Related papers: A variational approach to a fuzzy Boltzmann equati…
We consider the relativistic statistical mechanics of an ensemble of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau .$ We generalize the approach of Yang and Yao, based on the Wigner distribution…
We investigate the effects of the gravitational field on the quantum dynamics of non-relativistic particles. We consider N non-relativistic particles, interacting with the linearized gravitational field. Using the Feynman - Vernon influence…
This paper considers a new fuzzy fractional differential variational inequality with integral boundary conditions comprising a fuzzy fractional differential inclusion with integral boundary conditions and a variational inequality in…
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…
We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
A linear Boltzmann equation with nonautonomous collision operator is rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with…
We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another particle, the leader. The follower chooses its leader…
Starting from a microscopic approach, we develop a covariant formalism to describe a set of interacting gases. For that purpose, we model the collision term entering the Boltzmann equation for a class of interactions and then integrate this…
This Thesis concentrates on the analysis of coupled RTA (relaxation time approximation) kinetic equations for bosons and fermions. Bosons are treated as massless particles, while fermions have a finite mass. Using analytic and numerical…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
We consider percolation and jamming transitions for particulate systems exposed to compression. For the systems built of particles interacting by purely repulsive forces in addition to friction and viscous damping, it is found that these…
Deformed correlated Gaussian basis functions are introduced and their matrix elements are calculated. These basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole…
We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive…
In dealing with veracity of data analytics, fuzzy methods are more and more relying on probabilistic and statistical techniques to underpin their applicability. Conversely, standard statistical models usually disregard to take into account…
Following the analytic approach to thermodynamics developed by Stueckelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations…
We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of…
In transport theory, physical phenomena are well described using the Boltzmann equation, which is efficiently simulated and discretized with the lattice Boltzmann method. The collision step defines the microscopic molecules behavior, and…
Although a precise description of microscopic physical problems requires a full quantum mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which…
A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled Hamilton-Heisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become…