Project "Thermocrystal"

Ballistic resonance and thermalization in FPU chain

TM > Project "Thermocrystal"

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

Publications

2023

• PNRPU 2023: R.V. Rubinova, O.S. Loboda, A.M. Krivtsov. Ballistic heat transfer in a one-dimensional crystal with long-range interactions. 2023, PNRPU Mechanics Bulletin, 5, 74-80 (download pdf)

• ASM 2023: E.V. Shishkina, S.N. Gavrilov. Localized Modes in a 1D Harmonic Crystal with a Mass-Spring Inclusion. 2023, Advances in Linear and Nonlinear Continuum and Structural Mechanics. Advanced Structured Materials, 461-479 (abstract, download pdf)

• DD 2023: S.N. Gavrilov, E.V. Shishkina, Yu.A. Mochalova. An example of the anti-localization of non-stationary quasi-waves in a 1D semi-infinite harmonic chain. 2023, Days on Difraction , 67–72 (abstract, download pdf)

• PRE2 2023: S.V. Dmitriev, V.A. Kuzkin, A.M. Krivtsov. Nonequilibrium thermal rectification at the junction of harmonic chains. 2023, Phys. Rev. E, 108, 054221 (abstract, download pdf)

• CMT1 2023: S.D. Liazhkov. Unsteady thermal transport in an instantly heated semi-infinite free end Hooke chain. 2023, Continuum Mechanics and Thermodynamics, 35(2), 413-430 (abstract, download pdf)

• PRE1 2023: V.A. Kuzkin. Acoustic transparency of the chain-chain interface. 2023, Phys. Rev. E, 107, 065004 (abstract, download pdf)

• PRE 2023: J. A. Baimova, N.M. Bessonov, A.M. Krivtsov. Motion of localized disturbances in scalar harmonic lattices. 2023, Phys. Rev. E, 107(6) (abstract, download pdf)

• CMT 2023: E.V. Shishkina, S.N. Gavrilov. Unsteady ballistic heat transport in a 1D harmonic crystal due to a source on an isotopic defect. 2023, Continuum Mechanics and Thermodynamics, 35, 431–456 (abstract, download pdf)

2022

• ASM1 2022: A.A. Sokolov, W.H. Müller, A.M. Krivtsov, A.V. Porubov. Signatures of Transient Purely Ballistic Heat Conduction: Theory and Experimental Investigation. 2022, Mechanics and Control of Solids and Structures, Advanced Structured Materials 164 (abstract, download pdf)

• MPM 2022: R.V. Rubinova, O.S. Loboda, A.M. Krivtsov. Heat transfer in infinite one-dimensional crystal considering the third coordination sphere. 2022, Materials Physics and Mechanics, 50(3), 365-372. (abstract, download pdf)

• JHMT 2022: S.N. Gavrilov. Discrete and continuum fundamental solutions describing heat conduction in a 1D harmonic crystal: Discrete-to-continuum limit and slow-and-fast motions decoupling. 2022, International Journal of Heat and Mass Transfer, 194, 123019 (abstract, download pdf) .

• PRE 2022: S.D. Liazhkov, V.A. Kuzkin. Unsteady two-temperature heat transport in mass-in-mass chains. 2022, Phys. Rev. E, 105, 054145 (abstract, download pdf)

• ASM 2022: E.A. Podolskaya, A.M. Krivtsov, V.A. Kuzkin. Discrete thermomechanics: From thermal echo to ballistic resonance (A review). 2022, In: Polyanskiy, V.A., K. Belyaev, A. (eds) Mechanics and Control of Solids and Structures. Advanced Structured Materials, 164. Springer, Cham. (download pdf)

• ZAMM 2022: A.M. Krivtsov. Dynamics of matter and energy. 2022, Zeitschrift fur Angewandte Mathematik und Mechanik, 103, e202100496 (abstract, download pdf)

• JPCM1 2022: A.M. Krivtsov, A.S. Murachev, D.V. Tsvetkov. Transient diffusion and thermal processes in a finite one-dimensional harmonic crystal. 2022, Journal of Physics: Condensed Matter, 34(9), 095401 (abstract, download pdf)

