Variational discretization of thermodynamical simple systems on Lie groups

DOI10.3934/dcdss.2020064zbMath1443.37061arXiv1806.09897OpenAlexW2963288691WikidataQ128009890 ScholiaQ128009890MaRDI QIDQ2180358

Benjamin Couéraud, François Gay-Balmaz

Publication date: 13 May 2020

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.09897

zbMATH Keywords

entropynonequilibrium thermodynamicsvariational integratorsdiscrete Lagrangian formulationstructure-preserving discretization

Mathematics Subject Classification ID

Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics (82C21) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Variational principles of physics (49S05) Variational methods applied to problems in thermodynamics and heat transfer (80M30)

Related Items

From variational to bracket formulations in nonequilibrium thermodynamics of simple systems

Cites Work

• A Lagrangian variational formulation for nonequilibrium thermodynamics. I: Discrete systems.
• A Lagrangian variational formulation for nonequilibrium thermodynamics. II: Continuum systems.
• Variational discretization for rotating stratified fluids
• Reduction theory for symmetry breaking with applications to nematic systems
• Structure-preserving discretization of incompressible fluids
• Geometric, variational discretization of continuum theories
• Integrators for nonholonomic mechanical systems
• The geometric structure of complex fluids
• Hamilton-Pontryagin integrators on Lie groups. I: Introduction and structure-preserving properties
• Lagrangian reduction and the double spherical pendulum
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products
• Variational integrators and time-dependent Lagrangian systems
• The Euler-Poincaré equations and double bracket dissipation
• Finite-mode analogs of 2D ideal hydrodynamics: Coadjoint orbits and local canonical structure
• Towards a geometric variational discretization of compressible fluids: the rotating shallow water equations
• Lagrangian reduction by stages
• Discrete mechanics and variational integrators
• Symplectic-energy-momentum preserving variational integrators
• Variational discretization of the nonequilibrium thermodynamics of simple systems
• Discrete Euler-Poincaré and Lie-Poisson equations
• Geometric Numerical Integration
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