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[[Main_Page|Кафедра ТМ]] > '''Project "Thermocrystal"''' <HR>


''The project is devoted to development of analytical models of unsteady thermal processes in ultrapure crystals.''

== Publications ==

* CMT 2020: [http://www.pdmi.ras.ru/~serge/index.html S.N. Gavrilov], [[A.M. Krivtsov]]. '''Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source.''' 2020, Continuum Mechanics and Thermodynamics, 32(1), с. 41-61 (download [[media:Gavrilov_CMT_2020.pdf|pdf]])

* PM 2020: [[A.M. Krivtsov]], [[M.B. Babenkov]], [[D.V. Tsvetkov]]. '''Heat Propagation in a One-Dimensional Harmonic  Crystal on an Elastic Foundation.''' 2020, [http://www.ispms.ru/ru/52/ Physical Mesomechanics], Vol. 23, No. 2, pp. 109–119 ([[media:Krivtsov_Babenkov_PM_2020.pdf |pdf]]).

*PR 2020: [[V.A. Kuzkin]], [[A.M. Krivtsov]]. '''Ballistic resonance and thermalization in the Fermi-Pasta-Ulam-Tsingou chain at finite temperature'''. 2020, Physical Review, E 101, 042209 (download [[media:Kuzkin_2020_PRE.pdf|pdf]])

* MPM 2019: [[A.M. Krivtsov]], [[E.A. Podolskaya]], [[V.Yu. Shubina]]. '''Asymptotics of a thermal wave in a one-dimensional harmonic crystal.''' 2019, [http://www.ipme.ru/e-journals/MPM/ Materials Physics and Mechanics], Vol. 42, pp. 837-845 (download [[media:MPM642_15_krivtsov.pdf | pdf]]). 

* AR 2019: [[A.M. Krivtsov]], [[A.S. Murachev]]. '''Transition to thermal equilibrium in a deformed crystal'''. 2019, ArXiv:1908.05464 ([https://arxiv.org/abs/1908.05464 abstract], download [http://mech.spbstu.ru/images/c/c3/Murachev_2019_ArXiv.pdf pdf])

* PR1 2019: [http://www.pdmi.ras.ru/~serge/index.html S.N. Gavrilov], [[A.M. Krivtsov]]. '''Thermal equilibration in a one-dimensional damped harmonic crystal'''. 2019, [https://journals.aps.org/pre/ Physical review E], E100, 022117 ([https://journals.aps.org/pre/accepted/3d070R5aS2d1102d302744d735916715cb09ce08f abstract], download [[media:Gavrilov_Krivtsov_PhysRev_2019.pdf|pdf]])

* ZAM 2019: [[O.S. Loboda]], [[A.M. Krivtsov]], [http://www.ipme.ru/ipme/ru/indexr.html A.V. Porubov], [[D.V. Tsvetkov]]. '''Thermal processes in a one-dimensional crystal with regard for the second coordination sphere'''. 2019, [https://onlinelibrary.wiley.com/journal/15214001 ZAMM]. 13 p. ([[media:Loboda_Zamm_19.pdf |pdf]]).

* CM3 2019: [[V.A. Kuzkin]]. '''Unsteady ballistic heat transport in harmonic crystals with polyatomic unit cell.''' [https://rd.springer.com/journal/161 Continuum Mechanics and Thermodynamics]. 2019, 26 p. ([[media:Kuzkin_2019_CMAT.pdf |pdf]]). 

* PR 2019: [[A.A. Sokolov]], [[A.M. Krivtsov]], [http://www.lkm.tu-berlin.de/menue/mitarbeiterinnen_sprechstunden/prof_dr_rer_nat_w_h_mueller/ W.H. Müller], [[E.N. Vilchevskaya]]. '''Change of entropy for one-dimensional ballistic heat equation — sinusoidal initial perturbation.''' [https://journals.aps.org/pre/ Physical Review E]. 2019, Vol. 99, 042107 ([https://journals.aps.org/pre/accepted/53079Rb3I7211316f7091ae76420724fca5745d95 abstract], [[Media:Sokolov_PhysRev_2019.pdf|pdf]]). 

