
S. Piekarski:
On the modified Fick law and its potential applications

K. Pawluk:
Integrals of LipschitzHankel type in analysis of magnetostatic fields

T. J. Hoffmann D. Wróbel:
Extended phenomenological electrodynamics of dyesolvent mixture

V. HenčBartolić, E. Kovačević, H.J. Kunze, M. Stubičar:
Laserproduced copper plasmas

B. Atamaniuk K. Żuchowski:
Charge fluctuation of dust grains and its impact on dusty wave propagation

J. Avsec:
Calculation of equilibrium and nonequilibrium thermophysical properties by means
of statistical mechanics

A. Ciarkowski:
Dependence of the Brillouin precursor form on the initial signal risetime

A. J. Turski, B. Atamaniuk, E. Turska:
Fractional derivative analysis of Helmholtz and paraxialwave equations

A. Chanda, J. Das:
Measures of complexity in wind direction

R. Brojewski, J. Jasiński:
Influence of the method of dry convection in the atmosphere modeling
on the dynamic properties of the model
 S. Piekarski:
On the modified Fick law and its potential applications

It can be observed that the standard
EinsteinSmoluchowski equation for isothermal processes can be written in the two
equivalent forms which, however, become distinct when the temperature becomes
spatially varying. Therefore, we have two different equations which could
potentially describe the flux of diffusing particles subjected to the potential
external forces and variable temperature. The first is the standard
EinsteinSmoluchowski equation, while the second is its modification containing
an additional term proportional to the temperature gradient. In order to fix the
terminology, the above mentioned modification of standard EinsteinSmoluchowski
equation shall be called "the modified Fick law". In this paper, we shall
discuss the origin of this equation and we shall try to make a preliminary
discussion of its solutions and potential applications to thermodiffusion. We
propose two models: one exploiting Onsager's thermodynamics and the second one
independent from it. Elementary solutions of both models are identical in the
limit of small concentrations.
Contents
 K. Pawluk:
Integrals of LipschitzHankel type in analysis
of magnetostatic fields

A boundaryintegral model of the static magnetic field
due to cylindrical permanent magnets that is put in free space is
considered. Magnetic scalar potential quantities created by a
virtual quantity "surface magnetic charge density" is expressed by
means of LipschitzHankel integrals that for the considered case
are reducible (by the way of hypergeometric series) to some
algebraic expressions, in which elliptic integrals of various
kinds occur. This approach seems to be more effective than that
can be reached by the use of a typical professional software for
the field problems in which numerical integration, being not quite
conform to the considered case, is common. The magnet subjected to
the analysis has to be virtually subdivided in some number of
elementary pieces, inside of which the uniform distribution of the
inherent magnetization is supposed.
Contents
 T. J. Hoffmann D. Wróbel:
Extended phenomenological electrodynamics of
dyesolvent mixture

In the paper, the description of dynamics of the electromagnetic fields in
dyesolvent mixture in the concept of extended phenomenological electrodynamics
is presented. For the description of the structure of material, a phenomenological
model of the multicomponent body is used. Such a model is based on the following
assumptions:
1) a body consists of many homogeneously (ideally mixed) different
components and
2) all components are located in each space point occupied by the body.
It seems that the dyesolvent mixture fulfils the above
phenomenological supposition for the multicomponent body.
Dynamics of the electromagnetic field has been expressed in the
LagrangeHamiltonian formalism, and can be used in investigation
of the local electromagnetic field in dyesolvent mixture.
Contents
 V. HenčBartolić, E. Kovačević, H.J. Kunze,
M. Stubičar:
Laserproduced copper plasmas

