Tensorial Euler-Lagrange expressions and conservation laws.
Tensorial Euler-Lagrange expressions and conservation laws. (Short Communication).
The calculus of variations on jet bundles as a universal approach for a variational formulation of fundamental physical theories
As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples of physical...
The concentration-compactness principle in the calculus of variations. The locally compact case, part 1
The inverse problem for flat kinetic minus potencial Lagrangians.
The Jacobi variational principle revisited
The origin of variational principles
The principle of stationary action in the calculus of variations
We review some techniques from non-linear analysis in order to investigate critical paths for the action functional in the calculus of variations applied to physics. Our main intention in this regard is to expose precise mathematical conditions for critical paths to be minimum solutions in a variety of situations of interest in Physics. Our claim is that, with a few elementary techniques, a systematic analysis (including the domain for which critical points are genuine minima) of non-trivial models...
The Regularization of the Second Order Lagrangians in Example
This paper is devoted to geometric formulation of the regular (resp. strongly regular) Hamiltonian system. The notion of the regularization of the second order Lagrangians is presented. The regularization procedure is applied to concrete example.
The shape and smoothness of stable plasma configurations
The structure of extremals of a class of second order variational problems
The symmetry reduction of variational integrals
The Routh reduction of cyclic variables in the Lagrange function and the Jacobi-Maupertuis principle of constant energy systems are generalized. The article deals with one-dimensional variational integral subject to differential constraints, the Lagrange variational problem, that admits the Lie group of symmetries. Reduction to the orbit space is investigated in the absolute sense relieved of all accidental structures. In particular, the widest possible coordinate-free approach to the underdetermined...
The symmetry reduction of variational integrals, complement
Some open problems appearing in the primary article on the symmetry reduction are solved. A new and quite simple coordinate-free definition of Poincaré-Cartan forms and the substance of divergence symmetries (quasisymmetries) are clarified. The unbeliavable uniqueness and therefore the global existence of Poincaré-Cartan forms without any uncertain multipliers for the Lagrange variational problems are worth extra mentioning.
Theoretical study and optimization of a fluid-structure interaction problem
Théorie classique des champs en interaction : théorie de jauge et interprétation géométrique
Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion
We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine a-priori estimates are derived, and convergence is proved by careful successive...
Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion*
We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine a-priori estimates are derived, and convergence is proved by careful...
Two Hartree-Fock models for the vacuum polarization
We review recent results about the derivation and the analysis of two Hartree-Fock-type models for the polarization of vacuum. We pay particular attention to the variational construction of a self-consistent polarized vacuum, and to the physical agreement between our non-perturbative construction and the perturbative description provided by Quantum Electrodynamics.