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François Gay-Balmaz

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Related publications (34)

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Infinite dimensional geodesic flows and the universal Teichmüller space

François Gay-Balmaz

The subject of this thesis lies in the intersection of differential geometry and functional analysis, a domain usually called global analysis. A central object in this work is the group Ds(M) of all orientation preserving diffeomorphisms of a compact manif ...

EPFL2009

Clebsch Optimal Control Formulation In Mechanics

Tudor Ratiu, François Gay-Balmaz

This paper introduces and studies a class of optimal control problems based on the Clebsch approach to Euler-Poincare dynamics. This approach unifies and generalizes a wide range of examples appearing in the literature: the symmetric formulation of N-dimen ...

2011

Flexible beam in R3 under large overall motions and Asynchronous Variational Integrators

Tudor Ratiu, Yves Weinand, François Gay-Balmaz, François Marie Alain Demoures

The theory of discrete variational mechanics has its roots in the optimal control literature of the 1960's. The past ten years have seen a major development of discrete variational mechanics and corresponding numerical integrators, due largely to pioneerin ...

IABSE ETH Zurich2011

The geometric structure of complex fluids

Tudor Ratiu, François Gay-Balmaz

This paper develops the theory of affine Euler-Poincare and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids, spin glasses, microf ...

Elsevier2009

Symmetry Reduced Dynamics of Charged Molecular Strands

Tudor Ratiu, François Gay-Balmaz

The equations of motion are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting rigid charge conformations. The new feature is that these equations are nonloca ...

Springer-Verlag2010

Reduction theory for symmetry breaking with applications to nematic systems

François Gay-Balmaz, Cesare Tronci

We formulate Euler-Poincare and Lagrange-Poincare equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial liquid crystals. Th ...

2010

Lagrange-Poincare field equations

Tudor Ratiu, François Gay-Balmaz

The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original ...

2011

A New Lagrangian Dynamic Reduction In Field Theory

Tudor Ratiu, François Gay-Balmaz

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 symmetric covariant Lagrangian density defined on the first jet bundle of a ...

2010

On the classification of the coadjoint orbits of the Sobolev Bott-Virasoro group

François Gay-Balmaz

The purpose of this paper is to give the classification of the Bott-Virasoro coadjoint orbits, with nonzero central charge, in the functional analytic setting of smooth Hilbert manifolds. The central object of the paper is thus the completion of the Bott-V ...

2009

Integrable G-strands on semisimple Lie groups

Tudor Ratiu, François Gay-Balmaz

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 determines the general form of Hamilton's principles and Hamiltonians for these s ...

Iop Publishing Ltd2014

A multisymplectic integrator for elastodynamic frictionless impact problems

Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

We present a structure preserving numerical algorithm for the collision of elastic bodies. Our integrator is derived from a discrete version of the field-theoretic (multisymplectic) variational description of nonsmooth Lagrangian continuum mechanics, combi ...

Elsevier2017

Multisymplectic Variational Integrators For Nonsmooth Lagrangian Continuum Mechanics

Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

This paper develops the theory of multisymplectic variational integrators for nonsmooth continuum mechanics with constraints. Typical problems are the impact of an elastic body on a rigid plate or the collision of two elastic bodies. The integrators are ob ...

Cambridge Univ Press2016

The Momentum Map Representation of Images

Tudor Ratiu, François Gay-Balmaz, Martins Bruveris

This paper discusses the mathematical framework for designing methods of Large Deformation Diffeomorphic Matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, we prove a ...

Springer Verlag2011

Variational Principles For Spin Systems And The Kirchhoff Rod

Tudor Ratiu, François Gay-Balmaz

We obtain the affine Euler-Poincare equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in deriving the equations of motion for continuum spin systems and Kirchhoff's ...

2009

Lagrangian Reductions and Integrable Systems in Condensed Matter

Tudor Ratiu, François Gay-Balmaz

We consider a general approach for the process of Lagrangian and Hamiltonian reduction by symmetries in chiral gauge models. This approach is used to show the complete integrability of several one dimensional texture equations arising in liquid Helium phas ...

Springer2015

Discrete variational Lie group formulation of geometrically exact beams dynamics

Tudor Ratiu, Yves Weinand, François Gay-Balmaz, François Marie Alain Demoures

The goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics, by using a Lie group variational integrator. Both spatial and temporal discretization are implemented in a geometry preserving manner. The resultin ...

Springer2015

The helicity and vorticity of liquid-crystal flows

François Gay-Balmaz, Cesare Tronci

We present explicit expressions of the helicity conservation in nematic liquid-crystal flows, for both the Ericksen-Leslie and Landau-de Gennes theories. This is done by using a minimal coupling argument that leads to an Euler-like equation for a modified ...

2011

Exact geometric theory of dendronized polymer dynamics

Tudor Ratiu, François Gay-Balmaz

Dendronized polymers consist of an elastic backbone with a set of iterated branch structures (dendrimers) attached at every base point of the backbone. The conformations of such molecules depend on the elastic deformation of the backbone and the branches, ...

2012

Multisymplectic variational integrators and space/time symplecticity

Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

Multisymplectic variational integrators are structure-preserving numerical schemes especially designed for PDEs derived from covariant spacetime Hamilton principles. The goal of this paper is to study the properties of the temporal and spatial discrete evo ...

World Scientific Publ Co Pte Ltd2016

Affine Lie-Poisson reduction, Yang-Mills magnetohydrodynamics, and superfluids

Tudor Ratiu, François Gay-Balmaz

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 this approach, the associated Poisson brackets are obtained by reduction of ...

2008