Random motions in inhomogeneous media
Enzo Orsingher,Nikita Ratanov +1 more
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In this article, the authors considered space inhomogeneous random motions of particles on the line and in the plane, and the changes of the movement direction are driven by a Poisson process.Abstract:
Space inhomogeneous random motions of particles on the line and in the plane are considered in the paper. The changes of the movement direction are driven by a Poisson process. The particles are assumed to move according to a finite velocity field that depends on a spatial argument. The explicit distribution of particles is obtained in the paper for the case of dimension 1 in terms of characteristics of the governing equations. In the case of dimension 2, the distribution is obtained if a rectifying diffeomorphism exists.read more
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Branching random motions, nonlinear hyperbolic systems and traveling waves
TL;DR: In this paper, a branching random motion on a line, with abrupt changes of direction, is studied, and the convergence of solutions with Heaviside terminal data to the traveling waves is discussed.
References
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Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
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Ordinary differential equations
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
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Ordinary Differential Equations
TL;DR: In this paper, differential equations on manifolds have been used to prove linear systems and linear systems are proven to be linear systems with differential equations on manifolds.
Journal ArticleDOI
Probability and Related Topics in Physical Sciences.
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Models of dispersal in biological systems
TL;DR: Two stochastic processes that model the major modes of dispersal that are observed in nature are introduced, and explicit expressions for the mean squared displacement and other experimentally observable quantities are derived.
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