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François Gay-Balmaz

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Related publications (33)

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Equivalent Theories of Liquid Crystal Dynamics

Tudor Ratiu, François Gay-Balmaz, Cesare Tronci

There are two competing descriptions of nematic liquid crystal dynamics: the Ericksen-Leslie director theory and the Eringen micropolar approach. Up to this day, these two descriptions have remained distinct in spite of several attempts to show that the mi ...

Springer Verlag2013

Invariant Higher-Order Variational Problems

Tudor Ratiu, François Gay-Balmaz

We investigate higher-order geometric k-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudinal studies of Computational Anatomy. Our approach formulat ...

2012

Euler-Poincare Approaches to Nematodynamics

Tudor Ratiu, François Gay-Balmaz, Cesare Tronci

Nematodynamics is the orientation dynamics of flowless liquid-crystals. We show how Euler-Poincar, reduction produces a unifying framework for various theories, including Ericksen-Leslie, Luhiller-Rey, and Eringen's micropolar theory. In particular, we sho ...

Springer Netherlands2012

Invariant Higher-Order Variational Problems II

Tudor Ratiu, François Gay-Balmaz

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as ...

Springer Verlag2012

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

Reduced Variational Formulations in Free Boundary Continuum Mechanics

Tudor Ratiu, François Gay-Balmaz

We present the material, spatial, and convective representations for elasticity and fluids with a free boundary from the Lagrangian reduction point of view, using the material and spatial symmetries of these systems. The associated constrained variational ...

Springer-Verlag2012

Geometry of nonabelian charged fluids

Tudor Ratiu, François Gay-Balmaz

The goal of this paper is to derive the Hamiltonian structure of polarized and magnetized Euler-Maxwell fluids by reduction of the canonical symplectic form on phase space, and to generalize the dynamics to the nonabelian case. The Hamiltonian function we ...

2011

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

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

Yves Weinand, Tudor Ratiu, 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

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