Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 10/2014, Volume 19, Issue 10, pp. 3492 - 3512

•We discretize the covariant formulation of the geometrically exact beam model.•The discrete covariant principle is established on a triangular spacetime...

Multisymplectic integrator | Variational integrator | Energy conservation | Geometrically exact beam | Discrete Noether theorem

Multisymplectic integrator | Variational integrator | Energy conservation | Geometrically exact beam | Discrete Noether theorem

Journal Article

Quarterly Journal of the Royal Meteorological Society, ISSN 0035-9009, 04/2019, Volume 145, Issue 720, pp. 1070 - 1088

We develop a variational integrator for the shallow‐water equations on a rotating sphere. The variational integrator is built around a discretization of the...

variational integrator on sphere | rotating shallow‐water equations | structure‐preserving discretization | DISCRETIZATION | ENERGY | POTENTIAL ENSTROPHY | NUMERICAL-INTEGRATION | rotating shallow-water equations | structure-preserving discretization | METEOROLOGY & ATMOSPHERIC SCIENCES | SCHEMES | Hydrodynamics | Equations | Framework | Mathematics | Nonlinear Sciences

variational integrator on sphere | rotating shallow‐water equations | structure‐preserving discretization | DISCRETIZATION | ENERGY | POTENTIAL ENSTROPHY | NUMERICAL-INTEGRATION | rotating shallow-water equations | structure-preserving discretization | METEOROLOGY & ATMOSPHERIC SCIENCES | SCHEMES | Hydrodynamics | Equations | Framework | Mathematics | Nonlinear Sciences

Journal Article

Journal of Nonlinear Science, ISSN 0938-8974, 6/2018, Volume 28, Issue 3, pp. 873 - 904

... Fluid Flows François Gay-Balmaz 1 · Darryl D. Holm 2 Received: 16 August 2017 / Accepted: 2 December 2017 / Published online: 17 January 2018 © The Author(s) 2018...

Euler-Poincaré theory | 37J15 | 60H10 | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Mathematics | Stochastic geometric mechanics | 37H10 | Geophysical fluid dynamics | Analysis | Mathematical and Computational Engineering | Coadjoint orbits | MATHEMATICS, APPLIED | Euler-Poincare theory | EQUATIONS | PHYSICS, MATHEMATICAL | SPACE | MECHANICS | REDUCTION | SYSTEMS | SEMIDIRECT PRODUCTS | TURBULENT FLOWS | Fluid dynamics | Environmental law | Physics - Chaotic Dynamics

Euler-Poincaré theory | 37J15 | 60H10 | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Mathematics | Stochastic geometric mechanics | 37H10 | Geophysical fluid dynamics | Analysis | Mathematical and Computational Engineering | Coadjoint orbits | MATHEMATICS, APPLIED | Euler-Poincare theory | EQUATIONS | PHYSICS, MATHEMATICAL | SPACE | MECHANICS | REDUCTION | SYSTEMS | SEMIDIRECT PRODUCTS | TURBULENT FLOWS | Fluid dynamics | Environmental law | Physics - Chaotic Dynamics

Journal Article

Entropy, ISSN 1099-4300, 03/2018, Volume 20, Issue 3, p. 163

...entropy Article A Variational Formulation of Nonequilibrium Thermodynamics for Discrete Open Systems with Mass and Heat Transfer François Gay-Balmaz 1...

