Kinetic equations of soft active matter

Gerasimenko, V. I.; Fedchun, Yu. Yu.

doi:10.15407/dopovidi2014.05.011

Cited by 2 publications

(3 citation statements)

References 7 publications

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“…If the initial state is completely specified by a one-particle distribution function and a sequence of correlation functions (23), then, using a non-perturbative solution of the dual BBGKY hierarchy (9), in [31,32] it was proved that all possible states at the arbitrary moment of time can be described within the framework of a one-particle distribution function governed by the non-Markovian generalized kinetic equation with initial correlations, i.e. without any approximations like in scaling limits as above.…”

Section: The Non-markovian Generalized Kinetic Equation With Initial mentioning

confidence: 99%

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Kinetic Equations of Active Soft Matter

Gerasimenko¹

2018

Kinetic Theory

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Section: The Non-markovian Generalized Kinetic Equation With Initial mentioning

confidence: 99%

“…where the following notations used: Y (1, … , s), X \ Y (s +1, … , s + n) and the generating operators V 1þn t ðÞ ,n≥ 0, are defined by the expansions [31]: ,k≥ 1. We adduce some examples of evolution operators (27):…”

Section: The Non-markovian Generalized Kinetic Equation With Initial mentioning

confidence: 99%

Kinetic Equations of Active Soft Matter

Gerasimenko¹

2018

Kinetic Theory

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“…The sequence B(t) = U(t)B 0 of marginal observables determined by semigroup (23) is a classical nonperturbative solution of the Cauchy problem of the dual BBGKY hierarchy for entities [14].…”

Section: Stochastic Dynamics Of Many-entity Systemsmentioning

confidence: 99%

On Semigroups of Large Particle Systems and Their Scaling Asymptotic Behavior

Gerasimenko

Fedchun

2014

Springer Proceedings in Mathematics &Amp; Statistics

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Abstract. We consider semigroups of operators for hierarchies of evolution equations of large particle systems, namely, of the dual BBGKY hierarchy for marginal observables and the BBGKY hierarchy for marginal distribution functions. We establish that the generating operators of the expansions for one-parametric families of operators of these hierarchies are the corresponding order cumulants (semiinvariants) of semigroups for the Liouville equations. We also apply constructed semigroups to the description of the kinetic evolution of interacting stochastic Markovian processes, modeling the microscopic evolution of soft active matter. For this purpose we consider the mean field asymptotic behavior of the semigroup generated by the dual BBGKY hierarchy for marginal observables. The constructed scaling limit is governed by the set of recurrence evolution equations, namely, by the Vlasov-type dual hierarchy. Moreover, the relationships of this hierarchy of evolution equations with the Vlasov-type kinetic equation with initial correlations are established.

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Kinetic equations of soft active matter

Cited by 2 publications

References 7 publications

Kinetic Equations of Active Soft Matter

Kinetic Equations of Active Soft Matter

On Semigroups of Large Particle Systems and Their Scaling Asymptotic Behavior

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