Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the appearance of chaotic attractor. The attractor exists in an invariant region of phase space bounded by the manifolds of the saddle fixed point and the saddle periodic point. The oscillations from the chaotic attractor have a spike-burst shape with anti-phase synchronized spiking.Comment: To be published in CHAO

Self-similar turbulent dynamo

The amplification of magnetic fields in a highly conducting fluid is studied numerically. During growth, the magnetic field is spatially intermittent: it does not uniformly fill the volume, but is concentrated in long thin folded structures. Contrary to a commonly held view, intermittency of the folded field does not increase indefinitely throughout the growth stage if diffusion is present. Instead, as we show, the probability-density function (PDF) of the field strength becomes self-similar. The normalized moments increase with magnetic Prandtl number in a powerlike fashion. We argue that the self-similarity is to be expected with a finite flow scale and system size. In the nonlinear saturated state, intermittency is reduced and the PDF is exponential. Parallels are noted with self-similar behavior recently observed for passive-scalar mixing and for map dynamos.Comment: revtex, 4 pages, 5 figures; minor changes to match published versio

Magnetic Field Amplification by Small-Scale Dynamo Action: Dependence on Turbulence Models and Reynolds and Prandtl Numbers

The small-scale dynamo is a process by which turbulent kinetic energy is converted into magnetic energy, and thus is expected to depend crucially on the nature of turbulence. In this work, we present a model for the small-scale dynamo that takes into account the slope of the turbulent velocity spectrum v(l) ~ l^theta, where l and v(l) are the size of a turbulent fluctuation and the typical velocity on that scale. The time evolution of the fluctuation component of the magnetic field, i.e., the small-scale field, is described by the Kazantsev equation. We solve this linear differential equation for its eigenvalues with the quantum-mechanical WKB-approximation. The validity of this method is estimated as a function of the magnetic Prandtl number Pm. We calculate the minimal magnetic Reynolds number for dynamo action, Rm_crit, using our model of the turbulent velocity correlation function. For Kolmogorov turbulence (theta=1/3), we find that the critical magnetic Reynolds number is approximately 110 and for Burgers turbulence (theta=1/2) approximately 2700. Furthermore, we derive that the growth rate of the small-scale magnetic field for a general type of turbulence is Gamma ~ Re^((1-theta)/(1+theta)) in the limit of infinite magnetic Prandtl numbers. For decreasing magnetic Prandtl number (down to Pm approximately larger than 10), the growth rate of the small-scale dynamo decreases. The details of this drop depend on the WKB-approximation, which becomes invalid for a magnetic Prandtl number of about unity.Comment: 13 pages, 8 figures; published in Phys. Rev. E 201

Professional readiness of the teacher of physical culture to work in conditions of inclusive education

Analyzes the effectiveness of implementation in the educational system, inclusive approach. Shows the problems and the importance of preparation of qualified pedagogical staff, including in the field of physical culture and sports. Considered professional readiness pedagog for physical cultureАнализируется эффективность внедрения в образовательную систему инклюзивного подхода. Показаны проблемы и значимость подготовки квалифицированных педагогических кадров, в том числе в области физической культуры и спорта. Рассматривается профессиональная готовность педагога по физической культур

Turbulent Origin of the Galactic-Center Magnetic Field: Nonthermal Radio Filaments

A great deal of study has been carried out over the last twenty years on the origin of the magnetic activity in the Galactic center. One of the most popular hypotheses assumes milli-Gauss magnetic field with poloidal geometry, pervading the inner few hundred parsecs of the Galactic-center region. However, there is a growing observational evidence for the large-scale distribution of a much weaker field of B \lesssim 10 micro G in this region. Here, we propose that the Galactic-center magnetic field originates from turbulent activity that is known to be extreme in the central hundred parsecs. In this picture the spatial distribution of the magnetic field energy is highly intermittent, and the regions of strong field have filamentary structures. We propose that the observed nonthermal radio filaments appear in (or, possibly, may be identified with) such strongly magnetized regions. At the same time, the large-scale diffuse magnetic field is weak. Both results of our model can explain the magnetic field measurements of the the Galactic-center region. In addition, we discuss the role of ionized outflow from stellar clusters in producing the long magnetized filaments perpendicular to the Galactic plane.Comment: 11 pages, accepted to ApJ Letter

Simple model of complex dynamics of activity patterns in developing networks of neuronal cultures

Living neuronal networks in dissociated neuronal cultures are widely known for their ability to generate highly robust spatiotemporal activity patterns in various experimental conditions. These include neuronal avalanches satisfying the power scaling law and thereby exemplifying self-organized criticality in living systems. A crucial question is how these patterns can be explained and modeled in a way that is biologically meaningful, mathematically tractable and yet broad enough to account for neuronal heterogeneity and complexity. Here we propose a simple model which may offer an answer to this question. Our derivations are based on just few phenomenological observations concerning input-output behavior of an isolated neuron. A distinctive feature of the model is that at the simplest level of description it comprises of only two variables, a network activity variable and an exogenous variable corresponding to energy needed to sustain the activity and modulate the efficacy of signal transmission. Strikingly, this simple model is already capable of explaining emergence of network spikes and bursts in developing neuronal cultures. The model behavior and predictions are supported by empirical observations and published experimental evidence on cultured neurons behavior exposed to oxygen and energy deprivation. At the larger, network scale, introduction of the energy-dependent regulatory mechanism enables the network to balance on the edge of the network percolation transition. Network activity in this state shows population bursts satisfying the scaling avalanche conditions. This network state is self-sustainable and represents a balance between global network-wide processes and spontaneous activity of individual elements

Resonant Diffraction Radiation from an Ultrarelativistic Particle Moving Close to a Tilted Grating

A simple model for calculating the diffraction radiation characteristics from an ultrarelativistic charged particle moving close to a tilted ideally conducting strip is developed. Resonant diffraction radiation (RDR) is treated as a superposition of the radiation fields for periodically spaced strips. The RDR characteristics have been calculated as a function of the number of grating elements, tilted angle, and initial particle energy. An analogy with both the resonant transition radiation in absorbing medium and the parametric X-ray radiation is noted.Comment: 17 pages, 12 figures, RevTe

Thomson Scattering of Coherent Diffraction Radiation by an Electron Bunch

The paper considers the process of Thomson scattering of coherent diffraction radiation (CDR) produced by the preceding bunch of the accelerator on one of the following bunches. It is shown that the yield of scattered hard photons is proportional to N$_e^3$, where N$_e$ is the number of electrons per bunch. A geometry is chosen for the CDR generation and an expression is obtained for the scattered photon spectrum with regard to the geometry used, that depends in an explicit form on the bunch size. A technique is proposed for measuring the bunch length using scattered radiation characteristics.Comment: 14 pages, LATEX, 6 ps.gz figures, submitted to Phys.Rev.

Synthesis of substituted tetrahydro-1,3-oxazines

A number of mono-, di-, tri-, and tetrasubstituted tetrahydro-1,3-oxazines were synthesized by the reaction of 3-amino- and 3-methylamino-1-propanols with aldehydes. © 1975 Consultants Bureau