Related papers: Simulation and Analysis of Two Toy Models
The dissipation rate due to inelastic collisions between equally charged, insulating particles in a dilute granular medium is calculated. It is equal to the known dissipation rate for uncharged granular media multiplied by a Boltzmann-like…
We develop two further numerical tests of parton cascade models: the ideal gas equation of state and the collision frequency tests. The equation of state test checks the initial momentum distribution generator and free expansion dynamics in…
We study uncertainty quantification for a Boltzmann-Poisson system that models electron transport in semiconductors and the physical collision mechanisms over the charges. We use the stochastic Galerkin method in order to handle the…
A two-temperature lattice gas model with repulsive nearest-neighbour interactions is studied using Monte Carlo simulations and dynamical mean-field approximation. The evolution of the two-dimensional, half-filled system is described by an…
For more than a century Liesegang patterns -- self-organized, quasi-periodic structures occurring in diffusion-limited chemical reactions with two components -- have been attracting scientists. The pattern formation can be described by four…
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of…
Extending the famous Model B for the time evolution of a liquid mixture, we derive an approximate expression for the mobility matrix that couples the different mixture components. This approach is based on a single component fluid with…
Collisional reservoirs are becoming a major tool for modelling open quantum systems. In their simplest implementation, an external agent switches on, for a given time, the interaction between the system and a specimen from the reservoir.…
The correlation length $\xi$, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields…
In spite of its simplicity, the central limit theorem captures one of the most outstanding phenomena in mathematical physics, that of universality. While this classical result is well understood it is still not very clear what happens to…
The zero-temperature and finite-temperature thermodynamics of two-component Fermi gases with finite-range attractive interaction suffer from fermion sign problem, which seems like an insurmountable problem in exact numerical simulations. In…
Diffusion models are increasingly used as powerful conditional generators, yet real deployments often involve multiple target distributions arising from different tasks, e.g., diverse prompt domains in text-to-image generation, or multiple…
A mixture of spin-1/2 fermionic atoms and molecules of paired fermionic atoms is studied in an optical lattice. The molecules are formed by an attractive nearest-neighbor interaction. A functional integral is constructed for this many-body…
In a granular gas experiment of magnetized particles confined in a thin layer, the rate of dissipative collisions is tuned by adjusting the amplitude of an external magnetic field. The velocity statistics are analyzed using the dynamic and…
Infinite-range spin-glass models with Levy-distributed interactions show a spin-glass transition with similarities to both the Sherrington-Kirkpatrick model and to disordered spin systems on finite connectivity random graphs. Despite the…
We develop a microscopic theory to analyze the phase behaviour and compute correlation functions of dense assemblies of soft repulsive particles both at finite temperature, as in colloidal materials, and at vanishing temperature, a…
The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to…
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…
The most general exclusion single species reaction-diffusion models with nearest-neighbor interactions one a one dimensional lattice are investigated, for which the evolution of full intervals are closed. Using a generating function method,…
Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective,…