Billiards with polynomial mixing rates

While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are intermittent between regular and chaotic, which makes them particularly interesting in physical studies. However, mathematical methods for the analysis of systems with slow mixing rates were developed just recently and are still difficult to apply to realistic models. Here we reduce those methods to a practical scheme that allows us to obtain a nearly optimal bound on mixing rates. We demonstrate how the method works by applying it to several classes of chaotic billiards with slow mixing as well as discuss a few examples where the method, in its present form, fails.Comment: 39pages, 11 figue

Personality regulation of students’ cognitive states during sports and educational activities

The article is devoted to the study of cognitive mental states and personality properties relationship during educational activities. In practical terms, the most important task in the field of educational psychology is to develop methods for updating and regulation of cognitive states. The study of cognitive states carried out in various forms of educational activity: in an ordinary situation (a lecture) and in a tense situation of training (an exam). N = 90, 1-st year students at the Kazan Federal University. During the research used different questionnaires to diagnose the personality traits and the intensity of students’ cognitive states, such as interest, reflection, concentration, mental stress etc. The data analysis included frequency analysis, the polar group method and the MANOVA method. Revealed that in an everyday situation of educational activity (lecture) the most often experienced states are thoughtfulness, interest and concentration, while in a tense situation of an exam - mental stress, doubt and concentration. In everyday situations, a state of thoughtfulness is observed in individuals with high Conscientiousness, and prevails in friendly, open-minded and emotionally stable students with a focus on the task. During the exam students with high activity, extraversion, and focus on the task experience the state of mental stress. Results of this research will find application in educational systems increasing the effectiveness of educational, scientific and creative activities, through the updating of students’ positive cognitive states. Cognitive states stimulate and regulate cognitive activity, performing the function of development of cognitive processes and intellectual abilities. The influence of personality properties on cognitive states is mediated by both the intensity of educational activity and the interaction of the personality traits.The study was carried out with the financial support of the Russian Foundation for Basic Research, project No. 19-013-00325

Beam propagation in a Randomly Inhomogeneous Medium

An integro-differential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random times. The expressions obtained for the mean square deviation from the initial direction of beam propagation generalize the "3/2 law".Comment: 4 page

Vacuum shell in the Schwarzschild-de Sitter world

We construct the classification scheme for all possible evolution scenarios and find the corresponding global geometries for dynamics of a thin spherical vacuum shell in the Schwarzschild-de Sitter metric. This configuration is suitable for the modelling of vacuum bubbles arising during cosmological phase transitions in the early Universe. The distinctive final types of evolution from the local point of view of a rather distant observer are either the unlimited expansion of the shell or its contraction with a formation of black hole (with a central singularity) or wormhole (with a baby universe in interior).Comment: 15 pages, 8 figure

Bacterial Phytochromes, Cyanobacteriochromes and Allophycocyanins as a Source of Near-Infrared Fluorescent Probes

Bacterial photoreceptors absorb light energy and transform it into intracellular signals that regulate metabolism. Bacterial phytochrome photoreceptors (BphPs), some cyanobacteriochromes (CBCRs) and allophycocyanins (APCs) possess the near-infrared (NIR) absorbance spectra that make them promising molecular templates to design NIR fluorescent proteins (FPs) and biosensors for studies in mammalian cells and whole animals. Here, we review structures, photochemical properties and molecular functions of several families of bacterial photoreceptors. We next analyze molecular evolution approaches to develop NIR FPs and biosensors. We then discuss phenotypes of current BphP-based NIR FPs and compare them with FPs derived from CBCRs and APCs. Lastly, we overview imaging applications of NIR FPs in live cells and in vivo. Our review provides guidelines for selection of existing NIR FPs, as well as engineering approaches to develop NIR FPs from the novel natural templates such as CBCRs.Peer reviewe

A simple piston problem in one dimension

We study a heavy piston that separates finitely many ideal gas particles moving inside a one-dimensional gas chamber. Using averaging techniques, we prove precise rates of convergence of the actual motions of the piston to its averaged behavior. The convergence is uniform over all initial conditions in a compact set. The results extend earlier work by Sinai and Neishtadt, who determined that the averaged behavior is periodic oscillation. In addition, we investigate the piston system when the particle interactions have been smoothed. The convergence to the averaged behavior again takes place uniformly, both over initial conditions and over the amount of smoothing.Comment: Accepted by Nonlinearity. 27 pages, 2 figure