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Cesare Tronci

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Publications associées (9)

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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

Euler-Poincare Formulation Of Hybrid Plasma Models

Cesare Tronci

Three different hybrid Vlasov-fluid systems are derived by applying reduction by symmetry to Hamilton's variational principle. In particular, the discussion focuses on the Euler-Poincare formulation of three major hybrid MHD models, which are compared in t ...

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

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

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

Double-bracket dissipation in kinetic theory for particles with anisotropic interactions

Cesare Tronci

We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double-bracket approach (double-bracket Vlasov, or DBV). The moments of the DBV equation lead ...

2010

Hamiltonian approach to hybrid plasma models

Cesare Tronci

The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling schemes for an ord ...

2010

Geodesic Vlasov Equations And Their Integrable Moment Closures

Cesare Tronci

Various integrable geodesic flows on Lie groups are shown to arise by taking moments of a geodesic Vlasov equation on the group of canonical transformations. This was already known for both the one- and two-component Camassa-Holm systems [18, 19]. The pres ...

2009

Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions

Cesare Tronci

The EPDiff equation (or dispersionless Camassa-Holm equation in 1D) is a well known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its recent two-component extension governs geodesic motion on the semidirect produ ...

2009