595 research outputs found
About Calculation of the Hankel Transform Using Preliminary Wavelet Transform
The purpose of this paper is to present an algorithm for evaluating Hankel
transform of the null and the first kind. The result is the exact analytical
representation as the series of the Bessel and Struve functions multiplied by
the wavelet coefficients of the input function. Numerical evaluation of the
test function with known analytical Hankel transform illustrates the proposed
algorithm.Comment: 5 pages, 2 figures. Some misprints are correcte
On discrete integrable equations of higher order
We study 2D discrete integrable equations of order 1 with respect to one
independent variable and with respect to another one. A generalization of
the multidimensional consistency property is proposed for this type of
equations. The examples are related to the B\"acklund--Darboux transformations
for the lattice equations of Bogoyavlensky type.Comment: 20 pages, 2 figure
Linear problems and B\"acklund transformations for the Hirota-Ohta system
The auxiliary linear problems are presented for all discretization levels of
the Hirota-Ohta system. The structure of these linear problems coincides
essentially with the structure of Nonlinear Schr\"odinger hierarchy. The
squared eigenfunction constraints are found which relate Hirota-Ohta and
Kulish-Sklyanin vectorial NLS hierarchies.Comment: 11 pages, 1 figur
Brownian yet non-Gaussian diffusion in heterogeneous media: from superstatistics to homogenization
We discuss the situations under which Brownian yet non-Gaussian (BnG)
diffusion can be observed in the model of a particle's motion in a random
landscape of diffusion coefficients slowly varying in space. Our conclusion is
that such behavior is extremely unlikely in the situations when the particles,
introduced into the system at random at , are observed from the
preparation of the system on. However, it indeed may arise in the case when the
diffusion (as described in Ito interpretation) is observed under equilibrated
conditions. This paradigmatic situation can be translated into the model of the
diffusion coefficient fluctuating in time along a trajectory, i.e. into a kind
of the "diffusing diffusivity" model.Comment: 12 pages; 10 figure
Limits of structure stability of simple liquids revealed by study of relative fluctuations
We analyse the inverse reduced fluctuations (inverse ratio of relative volume
fluctuation to its value in the hypothetical case where the substance acts an
ideal gas for the same temperature-volume parameters) for simple liquids from
experimental acoustic and thermophysical data along a coexistence line for both
liquid and vapour phases. It has been determined that this quantity has a
universal exponential character within the region close to the melting point.
This behaviour satisfies the predictions of the mean-field (grand canonical
ensemble) lattice fluid model and relates to the constant average structure of
a fluid, i.e. redistribution of the free volume complementary to a number of
vapour particles. The interconnection between experiment-based fluctuational
parameters and self-diffusion characteristics is discussed. These results may
suggest experimental methods for determination of self-diffusion and structural
properties of real substances.Comment: 5 pages, 4 figure
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