Related papers: Dynamics of McMillan mappings II. Axially symmetri…
We apply round-off to planar rotations, obtaining a one-parameter family of invertible maps of a two-dimensional lattice. As the angle of rotation approaches pi/2, the fourth iterate of the map produces piecewise-rectilinear motion, which…
The relative motion of material, point-like observers is analysed in terms of coordinate maps between the respective rest-frame of each observer. Under the assumption these maps are $C^{2}$-regular, conservation laws are deduced, which in…
The premetric approach to electrodynamics provides a unified description of a wide class of electromagnetic phenomena. In particular, it involves axion, dilaton and skewon modifications of the classical electrodynamics. This formalism…
We examine the diffraction properties of lattice dynamical systems of algebraic origin. It is well-known that diverse dynamical properties occur within this class. These include different orders of mixing (or higher-order correlations), the…
The problem of light waves interaction with charged particles becomes more and more complex starting with the case of plane waves, where the analytical solution is well known, to more natural, though more complicated situations which…
We define affine transport lifts on the tangent bundle by associating a transport rule for tangent vectors with a vector field on the base manifold. The aim is to develop tools for the study of kinetic/ dynamical symmetries in relativistic…
Focused laser beams allow controlling mechanical motion of objects and can serve as a tool for assembling complex micro and nano structures in space. While in a vast majority of cases small particles experience attractive gradient forces…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
Plasma lensing provides compact focusing of electron beams, since they offer strong focusing fields (kT/m) in both planes simultaneously. This becomes particularly important for highly diverging beams with a large energy spread such as…
The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…
A formalism for describing relativistic ponderomotive effects, which occur in the dynamics of an electron driven by a focused relativisticaly intense optical envelope, is established on the basis of a rigorous asymptotic expansion of the…
Using mean-field approximations, this paper identifies a phase transition in a three-dimensional Electron Glass lattice model. The density of states of the eigenvalue distribution of the inverse susceptibility matrix is used to identify the…
This paper describes a package for analytical ray tracing of relatively simple optical systems. AESOP (An Extensible Symbolic Optics Package) enables analysis of the effects of small optical element misalignments or other perturbations. (It…
We consider Markovian dynamics modeling open mesoscopic systems which are driven away from detailed balance by a nonconservative force. A systematic expansion is obtained of the stationary distribution around an equilibrium reference, in…
Progress on the Intensity Frontier of high energy physics critically depends on record high intensity charged particles accelerators. Beams in such machines become operationally limited by coherent beam instabilities, particularly enhanced…
Quantum mechanics of bending of a nonrelativistic monoenergetic charged particle beam by a dipole magnet is studied in the paraxial approximation. The transfer map for the position and momentum components of a particle of the beam between…
Using the ``composite harmonic mapping method," we construct exact solutions for cylindrically symmetric gravitational and electromagnetic waves within the Einstein-Maxwell system, focusing on the conversion dynamics between these types of…
This paper begins with a critical analysis of the concept of 'material point particle'. We argue that this concept is incompatible with the force laws of action-at-a-distance electrodynamics, and we suggest that the trajectory of a particle…
In the paper [I], the first part of our work, we established the model of interaction of five elements: first, a unit time-like vector field, associated with the velocity of dynamic aether, second, the pseudoscalar field describing an…
Maxwell's equations and the Lorentz force density are expressed using an alternative simultaneity gauge. As a result, they describe electrodynamics for an observer travelling with a constant velocity through an isotropic medium. If desired,…