• CMT 2022: S.N. Gavrilov, A.M. Krivtsov. Steady-state ballistic thermal transport associated with transversal motions in a damped graphene lattice subjected to a point heat source. 2022, Continuum Mechanics and Thermodynamics, 34(1), 297–319 (abstract, download pdf)

• JPCM 2022: A.Y. Panchenko, V.A. Kuzkin, I.E. Berinskii. Unsteady ballistic heat transport in two-dimensional harmonic graphene lattice. 2022, Journal of Physics: Condensed Matter, 34(16) (abstract, download pdf)

2021

• AM 2021: V.A. Kuzkin, A.M. Krivtsov. Unsteady ballistic heat transport: linking lattice dynamics and kinetic theory. 2021, Acta Mechanica, 232(5), 1983-1996 (abstract, download pdf)

• JHMT 2021: A. A. Sokolov, W.H. Müller, A.V. Porubov, S.N. Gavrilov. Heat conduction in 1D harmonic crystal: Discrete and continuum approaches. 2021, International Journal of Heat and Mass Transfer, 176, 121442, (abstract, download pdf ).

• CMT 2021: O.S. Loboda, E.A. Podolskaya, D.V. Tsvetkov, A.M. Krivtsov. On the fundamental solution of the heat transfer problem in one-dimensional harmonic crystals. 2021, Continuum Mechanics and Thermodynamics, 33(2), pp. 485–496 (abstract, download pdf)

• JPCM 2021: A.M. Krivtsov, A.S. Murachev. Transition to thermal equilibrium in a crystal subjected to instantaneous deformation. 2021, Journal of Physics: Condensed Matter, 33(21), 215403 (abstract, download pdf)

2020

• PRE2 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 (abstract, download pdf)

• PRE1 2020: E.A. Korznikova , V.A. Kuzkin, A.M. Krivtsov, D. Xiong , V.A. Gani , A.A. Kudreyko , S.V. Dmitriev. Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains. 2020, Phys. Rev. E 102, 062148 (abstract, download pdf)

• PRE 2020: V.A. Kuzkin, S.D. Liazhkov. Equilibration of kinetic temperatures in face-centered cubic lattices. 2020, Physical Rev. E, 102, 042219 (abstract, download pdf)

• CMT 2020: 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), 41-61 (abstract, download pdf)

2019

• MPM 2019: A.M. Krivtsov, E.A. Podolskaya, V.Yu. Shubina. Asymptotics of a thermal wave in a one-dimensional harmonic crystal. 2019, Materials Physics and Mechanics, 42, 837-845 (download pdf).

• ARX 2019: A.M. Krivtsov, A.S. Murachev. Transition to thermal equilibrium in a deformed crystal. 2019, ArXiv: 1908.05464 (abstract, download pdf)

• PRE1 2019: S.N. Gavrilov, A.M. Krivtsov. Thermal equilibration in a one-dimensional damped harmonic crystal. 2019, Phys. Rev. E, E100, 022117 (abstract, download pdf)

• ZAMM 2019: O.S. Loboda, A.M. Krivtsov, A.V. Porubov, D.V. Tsvetkov. Thermal processes in a one-dimensional crystal with regard for the second coordination sphere. 2019, Zeitschrift fur Angewandte Mathematik und Mechanik, 99, e201900008 (abstract, download pdf).

• CMT1 2019: V.A. Kuzkin. Unsteady ballistic heat transport in harmonic crystals with polyatomic unit cell. 2019, Continuum Mechanics and Thermodynamics, 31, 1573–1599 (abstract, download pdf).

• PMM 2019: A.M. Krivtsov, M.B. Babenkov, D.V. Tsvetkov. Heat Propagation in a One-Dimensional Harmonic Crystal on an Elastic Foundation. 2020, Physical Mesomechanics, 23, 2, 109–119 (abstract, download pdf)

• PRE 2019: A.A. Sokolov, A.M. Krivtsov, W.H. Müller, E.N. Vilchevskaya. Change of entropy for one-dimensional ballistic heat equation — sinusoidal initial perturbation. 2019, Phys. Rev. E, 99, 042107 (abstract, pdf).

