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Tudor Ratiu

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Publications associées (105)

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

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Tudor Ratiu

Bi-Jacobi fields are generalized Jacobi fields, and are used to efficiently compute approximations to Riemannian cubic splines in a Riemannian manifold M. Calculating bi-Jacobi fields is straightforward when M is a symmetric space such as bi-invariant SO(3 ...

Int Press Boston, Inc2016

Nematodynamics and random homogenization

Tudor Ratiu

We study the homogenization problem for the system of equations of dynamics of a mixture of liquid crystals with random structure. We consider a simplified form of the Ericksen-Leslie equations for an incompressible medium with inhomogeneous density with r ...

Taylor & Francis2016

On unique solvability of the full three-dimensional Ericksen-Leslie system

Tudor Ratiu

In this paper, we study the full three-dimensional Ericksen-Leslie system of equations for the nematodynamics of liquid crystals. We announce the short-time existence and uniqueness of strong solutions for the initial value problem in the periodic case and ...

Elsevier2016

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

L-2-cohomology and complete Hamiltonian manifolds

Tudor Ratiu

A classical theorem of Frankel for compact Kahler manifolds states that a Kahler S-1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when the Hodge theory holds on non-compact manifolds, Frankel's theorem st ...

Elsevier2015

Discrete variational Lie group formulation of geometrically exact beams dynamics

Tudor Ratiu, François Gay-Balmaz, Yves Weinand, 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

Quantum anomalies and logarithmic derivatives of feynman pseudomeasures

Tudor Ratiu

Connections between quantum anomalies and transformations of pseudomeasures of the type of Feynman pseudomeasures are studied. Mathematical objects related to the notion of the volume element in an infinite-dimensional space considered in the physics liter ...

Springer Verlag2015

Fiber connectivity and bifurcation diagrams of almost toric integrable systems

Tudor Ratiu

We describe the bifurcation diagrams of almost toric integrable Hamiltonian systems on a four dimensional symplectic manifold M, not necessarily compact. We prove that, under a weak assumption, the connectivity of the fibers of the induced singular Lagrang ...

Int Press Boston, Inc2015

Existence and Uniqueness Theorems in Two-Dimensional Nematodynamics. Finite Speed of Propagation

Tudor Ratiu

The paper is devoted to the two-dimensional Ericksen-Leslie system describing the nematodinamics of liquid crystals. The moment of inertia of molecules is supposed to be strictly positive. The existence of the solution was proved in the case of periodic do ...

Springer Verlag2015

Noether's theorem for dissipative quantum dynamical semi-groups

Tudor Ratiu

Noether's theorem on constants of the motion of dynamical systems has recently been extended to classical dissipative systems (Markovian semi-groups) by Baez and Fong [J. Math. Phys. 54, 013301 (2013)]. We show how to extend these results to the fully quan ...

Amer Inst Physics2015

Dynamics of particles with anisotropic mass depending on time and position

Tudor Ratiu

Representations of solutions of equations describing the diffusion and quantum dynamics of particles in a Riemannian manifold are discussed under the assumption that the mass of particles is anisotropic and depends on both time and position. These equation ...

Springer Verlag2015

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

The geometry of the universal Teichmuller space and the Euler-Weil-Petersson equation

Tudor Ratiu, François Gay-Balmaz

On the identity component of the universal Teichmuller space endowed with the Takhtajan-Teo topology, the geodesics of the Weil Petersson metric are shown to exist for all time. This component is naturally a subgroup of the quasisymmetric homeomorphisms of ...

Elsevier2015

Wigner Quantization of Hamilton-Dirac Systems

Tudor Ratiu

Springer Verlag2015

The U (n) free rigid body: Integrability and stability analysis of the equilibria

Tudor Ratiu

A natural extension of the free rigid body dynamics to the unitary group U (n) is considered. The dynamics is described by the Euler equation on the Lie algebra u(n), which has a bi-Hamiltonian structure, and it can be reduced onto the adjoint orbits, as i ...

Elsevier2015

Hamiltonian Structures in the Quantum Theory of Hamilton-Dirac Systems

Tudor Ratiu

Springer Verlag2015

Integrable Systems of Neumann Type

Tudor Ratiu

We construct families of integrable systems that interpolate between -dimensional harmonic oscillators and Neumann systems. This is achieved by studying a family of integrable systems generated by the Casimir functions of the Lie algebra of real skew-symme ...

Springer Verlag2015

Wigner measures and quantum control

Tudor Ratiu

Springer Verlag2015

Geometry of non-holonomic diffusion

Tudor Ratiu, Simon Hochgerner

We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For G-Chap ...

European Mathematical Soc2015

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