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- W4297675786 abstract "A self-organizing joint system classical oscillator + random environment is considered within the framework of a complex probabilistic process that satisfies a Langevin-type stochastic differential equation. Various types of randomness generated by the environment are considered. In the limit of statistical equilibrium (SEq), second-order partial differential equations (PDE) are derived that describe the distribution of classical environmental fields. The mathematical expectation of the oscillator trajectory is constructed in the form of a functional-integral representation, which, in the SEq limit, is compactified into a two-dimensional integral representation with an integrand - the solution of the second-order complex PDE. It is proved that the complex PDE in the general case is reduced to two independent PDEs of the second-order with spatially deviating arguments. The geometric and topological features of the two-dimensional subspace on which these equations arise are studied in detail. An algorithm for parallel modeling of the problem has been developed." @default.
- W4297675786 created "2022-09-30" @default.
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- W4297675786 date "2022-09-06" @default.
- W4297675786 modified "2023-09-27" @default.
- W4297675786 title "Theoretical and Numerical Study of Self-Organizing Processes In a Closed System Classical Oscillator + Random Environment" @default.
- W4297675786 doi "https://doi.org/10.48550/arxiv.2209.02771" @default.
- W4297675786 hasPublicationYear "2022" @default.
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