• DPG 2019: A.M. Krivtsov. The Ballistic Heat Equation for a One-Dimensional Harmonic Crystal. 2019, Altenbach H., Belyaev A., Eremeyev V., Krivtsov A., Porubov A. (eds) Dynamical Processes in Generalized Continua and Structures. Advanced Structured Materials, Springer, 103, 345–358 (abstract, pdf).

• JPCM 2019: A.S. Murachev, A.M. Krivtsov, D.V. Tsvetkov. Thermal echo in a one-dimensional harmonic crystal. 2019, Journal of Physics: Condensed Matter, 31(9). (abstract, pdf).

• CMT 2019: V.A. Kuzkin. Thermal equilibration in infinite harmonic crytals. 2019, Continuum Mechanics and Thermodynamics,31, 1401–1423 (abstract, pdf).

2018

• MPM 2018: E.A. Podolskaya, A.M. Krivtsov, D.V. Tsvetkov. Anomalous heat transfer in one-­dimensional diatomic harmonic crystal. 2018, Materials Physics and Mechanics, 40, 172–180 (abstract, download pdf).
• CMT 2018: 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. 2018, Continuum Mechanics and Thermodynamics, 31, 255–272 (abstract, pdf)

• AMM 2018: A.M. Krivtsov, A.A. Sokolov, W.H. Müller, A.B. Freidin. One-Dimensional Heat Conduction and Entropy Production. 2018, Advances in Mechanics of Microstructured Media and Structures, 87, 197–214 (abstract, download pdf).

• ECM 2018: A.M. Krivtsov, V.A. Kuzkin. Discrete and continuum thermomechanics. 2018, Altenbach H., Öchsner A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. (abstract, download pdf)

• LMA 2018: V.A. Tsaplin, V.A. Kuzkin. Temperature oscillations in harmonic triangular lattice with random initial velocities. 2018, Letters on Materials, 8(1), 16–20 (abstract, download pdf).

2017

• JPCM 2017: V.A. Kuzkin, A.M. Krivtsov. Fast and slow thermal processes in harmonic scalar lattices. 2017, Journal of Physics: Condensed Matter, 29 (50) (abstract, pdf).

• АRX 2017: A.M. Krivtsov. On heat transfer in a thermally perturbed harmonic chain. ArXiv:1709.07924. 2017, 2 p. (abstract, download pdf).

• PMM 2017: A.A. Sokolov, A.M. Krivtsov, W.H. Müller. Localized heat perturbation in harmonic 1D crystals: Solutions for an equation of anomalous heat conduction. 2017, Physical Mesomechanics, 20 (3), 305–310 (download pdf).

• PSS 2017: V.A. Kuzkin, A.M. Krivtsov. An analytical description of transient thermal processes in harmonic crystals. Physics of the Solid State. 2017, Vol. 59, No. 5, pp. 1051–1062, (abstract, pdf).

• DAN 2017: V.A. Kuzkin, A. M. Krivtsov High-frequency thermal processes in harmonic crystals.2017, Doklady Physics, 5, 529–533 (abstract, download pdf). (Обобщение ДАН 2014 на двух- и трехмерный случай).

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• V.A. Kuzkin, S.D. Liazhkov, Equilibration of kinetic temperatures in face-centered cubic lattices. 2020, Physical Review E, 102, 042219 (abstract, download pdf)

• 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 (abstract, download pdf)

• A.M. Krivtsov, M.B. Babenkov, D.V. Tsvetkov. Heat Propagation in a One-Dimensional Harmonic Crystal on an Elastic Foundation. 2020, Physical Mesomechanics, Vol. 23, No. 2, pp. 109–119 (abstract, download pdf)

• 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 (abstract, download pdf)

• A.M. Krivtsov, E.A. Podolskaya, V.Yu. Shubina. Asymptotics of a thermal wave in a one-dimensional harmonic crystal. 2019, Materials Physics and Mechanics, Vol. 42, pp. 837-845 (download pdf).

