منابع مشابه
Discreteness-Induced Oscillatory Instabilities of Dark Solitons
We reveal that even weak inherent discreteness of a nonlinear model can lead to instabilities of the localized modes it supports. We present the first example of an oscillatory instability of dark solitons, and analyse how it may occur for dark solitons of the discrete nonlinear Schrödinger and generalized Ablowitz-Ladik equations. PACS numbers: 03.40.Kf, 42.65.Tg, 63.20.Pw Typeset using REVTEX...
متن کاملDiscreteness-Induced Transitions in Autocatalytic Systems
To study the dynamics of chemical processes, we often adopt rate equations to observe the change in chemical concentrations. However, when the number of the molecules is small, the fluctuations cannot be neglected. We often study the effects of fluctuations with the help of stochastic differential equations. Chemicals are composed of molecules on a microscopic level. In principle, the number of...
متن کاملDiscreteness-induced transitions in multibody reaction systems.
A decrease in system size can induce qualitatively different behavior compared to the macroscopic behavior of the corresponding large-size system. The mechanisms of this transition, which is known as the small-size transition, can be attributed to either a relative increase in the noise intensity or to the discreteness of the state space due to the small system size. The former mechanism has be...
متن کاملTheoretical analysis of discreteness-induced transition in autocatalytic reaction dynamics.
Transitions in the qualitative behavior of chemical reaction dynamics with a decrease in molecule number have attracted much attention. Here, a method based on a Markov process with a tridiagonal transition matrix is applied to the analysis of this transition in reaction dynamics. The transition to bistability due to the small-number effect and the mean switching time between the bistable state...
متن کاملTransition phenomena induced by internal noise and the discreteness
We study a simple chemical reaction system and effects of the internal noise. Although stochastic differential equations are often used in order to study the fluctuations, they can not treat the discreteness in the number of components (molecules, individuals, and so on) because they are based on the continuum approximation which is justified by the large system size. The discreteness of compon...
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ژورنال
عنوان ژورنال: Physica A: Statistical Mechanics and its Applications
سال: 2015
ISSN: 0378-4371
DOI: 10.1016/j.physa.2015.06.011