Levy flights from a continuous-time process

The Levy-flight dynamics can stem from simple random walks in a system whose operational time (number of steps n) typically grows superlinearly with physical time t. Thus, this processes is a kind of continuous-time random walks (CTRW), dual to usual Scher-Montroll model, in which $n$ grows sublinearly with t. The models in which Levy-flights emerge due to a temporal subordination let easily discuss the response of a random walker to a weak outer force, which is shown to be nonlinear. On the other hand, the relaxation of en ensemble of such walkers in a harmonic potential follows a simple exponential pattern and leads to a normal Boltzmann distribution. The mixed models, describing normal CTRW in superlinear operational time and Levy-flights under the operational time of subdiffusive CTRW lead to paradoxical diffusive behavior, similar to the one found in transport on polymer chains. The relaxation to the Boltzmann distribution in such models is slow and asymptotically follows a power-law

Features of the methodology of the development of cadets’ physical qualities during kettlebell lifting activities

La metodología de los autores sobre el desarrollo de las cualidades físicas de los cadetes durante las actividades de levantamiento de pesas se confirma en el artículo y se verifica su eficiencia. 86 cadetes participaron en la investigación. Se formaron los grupos experimentales (EG, n=29) y control (CG, n=57). La investigación se realizó de acuerdo con las siguientes pruebas: carrera de 100 m, carrera de 3 km, inclinación hacia adelante del cuerpo, mantener el cuerpo en posición horizontal, ejercicio de barra de levantamiento, balanceo de cadera, flexión en barras paralelas, ejercicio de poder complejo. Al final del estudio, la mayoría de las pruebas establecieron un nivel significativamente mejor del desarrollo de las cualidades físicas de los cadetes. The authors’ methodology of the development of the physical qualities of cadets during kettlebell lifting activities is substantiated in the article and its efficiency is checked. 86 cadets participated in the research. The experimental (EG, n=29) and control (CG, n=57) groups were formed. The research was conducted according to the following tests: 100 m race, 3 km race, forward inclination of the body, holding the body in a horizontal position, pull-up bar exercise, hipswing-up, push-up on parallel bars, complex power exercise. At the end of the study, a significantly better level of the physical qualities’ development of cadets engaged in kettlebell lifting activities according to the authors’ methodology was established by the majority of tests

Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution

The nonlinear diffusion equation $\frac{\partial \rho}{\partial t}=D \tilde{\Delta} \rho^\nu$ is analyzed here, where $\tilde{\Delta}\equiv \frac{1}{r^{d-1}}\frac{\partial}{\partial r} r^{d-1-\theta} \frac{\partial}{\partial r}$, and $d$, $\theta$ and $\nu$ are real parameters. This equation unifies the anomalous diffusion equation on fractals ($\nu =1$) and the spherical anomalous diffusion for porous media ($\theta=0$). Exact point-source solution is obtained, enabling us to describe a large class of subdiffusion ($\theta > (1-\nu)d$), normal diffusion ($\theta= (1-\nu)d$) and superdiffusion ($\theta < (1-\nu)d$). Furthermore, a thermostatistical basis for this solution is given from the maximum entropic principle applied to the Tsallis entropy.Comment: 3 pages, 2 eps figure

On the Evolution of the Neutrino State inside the Sun

We reexamine the conventional physical description of the neutrino evolution inside the Sun. We point out that the traditional resonance condition has physical meaning only in the limit of small values of the neutrino mixing angle, theta<<1. For large values of theta, the resonance condition specifies neither the point of the maximal violation of adiabaticity in the nonadiabatic case, nor the point where the flavor conversion occurs at the maximal rate in the adiabatic case. The corresponding correct conditions, valid for all values of theta including theta>pi/4, are presented. An adiabaticity condition valid for all values of theta is also described. The results of accurate numerical computations of the level jumping probability in the Sun are presented. These calculations cover a wide range of Delta m^2, from the vacuum oscillation region to the region where the standard exponential approximation is good. A convenient empirical parametrization of these results in terms of elementary functions is given. The matter effects in the so-called "quasi-vacuum oscillation regime" are discussed. Finally, it is shown how the known analytical results for the exponential, 1/x, and linear matter distributions can be simply obtained from the formula for the hyperbolic tangent profile. An explicit formula for the jumping probability for the distribution N_e ~ (coth(x/l) +- 1) is obtained.Comment: 34 pages, 8 figure