79 citations · 763 across the 53 of their papers we have counts for
17 papers · 1 filter
Dirac structures in nonequilibrium thermodynamics for simple open systems
François Gay-Balmaz, Hiroaki Yoshimura
Dirac structures are geometric objects that generalize Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechani…
Madelung transform and probability densities in hybrid classical-quantum dynamics
François Gay-Balmaz, Cesare Tronci
This paper extends the Madelung-Bohm formulation of quantum mechanics to describe the time-reversible interaction of classical and quantum systems. The symplectic geometry of the M…
Dirac structures and port-Lagrangian systems in thermodynamics
Hiroaki Yoshimura, François Gay-Balmaz
In this paper, we introduce the notion of port-Lagrangian systems in nonequilibrium thermodynamics, which is constructed by generalizing the notion of port-Lagrangian systems for n…
From variational to bracket formulations in nonequilibrium thermodynamics of simple systems
François Gay-Balmaz, Hiroaki Yoshimura
A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends th…
From Lagrangian mechanics to nonequilibrium thermodynamics: a variational perspective
François Gay-Balmaz, Hiroaki Yoshimura
In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite dimensional case of discrete systems as well as for the i…
A Variational Formulation of Nonequilibrium Thermodynamics for Discrete Open Systems with Mass and Heat Transfer
François Gay-Balmaz, Hiroaki Yoshimura
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our…
Koopman wavefunctions and classical-quantum correlation dynamics
Denys I. Bondar, François Gay-Balmaz, Cesare Tronci
Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory…
A free energy Lagrangian variational formulation of the Navier-Stokes-Fourier system
François Gay-Balmaz, Hiroaki Yoshimura
We present a variational formulation for the Navier-Stokes-Fourier system based on a free energy Lagrangian. This formulation is a systematic infinite dimensional extension of the…
Dirac structures in nonequilibrium thermodynamics
François Gay-Balmaz, Hiroaki Yoshimura
Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained me…
A variational derivation of the nonequilibrium thermodynamics of a moist atmosphere with rain process and its pseudoincompressible approximation
François Gay-Balmaz
Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation of the evolution equations fo…
A Lagrangian formalism for nonequilibrium thermodynamics
François Gay-Balmaz, Hiroaki Yoshimura
In this paper, we present a Lagrangian formalism for nonequilibrium thermodynamics. This formalism is an extension of the Hamilton principle in classical mechanics that allows the…
Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions
François Gay-Balmaz, Darryl D. Holm, Tudor S. Ratiu
Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework for Lagrangian and Hamiltonian…
A new Lagrangian dynamic reduction in field theory
François Gay-Balmaz, Tudor S. Ratiu
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a…
Integrable G-Strands on semisimple Lie groups
François Gay-Balmaz, Darryl D. Holm, Tudor S. Ratiu
The present paper derives systems of partial differential equations that admit a quadratic zero curvature representation for an arbitrary real semisimple Lie algebra. It also deter…
Clebsch variational principles in field theories and singular solutions of covariant EPDiff equations
François Gay-Balmaz
This paper introduces and studies a field theoretic analogue of the Clebsch variational principle of classical mechanics. This principle yields an alternative derivation of the cov…
The Geometric Structure of Complex Fluids
François Gay-Balmaz, Tudor S. Ratiu
This paper develops the theory of affine Euler-Poincaré and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills an…
Affine Lie-Poisson Reduction, Yang-Mills magnetohydrodynamics, and superfluids
François Gay-Balmaz, Tudor S. Ratiu
This paper develops the theory of affine Lie-Poisson reduction and applies this process to Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids. As a consequence of…