229 research outputs found
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
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