2,895 research outputs found

    On eigenfunction approximations for typical non-self-adjoint Schroedinger operators

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    We construct efficient approximations for the eigenfunctions of non-self-adjoint Schroedinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schroedinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable adaptation of the JWKB method is able to provide accurate lobal approximations to them.Comment: 17 pages, 11 figure

    Hydrometallurgical processing of gold-containing ore and its washed products

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    This article presents the results of hydrometallurgical studies of gold-bearing ore. The experiments were carried out on 2 parallel weighed portions with the analysis of products by assay (cake) and atomic absorption (solution) analyzes of gold. To determine the technological properties, tests were carried out on the direct and sorption cyanidation of ore samples using different material sizes, the concentration of the complexing agent in the solution and the preliminary treatment of the pulp with lime. The study of the sorption activity of the ore, as well as the dynamics of gold dissolution was carried out

    On the kinetic equation approach to pair production by time-dependent electric field

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    We investigate the quantum kinetic approach to pair production from vacuum by time-dependent electric field. Equivalence between this approach and the more familiar S-matrix approach is explicitly established for both scalar and fermion cases. For the particular case of a constant electric field exact solution for kinetic equations is provided and the accuracy of low-density approximation is estimated.Comment: 8 pages, 4 figure

    Phenomenological model of mechanoelectric transformations in rocks

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    A phenomenological model is proposed on the example of the rock destruction development in underground mines. The characteristics of the electromagnetic signal generated due to the appearance and change of the dipole moment of cracks, whose beads are charged when the discontinuity is disturbed, are analytically investigated. The model is constructed using the theory of reliability and percolation theory, which allows to take into account the non-synchronism of the mechanical converters

    The scattering from generalized Cantor fractals

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    We consider a fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from zero to one in one dimension and from zero to three in three dimensions. The intensity profile of small-angle scattering from the generalized Cantor fractal in three dimensions is calculated. The system is generated by a set of iterative rules, each iteration corresponding to a certain fractal generation. Small-angle scattering is considered from monodispersive sets, which are randomly oriented and placed. The scattering intensities represent minima and maxima superimposed on a power law decay, with the exponent equal to the fractal dimension of the scatterer, but the minima and maxima are damped with increasing polydispersity of the fractal sets. It is shown that for a finite generation of the fractal, the exponent changes at sufficiently large wave vectors from the fractal dimension to four, the value given by the usual Porod law. It is shown that the number of particles of which the fractal is composed can be estimated from the value of the boundary between the fractal and Porod regions. The radius of gyration of the fractal is calculated analytically.Comment: 8 pages, 4 figures, accepted for publication in J. Appl. Crys

    A toy model of fractal glioma development under RF electric field treatment

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    A toy model for glioma treatment by a radio frequency electric field is suggested. This low-intensity, intermediate-frequency alternating electric field is known as the tumor-treating-field (TTF). In the framework of this model the efficiency of this TTF is estimated, and the interplay between the TTF and the migration-proliferation dichotomy of cancer cells is considered. The model is based on a modification of a comb model for cancer cells, where the migration-proliferation dichotomy becomes naturally apparent. Considering glioma cancer as a fractal dielectric composite of cancer cells and normal tissue cells, a new effective mechanism of glioma treatment is suggested in the form of a giant enhancement of the TTF. This leads to the irreversible electroporation that may be an effective non-invasive method of treating brain cancer.Comment: Submitted for publication in European Physical Journal

    Migration and proliferation dichotomy in tumor cell invasion

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    We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW) we formulate a system of the balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration. The transport process is formulated in terms of the CTRW with an arbitrary waiting time distribution law. Proliferation is modeled by a standard logistic growth. We apply hyperbolic scaling and Hamilton-Jacobi formalism to determine the overall rate of tumor cell invasion. In particular, we take into account both normal diffusion and anomalous transport (subdiffusion) in order to show that the standard diffusion approximation for migration leads to overestimation of the overall cancer spreading rate.Comment: 9 page
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