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We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
We study a general class of nonlinear mean field Fokker-Planck equations in relation with an effective generalized thermodynamical formalism. We show that these equations describe several physical systems such as: chemotaxis of bacterial…
The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…
Understanding the behavior of particles in a dispersed phase system via population balances holds fundamental importance in studies of particulate sciences across various fields. Particle behavior, however, is sophisticated as a single…
By studying a system of Brownian particles, interacting only through a local social-like force (velocity alignment), we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped…
The main concern of the present paper is the study of the multi-scale dynamics of thermonuclear fusion plasmas via a multi-species Fokker-Planck kinetic model. One of the goals is the generalization of the standard Fokker-Planck collision…
Self-propulsion allows living systems to display unusual collective behavior. Unlike passive systems in thermal equilibrium, active matter systems are not constrained by conventional thermodynamic laws. A question arises however as to what…
We derive a Fokker-Planck equation for joint probability density for an active particle coupled two heat reservoirs with harmonic, viscous, random forces. The approximate solution for the joint distribution density of all-to-all and three…
We propose and investigate a one-parameter probabilistic mixture of one-dimensional elementary cellular automata under the guise of a model for the dynamics of a single-species unstructured population with nonoverlapping generations in…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation…
A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…
Concepts of everyday use like energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and with the general…
Collective motion and self-organization of interacting particles, such as flocking and swarming, can be viewed as nonequilibrium analogues of collective dynamics in gases. Motivated by the analogy between gas mixtures and Cucker--Smale…
This paper derives the Fokker-Planck (FP) equation for a particle moving in potential by a randomly modulated dipole. The FP equation describes the anomalous diffusion observed in the companion paper [1] and breaks the conservation of the…
The dynamics of a reaction-diffusion-advection benthic-drift population model that links changes in the flow regime and habitat availability with population dynamics is studied. In the model, the stream is divided into drift zone and…
We study generic aspects of bubble dynamics in DNA under time dependent perturbations, for example temperature change, by mapping the associated Fokker-Planck equation to a quantum time-dependent Schroedinger equation with imaginary time.…
We propose and investigate different kinetic models for opinion formation, when the opinion formation process depends on an additional independent variable, e.g. a leadership or a spatial variable. More specifically, we consider:(i) opinion…
We study the main properties of the solution of a Fokker-Planck equation characterized by a variable diffusion coefficient and a polynomial superlinear drift, modeling the formation of consensus in a large interacting system of individuals.…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…