Related papers: Lorenz cycle for the Lorenz attractor
This article discusses the search procedure for the Poincar\'e recurrences to classify solutions on an attractor of a fourth-order nonlinear dynamical system using a previously developed high-precision numerical method. For the resulting…
Lorenz attractors are important objects in the modern theory of chaos. The reason from one side is that they are met in various natural applications (fluid dynamics, mechanics, laser dynamics, etc.). At the same time, Lorenz attractors are…
We present a mechanism to endow the polariton gas with attractive interactions. The scheme relies on an exciton reservoir, which can be formed even if excitons lie outside of the light-cone. Such an attractive interaction should open new…
Ligand-receptor interactions are ubiquitous in biology and have become popular in materials in view of their applications to programmable self-assembly. Although, complex functionalities often emerge from the simultaneous interaction of…
The classical dynamical $r$-matrix structure for the periodic elliptic Ruijsenaars chain is described. The Poisson brackets for the monodromy matrix are calculated as well, thus providing Liouville integrability of the model. Next, we study…
The structure of cylindrical double layers is studied using a modified Poisson Boltzmann theory and the density functional approach. In the model double layer, the electrode is a cylindrical polyion that is infinitely long, impenetrable,…
Study of various interesting features related to the nonlinear electrical response in composite materials through a model bond percolative system.
We study some topological properties of attractors.
The generalized Floquet exponent and the attractiveness portrait (or A-portrait for short) of the attractor and of the smallest invariant closed set are suggested to be used for the study of dynamical systems. Based on the A-portrait, some…
We derive a formally simple approximate analytical solution to the Poisson-Boltzmann equation for the spherical system via a geometric mapping. Its regime of applicability in the parameter space of the spherical radius and the surface…
This document presents an overview of the physics potential of a future electron-positron linear collider. It represents a common input from the CLIC and ILC communities.
In this paper, a new class of energy-preserving integrators is proposed and analysed for Poisson systems by using functionally-fitted technology. The integrators exactly preserve energy and have arbitrarily high order. It is shown that the…
The grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for existence of a grazing family of periodic solutions, is given. The properties of these periodic…
We consider a system of two identical linearly coupled Lorenz oscillators, presenting synchro- nization of chaotic motion for a specified range of the coupling strength. We verify the existence of global synchronization and…
The energy band structure of excitons is studied in periodic potentials produced by the short-range interaction between the exciton and electrons of Wigner or Moir\'{e} lattices. Treating the exciton as a point-like dipole that interacts…
In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation. It is also proved that if a Lie group acts…
The Zakharov system was originally proposed to study the propagation of Langmuir waves in an ionized plasma. In this paper, motivated by earlier work of the first and third authors, we numerically and analytically investigate the dynamics…
A linearly polarized Laguerre-Gaussian (LP-LG) laser beam with a twist index $l = -1$ has field structure that fundamentally differs from the field structure of a conventional linearly polarized Gaussian beam. Close to the axis of the LP-LG…
We calculate directly the interaction energy of the eigenstate with the single particle and the single hole for the XXZ-spin chain. We find the connection of this addition to the energy with the two-particle forward scattering phase shift…
The role of dielectric screening of electron-hole interaction in van der Waals heterostructures is theoretically investigated. A comparison between models available in the literature for describing these interactions is made and the…