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

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