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Search results for: fokker-planck equation

  • Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment

    Publication
    • P. Weber
    • P. Bełdowski
    • M. Bier
    • A. Gadomski

    - ENTROPY - Year 2018

    We study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to k_{B}T, which is the “quantum” of Brownian energy. Especially for polymers, the conformational energy landscape is often rough and has been commonly modeled as being self-similar...

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  • KOLMOGOROV EQUATION SOLUTION: MULTIPLE SCATTERING EXPANSION AND PHOTON STATISTICS EVOLUTION MODELING

    Publication

    We consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon...

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  • Equivariant Morse equation

    The paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.

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  • Dimensionally Consistent Nonlinear Muskingum Equation

    Although the Muskingum equation was proposed nearly 75 years ago, it is still a subject of active research. Despite of its simple form, the real properties of this equation have not been comprehensively explained. This paper proposes a new interpretation of the linear McCarthy’s relation. This relation can be interpreted only together with the storage equation, whereas the Muskingum equation can be derived directly from the system...

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  • Newton’s Method for the McKendrick-von Foerster Equation

    Publication

    - Year 2020

    In the paper we study an age-structured model which describes the dynamics of one population with growth, reproduction and mortality rates. We apply Newton’smethod to the McKendrick-von Foerster equation in the semigroup setting. We prove its first- and second-order convergence.

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