*DPG 2019: [[A.M. Krivtsov]]. '''The Ballistic Heat Equation for a One-Dimensional Harmonic Crystal.''' [https://link.springer.com/book/10.1007/978-3-030-11665-1 Dynamical Processes in Generalized Continua and Structures]. 2019, Vol. 103, pp. 345–358 ([https://link.springer.com/chapter/10.1007/978-3-030-11665-1_19 abstract], [[media: Krivtsov_Ballistic.pdf|pdf]]). 

* CM2 2019: [http://www.pdmi.ras.ru/~serge/index.html S.N. Gavrilov], [[A.M. Krivtsov]]. '''Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source.''' [https://rd.springer.com/journal/161 Continuum Mechanics and Thermodynamics]. 2019, Vol. 31, 21 p. ([https://rd.springer.com/article/10.1007/s00161-019-00782-2 abstract], [[media: Gavrilov-Krivtsov2019_Article_Steady-stateKineticTemperature.pdf|pdf]]). 

* IOP 2019: [[A.S. Murachev]], [[A.M. Krivtsov]], [[D.V. Tsvetkov]]. '''Thermal echo in a one-dimensional harmonic crystal.''' [https://iopscience.iop.org/journal/0953-8984 Journal of Physics: Condensed Matter]. 2019, Vol. 31, Num. 9. ([http://iopscience.iop.org/article/10.1088/1361-648X/aaf3c6/meta abstract], [[media: Murachev_Krivtsov_Tsvetkov.pdf|pdf]]). 

* CMT 2019: [[V.A. Kuzkin]]. '''Thermal equilibration in infinite harmonic crytals'''. [https://rd.springer.com/journal/161 Continuum Mechanics and Thermodynamics]. 2019, 23 p. ([https://rd.springer.com/article/10.1007/s00161-019-00758-2#citeas abstract], [[media: Kuzkin2019_Article_ThermalEquilibrationInInfinite.pdf|pdf]]). 

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* AR2 2018: [[V.A. Kuzkin]]. '''Fast and slow thermal processes in harmonic crystals with polyatomic lattice'''. arXiv:1808.07255. 2018, 34 p. ([https://arxiv.org/abs/1808.07255 abstract], [https://arxiv.org/pdf/1808.07255.pdf pdf]).
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* MPM 2018: [[E.A. Podolskaya]], [[A.M. Krivtsov]], [[D.V. Tsvetkov]]. '''Anomalous heat transfer in one-dimensional diatomic harmonic crystal.''' [http://www.ipme.ru/e-journals/MPM/ Materials Physics and Mechanics]. 2018, 40, pp. 172–180 ([[media:MPM240_05_podolskaya.pdf‎ |pdf]]). 

* CMT 2018: [http://www.pdmi.ras.ru/~serge/index.html S.N. Gavrilov], [[A.M. Krivtsov]], [[D.V. Tsvetkov]]. '''Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply.''' [https://link.springer.com/journal/161/ Continuum Mechanics and Thermodynamics]. 2018, Vol. 31, pp. 255–272 ([https://link.springer.com/article/10.1007/s00161-018-0681-3 abstract], [[media: Gavrilov_Krivtsov_Tsvetkov_Heat_Transfer.pdf|pdf]]) 

* AMM 2018: [[A.M. Krivtsov]], [[A.A. Sokolov]], [http://www.lkm.tu-berlin.de/menue/mitarbeiterinnen_sprechstunden/prof_dr_rer_nat_w_h_mueller/ W.H. Müller], [http://mc.spbstu.ru/uPeople/profile/112/ A.B. Freidin]. '''One-Dimensional Heat Conduction and Entropy Production.''' [https://link.springer.com/book/10.1007%2F978-3-319-73694-5 Advances in Mechanics of Microstructured Media and Structures]. 2018, Vol. 87, pp. 197–214 ([[media: A._M._Krivtsov,_A._A._Sokolov,_W.H._Müller,_A._B._Freidin.pdf |pdf]]). 

