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07/2020
We derive the equations of motion for the dynamics of a porous media filled with an incompressible fluid. We use a variational approach with a Lagrangian... 
Journal Article
Acta mechanica, ISSN 0001-5970, 07/2020
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 07/2020, Volume 412, p. 109439
•A scheme for the incompressible Euler equations with variable density is presented.•It exactly preserves mass, total squared density, energy, and... 
Incompressible flow | Exactly divergence-free | Energy-conserving | Variable density | Finite element | Inviscid | ENERGY | ENSTROPHY | PHYSICS, MATHEMATICAL | STOKES | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PROJECTION METHOD | MASS | FLOWS | SCHEMES
Journal Article
Journal of physics. A, Mathematical and theoretical, ISSN 1751-8113, 05/2020
Journal Article
Entropy (Basel, Switzerland), ISSN 1099-4300, 04/2020, Volume 22, Issue 5, p. 498
In this paper, we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which... 
Lie group actions | (multi)symplectic integrators | momentum maps | cocycles | variational integrators | coadjoint orbits
Journal Article
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, ISSN 1937-1632, 04/2020, Volume 13, Issue 4, pp. 1075 - 1102
This paper presents the continuous and discrete variational formulations of simple thermodynamical systems whose configuration space is a (finite dimensional)... 
MATHEMATICS, APPLIED | entropy | nonequilibrium thermodynamics | structure preserving discretization | discrete Lagrangian formulation | EULER-POINCARE EQUATIONS | Variational integrators | INTEGRATORS | FORMULATION | LAGRANGIAN REDUCTION
Journal Article
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, ISSN 1937-1632, 04/2020, Volume 13, Issue 4, pp. 1229 - 1242
We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear... 
Dimension theory | MATHEMATICS, APPLIED | multifractal analysis | Poincare recurrences
Journal Article
10/2019
We construct a finite element discretization and time-stepping scheme for the incompressible Euler equations with variable density that exactly preserves total... 
Journal Article
10/2019
We present a finite element variational integrator for compressible flows. The numerical scheme is derived by discretizing, in a structure preserving way, the... 
Journal Article
09/2019
We describe the coadjoint orbits of the group of volume preserving diffeomorphisms of $\mathbb{R}^3$ associated to the motion of closed vortex sheets in ideal... 
Mathematics - Symplectic Geometry
Journal Article
07/2019
Dirac structures are geometric objects that generalize Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation... 
Journal Article
07/2019
This paper extends the Madelung-Bohm formulation of quantum mechanics to describe the time-reversible interaction of classical and quantum systems. The... 
Journal Article
06/2019
In this paper, we introduce the notion of port-Lagrangian systems in nonequilibrium thermodynamics, which is constructed by generalizing the notion of... 
Journal Article
04/2019
A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This... 
Journal Article
JOURNAL OF SYMPLECTIC GEOMETRY, ISSN 1527-5256, 2019, Volume 17, Issue 3, pp. 663 - 702
We describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms of a symplectic manifold (S, omega) by implementing symplectic reduction... 
MATHEMATICS | MANIFOLDS | PRINCIPAL BUNDLES
Journal Article
JOURNAL OF GEOMETRIC MECHANICS, ISSN 1941-4889, 12/2019, Volume 11, Issue 4, pp. 511 - 537
The anelastic and pseudo-incompressible equations are two wellknown soundproof approximations of compressible flows useful for both theoretical and numerical... 
soundproof approximations | SCALE ANALYSIS | MATHEMATICS, APPLIED | DISCRETIZATION | VORTICES | DEEP | CONVECTION | structure-preserving schemes | Euler-Poincare formulation | PHYSICS, MATHEMATICAL | fluid dynamics | Geometric discretization
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
Journal Article
11/2018
The equations of reversible (inviscid, adiabatic) fluid dynamics have a well-known variational formulation based on Hamilton's principle and the Lagrangian, to... 
Physics - Classical Physics
Journal Article
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