Related papers: Stochastic Methods and Dynamical Wave-function Col…
Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a mechanical structure even for realistic…
The internal phase dynamics of a quantum system is revealed in details. Theoretical and experimental evidences of existence of a causal relation of the phase of the wave function with the dynamics of the quantum system are presented…
In this paper we study the dynamics of stochastic microorganism flocculation models. Given the strong influence of environmental and seasonal fluctuations that are present in these models, we propose a stochastic model that includes…
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
We present a discussion on some physical aspects of gravitational collapse which is based on a list of questions related to relevant issues in the study of that phenomenon. Providing answers to those questions we bring out the role played…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equations on cylindrical domains. In particular, we use a…
Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and…
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…
We study stochastic resonance in an over-damped approximation of the stochastic Duffing oscillator from a random dynamical systems point of view. We analyse this problem in the general framework of random dynamical systems with a…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
Advanced measurement techniques and high performance computing have made large data sets available for a wide range of turbulent flows that arise in engineering applications. Drawing on this abundance of data, dynamical models can be…
We express the probabilistic character associated to the wave function by treating it as a stochastic variable. This is accomplished by means of a stochastic equation for the wave function whose noise changes the phase of the wave function…
The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
On the basis of a proposed model of wave function collapse, we investigate spontaneous localization of a quantum state. The model is similar to the Ghirardi-Rimini-Weber model, while we postulate the localization functions to depend on the…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…