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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:20260611T222328Z
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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BEGIN:VEVENT
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:20260611T222328Z
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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BEGIN:VEVENT
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:20260611T222328Z
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/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calculation of thermodynamic potential for Bose system near conden
 sate point
DTSTART;VALUE=DATE-TIME:20181204T100500Z
DTEND;VALUE=DATE-TIME:20181204T102500Z
DTSTAMP;VALUE=DATE-TIME:20260611T222328Z
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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BEGIN:VEVENT
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:20260611T222328Z
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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