Related papers: Lorenz cycle for the Lorenz attractor
The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which…
The solvable quantum mechanical model for the relativistic two-body system composed of spin-1/2 and spin-0 particles is constructed. The model includes the oscillator-type interaction through a combination of Lorentz-vector and -tensor…
Using the multisymplectic Hamiltonian formalism, we propose a Poisson bracket for the electromagnetic field that, in addition to satisfying the restricted principle of relativity, reproduces well-established results from the standard…
We study a class of geometric Lorenz flows, introduced independently by Afraimovic, Bykov & Sil'nikov and by Guckenheimer & Williams, and give a verifiable condition for such flows to be mixing. As a consequence, we show that the classical…
Relativistic many-body perturbation theory is applied to study properties of ions of the francium isoelectronic sequence. Specifically, energies of the 7s, 7p, 6d, and 5f states of Fr-like ions with nuclear charges Z = 87 - 100 are…
Chaotic bursting behaviors have been observed by many authors in neural dynamics mainly in the transition between different kinds of bursting behavior. As a well-known three-dimensional ODEs model with various bursting solutions, the…
This thesis presents our results on Liouville integrable systems of Calogero-Ruijsenaars type: 1. We prove an explicit formula providing canonical spectral coordinates for the rational Calogero-Moser system. 2. We explore action-angle…
A method is presented for calculating binding energies and other properties of extended interacting systems using the projected density of transitions (PDoT) which is the probability distribution for transitions of different energies…
We prove energy estimates for solutions to a tensorial system of coupled non-linear wave equations, in a way that is suitable to deal with the structure of the non-linearity that arises from the Einstein-Yang-Mills system in the Lorenz…
The Lorentz gas of $\mathbb{Z}^2$-periodic scatterers (or the so called Sinai billiards) can be used to model motion of electrons on an ionized medal. We investigate the linear response for the system under various external forces (during…
The isospin, spin and parity dependent potential of a pair of static-light mesons is computed using Wilson twisted mass lattice QCD with two flavors of degenerate dynamical quarks. From the results a simple rule can be deduced stating,…
We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and…
Lie-Poisson electrodynamics describes the semi-classical limit of non-commutative $U(1)$ gauge theory, characterized by Lie-algebra-type non-commutativity. We focus on the mechanics of a charged point-like particle moving in a given gauge…
Adsorbed gases within, or outside of, carbon nanotubes may be analyzed with an approximate model of adsorption on lattice sites situated on a cylindrical surface. Using this model, the ground state energies of alternative lattice structures…
We define a 1-parameter family of $r$-matrices on the loop algebra of $sl_{2}$, defining compatible Poisson structures on the associated loop group, which degenerate into the rational and trigonometric structures, and study the Manin…
We investigate the dynamics of a single phonon (oscillator) mode linearly coupled to an electronic few-level system in contact with external particle reservoirs (leads). A stationary electronic current through the system generates…
In a recent paper, we presented an intelligent evolutionary search technique through genetic programming (GP) for finding new analytical expressions of nonlinear dynamical systems, similar to the classical Lorenz attractor's which also…
Structure of spinning particle based on the rotating black hole solution is considered. It has gyromagnetic ratio $g=2$ and a nontrivial twistorial and stringy systems. The mass and spin appear from excitations of the Kerr circular string,…
In this article we construct the parameter region where the existence of a homoclinic orbit to a zero equilibrium state of saddle type in the Lorenz-like system will be analytically proved in the case of a nonnegative saddle value. Then,…
We show that oscillations are excited in a complex system under the influence of the external force, if the parameters of the system experience rapid change due to the changes in its internal structure. This excitation is collision-like and…