• A.M. Krivtsov, A.S. Murachev. Transition to thermal equilibrium in a deformed crystal. 2019, ArXiv:1908.05464 (abstract, download pdf)

• S.N. Gavrilov, A.M. Krivtsov. Thermal equilibration in a one-dimensional damped harmonic crystal. 2019, Physical review E, E100, 022117 (abstract, download pdf)

• O.S. Loboda, A.M. Krivtsov, A.V. Porubov, D.V. Tsvetkov. Thermal processes in a one-dimensional crystal with regard for the second coordination sphere. 2019, ZAMM. 13 p. (pdf).

• V.A. Kuzkin. Unsteady ballistic heat transport in harmonic crystals with polyatomic unit cell. Continuum Mechanics and Thermodynamics. 2019, 26 p. (pdf).

• A.A. Sokolov, A.M. Krivtsov, W.H. Müller, E.N. Vilchevskaya. Change of entropy for one-dimensional ballistic heat equation — sinusoidal initial perturbation. Physical Review E. 2019, Vol. 99, 042107 (abstract, pdf).

• A.M. Krivtsov. The Ballistic Heat Equation for a One-Dimensional Harmonic Crystal. Dynamical Processes in Generalized Continua and Structures. 2019, Vol. 103, pp. 345–358 (abstract, pdf).

• 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. Continuum Mechanics and Thermodynamics. 2019, Vol. 31, 21 p. (abstract, pdf).

• A.S. Murachev, A.M. Krivtsov, D.V. Tsvetkov. Thermal echo in a one-dimensional harmonic crystal. Journal of Physics: Condensed Matter. 2019, Vol. 31, Num. 9. (abstract, pdf).

• V.A. Kuzkin. Thermal equilibration in infinite harmonic crytals. Continuum Mechanics and Thermodynamics. 2019, 23 p. (abstract, pdf).

• E.A. Podolskaya, A.M. Krivtsov, D.V. Tsvetkov. Anomalous heat transfer in one-­dimensional diatomic harmonic crystal. Materials Physics and Mechanics. 2018, 40, pp. 172–180 (pdf).

• 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. Continuum Mechanics and Thermodynamics. 2018, Vol. 31, pp. 255–272 (abstract, pdf)

• A.M. Krivtsov, A.A. Sokolov, W.H. Müller, A.B. Freidin. One-Dimensional Heat Conduction and Entropy Production. Advances in Mechanics of Microstructured Media and Structures. 2018, Vol. 87, pp. 197–214 (pdf).

• A.M. Krivtsov, V.A. Kuzkin. Discrete and continuum thermomechanics. Encyclopedia of Continuum Mechanics. 2018, 16 p. (pdf)

• V.A. Tsaplin, V.A. Kuzkin. Temperature oscillations in harmonic triangular lattice with random initial velocities. Letters on Materials. 2018, 8(1), pp. 16–20 (pdf).

• V.A. Kuzkin, A.M. Krivtsov. Fast and slow thermal processes in harmonic scalar lattices. 2017, Journal of Physics: Condensed Matter. 2017, Vol. 29, No. 50, 14 p. (abstract, pdf).

• A.M. Krivtsov. On heat transfer in a thermally perturbed harmonic chain. ArXiv:1709.07924. 2017, 2 p. (abstract, pdf).

• A.A. Sokolov, A.M. Krivtsov, 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 (pdf).

• V.A. Kuzkin, A.M. Krivtsov. An analytical description of transient thermal processes in harmonic crystals. Physics of the Solid State. 2017, Vol. 59, No. 5, pp. 1051–1062, pdf.

• V.A. Kuzkin, A.M. Krivtsov High-frequency thermal processes in harmonic crystals. Doklady Physics. 2017, №5, pp. 529–533 (abstract, pdf).

• M.B. Babenkov, A.M. Krivtsov, D.V. Tsvetkov. Unsteady heat conduction processes in a harmonic crystal with a substrate potential. Proc. of XXIV ICTAM, 21-26 August 2016, Montreal, Canada, pp. 2440–2441 (pdf).

• M.B. Babenkov, A.M. Krivtsov, D.V. Tsvetkov. Energy oscillations in a one-dimensional harmonic crystal on an elastic substrate. Phys. Mesomech.. 2016, 19, No. 3, pp. 282–290 (pdf).

