

Abstract. We consider the following simplified model for the Belousou-Zhabotinskii(B-Z)reaction:     

The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.     

Small ball probabilities for a Wiener process under weighted sup-norms,with an application to the supremum of bessel local times

LetR be the radial part of ad-dimensional Wiener process, starting from 0. In this paper, small ball probabilities are evaluated for sup_0<11(t ^–p R(t)) and sup _t 0(e ^–1 R(t)), withp[0, 1/2]. Chung's law of the iterated logarithm is established for the supremum of the local times of a two-dimensional Bessel process.