2,902 research outputs found
On eigenfunction approximations for typical non-self-adjoint Schroedinger operators
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
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
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
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
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
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
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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