image/svg+xml Advected fibers: compatible with natural configurations   General Equation for Non-Equilibrium Reversible-Irreversible Coupling GENERIC functional of state variables Poisson bracket energy dissipation potential entropy   classical mechanics, kinetic theory, electromagnetism, fluid dynamics, elasticity, plasticity, viscoelasticity, mixtures, heat conduction, hyperbolic heat conduction, complex fluids, turbulence, ... reversible irreversible Dissipation potential quadratic - Fourier, Fick, Navier-Stokes chemical reactions, Boltzmann collisions Second law of thermodynamics Poisson bracket energy (Hamiltonian) Hamilton canonical equations Non-Newtonian fluids within GENERIC Michal Pavelka Symmetric hyperbolic thermodynamically compatible (SHTC) equations density momentum density entropy density distortion matrix Total energy temperature relaxation time S. K. Godunov, I. Peshkov, E. Romenskii Unified framework for fluids (viscoelastic) and solids (visco-elasto-plastic). bilinearantisymmetricLeibniz ruleJacobi identity Kinematics of fluid mechanics and phonons total momentum Grmela, Lebon, Dubois, Phys. Rev. E 2011 Peshkov, Pavelka, Romensky, Grmela, CMAT 2018 joint work with Petr Pelech, Karel Tůma and Josef Málek Miroslav GrmelaHans Christian Öttinger densitymomentum densityentropy density  Euler equations for fluids H. C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley 2005Michal Pavelka, Václav Klika and Miroslav Grmela. Multiscale Thermo-Dynamics, de Gruyter 2018 H. C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley 2005Michal Pavelka, Václav Klika and Miroslav Grmela. Multiscale Thermo-Dynamics, de Gruyter 2018 H. C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley 2005M. Pavelka, V. Klika, M. Grmela, Multiscale Thermo-Dynamics, de Gruyter 2018 convex in conservation symmetric, positive semidefinite V.I. Arnold. Sur la géometrie différentielle des groupes de Lie de dimension infini et ses applications dans l’hydrodynamique des fluides parfaits. Annales de l’institut Fourier,16(1):319–361, 1966.Annals of PhysicsVolume 125, Issue 1, March 1980, Pages 67-97Annals of PhysicsPoisson brackets in condensed matter physicsAuthor links open overlay panelI.E.DzyaloshinskiiG.E.Volovick   Peshkov, Romenskii, 2017 Peshkov, Pavelka, Romensky, Grmela, CMAT 2018 Compatible with GENERIC. How to derive Poisson brackets? Projection from kinetic theory. Lie groups and differential geometry. ? weak X strong formulation ? Hyperbolicity Novikov, Dubrovin, Tsarev Hamiltonian in 1D hyperbolicity Local in time existence, uniqueness Continuous dependence on data characteristics Until characteristics cross Choose the characteristic with higher entropy Does it work in 3D? Advected vector field Semidireict product J. Marsden, T. Ratiu, A. Weinstein, O, Esen cotangent bundle Advection of a tensor field Explicit formula for stress Kinetic theory Pavelka, Klika, Grmela, Esen, Physica D 2016 linear force-flux relations law of mass action Fluid mechanics
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  1. intro
  2. GENERIC
  3. books
  4. book
  5. book
  6. pb
  7. HCE
  8. Euler
  9. Euler PER PARTES
  10. Euler rovnice
  11. Euler rovnice detail
  12. GENERIC
  13. GENERIC aplicace
  14. GENERIC weak strong
  15. disip
  16. GENERIC
  17. GENERIC
  18. heat equations
  19. shtc
  20. distortion
  21. SHTC GEneric
  22. attenuation
  23. hyperbolicity
  24. generic
  25. brackets
  26. b
  27. b bracket
  28. b bracket
  29. tensor
  30. tensor more
  31. tensor more
  32. tensor more
  33. end
  34. end