* ECM 2018: [[A.M. Krivtsov]],  [[V.A. Kuzkin]]. '''Discrete and continuum thermomechanics.''' [https://www.springer.com/gp/book/9783662557709 Encyclopedia of Continuum Mechanics]. 2018, 16 p. ([[media:Kuzkin_2018_Encyclopedia.pdf|pdf]]) 

* LMA 2018: V.A. Tsaplin, [[V.A. Kuzkin]]. '''Temperature oscillations in harmonic triangular lattice with random initial velocities.''' [https://lettersonmaterials.com/en Letters on Materials]. 2018, 8(1), pp. 16–20 ([[media:Kuzkin_2018_LettMat_TempOscil.pdf|pdf]]). 

* JPH 2017: [[V.A. Kuzkin]], [[A.M. Krivtsov]]. '''Fast and slow thermal processes in harmonic scalar lattices.''' 2017, [http://iopscience.iop.org/journal/0953-8984/ Journal of Physics: Condensed Matter]. 2017, Vol. 29, No. 50, 14 p.  ([http://iopscience.iop.org/article/10.1088/1361-648X/aa98eb abstract], [[media:Kuzkin_2017_JPhys_Condens_Matter.pdf |pdf]]). 

* АR2 2017: [[A.M. Krivtsov]]. '''On heat transfer in a thermally perturbed harmonic chain.''' ArXiv:1709.07924. 2017, 2 p. ([https://arxiv.org/abs/1709.07924 abstract], [https://arxiv.org/pdf/1709.07924.pdf pdf]). 

* ФММ 2017: [[A.A. Sokolov]], [[A.M. Krivtsov]], [http://www.lkm.tu-berlin.de/menue/mitarbeiterinnen_sprechstunden/prof_dr_rer_nat_w_h_mueller/ W.H. Müller]. '''Localized heat perturbation in harmonic 1D crystals: Solutions for an equation of anomalous heat conduction.''' Physical Mesomechanics. 2017, Vol. 20, No. 3, pp. 305–310 ([[media: Sokolov 2017 PMM eng.pdf |pdf]]). 

* ФТТ 2017: [[V.A. Kuzkin]], [[A.M. Krivtsov]]. '''An analytical description of transient thermal processes in harmonic crystals.''' [https://link.springer.com/journal/11451 Physics of the Solid State]. 2017, Vol. 59, No. 5, pp. 1051–1062, [[media: Kuzkin 2017 PhysSolState Eng.pdf |pdf]]. 

* ДАН 2017: [[V.A. Kuzkin]], [[A.M. Krivtsov]] '''High-frequency thermal processes in harmonic crystals.''' [http://pleiades.online/en/journal/danphys/ Doklady Physics]. 2017, №5, pp. 529–533 ([https://link.springer.com/article/10.1134/S1028335817020070?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst abstract],  [[media:Krivtsov_Kuzkin_DAN_2017_eng.pdf |pdf]]). 

* ICT 2016: [[M.B. Babenkov]], [[A.M. Krivtsov]], [[D.V. Tsvetkov]]. '''Unsteady heat conduction processes in a harmonic crystal with a substrate potential.'''  Proc. of [http://www.ictam2016.org/ XXIV ICTAM], 21-26 August 2016, Montreal, Canada, pp. 2440–2441 ([[media:Babenkov_2016_ICTAM.pdf|pdf]]). 

* ФММ 2016: [[M.B. Babenkov]], [[A.M. Krivtsov]], [[D.V. Tsvetkov]]. '''Energy oscillations in a one-dimensional harmonic crystal on an elastic substrate.''' [http://www.ispms.ru/ru/53/ Phys. Mesomech.]. 2016, 19, No. 3, pp. 282–290 ([[media: Krivtsov_PhysMech_2016.pdf|pdf]]). 

* АRХ 2015: [[A.M. Krivtsov]]. '''On unsteady heat conduction in a harmonic crystal.''' 2015, ArXiv:1509.02506, 5 p. ([http://arxiv.org/abs/1509.02506 abstract], [http://arxiv.org/pdf/1509.02506v2.pdf pdf], [[:en:Heat transfer in a 1D harmonic crystal|simulation]]). 

* ДАН 2015: [[A.M. Krivtsov]]. '''Heat transfer in infinite harmonic one dimensional crystals.''' [http://pleiades.online/en/journal/danphys/ Doklady Physics]. 2015, Vol. 60, No. 9, pp. 407–411 ([[media: Krivtsov 2015 DAN eng.pdf.pdf|pdf]]). 