Nonequilibrium thermodynamics | Nonlinear nonholonomic constraint | Lagrangian variational formulation | Discrete open systems | ELEMENTS | MECHANICS | discrete open systems | PERMEABILITY | PHYSICS, MULTIDISCIPLINARY | nonequilibrium thermodynamics | COMPOSITE MEMBRANES | nonlinear nonholonomic constraint | Time dependence | Discrete systems | Heat exchange | Open systems | Entropy | Nonlinear systems | Heat transfer

Nonequilibrium thermodynamics | Nonlinear nonholonomic constraint | Lagrangian variational formulation | Discrete open systems | ELEMENTS | MECHANICS | discrete open systems | PERMEABILITY | PHYSICS, MULTIDISCIPLINARY | nonequilibrium thermodynamics | COMPOSITE MEMBRANES | nonlinear nonholonomic constraint | Time dependence | Discrete systems | Heat exchange | Open systems | Entropy | Nonlinear systems | Heat transfer

Journal Article

Geophysical & Astrophysical Fluid Dynamics: Mathematical Developments in Geophysical Fluid Dynamics: Structure, Vortices, and Waves. Guest Editors: Gualtiero Badin, Jörn Behrens, Christian Franzke, Marcel Oliver and Jens Rademacher, ISSN 0309-1929, 11/2019, Volume 113, Issue 5-6, pp. 428 - 465

Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation for...

irreversible processes | variational formulation | Moist atmosphere | lagrangian and eulerian formulations | nonequilibrium thermodynamics | IA SUPERNOVAE | CONVECTION | EQUATIONS | BRACKET FORMULATION | PRINCIPLES | SCALE ANALYSIS | GEOCHEMISTRY & GEOPHYSICS | DISCRETIZATION | MECHANICS | DEEP | ASTRONOMY & ASTROPHYSICS | Viscosity | Conductive heat transfer | Conduction | Approximation | Variational methods | Atmospheric models | Hamilton's principle | Derivation | Phase transitions | Phase changes | Irreversible processes | Heat conduction | Thermodynamics | Rain | Equations of state | Planets | Atmosphere | Conduction heating | Atmospheric precipitations | Nonequilibrium thermodynamics | Diffusion | Oceanic dynamics

irreversible processes | variational formulation | Moist atmosphere | lagrangian and eulerian formulations | nonequilibrium thermodynamics | IA SUPERNOVAE | CONVECTION | EQUATIONS | BRACKET FORMULATION | PRINCIPLES | SCALE ANALYSIS | GEOCHEMISTRY & GEOPHYSICS | DISCRETIZATION | MECHANICS | DEEP | ASTRONOMY & ASTROPHYSICS | Viscosity | Conductive heat transfer | Conduction | Approximation | Variational methods | Atmospheric models | Hamilton's principle | Derivation | Phase transitions | Phase changes | Irreversible processes | Heat conduction | Thermodynamics | Rain | Equations of state | Planets | Atmosphere | Conduction heating | Atmospheric precipitations | Nonequilibrium thermodynamics | Diffusion | Oceanic dynamics

Journal Article

Journal of Nonlinear Science, ISSN 0938-8974, 4/2019, Volume 29, Issue 2, pp. 377 - 414

...: Equations, Solutions and Shock Waves François Gay-Balmaz 1 · Vakhtang Putkaradze 2 Received: 24 May 2018 / Accepted: 23 August 2018 / Published online: 4 September 2018...

76Z05 | Variational methods | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Fluid-structure interactions | Mathematics | Compressible fluid dynamics | 74L15 | Compliant tubes conveying fluid | Shock waves | 70H30 | 76L05 | Analysis | Mathematical and Computational Engineering | 74F10 | Blood flow models | SYSTEM | MATHEMATICS, APPLIED | STABILITY | VIBRATIONS | PIPES | PHYSICS, MATHEMATICAL | FLOWING FLUID | MECHANICS | NONLINEAR DYNAMICS | CIRCULAR CYLINDRICAL-SHELLS | Fluid dynamics | Environmental law | Nonlinear Sciences

76Z05 | Variational methods | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Fluid-structure interactions | Mathematics | Compressible fluid dynamics | 74L15 | Compliant tubes conveying fluid | Shock waves | 70H30 | 76L05 | Analysis | Mathematical and Computational Engineering | 74F10 | Blood flow models | SYSTEM | MATHEMATICS, APPLIED | STABILITY | VIBRATIONS | PIPES | PHYSICS, MATHEMATICAL | FLOWING FLUID | MECHANICS | NONLINEAR DYNAMICS | CIRCULAR CYLINDRICAL-SHELLS | Fluid dynamics | Environmental law | Nonlinear Sciences

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 01/2018, Volume 59, Issue 1, p. 12701

Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the...

