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SUMMARY:Linear-in-gradients hydrodynamic equations for a system with small
interaction
DTSTART;VALUE=DATE-TIME:20181204T084500Z
DTEND;VALUE=DATE-TIME:20181204T090500Z
DTSTAMP;VALUE=DATE-TIME:20230205T104956Z
UID:indico-contribution-3-14@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Vyacheslav Gorev (National Mining University)\nThe s
ystem under consideration is a one-component weakly non-uniform gas with s
mall potential interaction. The investigation is based on the kinetic equa
tion in the case of small interaction with a nonlocal collision integral [
1]. In [2] it is shown that the system kinetic energy is not conserved on
the basis of the nonlocal collision integral. So the system temperature sh
ould be defined on the basis on the total system energy rather than the ki
netic one. The following hydrodynamic equations are obtained up to the fir
st order in small gradients and the second order in small interaction:\n\n
$ \\frac{{\\partial n}}{{\\partial t}} = - n\\frac{{\\partial {\\upsilon
_n}}}{{\\partial {x_n}}} - {\\upsilon _n}\\frac{{\\partial n}}{{\\partial
{x_n}}}\, \\quad \\frac{{\\partial {\\upsilon _n}}}{{\\partial t}} = - {\
\upsilon _l}\\frac{{\\partial {\\upsilon _n}}}{{\\partial {x_l}}} + \\left
[ { - \\frac{T}{{nm}} - \\frac{1}{m}V\\left( {k = 0} \\right) + } \\right.
$\n\n$ \\left. { + \\frac{1}{{2{\\pi ^2}mT}}\\left( {A + \\frac{B}{3}} \\
right)} \\right]\\frac{{\\partial n}}{{\\partial {x_n}}} + \\left[ { - \\f
rac{1}{m} - \\frac{n}{{4{\\pi ^2}m{T^2}}}\\left( {A + \\frac{B}{3}} \\righ
t)} \\right]\\frac{{\\partial T}}{{\\partial {x_n}}}\, $\n\n$ \\frac{{\\pa
rtial T}}{{\\partial t}} = \\left[ { - \\frac{2}{3}T + \\frac{n}{{9{\\pi ^
2}T}}\\left( {A + \\frac{B}{2}} \\right)} \\right]\\frac{{\\partial {\\ups
ilon _n}}}{{\\partial {x_n}}} - {\\upsilon _n}\\frac{{\\partial T}}{{\\par
tial {x_n}}}\, $\n\n$ A = \\int\\limits_0^\\infty {dk} {k^2}{V^2}\\left(
k \\right)\, \\quad B = \\int\\limits_0^\\infty {dk{k^3}V\\left( k \\righ
t)\\frac{{\\partial V\\left( k \\right)}}{{\\partial k}}} $\n\nwhere $n$ i
s the particle number density\, $\\upsilon_l$ is the velocity\, $T$ is the
temperature\, and $V(k)$ is the Fourier transform of the system pair pote
ntial. In fact\, these equations are non-dissipative hydrodynamic equation
s and in the leading-in-interaction order they coincide with corresponding
equations in the framework of standard hydrodynamics. The obtained equati
ons may be a basis for the investigation of the system dissipative hydrody
namics and system kinetic coefficients. \n\n[1] A.I. Akhiezer and S.V. Pel
etminsky\, Methods of Statistical Physics\, Oxford\, Pergamon Press\, 1981
\, 376 p.\n[2] V.N. Gorev and A.I. Sokolovsky\, Visnik Dnipropetrovs'kogo
Universitetu. Seria Fizika\, radioelektronika\, 25\, issue 24\, 14 (2017).
\n\nhttps://indico.bitp.kiev.ua/event/2/contributions/14/
LOCATION:
URL:https://indico.bitp.kiev.ua/event/2/contributions/14/
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SUMMARY:Relation between firing statistics of spiking neuron with delayed
feedback and without feedback
DTSTART;VALUE=DATE-TIME:20181204T102500Z
DTEND;VALUE=DATE-TIME:20181204T104500Z
DTSTAMP;VALUE=DATE-TIME:20230205T104956Z
UID:indico-contribution-3-30@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Olha Shchur (Bogolyubov Institute for Theoretical Ph
ysics of the National Academy of Sciences of Ukraine)\nWe consider a class
of spiking neuronal models with threshold 2\, defined by a set of conditi
ons typical for basic threshold-type models\, such as the leaky integrate-
and-fire or the binding neuron model and also for some artificial neurons.