* ДАН 2014: [[A.M. Krivtsov]]. '''Energy Oscillations in a One-Dimensional Crystal'''. [http://pleiades.online/en/journal/danphys/ Doklady Physics]. 2014, Vol. 59, No. 9, pp. 427–430 ([[media: Krivtsov_2014_DAN_eng_corrected.pdf|pdf]]).

== Additional publications ==

* [[A.A. Le-Zakharov]], [[A.M. Krivtsov]], [http://www.ipme.ru/ipme/ru/indexr.html A.V. Porubov]. '''Relation between defects and crystalline thermal conduction'''. 2019, [https://rd.springer.com/journal/161 Continuum Mechanics and Thermodynamics], ISSN 0935-1175, Volume 31, Number 6, pp. 1873–1881 (download [[media: CMAT19dfg.pdf|pdf]]).

* [[A.A. Le-Zakharov]], [[A.M. Krivtsov]]. ''' Molecular dynamics investigation of heat conduction in crystals with defects.''' [http://www.maik.rssi.ru/cgi-perl/journal.pl?name=danphys&page=main Doklady Physics], 2008, № 5, pp. 261–264. ([[media:Le_2008_DAN_eng.pdf |pdf]]).

== Preprints ==

* [[A.M. Krivtsov]], [[E.A. Podolskaya]], V.Yu. Shubina. '''Asymptotics of a thermal wave in a one-dimensional harmonic crystal.''' [http://www.ipme.ru/e-journals/MPM/ Materials Physics and Mechanics]. 2019. 
* [[A.M. Krivtsov]], [[A.S. Murachev]]. Transition to thermal equilibrium in a deformed crystal.
* S.N. Gavrilov, [[A.M. Krivtsov]]. Thermal equilibration in a one-dimensional harmonic crystal lying in a viscous environment. 
* [[A.A. Sokolov]], [[A.M. Krivtsov]], [http://www.lkm.tu-berlin.de/menue/mitarbeiterinnen_sprechstunden//prof_dr_rer_nat_w_h_mueller/ W.H. Müller]. Energy transfer in discrete and continuous one-dimensional media.

== [[Virtual laboratory]] ==
*[http://tm.spbstu.ru/Динамика_одномерного_кристалла  Dynamics of 1D harmonic crystal]
*[http://tm.spbstu.ru/Динамика_одномерного_нелинейного_кристалла  Dynamics of 1D anharmonic crystal]
*[http://tm.spbstu.ru/Колебания_энергий_в_одномерном_кристалле  Oscillations of energies in 1D crystal]
*[http://tm.spbstu.ru/Диффузионные_процессы_в_одномерном_кристалле   Diffusive processses in 1D crystal] 
*[http://tm.spbstu.ru/Распространение_тепла_в_гармоническом_одномерном_кристалле   Heat transport in 1D crystal]  (see also [http://tm.spbstu.ru/Распространение_тепла_в_гармоническом_одномерном_кристалле:_регулярная_температура uniform] and [http://tm.spbstu.ru/Распространение_тепла_в_гармоническом_одномерном_кристалле:_периодическая_температура periodic] temperature)
*[http://tm.spbstu.ru/Колебания_энергий_в_одномерном_кристалле_с_подложкой   Oscillations of energies in 1D crystal on elastic substrate][http://tm.spbstu.ru/Статистические_распределения_в_двумерном_кристалле_с_треугольной_решеткой  Distribution function in 2D triangular lattice]
*[http://tm.spbstu.ru/ФПУ_термокристалл   Fermi-Pasta-Ulam crystal] ([http://tm.spbstu.ru/ФПУ_термокристалл:_аналитическое_решение   Fermi-Pasta-Ulam crystal (analytics)])
*[http://tm.spbstu.ru/Моделирование_распространения_тепла_в_треугольной_кристаллической_решетке  Heat tranport in triangular lattice]
* Transition of mechanical energy to heat:
**[http://tm.spbstu.ru/Преобразования_энергии_в_нелинейном_кристалле:_осцилляции   oscillations ]
**[http://tm.spbstu.ru/Преобразования_энергии_в_нелинейном_кристалле:_бегущая_волна  traveling wave]
**[http://tm.spbstu.ru/Преобразования_энергии_в_нелинейном_кристалле:_Гаусс  Gauss]
* Heat supply:
**[http://tm.spbstu.ru/Одномерное_броуновское_движение  Brownian motion]
**[http://tm.spbstu.ru/Нагрев_одномерного_кристалла   behavior of displacements and velocities)]
**[http://tm.spbstu.ru/Нагрев_одномерного_кристалла:_температура    behavior of temperature]
*[http://tm.spbstu.ru/Сравнение_групповой_и_фазовой_скоростей   Group velocity vs. phase velocity]
*[http://tm.spbstu.ru/Сравнение_солитона_с_волной  Soliton vs. harmonic wave]

