The world of strategies with memory

As part of a generalized ”prisoners’ dilemma”, is considered that the evolution of a population with a full set of behavioral strategies limited only by the depth of memory. Each subsequent generation of the population successively loses the most disadvantageous strategies of behavior of the previous generation. It is shown that an increase in memory in a population is evolutionarily beneficial. The winners of evolutionary selection invariably refer to agents with maximum memory. The concept of strategy complexity is introduced. It is shown that strategies that win in natural selection have maximum or near maximum complexity. Despite the fact that at a separate stage of evolution, according to the payout matrix, the individual gain, while refusing to cooperate, exceeded the gain obtained while cooperating. The winning strategies always belonged to the so-called respectable strategies that are clearly prone to cooperation

Alternative mechanisms of stochasticity in maps with discontinuities

The maps with discontinuities dynamic chaos research is made. The borders of stability and bifurcation of cycles cutting are obtained. The structure of the stable cycles tree is determined. A new mechanism of spontaneous transition to chaos caused by non-local bifurcation of stable cycles cutting is found out

Singularities Motion Equations in 2-Dimensional Ideal Hydrodynamics of Incompressible Fluid

In this paper, we have obtained motion equations for a wide class of one-dimensional singularities in 2-D ideal hydrodynamics. The simplest of them, are well known as point vortices. More complicated singularities correspond to vorticity point dipoles. It has been proved that point multipoles of a higher order (quadrupoles and more) are not the exact solutions of two-dimensional ideal hydrodynamics. The motion equations for a system of interacting point vortices and point dipoles have been obtained. It is shown that these equations are Hamiltonian ones and have three motion integrals in involution. It means the complete integrability of two-particle system, which has a point vortex and a point dipole.Comment: 9 page

Relaxation of high-energy quasiparticle distributions: electron-electron scattering in a two-dimensional electron gas

A theory is developed for the evolution of the non-equilibrium distribution of quasiparticles when the scattering rate decreases due to particle collisions. We propose a "modified one-collision approximation" which is most effective for high-energy quasiparticle distributions. This method is used to explain novel measurements of the non-monotonic energy dependence of the signal of scattered electrons in a 2D system. The observed effect is related to a crossover from the ballistic to the hydrodynamic regime of electron flow.Comment: 6 pages, 3 figure

Stochastic resonance in nuclear fission

Fission decay of highly excited periodically driven compound nuclei is considered in the framework of Langevin approach. We used residual-time distribution (RTD) as a tool for studying the dynamic features in the presence of periodic perturbation. The structure of RTD essentially depends on the relation between Kramers decay rate and the frequency w of periodic perturbation. In particular, the intensity of the first peak in RTD has a sharp maximum at certain nuclear temperature depending on w. This maximum should be considered as fist-hand manifestation of stochastic resonance in nuclear dynamics

The electrical resistance of spatially varied magnetic interface. The role of normal scattering

We investigate the diffusive electron transport in conductors with spatially inhomogeneous magnetic properties taking into account both impurity and normal scattering. It is found that the additional interface resistance that arises due to the magnetic inhomogeneity depends essentially on their spatial characteristics. The resistance is proportional to the spin flip time in the case when the magnetic properties of the conducting system vary smoothly enough along the sample. It can be used to direct experimental investigation of spin flip processes. In the opposite case, when magnetic characteristics are varied sharply, the additional resistance depends essentially on the difference of magnetic properties of the sides far from the interface region. The resistance increases as the frequency of the electron-electron scattering increases. We consider also two types of smooth interfaces: (i) between fully spin-polarized magnetics and usual magnetic (or non-magnetic) conductors, and (ii) between two fully oppositely polarized magnetic conductors. It is shown that the interface resistance is very sensitive to appearing of the fully spin-polarized state under the applied external field

Levy Anomalous Diffusion and Fractional Fokker--Planck Equation

We demonstrate that the Fokker-Planck equation can be generalized into a 'Fractional Fokker-Planck' equation, i.e. an equation which includes fractional space differentiations, in order to encompass the wide class of anomalous diffusions due to a Levy stable stochastic forcing. A precise determination of this equation is obtained by substituting a Levy stable source to the classical gaussian one in the Langevin equation. This yields not only the anomalous diffusion coefficient, but a non trivial fractional operator which corresponds to the possible asymmetry of the Levy stable source. Both of them cannot be obtained by scaling arguments. The (mono-) scaling behaviors of the Fractional Fokker-Planck equation and of its solutions are analysed and a generalization of the Einstein relation for the anomalous diffusion coefficient is obtained. This generalization yields a straightforward physical interpretation of the parameters of Levy stable distributions. Furthermore, with the help of important examples, we show the applicability of the Fractional Fokker-Planck equation in physics.Comment: 22 pages; To Appear in Physica

Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires

We study the role of electron-electron collisions in the formation of spin-polarized current states in a "spin guide" which is a system consisting of a non-magnetic conducting channel wrapped in the grounded nanoscale magnetic shell. It is shown that under certain conditions the spin guide may generate and transport over long distances the non-equilibrium electron density with a high level of spin polarization, even though the frequent electron-electron scattering leads to a common drift of non-equilibrium electrons. We also propose some ways to convert the spin-polarized electron density into a spin-polarized electric current

Effects of Electron-Electron Scattering on Electron-Beam Propagation in a Two-Dimensional Electron-Gas

We have studied experimentally and theoretically the influence of electron-electron collisions on the propagation of electron beams in a two-dimensional electron gas for excess injection energies ranging from zero up to the Fermi energy. We find that the detector signal consists of quasiballistic electrons, which either have not undergone any electron-electron collisions or have only been scattered at small angles. Theoretically, the small-angle scattering exhibits distinct features that can be traced back to the reduced dimensionality of the electron system. A number of nonlinear effects, also related to the two-dimensional character of the system, are discussed. In the simplest situation, the heating of the electron gas by the high-energy part of the beam leads to a weakening of the signal of quasiballistic electrons and to the appearance of thermovoltage. This results in a nonmonotonic dependence of the detector signal on the intensity of the injected beam, as observed experimentally.Comment: 9 pages, 7 figure

Minimal Fermi model

In this work, we consider the simple model for Fermi acceleration of a particle between two periodically oscillating walls, The law of wall movement is continuous but not smooth. Exact mapping for this system has been obtained. A fractal saet of trajectories with infinitely increasing speed is shown to exist. The main characteristic of such trajectories are discussed. A comparison with heigh-energy approach has been carried out. Quanlitative differences in behavior of exact and approximate description have been found. For example, in heigh-energy approach, there are no trajectories with unlimited speed increase