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The present paper is concerned with Ekeland Variational Principle (EkVP) and its equivalents (Caristi-Kirk fixed point theorem, Takahashi minimization principle, Oettli-Th\'era equilibrium version of EkVP) in quasi-uniform spaces. These…
We derive the Planck law from a classical variational principle over probability densities, without invoking quantum states, quantized oscillator energies, or ensemble averages. We construct a generalized free energy functional involving…
A variational method is discussed, based on the principle of minimal variance. The method seems to be suited for gauge interacting fermions, and the simple case of quantum electrodynamics is discussed in detail. The issue of renormalization…
We show that the minimal speed for the existence of monotonic fronts of the equation $u_t = (u^m)_{xx} + f(u)$ with $f(0) = f(1) = 0$, $m >1$ and $f>0$ in $(0,1)$ derives from a variational principle. The variational principle allows to…
Here we obtain explicit formulae for bounds on the complex electrical polarizability at a given frequency of an inclusion with known volume that follow directly from the quasistatic bounds of Bergman and Milton on the effective complex…
This paper presents the notion of a variation entropy. This concept is an entropy framework for the gradient of the solution of a conservation law instead of on the solution itself. It appears that all semi-norms are admissible variation…
This work focuses on the frequency-domain modeling of a control system with a flexible beam and a rigid body. A simply supported beam is equipped with a spring-loaded control actuator and possesses local damping effect. Using Hamilton's…
By applying a variational principle on a magnetic system within the framework of extended irreversible thermodynamics, we find that the presence of a temperature gradient in a ferromagnet leads to a generalisation of the Landau-Lifshitz…
The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the…
Variational principles are proved for self-adjoint operator functions arising from variational evolution equations of the form \[ \langle\ddot{z}(t),y \rangle + \mathfrak{d}[\dot{z} (t), y] + \mathfrak{a}_0 [z(t),y] = 0. \] Here…
We develop an elementary method to give a Lipschitz estimate for the minimizers in the problem of Herglotz' variational principle proposed in \cite{CCWY2018} in the time-dependent case. We deduce Erdmann's condition and the Euler-Lagrange…
The principle of minimal energy, which has been set up in the preceding papers for systems of non-identical particles (e.g. positronium), is now generalized to include also identical particles. Since the latter kind of particles feels also…
A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational…
The time-dependent variational principle is used to optimize the linear and nonlinear parameters of Gaussian basis functions to solve the time-dependent Schrodinger equation in 1 and 3 dimensions for a one-body soft Coulomb potential in a…
In this work, a second order smoothed particle hydrodynamics is derived for the study of relativistic heavy ion collisions. The hydrodynamical equation of motion is formulated in terms of the variational principle. In order to describe the…
We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original…
Variational principles are important in the investigation of large classes of physical systems. They can be used both as analytical methods as well as starting points for the formulation of powerful computational techniques such as…
In this paper two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to…
The Eulerian variational principle for the Vlasov-Poisson-Amp\`{e}re system of equations in a general coordinate system is presented. The invariance of the action integral under an arbitrary spatial coordinate transformation is used to…
Variational inference is a powerful tool for approximate inference. However, it mainly focuses on the evidence lower bound as variational objective and the development of other measures for variational inference is a promising area of…