SYSTEMS | LAGRANGIAN VARIATIONAL FORMULATION | PART II | PHYSICS, MATHEMATICAL

SYSTEMS | LAGRANGIAN VARIATIONAL FORMULATION | PART II | PHYSICS, MATHEMATICAL

Journal Article

Nonlinearity, ISSN 0951-7715, 03/2018, Volume 31, Issue 4, pp. 1673 - 1705

In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a...

entropy | nonequilibrium thermodynamics | variational integrators | discrete Lagrangian formulation | structure preserving discretization | MATHEMATICS, APPLIED | FACTORIZATION | MECHANICS | INTEGRATORS | FORMULATION | PHYSICS, MATHEMATICAL | Mathematics - Numerical Analysis

entropy | nonequilibrium thermodynamics | variational integrators | discrete Lagrangian formulation | structure preserving discretization | MATHEMATICS, APPLIED | FACTORIZATION | MECHANICS | INTEGRATORS | FORMULATION | PHYSICS, MATHEMATICAL | Mathematics - Numerical Analysis

Journal Article

Analysis and Applications, ISSN 0219-5305, 05/2016, Volume 14, Issue 3, pp. 341 - 391

Multisymplectic variational integrators are structure-preserving numerical schemes especially designed for PDEs derived from covariant spacetime Hamilton...

variational integrator | Multisymplectic structure | discrete momentum map | discrete mechanics | discrete global Noether theorem | Lie group symmetry | BEAM | MATHEMATICS | MATHEMATICS, APPLIED | GEOMETRY

variational integrator | Multisymplectic structure | discrete momentum map | discrete mechanics | discrete global Noether theorem | Lie group symmetry | BEAM | MATHEMATICS | MATHEMATICS, APPLIED | GEOMETRY

Journal Article

Entropy, ISSN 1099-4300, 01/2019, Volume 21, Issue 1, p. 8

In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite-dimensional case of discrete...

Discrete thermodynamic systems | Irreversible processes | Nonequilibrium thermodynamics | Nonholonomic constraints | Continuum thermodynamic systems | Variational formulation | COMPLEX FLUIDS | continuum thermodynamic systems | PERMEABILITY | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | BRACKET FORMULATION | COMPOSITE MEMBRANES | PRINCIPLES | variational formulation | nonholonomic constraints | nonequilibrium thermodynamics | PRODUCTS | HAMILTONIAN-SYSTEMS | FLUCTUATIONS | discrete thermodynamic systems | irreversible processes | DYNAMICS | Nonlinear Sciences

Discrete thermodynamic systems | Irreversible processes | Nonequilibrium thermodynamics | Nonholonomic constraints | Continuum thermodynamic systems | Variational formulation | COMPLEX FLUIDS | continuum thermodynamic systems | PERMEABILITY | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | BRACKET FORMULATION | COMPOSITE MEMBRANES | PRINCIPLES | variational formulation | nonholonomic constraints | nonequilibrium thermodynamics | PRODUCTS | HAMILTONIAN-SYSTEMS | FLUCTUATIONS | discrete thermodynamic systems | irreversible processes | DYNAMICS | Nonlinear Sciences

Journal Article

Journal of Fluids and Structures, ISSN 0889-9746, 04/2018, Volume 78, pp. 146 - 174

We study the linear stability of elastic collapsible tubes conveying fluid, when the equilibrium configuration of the tube is helical. A particular case of...

