Related papers: One-dimensional relativistic particle as a movable…
The dynamics of several light filaments (spatial optical solitons) propagating in an optically nonlinear and non-local random medium is investigated using the paradigms of the physics of complexity. Cluster formation is interpreted as a…
We study the dynamics of three elastic particles in a finite interval where two light particles are separated by a heavy ``piston''. The piston undergoes surprisingly complex motion that is oscillatory at short time scales but seemingly…
We study the dynamics of a one-dimensional discrete flow with open boundaries - a series of moving point particles connected by ideal springs. These particles flow towards an inlet at constant velocity, pass into a region where they are…
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a…
We introduce a spacetime discretization of the Dirac equation that has the form of a quantum automaton and that is invariant upon changing the representation of the Clifford algebra, as the Dirac equation itself. Our derivation follows…
Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…
I outline a possible logical path from the formulation of physics of classical mechanics to "abstract" systems like cellular automata. The goal of this article is that of illustrating why physicists often study extremely simplified models,…
The system describing a single Dirac electron field coupled with classically moving point nuclei is presented and studied. The model is a semi-relativistic extension of corresponding time-dependent one-body Hartree-Fock equation coupled…
Generalizing the motion representation we introduced for number-conserving rules, we give a systematic way to construct a generalized motion representation valid for non-conservative rules using the expression of the current, which appears…
Physical self-adjoint extensions and their spectra of the one-dimensional Dirac type Hamiltonian operator in which both the mass and velocity are constant except for a finite jump at one point of the real axis are correctly found. Different…
We have proposed a simple one-dimensional model of internal particle dynamics. The model is based on the assumption that self-interaction can be represented by a nonlinear feedback and described by a quadratic recurrent map. Charge plays…
In this paper, we give a singular function on a unit interval derived from the dynamic of the one-dimensional elementary cellular automaton Rule 150. We describe properties of the resulting function, that is strictly increasing, uniformly…
We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program…
Dirac particle represents a fundamental constituent of our nature. Simulation of Dirac particle dynamics by a controllable quantum system using quantum walks will allow us to investigate the non-classical nature of dynamics in its discrete…
We show that the full features of the dynamics towards the Feigenbaum attractor, present in all low-dimensional maps with a unimodal leading component, form a hierarchical construction with modular organization that leads to a clear-cut…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
In order to understand the origin of one-body dissipation in nuclei, we analyze the behavior of a gas of classical particles moving in a two-dimensional cavity with nuclear dimensions. This "nuclear" billiard has multipole-deformed walls…
Let A^Z be the Cantor space of bi-infinite sequences in a finite alphabet A, and let sigma be the shift map on A^Z. A `cellular automaton' is a continuous, sigma-commuting self-map Phi of A^Z, and a `Phi-invariant subshift' is a closed,…
Single particle dynamics in electron microscopes, ion or electron lithographic instruments, particle accelerators, and particle spectrographs is described by weakly nonlinear ordinary differential equations. Therefore, the linear part of…
We study the dynamics of three particles in a finite interval, in which two light particles are separated by a heavy ``piston'', with elastic collisions between particles but inelastic collisions between the light particles and the interval…