Fractional Models of Cosmic Ray Acceleration in the Galaxy

Possible formulations of the problem of cosmic rays acceleration in the interstellar galactic medium are considered with the use of fractional differential equations. The applied technique has been physically justified. A Fermi result has been generalized to the case of the acceleration of particles in shock waves in the supernovae remnants fractally distributed in the Galaxy.Comment: 10 page

High-T(sub c) squid application in medicine and geophysics

In the Laboratory a high-T(sub c) one-hole squid was built from Y1Ba2Cu3O(7-x) ceramics obtained by a standard procedure of solid state reaction. The ceramics with critical current density J(sub c) is greater than 100 A/sq cm was selected. In the middle of 10 x 10 x 2 mm ceramics pellet a 0.8 mm hole was drilled in which superconducting loop of the squid was located. Between the hole and the edge of the pellet a cut was mechanically filed out with a bridge inside it connecting the superconducting ring. A scheme of the magnetometer is presented. The resonant frequency shift of the tank circuit, the connection of the squid with this circuit, and the squid inductance are evaluated. One of the most interesting fields of the squid-based magnetometer application is biomagnetism, particularly, the human heart magnetocardiogram measuring. The low-temperature squids were used in this area and many interesting and important scientific results have been obtained. The observations have shown that the main noise contribution was not due to the squid but to the Earth's magnetic field variations, industrial inductions, and mainly to the vibrations caused by liquid nitrogen boiling and by vibrations of the box. Further attempts are needed to reduce the magnetic noise inductions. Nevertheless, the estimations promise the maximum signal/noise relation of the high-T(sub c) squid-magnetocardiometer to be not less than 10:1 in a bandwidth of 60 Hz. Apparently, such resolution would be enough not only for steady cardiogram reading but even for thin structure investigation at average technique application

High-T(c) squid application in medicine and geophysics

In our laboratory of high-T(sub c), a one-hole squid was built from Y1Ba2Cu3O(7-x) ceramics obtained by a standard procedure of solid state reaction. The ceramics with critical current density J(sub c) is greater than 100 A/sq cm was selected. In the middle of a 10 x 10 x 2 mm ceramics pellet, a 0.8 mm hole was drilled in which the superconducting loop of the squid was located. Between the hole and the edge of the pellet, a cut was mechanically filed out with a bridge inside it connecting the superconducting ring. A scheme of the magnetometer is presented. The resonant frequency shift of the tank circuit, the connection of the squid with this circuit, and the squid inductance are evaluated. One of the most interesting fields of the squid-based magnetometer application is biomagnetism, particularly, the human heart magnetocardiogram measuring. The low-temperature squids were used in this area and many interesting and important scientific results have been obtained. The observations have shown that the main noise contribution was not due to the squid but to the Earth's magnetic field variations, industrial inductions, and mainly to the vibrations caused by liquid nitrogen boiling and by vibrations of the box. Further attempts are needed to reduce the magnetic noise inductions. Nevertheless, the estimations promise the maximum signal/noise relation of the high-T(sub c) squid-magnetocardiometer to be not less than 10:1 in a bandwidth of 60 Hz. Apparently, such resolution would be enough not only for steady cardiogram reading but even for thin structure investigation at average technique application

Truncated Levy statistics for transport in disordered semiconductors

Probabilistic interpretation of transition from the dispersive transport regime to the quasi-Gaussian one in disordered semiconductors is given in terms of truncated Levy distributions. Corresponding transport equations with fractional order derivatives are derived. We discuss physical causes leading to truncated waiting time distributions in the process and describe influence of truncation on carrier packet form, transient current curves and frequency dependence of conductivity. Theoretical results are in a good agreement with experimental facts.Comment: 6 pages, 4 figures, presented in "Nonlinear Science and Complexity - 2010" (Turkey, Ankara

Fractional processes: from Poisson to branching one

Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Levy stable densities are discussed and used for construction of the Monte Carlo algorithm for simulation of random waiting times in fractional processes. Numerical calculations are performed and limit distributions of the normalized variable Z=N/ are found for both processes.Comment: 11 pages, 6 figure