Structure of inhomogeneous media within the random fractal model

The porosity of inhomogeneous media was treated within the random fractal model. Analytic expressions were obtained for the size distribution curves of bulk mesopores. The expressions were verified by analyzing previously obtained experimental data

Structure of inhomogeneous media within the random fractal model

The porosity of inhomogeneous media is treated within the random fractal model. Analytic expressions are obtained for the size distribution curves of bulk mesopores. © 1990 Plenum Publishing Corporation

Evidences of the fractional kinetics in temperature region: Evolution of extreme points in ibuprofen

Based on a new approach presented in detail in this paper one can find new evidences of existence of the fractional kinetics not only in the frequency range. One can find rather general principles of detection of different collective motions in temperature region. These principles can be expressed in terms of an algorithm (defined in the paper as an approach). This approach includes some steps that help to separate a couple of the neighboring collective motions (expressed in the frequency range as a linear combination of two power-law exponents) from each other and establish the temperature evolution of the extreme point that follows to the generalized Vogel-Fulcher-Tamman (VFT)-equation. This experimentally confirmed fact gives new evidences for supporting of the theory of dielectric relaxation based on the fractional kinetics on the frequency/temperature domain. As an example for verification of this new approach the ibuprofen complex permittivity data measured in the wide frequency/temperature range were chosen. The reason of such selection was the following. It helps to compare the conventional study of this complex substance recently published in [1] and use possibilities of the developed approach that can add some new features to the picture obtained in the frame of the conventional treatment. We suppose that possibilities presented by new approach will be extremely useful for detection of different collective motions in other substances studied by the method of broadband dielectric spectroscopy (BDS). © 2009 Elsevier B.V. All rights reserved

An algorithm for determining dispersion and Doppler line widths from limited experimental data

We present an algorithm that allows the efficient determination of the dispersion and Doppler contributions to a Voigt profile from limited experimental data. For this purpose, we use the measured intensity profiles, as well as their first and second derivatives. © 1991

Time fractional Schrodinger equation

The Schrodinger equation is considered with the first order time derivative changed to a Caputo fractional derivative, the time fractional Schrodinger equation. The resulting Hamiltonian is found to be non-Hermitian and non-local in time. The resulting wave functions are thus not invariant under time reversal. The time fractional Schrodinger equation is solved for a free particle and for a potential well. Probability and the resulting energy levels are found to increase over time to a limiting value depending on the order of the time derivative. New identities for the Mittag-Leffler function are also found and presented in an appendix.Comment: 23 page

A few exact solutions for the model of equal spin-spin interactions

For the model of equal spin-spin interactions, we obtain exact Heisenberg expressions for the spin operator components and use them to find the relations that hold for spin operators appearing in the thermodynamic mean. We use the obtained exact relations for the means to describe the thermodynamics of the model under consideration. © 2005 Springer Science+Business Media, Inc

Thermodynamics of the interacting Fermi-system in the Static Fluctuation Approximation

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the frame of the static fluctuation approximation (SFA) method. This method based only on the single and controllable approximation allows to obtain the so-called far-distance equations (FDEs). These equations connecting the quantum states of a Fermi particle with variables of the local field operator contains all necessary information related to calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system considered. The basic expressions for the mean energy and heat capacity for electron gas at low temperatures in the limit of high density were obtained. All expressions are given in the units of r_s,where r_s determines the ratio of a mean distance between electrons to the Bohr radius a_0. In these expressions we calculated the terms of the order r_s and r_s^2, correspondingly. It was shown also that the SFA allows to find the terms related with high orders of the decomposition with respect to the parameter r_s.Comment: 22 pages, 5 figure

Reproductive Biology and Scale of Maturity Stage of Reproductive Systemof Female Squid (Illex illecebrosus)

Oogenesis and the development of the reproductive organs in Illex illecebrosus females was studied. The sample analyses were obtained from the area between Cape Hatteras and the Grand Bank in 1966-1983. To investigate the oogenesis, 10 gonads were taken from the females with the mantle length of 15-30 cm at allmaturity stages (except spawning). Approximately 2,000 specimens were studied to obtain knowledge of thedevelopment of the reproductive system organs during the ontogenesis. More than 50,000 females were sampled to analyse the maturation dynamics and the distribution during their life cycle. Data on the spawning andspent females were obtained for Illex argentinus