Elastic tubes conveying fluid | Linear stability | Collapsible tubes | Variational methods | Helical equilibria | INSTABILITY | EQUATIONS | PIPES | FLOW | ENGINEERING, MECHANICAL | UNSTABLE OSCILLATION | MECHANICS | MOTION | DYNAMICS

Elastic tubes conveying fluid | Linear stability | Collapsible tubes | Variational methods | Helical equilibria | INSTABILITY | EQUATIONS | PIPES | FLOW | ENGINEERING, MECHANICAL | UNSTABLE OSCILLATION | MECHANICS | MOTION | DYNAMICS

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 02/2019, Volume 16

We present a variational formulation for the Navier-Stokes-Fourier system based on a free energy Lagrangian. This formulation is a systematic...

Navier-Stokes-Fourier system | nonequilibrium thermodynamics | Variational formulation | PHYSICS, MATHEMATICAL

Navier-Stokes-Fourier system | nonequilibrium thermodynamics | Variational formulation | PHYSICS, MATHEMATICAL

Journal Article

Comptes rendus - Mécanique, ISSN 1631-0721, 11/2016, Volume 344, Issue 11-12, pp. 769 - 775

We derive a variational approach for discretizing fluid–structure interactions, with a particular focus on the dynamics of fluid-conveying elastic tubes. Our...

Tubes avec écoulement interne | Fluid–structure interaction | Intégrateurs variationnels | Variational integrators | Fluid-conveying tubes | Interaction fluide–structure | UNSTABLE OSCILLATION | MECHANICS | PIPES | STABILITY | Environmental law | Analysis | Numerical analysis

Tubes avec écoulement interne | Fluid–structure interaction | Intégrateurs variationnels | Variational integrators | Fluid-conveying tubes | Interaction fluide–structure | UNSTABLE OSCILLATION | MECHANICS | PIPES | STABILITY | Environmental law | Analysis | Numerical analysis

Journal Article

Physical Review Letters, ISSN 0031-9007, 12/2012, Volume 109, Issue 24, p. 244303

One of the most challenging and basic problems in elastic rod dynamics is a description of rods in contact that prevents any unphysical self-intersections....

KIRCHHOFF RODS | SYSTEMS | PHYSICS, MULTIDISCIPLINARY | DNA | SELF-CONTACT | Models, Theoretical | Elasticity | Friction | Surface Properties | Chaotic Dynamics | Dynamical Systems | Biological Physics | Nonlinear Sciences | Mathematics | Physics

KIRCHHOFF RODS | SYSTEMS | PHYSICS, MULTIDISCIPLINARY | DNA | SELF-CONTACT | Models, Theoretical | Elasticity | Friction | Surface Properties | Chaotic Dynamics | Dynamical Systems | Biological Physics | Nonlinear Sciences | Mathematics | Physics

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 1/2012, Volume 309, Issue 2, pp. 413 - 458

... V ariational Problems François Gay-Balmaz 1 , Darryl D. Holm 2 , David M. Meier 2 , Tudor S. Ratiu 3 , François-Xavier Vialard 2 1 Laboratoire de Météorologie...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | EQUATIONS | SPLINES | REDUCTION | PHYSICS, MATHEMATICAL | METRICS | GEOMETRY | Mathematical Physics | Data Analysis, Statistics and Probability

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | EQUATIONS | SPLINES | REDUCTION | PHYSICS, MATHEMATICAL | METRICS | GEOMETRY | Mathematical Physics | Data Analysis, Statistics and Probability

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 12/2013, Volume 210, Issue 3, pp. 773 - 811

...Digital Object Identiﬁer (DOI) 10.1007/s00205-013-0673-1 Arch. Rational Mech. Anal. 210 (2013) 773–811 Equivalent Theories of Liquid Crystal Dynamics François...