== Conferences talks ==


* [[A.M. Krivtsov]]. October 2, 2019: '''Ballistic and diffusive heat process in ultrapure materials'''. ''Plenary lecture.'' Tomsk, [http://www.ispms.ru/en/ispmsconf/10/ The International Workshop "Multiscale Biomechanics and Tribology of Inorganic and Organic Systems" in Memory of Professor Sergey Grigor'evich Psakhie].
* [[A.M. Krivtsov]]. June 25, 2019: '''Wave and diffusive heat processes in ultrapure materials'''. ''Plenary lecture.'' St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2019].
* [[V.A. Kuzkin]]. June 25, 2019: '''Unsteady ballistic heat transport in harmonic crystals with polyatomic unit cell'''. St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2019].
* [http://www.pdmi.ras.ru/~serge/index.html S.N. Gavrilov]. June 25, 2019: '''Steady-state kinetic temperature distribution in a two-dimensional harmonic scalar lattice lying in a viscous environment and subjected to a point heat source'''. St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2019].
* [[A.S. Murachev]]. June 25, 2019: '''Transition to thermal equilibrium in a deformed crystal'''. St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2019].
* [[A.A. Sokolov]]. June 25, 2019: '''Heat conduction in 1D harmonic crystal. Finite or infinite? The comparison of two approaches'''. St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2019].
* A.S. Evseenkov. June 25, 2019: '''Ballistic and diffusion heat transfer in onedimensional harmonic crystal with defects'''. St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2019].
* [[A.M. Krivtsov]]. June 26, 2018: '''Ballistic heat conduction at nano- and microscale'''. ''Plenary lecture.'' St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2018].
* [[V.A. Kuzkin]]. June 26, 2018: '''Transition to thermal equilibrium and nonequipartition of energy in harmonic crystals '''. St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2018].
* [http://www.pdmi.ras.ru/~serge/index.html S.N. Gavrilov]. June 26, 2018: '''Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply'''. St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2018].
* E.B. Starobinskii. June 26, 2018: '''Mechanical and thermal oscillations in crystals of different dimensions '''. St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2018].
* [[A.S. Murachev]]. June 26, 2018: '''Non-stationary thermodiffusion processes in a finite one-dimensional crystal'''. St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2018].
*  [[A.A. Sokolov]]. June 26, 2018: '''Entropy production for one-dimensional ballistic heat equation - sinusoidal initial perturbation'''. St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2018].
* [[A.M. Krivtsov]]. June 23, 2018: '''Unsteady thermal processes in harmonic crystals'''. ''Plenary lecture.'' St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2017].
*  [[A.A. Sokolov]]. September 17, 2016. '''Localized heat impulses and non-Fourier heat propagation in 1-D crystals'''. Tomsk, [http://www.ispms.ru/en/IWCMM26/ 26th INTERNATIONAL WORKSHOP ON COMPUTATIONAL MECHANICS OF MATERIALS].

* [[A.M. Krivtsov]]. June 25, 2016. '''On unsteady heat conduction in a harmonic crystal'''. Sheffield, UK, [http://www.sheffield.ac.uk/materials/nesc/index Non-Equilibrium Simulation Conference (NESC 2016)].
* [[A.M. Krivtsov]]. June 27, 2016. '''Unsteady thermal processes in harmonic crystals'''. ''Plenary lecture.'' St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2016].

* [[A.M. Krivtsov]]. June 22, 2015. '''One-dimensional crystals and heat superconductivity.''' ''Plenary lecture.'' St. Petersburg, [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics” 2015].

== Links ==
* [[Main_Page | Department "Theoretical Mechanics"]]