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Wealth Distribution Involving Psychological Traits and Non-Maxwellian Collision Kernel.
Entropy (Basel)
January 2025
School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China.
A kinetic exchange model is developed to investigate wealth distribution in a market. The model incorporates a value function that captures the agents' psychological traits, governing their wealth allocation based on behavioral responses to perceived potential losses and returns. To account for the impact of transaction frequency on wealth dynamics, a non-Maxwellian collision kernel is introduced.
View Article and Find Full Text PDFToward Grid-Based Models for Molecular Association.
J Chem Theory Comput
January 2025
Department of Biology, Chemistry and Pharmacy, Freie Universität Berlin, Arnimallee 22, 14195 Berlin, Germany.
This paper presents a grid-based approach to model molecular association processes as an alternative to sampling-based Markov models. Our method discretizes the six-dimensional space of relative translation and orientation into grid cells. By discretizing the Fokker-Planck operator governing the system dynamics via the square-root approximation, we derive analytical expressions for the transition rate constants between grid cells.
View Article and Find Full Text PDFIntermediate scattering function of a gravitactic circle swimmer.
Phys 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 PDFBrownian non-Gaussian polymer diffusion in non-static media.
Chaos
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 PDFPhase transition in a kinetic mean-field game model of inertial self-propelled agents.
Chaos
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.
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