A neuron is fed with a Poisson process. Each output impulse is applied to
the neuron itself after a finite delay $\\Delta$. This impulse is identi
cal to those delivered from the input stream. We derive a general relation
which allows calculating exactly the probability density function (pdf) $
p(t)$ of output interspike intervals of a neuron with feedback based on kn
own pdf $p^0(t)$ for the same neuron without feedback\, intensity of the i
nput stream and the properties of the feedback line (the $\\Delta$ value)
.\n In addition to this\, we calculate exactly the model-independent ini
tial segment of pdf $p(t)$ for a neuron with feedback that is the same for
any neuron satisfying the imposed conditions. Also\, relations between mo
ments of pdf $p(t)$ for a neuron with feedback and pdf $p^0(t)$ for the s
ame neuron without feedback are derived. The obtained expressions are chec
ked numerically by means of Monte Carlo simulation.\nThe course of $p(t)$
has a $\\delta$-function peculiarity\, which makes it impossible to approx
imate $p(t)$ by Poisson or another simple stochastic process.\n\nhttps://i
ndico.bitp.kiev.ua/event/2/contributions/30/
LOCATION:
URL:https://indico.bitp.kiev.ua/event/2/contributions/30/
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SUMMARY:The influence of inhomogeneities on physical characteristics of fe
rromagnetic clusters inside of antiferromagnetic matrix in an external fie
ld
DTSTART;VALUE=DATE-TIME:20181204T092500Z
DTEND;VALUE=DATE-TIME:20181204T094500Z
DTSTAMP;VALUE=DATE-TIME:20230205T104956Z
UID:indico-contribution-3-17@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Oleksii Kryvchikov (B. Verkin ILTPE of NASU)\nThe pr
oblem of the influence of an external field on the magnetic moments of fer
romagnetic clusters surrounded by an antiferromagnet is studied in this pa
per. Clusters interact with each other magneticaly. In the case of strong
anisotropy such a system can be described by a one-dimensional Ising model
with a random exchange in the presence of an effective local field. The i
nhomogeneity of the interface between clusters and an antiferromagnet repr
esents the random effective field. The ground state of such a model turns
out to be the set of domains of different lengths in fields smaller than t
he saturation field. In contrast to the one-dimensional Ising model in a h
omogeneous field\, linear dependence of the magnetization on the external
field in the presence of a random effective field in the region of small f
ields is observed. The magnitude of the exchange bias of the magnetization
curve depends on the average of the random effective field\, and the slop
e of the curve depends on the variance of the random effective field. The
use of such a model allows drawing conclusions about the properties of the
boundary between subsystems from experimental data. The results obtained
within the framework of such model allow to estimate the properties of the
boundary between subsystems basing on experimental data. A formula that e
stimates the quality of the interface in the case of the cylindrical geome
try of the sample is obtained.\n\nhttps://indico.bitp.kiev.ua/event/2/cont
ributions/17/
LOCATION:
URL:https://indico.bitp.kiev.ua/event/2/contributions/17/
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SUMMARY:Calculation of thermodynamic potential for Bose system near conden
sate point
DTSTART;VALUE=DATE-TIME:20181204T100500Z
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DTSTAMP;VALUE=DATE-TIME:20230205T104956Z
UID:indico-contribution-3-25@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Kseniia Haponenko (Oles Honchar Dnipro National Univ
ersity)\nBose system in the presence of the condensate is investigated in
the Bogolyubov model of the separated condensate (see about in [1]). In th
is state occupation number ${{n}_{0}}$ of one-particle state with momentu
m ${p}=0$ is macroscopic one. In this model the system is described by the
statistical operator\n\n$\nw({{n}_{0}})={{e}^{\\beta [\\Omega ({{n}_{0}})
-\\hat{H}({{n}_{0}})+\\mu \\hat{N}({{n}_{0}})]}}\, \\quad \\mathrm{S
p}w({{n}_{0}})=1\n $\n\nwhere operators $\\hat{H}({{n}_{0}})$\, $\\hat{N}(
{{n}_{0}})$ are given by Hamiltonian of the system $\\hat{H}$ and operator
of particle number $\\hat{N}$ after substitution $n_{0}^{1/2}$ instead of
the Bose operators ${{a}_{0}}$\, ${{a}_{0}}^{+}$ ($\\beta $\,$\\mu $ are
the reverse temperature and the chemical potential). According to Bogolyub
