Alexander Loskutov

Properties of some chaotic billiards with time-dependent boundaries

A dispersing billiard (Lorentz gas) and focusing billiards (in the form of a stadium) with time-dependent boundaries are considered. The problem of particle acceleration in such billiards is studied. For the Lorentz gas two cases of the time dependence are investigated: stochastic perturbations of the boundary and its periodic oscillations. Two types of focusing billiards with periodically forced boundaries are explored: a stadium with strong chaotic properties and a near-rectangle stadium. It is shown that in all cases billiard particles can reach unbounded velocities. Average velocities of the particle ensemble as functions of time and the number of collisions are obtained.

Particle Dynamics in Time-Dependent Stadium-Like Billiards

Billiards in the form of a stadium with perturbed boundaries are considered. Investigations are primarily devoted to billiards having a near-rectangle form, but the results regarding the “classical” stadium with the boundary that consists of two semicircles and two parallel segments tangent to them, are also described. In the phase plane, areas corresponding to decrease and increase of the velocity of billiard particles are found. The average velocity of the particle ensemble as a function of the number of collisions with the boundary is obtained.

Control of dynamical systems behavior by parametric perturbations: An analytic approach

The problem of parametric suppression of deterministic chaos is considered. It is proved that certain parametric perturbations of a one-dimensional map with chaotic dynamics can lead to a transition of that map into a regime of regular behavior.

Fermi acceleration and scaling properties of a time dependent oval billiard

We consider the phenomenon of Fermi acceleration for a classical particle inside an area with a closed boundary of oval shape. The boundary is considered to be periodically time varying and collisions of the particle with the boundary are assumed to be elastic. It is shown that the breathing geometry causes the particle to experience Fermi acceleration with a growing exponent rather smaller as compared to the no breathing case. Some dynamical properties of the particles velocity are discussed in the framework of scaling analysis.

Chromosome evolution with naked eye: Palindromic context of the life origin

Based on the representation of the DNA sequence as a two-dimensional (2D) plane walk, we consider the problem of identification and comparison of functional and structural organizations of chromosomes of different organisms. According to the characteristic design of 2D walks we identify telomere sites, palindromes of various sizes and complexity, areas of ribosomal RNA, transposons, as well as diverse satellite sequences. As an interesting result of the application of the 2D walk method, a new duplicated gigantic palindrome in the X human chromosome is detected. A schematic mechanism leading to the formation of such a duplicated palindrome is proposed. Analysis of a large number of the different genomes shows that some chromosomes (or their fragments) of various species appear as imperfect gigantic palindromes, which are disintegrated by many inversions and the mutation drift on different scales. A spread occurrence of these types of sequences in the numerous chromosomes allows us to develop a new insight of some accepted points of the genome evolution in the prebiotic phase.

Dynamics control of chaotic systems by parametric destochastization

It is shown, that deterministic noise (chaos) appearing via destruction of the quasiperiodic motion may be easily suppressed by weak parametric perturbation of the system.

MODEL OF CARDIAC TISSUE AS A CONDUCTIVE SYSTEM WITH INTERACTING PACEMAKERS AND REFRACTORY TIME

The model of the cardiac tissue as a conductive system with two interacting pacemakers and a refractory time is proposed. In the parametric space of the model the phase locking areas are investigated in detail. The obtained results make possible to predict the behavior of excitable systems with two pacemakers, depending on the type and intensity of their interaction and the initial phase. Comparison of the described phenomena with intrinsic pathologies of cardiac rhythms is given.

TIME SERIES ANALYSIS OF ECG: A POSSIBILITY OF THE INITIAL DIAGNOSTICS

The methods of nonlinear dynamics are applied to reveal the pathologies of patients with different heart failures. Our approach is based on the analysis of the correlation and embedding dimensions of the RR-intervals of ECGs. We demonstrate that these characteristics are quite convenient tools for the initial diagnosis. Advantages and disadvantages of the method are discussed.

A family of stadium-like billiards with parabolic boundaries under scaling analysis

Some chaotic properties of a family of stadium-like billiards with parabolic focusing components, which is described by a two-dimensional nonlinear area-preserving map, are studied. Critical values of billiard geometric parameters corresponding to a sudden change of the maximal Lyapunov exponent are found. It is shown that the maximal Lyapunov exponent obtained for chaotic orbits of this family is scaling invariant with respect to the control parameters describing the geometry of the billiard. We also show that this behavior is observed for a generic one-parameter family of mapping with the nonlinearity given by a tangent function.

Intermittency as a universal characteristic of the complete chromosome DNA sequences of eukaryotes: From protozoa to human genomes

Large-scale dynamical properties of complete chromosome DNA sequences of eukaryotes are considered. Using the proposed deterministic models with intermittency and symbolic dynamics we describe a wide spectrum of large-scale patterns inherent in these sequences, such as segmental duplications, tandem repeats, and other complex sequence structures. It is shown that the recently discovered gene number balance on the strands is not of a random nature, and certain subsystems of a complete chromosome DNA sequence exhibit the properties of deterministic chaos.