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  • Title: Positing the problem of stationary distributions of active particles as third-order differential equation.
    Author: Frydel D.
    Journal: Phys Rev E; 2022 Aug; 106(2-1):024121. PubMed ID: 36109956.
    Abstract:
    In this work, we obtain a third-order linear differential equation for stationary distributions of run-and-tumble particles in two dimensions in a harmonic trap. The equation represents the condition j=0, where j is a flux. Since an analogous equation for passive Brownian particles is first-order, a second- and third-order term are features of active motion. In all cases, the solution has a form of a convolution of two distributions: the Gaussian distribution representing the Boltzmann distribution of passive particles, and the beta distribution representing active motion at zero temperature.
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