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Trapping for Newtonian Diffusion Processes

  • Ph. Blanchard
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 26/1984)

Abstract

In the first lecture I will try to explain a general mechanism for the formation of impenetrable barriers for diffusion processes (see [1]). I will consider a special class of diffusion processes, which we call Newtonian diffusions. This name is justified by the fact that such a diffusion process satisfies a Newton law in the mean. We will see how it is possible to define a mean stochastic acceleration a for diffusion processes. The Newton law in the mean
$$\mu a\, = \,F\, = \, - \nabla \nabla$$
where µ is the mass of a test-particle, plays the role of a constraint and allows to construct under some assumptions a family of possible probability distributions ρ of the stochastic diffusion process. We will also show that the nodal surfaces of \(N_\rho \, = \,\left\{ {x\, \in \,R^d |\rho \,(t,x)\, = \,0} \right\}\) can also be impenetrable barriers, splitting the family of typical particles into several groups. Since no particle can pass from one group to another we have to do with a segregation (confinement, trapping) mechanism.

Keywords

Diffusion Process Stochastic Differential Equation Central Body Dirichlet Form Radiation Belt 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Ph. Blanchard
    • 1
  1. 1.Theoretische Physik and BiBoSUniversität BielefeldBielefeld 1Germany

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