• A.M. Krivtsov. On unsteady heat conduction in a harmonic crystal. 2015, ArXiv:1509.02506, 5 p. (abstract, pdf, simulation).

• A.M. Krivtsov. Heat transfer in infinite harmonic one dimensional crystals. Doklady Physics. 2015, Vol. 60, No. 9, pp. 407–411 (pdf).

• A.M. Krivtsov. Energy Oscillations in a One-Dimensional Crystal. Doklady Physics. 2014, Vol. 59, No. 9, pp. 427–430 (pdf).

Additional publications

• A.A. Le-Zakharov, A.M. Krivtsov, A.V. Porubov. Relation between defects and crystalline thermal conduction. 2019, Continuum Mechanics and Thermodynamics, ISSN 0935-1175, Volume 31, Number 6, pp. 1873–1881 (download pdf).

• A.A. Le-Zakharov, A.M. Krivtsov. Molecular dynamics investigation of heat conduction in crystals with defects. Doklady Physics, 2008, № 5, pp. 261–264. (pdf).

Preprints

• 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, W.H. Müller. Energy transfer in discrete and continuous one-dimensional media.

Virtual laboratory

• Dynamics of 1D harmonic crystal
• Dynamics of 1D anharmonic crystal
• Oscillations of energies in 1D crystal
• Diffusive processses in 1D crystal
• Heat transport in 1D crystal (see also uniform and periodic temperature)
• Oscillations of energies in 1D crystal on elastic substrateDistribution function in 2D triangular lattice
• Fermi-Pasta-Ulam crystal (Fermi-Pasta-Ulam crystal (analytics))
• Heat tranport in triangular lattice
• Transition of mechanical energy to heat:
  • oscillations
  • traveling wave
  • Gauss
• Heat supply:
  • Brownian motion
  • behavior of displacements and velocities)
  • behavior of temperature
• Group velocity vs. phase velocity
• Soliton vs. harmonic wave

Conferences talks

• A.M. Krivtsov. June 22, 2020: Hooke’s chain. Keynote lecture. St. Petersburg, 48th International Summer School-Conference "Advanced Problems in Mechanics-2020 ONLINE".
• S.N. Gavrilov. June 22, 2020: Heat conduction in 1D harmonic crystal: discrete-to-continuum limit and slow-and-fast motions decoupling. St. Petersburg, 48th International Summer School-Conference "Advanced Problems in Mechanics-2020 ONLINE".
• V.A. Kuzkin. June 22, 2020: Ballistic resonance and thermalization in Fermi-Pasta-UlamTsingou chain at finite temperature. St. Petersburg, 48th International Summer School-Conference "Advanced Problems in Mechanics-2020 ONLINE".
• A.Yu. Panchenko. June 22, 2020: Ballistic heat propagation in a 2D harmonic graphene lattice. St. Petersburg, 48th International Summer School-Conference "Advanced Problems in Mechanics-2020 ONLINE".
• A.A. Sokolov. June 22, 2020: Ballistic heat conduction in graphene: The approach based on analytical results obtained from lattice dynamics and dispersion relations measured in MD simulations and experiments. St. Petersburg, 48th International Summer School-Conference "Advanced Problems in Mechanics-2020 ONLINE".
• A.M. Krivtsov. October 2, 2019: Ballistic and diffusive heat process in ultrapure materials. Plenary lecture. Tomsk, 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, 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, International Summer School-Conference “Advanced Problems in Mechanics” 2019.
• 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, 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, 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, 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, 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, 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, International Summer School-Conference “Advanced Problems in Mechanics” 2018.
• 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, 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, 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, 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, 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, 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, 26th INTERNATIONAL WORKSHOP ON COMPUTATIONAL MECHANICS OF MATERIALS.
• A.M. Krivtsov. June 25, 2016. On unsteady heat conduction in a harmonic crystal. Sheffield, UK, Non-Equilibrium Simulation Conference (NESC 2016).
• A.M. Krivtsov. June 27, 2016. Unsteady thermal processes in harmonic crystals. Plenary lecture. St. Petersburg, 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, International Summer School-Conference “Advanced Problems in Mechanics” 2015.

Links

• Higher school of theoretical mechanics