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | FLUIDS | EULER-POINCARE EQUATIONS | SYSTEMS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | DOUBLE-BRACKET DISSIPATION | Mathematical Physics

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | FLUIDS | EULER-POINCARE EQUATIONS | SYSTEMS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | DOUBLE-BRACKET DISSIPATION | Mathematical Physics

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2010, Volume 239, Issue 20, pp. 1929 - 1947

We formulate Euler–Poincaré and Lagrange–Poincaré equations for systems with broken symmetry. We specialize the general theory to present explicit equations of...

Euler–Poncaré and Lagrange–Poincaré reduction | Order parameter | Nematic liquid crystals | Symmetry breaking | EulerPoncar and LagrangePoincar reduction | FLUIDS | MATHEMATICS, APPLIED | DEFECTS | PHYSICS, MULTIDISCIPLINARY | NONLINEAR HYDRODYNAMICS | STABILITY | MAGNETOHYDRODYNAMICS | PHYSICS, MATHEMATICAL | Euler-Poncare and Lagrange-Poincare reduction | EULER-POINCARE-EQUATIONS | LIQUID-CRYSTALS | HAMILTONIAN-DYNAMICS | SEMIDIRECT PRODUCTS | Broken symmetry | Reduction | Tensors | Mathematical analysis | Matrices | Helicity | Invariants | Nematic

Euler–Poncaré and Lagrange–Poincaré reduction | Order parameter | Nematic liquid crystals | Symmetry breaking | EulerPoncar and LagrangePoincar reduction | FLUIDS | MATHEMATICS, APPLIED | DEFECTS | PHYSICS, MULTIDISCIPLINARY | NONLINEAR HYDRODYNAMICS | STABILITY | MAGNETOHYDRODYNAMICS | PHYSICS, MATHEMATICAL | Euler-Poncare and Lagrange-Poincare reduction | EULER-POINCARE-EQUATIONS | LIQUID-CRYSTALS | HAMILTONIAN-DYNAMICS | SEMIDIRECT PRODUCTS | Broken symmetry | Reduction | Tensors | Mathematical analysis | Matrices | Helicity | Invariants | Nematic

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 12/2012, Volume 53, Issue 12, p. 123502

By using the moment algebra of the Vlasov kinetic equation, we characterize the integrable Bloch-Iserles system on symmetric matrices [Bloch, A. M.,...

FLUIDS | EQUATIONS | SQUEEZED STATES | PHYSICS, MATHEMATICAL | STABILITY | Algebra | Dynamics | Mathematical analysis | Matrices | Kinetic theory | Inclusions | Matrix methods | Subgroups | Mathematical Physics | Physics

FLUIDS | EQUATIONS | SQUEEZED STATES | PHYSICS, MATHEMATICAL | STABILITY | Algebra | Dynamics | Mathematical analysis | Matrices | Kinetic theory | Inclusions | Matrix methods | Subgroups | Mathematical Physics | Physics

Journal Article

Forum of mathematics. Sigma, ISSN 2050-5094, 2016, Volume 4, pp. 1 - 54

... MECHANICS FRANÇOIS DEMOURES1,2, FRANÇOIS GAY-BALMAZ2 and TUDOR S. RATIU3,4 1 Department of Mathematics, Imperial College, London, UK; email: demoures@lmd.ens.fr 2 LMD...

Computational Mathematics | MATHEMATICS | FRICTIONAL CONTACT | MATHEMATICS, APPLIED | PENALTY | FONCTIONNELLE | CONTACT PROBLEMS | DYNAMICS | SYMPLECTICITY | MIXED FORMULATION | CONSTRAINTS | UNILATERAL CONTACT | OPTIMIZATION | Continuum mechanics | Integrators

Computational Mathematics | MATHEMATICS | FRICTIONAL CONTACT | MATHEMATICS, APPLIED | PENALTY | FONCTIONNELLE | CONTACT PROBLEMS | DYNAMICS | SYMPLECTICITY | MIXED FORMULATION | CONSTRAINTS | UNILATERAL CONTACT | OPTIMIZATION | Continuum mechanics | Integrators

Journal Article