Related papers: Simulation and Analysis of Two Toy Models
In ultra-relativistic heavy-ion collisions a strongly interacting complex system of quarks and gluons is formed. The nature of the system so created and the mechanism of multi-particle production in these collisions may be revealed by…
Chemical equilibrium is fully characterized by thermodynamics, while the rates of chemical reactions can be calculated for ideal solutions by using mass-action equations. The evaluation of the rates of reactions in a non-ideal system is…
The model of Fermi particles with random two-body interaction is investigated. This model allows to study the origin and accuracy of statistical laws in few-body systems, the role of interaction and chaos in thermalization, Fermi-Dirac…
A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…
The one dimensional probabilistic toy model of particle scattering theory is proposed. The toy model version of scattering probability is proved to be equal to the hypervolume of a n-dimensional figure. The solution for any n-particle toy…
Predicting nonequilibrium fluctuations requires a knowledge of nonequilibrium distribution functions. Despite the distributions' fractal character some theoretical results, "Fluctuation Theorems", reminiscent of but distinct from, Gibbs'…
Many processes in chemistry, physics, and biology depend on thermally activated events in which the system changes its state by surmounting an activation barrier. Examples range from chemical reactions, protein folding, and nucleation…
We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their…
We apply the random-matrix theory to the car-parking problem. For this purpose, we adopt a Coulomb gas model that associates the coordinates of the gas particles with the eigenvalues of a random matrix. The nature of interaction between the…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
This paper presents the first application of Gaussian Mixture Copula Models to the statistical modeling of driving scenarios for the safety validation of automated driving systems. Knowledge of the joint probability distribution of scenario…
In this paper, we present results of simulations of a model of the Galton board for various degrees of elasticity of the ball-to-nail collision.
Analytical and numerical studies on many-body stochastic processes with multiplicative interactions are reviewed. The method of moment relations is used to investigate effects of asymmetry and randomness in interactions. Probability…
We use a combination of perturbation theory and numerical techniques to study the equilibration of two interacting fields which are initially at thermal equilibrium at different temperatures. Using standard rules of quantum field theory, we…
Competition among particle evaporation, temperature gradient and flow is investigated in a phenomenological manner, based on a simultaneous analysis of quantum statistical correlations and momentum distributions for a non-relativistic,…
The use of machine learning algorithms is an attractive way to produce very fast detector simulations for scattering reactions that can otherwise be computationally expensive. Here we develop a factorised approach where we deal with each…
We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots. For chaotic dots, we use a normalized random wave model to obtain analytic expansions…
The packing of hard-core particles in contact with their neighbors is considered as the simplest model of disordered particulate media. We formulate the statically determinate problem which allows analytical investigation of the statistical…
In the Coulomb blockade regime of a ballistic quantum dot, the distribution of conductance peak spacings is well known to be incorrectly predicted by a single-particle picture; instead, matrix element fluctuations of the residual electronic…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…