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Thomson's theorem states that static charge distributions in conductors only exist at the conducting surfaces in an equipotential configuration, yielding a minimal electrostatic energy. In this work we present a proof for this theorem based…
Very recently, a new decay framework has been given by [51] for linearized dissipative hyperbolic systems satisfying the Kawashima-Shizuta condition on the framework of Besov spaces, which allows to pay less attention on the traditional…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
Variational principles for magnetohydrodynamics (MHD) were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of…
The McLachlan "minimum-distance" principle for optimizing approximate solutions of the time-dependent Schrodinger equation is revisited, with a focus on the local-in-time error accompanying the variational solutions. Simple, exact…
We consider the Ginzburg-Landau functional with a variable applied magnetic field in a bounded and smooth two dimensional domain. The applied magnetic field varies smoothly and is allowed to vanish non-degenerately along a curve. Assuming…
Stochastic mechanics is regarded as a physical theory to explain quantum mechanics with classical terms such that some of the quantum mechanics paradoxes can be avoided. Here we propose a new variational principle to uncover more insights…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
We generalize Wheeler-Feynman electrodynamics by the minimization of a finite action functional defined for variational trajectories that are required to merge continuously into given past and future boundary segments. We prove that the…
The following principle of minimum energy may be a powerful substitute to the dynamical perturbation method, when the latter is hard to apply. Fluid elements of self-gravitating barotropic flows, whose vortex lines extend to the boundary of…
A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…
This paper introduces an axiomatic basis for measuring the energy characteristic of vibrating dynamical systems. The basic approach is to compare non-modulated vs. modulated waveforms in measuring energy during the vibratory motion $m(t)$…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
A variational principle is introduced which minimizes an action formulated for configurations of vacuum Dirac seas. The action is analyzed in position and momentum space. We relate the corresponding Euler-Lagrange equations to the notion of…
Determining quantum excited states is crucial across physics and chemistry but presents significant challenges for variational methods, primarily due to the need to enforce orthogonality to lower-energy states, often requiring…
This paper presents symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group. Such variational principles yield deterministic as well as stochastic constrained…
We consider homogenization of random surfaces and study the variational principle for graph homomorphisms from subsets of $\mathbb{Z}^m$ into $\mathbb{Z}$, where the underlying uniform measure is perturbed by a random field. Motivated by…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a…