The Cu plasmas were produced by a ruby laser (5J, 694.3nm, 18ns, 140GWcm^{2}).
Timeresolved spectra of the plasmas were observed in the region of 824 nm. The electron
temperature was estimated to be about 40eV. A small depth of the crater (3μm) and the
surrounding ripples were observed at the Cu target surface. The trace of
deposited plasma was explained as the RayleighTaylor instability. Plasma was
transparent to the laser beam.
Contents
 B. Atamaniuk K. Żuchowski:
Charge fluctuation of dust grains and
its impact on dusty wave propagation
 In this paper we consider the influence of dust charge fluctuations on damping
of the dustionacoustic waves. Fluid approximation of longitudinal electrostatic
waves in unmagnetized plasmas is considered. We show that for a weak acoustic wave
the attenuation depends on a phenomenological charging coefficient.
Contents
 J. Avsec
: Calculation of equilibrium and
nonequilibrium thermophysical properties by means of statistical mechanics

The paper features the mathematical model of computing equilibrium and
nonequilibrium thermophysical properties of state in the liquid and gas domain
for pure refrigerants and mixtures with the help of classical thermodynamics and
statistical thermodynamics. The paper features all important contributions
(translation, rotation, internal rotation, vibration, intermolecular potential
energy and influence of electron and nuclei excitation). To calculate the
thermodynamic properties of real fluid, the models on the basis of LennardJones
intermolecular potential were applied. To calculate the thermodynamic properties
of real fluid by means of classical thermodynamics, we used the
TillnerRothWatanabeWagner (TRWW) equation on the base of Helmholtz type. We
have developed a mathematical model for the calculation of all equilibrium and
nonequilibrium thermodynamic functions of state for pure
refrigerants. The analytical results obtained by statistical thermodynamics are
compared with the TRWW model and show a relatively good agreement.
Contents
 A. Ciarkowski:
Dependence of the Brillouin precursor
form on the initial signal risetime

Propagation of a Brillouin precursor in a Lorentz dispersive medium is considered.
The precursor is excited by a sinemodulated initial signal, with its envelope
described by a hyperbolic tangent function. The purpose of the paper is to show how
the rate of growth of the signal affects the form of the Brillouin precursor. Uniform
asymptotic approach, pertinent to coalescing saddle points, is applied in the analysis.
The results are illustrated with numerical examples. Key words: Lorentz medium,
dispersive propagation, Brillouin precursor, uniform asymptotic expansions.
Contents
 A. J. Turski, B. Atamaniuk, E. Turska:
Fractional derivative analysis of
Helmholtz and paraxialwave equations

Fundamental rules and definitions of Fractional Calculus are outlined. Factorizing
1D and 2D Helmholtz equations, four semidifferential eigenfunctions are
determined. The functions exhibit incident and reflected plane waves as well as
diffracted incident and reflected waves on the halfplane edge. They allow to
construct the Sommerfeld halfplane diffraction solutions. ParabolicWave Equation
(PWE, LeontovichFock) for paraxial propagation is factorized and differential
fractional solutions of Fresnelintegral type are determined. We arrived at two
solutions, which are the mothers of known and new solutions.
Contents
 A. Chanda, J. Das:
Measures of complexity in wind
direction

In the present paper an attempt has been made to utilise two different forms of
complexity measures in directional change of wind. Two types of complexity
measures are average mutual information and multifractal dimensions. Four sets
of data have been studied. For each set, all the three measures have been
calculated. From the results, a comparative study of the properties of the two
measures of complexity visavis understanding the nature of complexity has been done.
Contents
 R. Brojewski, J. Jasiński:
Influence of the method of dry convection in the
atmosphere modeling on the dynamic properties of the model

This paper presents the problem of modeling dry convection in the atmosphere
based on scaling of the movement equations resulting from the assumption that
convection streams are mainly generated by the Archimedes draught force. This
approach leads to description of the atmosphere movement different than in the
Boussinesq approximation. The simplest case of Galerkin type equations in 3D
phase space was considered. The obtained equations have different dynamics than
the equations of the classical Lorenz model of dry convection. Lorenz model
dynamics is controlled by the configuration of 2 nondimensional numbers, while
the dynamics of the proposed model is controlled by 3 numbers. It is presented
in the language of symbolic dynamics, illustrated with numerous examples 
indicating its different character than in the classical Lorenz model, among
others: different values of Rayleigh number for which the systems loose
structural stability.
Contents
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