ov equilibrium value $n_{0}^{o}$ of the occupation number $n_{0}^{{}}$ can
be found from the minimum condition of the thermodynamic potential $\\Ome
ga ({{n}_{0}})$ i.e. it is the non-equilibrium one of the system. Near tra
nsition point from normal state to the state with the condensate occupatio
n number $n_{0}^{{}}$ is small in comparison with the total number of part
icles and the potential $\\Omega ({{n}_{0}})$ can be calculated in a pertu
rbation theory in powers of $n_{0}^{1/2}$.\nThe purpose of this paper is c
alculating of the potential $\\Omega ({{n}_{0}})$ in a modified thermodyna
mic perturbation theory with small parameter $n_{0}^{{}}$. The obtained ex
pression for $\\Omega ({{n}_{0}})$ can be used as the potential Landau in
his theory of the phase transitions of the second kind for the system unde
r consideration. The statistical operator $w({{n}_{0}})$ can be written in
the form $w({{n}_{0}})=\\exp \\beta \\\,[F-({{\\mathbf{\\hat{H}}}_{0}}+{{
{\\hat{U}}}_{1}}+{{{\\hat{U}}}_{2}})]$ where the operators ${{{\\hat{U}}}_
{1}}\\sim n_{0}^{1/2}\, {{{\\hat{U}}}_{2}}\\sim{{n}_{0}}$. The calculation
is substantially simplified by the fact that the independent on ${{n}_{0}
}$ operator ${{\\mathbf{\\hat{H}}}_{0}}$ commutes with the operator of the
number of particles. It is shown that only integer powers of this number
are present in expansion of the potential. Relatively compact expressions
for the coefficients of this series are obtained because operators describ
ing the interaction in the system commutate under T-product. For a Bose ga
s they are calculated in an additional perturbation theory in interaction
between particles. An analyze of the results with connection to the Landau
theory of phase transitions is given. \n\n[1] Akhiezer\, A.I. Methods of
Statistical Physics [Text] / A.I. Akhiezer\, A.I. and S.V. Peletminskii.
– Oxford: Pergamon Press\, 1981. – 450 p.\n\nhttps://indico.bitp.kiev.
ua/event/2/contributions/25/
LOCATION:
URL:https://indico.bitp.kiev.ua/event/2/contributions/25/
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SUMMARY:Towards the problem of the Nesterenko’s soliton waves propagatio
n in nonlinear inhomogeneous Hertzian chains
DTSTART;VALUE=DATE-TIME:20181204T090500Z
DTEND;VALUE=DATE-TIME:20181204T092500Z
DTSTAMP;VALUE=DATE-TIME:20230205T104956Z
UID:indico-contribution-3-22@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Andrii Spivak (Odesa State Environmental University)
\nWe consider theoretically the problem of the pulse transmission along 1D
vertical chain of hard spheres\, which interact with each other by pair-w
ise nonlinear Hertz law [1-3]. System is subject into gravity and therefor
e became inhomogeneous [2\,3]. We show\, that being excited form the bound
ary (from the top)\, system is able to exhibit complex multimode dynamics
of pulse propagation. After long-wave approximation has been used to study
the dynamics of week perturbation\, in the lowest approximation\, resulte
d governing equation is satisfy by either singular solutions\, or combinat
ions of cylindrical waves [2]. In the higher approximation we obtaine nonl
inear equation of motion (generalized in form of Bussinesq equation) which
bring us to solution of Nesterenko-type soliton [1] with a negligible dif
ferences in the amplitudes\, and dispersions.\nWe conclude that initially
weekly nonlinear and inhomogeneous chain\, already in the linear approxima
tion\, is able to transmit either normal or singular modes\, whenever\, th
e accounting\, of the nonlinearity leads to familiar Nesterenko-type solit
on’s [1].\nTherefore under the appropriate values of the parameters (non
linearity\, inhomogeneity\, signal amplitudes) linearized Hertzian chain s
upport both discontinuous as well as quasinormal mode scenarios of pulse t
ransmission.\n\n[1] Nesterenko\, V.F. Propagation of nonlinear compression
pulses in granular media. J. Appl. Mech. Tech. Phys. 24 (1) (1984) 733-74
3\; Translated from : Zh. Prikl. Mekh. Tekh. Fiz. (5) (1983) 136-148. [Rus
sian] \n[2] Sen\, S.\, Hong\, J.\, Bang\, J.\, Avalos\, E.\, and Doney\, R
. Solitary waves in the granular chain. Physics Reports 462 (2) (2008) 21-
66.\n[3] Gerasymov\, O.I. and Vandewalle\, N. On the exact solutions of th
e problem of impulsive propagation in an inhomogeneous granular chain. Dop
ov. Nac. acad. nauk Ukr. (8) (2012) 67-72. [Ukrainian]\n\nhttps://indico.b
itp.kiev.ua/event/2/contributions/22/
LOCATION:
URL:https://indico.bitp.kiev.ua/event/2/contributions/22/
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