A system of nonlocal electron transport equations for electrostatic perturbations in (omega,k) space in a high-Z plasma is derived from the Fokker-Planck equation for arbitrary relations between the time, space, and collisionality scales. The closed scheme for obtaining the longitudinal plasma susceptibility epsilon(omega,k) in the entire (omega,k) plane is proposed. Regions in the (omega,k) plane have been mapped for problems such as the relaxation of the local temperature enhancement with a time-dependent heat conductivity. The electron dielectric permittivity has been calculated over the entire range of parameters, including the transition region between Vlasov and Fokker-Planck equation solutions.
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http://dx.doi.org/10.1103/PhysRevLett.93.125002 | DOI Listing |
Comput Methods Biomech Biomed Engin
January 2025
Université de Lyon, VetAgro Sup, UPSP ICE 2021.A104, France.
Extrusion-based 3D printing is a widely utilized tool in tissue engineering, offering precise 3D control of bioinks to construct organ-sized biomaterial objects with hierarchically organized cellularized scaffolds. Topological properties in flowing polymers are determined by macromolecule conformation, namely orientation and stretch degree. We utilized the micro-macro approach to describe hydrogel macromolecule orientation during extrusion, offering a two-scale fluid behavior description.
View Article and Find Full Text PDFPhys Rev E
November 2024
Institut für Theoretische Physik, Technikerstraße 21-A, Universität Innsbruck, A-6020 Innsbruck, Austria.
We analyze gravitaxis of a Brownian circle swimmer by deriving and analytically characterizing the experimentally measurable intermediate scattering function (ISF). To solve the associated Fokker-Planck equation, we use a spectral-theory approach, finding formal expressions in terms of eigenfunctions and eigenvalues of the overdamped-noisy-driven pendulum problem. We further perform a Taylor series of the ISF in the wavevector to extract the cumulants up to the fourth order.
View Article and Find Full Text PDFChaos
December 2024
School of Mathematics and Statistics, State Key Laboratory of Natural Product Chemistry, Lanzhou University, Lanzhou 730000, China.
In nature, essentially, almost all the particles move irregularly in non-static media. With the advance of observation techniques, various kinds of new dynamical phenomena are detected, e.g.
View Article and Find Full Text PDFChaos
December 2024
California Institute of Technology, Pasadena, California 91125, USA.
The framework of mean-field games (MFGs) is used for modeling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative motile agents with inertial dynamics and finite-range interactions, where each agent is minimizing a biologically inspired cost function. By analyzing the associated coupled forward-backward in a time system of nonlinear Fokker-Planck and Hamilton-Jacobi-Bellman equations, we obtain conditions for closed-loop linear stability of the spatially homogeneous MFG equilibrium that corresponds to an ordered state with non-zero mean speed.
View Article and Find Full Text PDFPhys Rev E
October 2024
Institute for Solid State Physics and Optics, HUN-REN Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary.
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