Related papers: Symplectic bipotentials
We present a global approach of non-dissipative physics. Based on symplectic mechanics this technique allows us to obtain the solution of a very large class of problems in terms of a Taylor expand. We apply this method to the problem of…
To study temperature dependent elastic constants, a new computational method is proposed by combining continuum elasticity theory and first principles calculations. A Gibbs free energy function with one variable with respect to strain at…
The paper concerns the construction of a compressible liquid-vapor relaxation model which is able to capture the metastable states of the non isothermal van der Waals model as well as saturation states. Starting from the Gibbs formalism, we…
In this article, we first introduce the notion of a {\it continuous cover} of a manifold parametrised by any compact manifold endowed with a mass 1 volume-form. We prove that any such cover admits a partition of unity where the usual sum is…
The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between…
In this work, by considering an isentropic fluid-fluid interaction model with a large symmetric drag force, a commonly used simplified two-fluids flow model is justified as the asymptotic limit. Equations for each fluid component with an…
This article is based on the covariant canonical formalism and corresponding symplectic structure on phase space developed by Witten, Zuckerman and others in the context of field theory. After recalling the basic principles of this…
In this work one proves that, around each point of a dense open set (regular points), a real analytic or holomorphic bihamiltonian structure decomposes into a product of a Kronecker bihamiltonian structure and a symplectic one if a…
A new description of the endochronic and the Mroz model is discussed. It is based on the definition of a suitable pseudo-potential and the use of the generalized normality assumption. The key-point of this formulation is the dependence of…
We investigate the use of extended phase-space symplectic integration for simulating two different classes of electron dynamics. The first one, with one and a half degrees of freedom, comes from plasma physics and describes the classical…
A recent paper arXiv:1312.4890 on multi-symplectic magnetohydrodynamics (MHD) using Clebsch variables in an Eulerian action principle with constraints is further extended. We relate a class of symplecticity conservation laws to a vorticity…
In this paper we study non-commutative integrable systems on $b$-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering non-commutative systems on manifolds with boundary having the right…
An odd-symplectic form is a closed and maximally non-degenerate $2$-form on a compact odd-dimensional manifold. It describes the dynamics of an autonomous Hamiltonian system on a regular energy level. It is called Zoll if the induced…
In purely non-dissipative systems, Lagrangian and Hamiltonian reduction have proven to be powerful tools for deriving physical models with exact conservation laws. We have discovered a hint that an analogous reduction method exists also for…
The analysis of complex fibrous systems or materials on the micro- and nanoscale, which have a high practical relevance for many technical or biological systems, requires accurate analytical descriptions of the adhesive and repulsive forces…
The nonequilibrium free energy theorems show how distributions of work along nonequilibrium paths are related to free energy differences between the equilibrium states at the end points of these paths. In this paper we develop a natural way…
In this paper, a statistical physical derivation of thermodynamically consistent fluid mechanical equations is presented for non-isothermal viscous molecular fluids. The coarse-graining process is based on (i) the adiabatic expansion of the…
In this work we introduce an idempotent pressure to level-2 functions and its associated density entropy. All this is related to idempotent pressure functions which is the natural concept that corresponds to the meaning of probability in…
We study the nonextensive thermodynamics for open systems. On the basis of the maximum entropy principle, the dual power-law q-distribution functions are re-deduced by using the dual particle number definitions and assuming that the…
Boltzmann-Gibbs random fields are defined in terms of the exponential expression exp(-H), where H is a suitably defined energy functional of the field states x(s). This paper presents a new Boltzmann-Gibbs model which features local…