Related papers: A Hilbert-space formulation of and variational pri…
Within the framework of a Hilbert space theory, we develop a maximum-``power'' variational principle (MPVP) applicable to classical spontaneous electromagnetic radiation from relativistic electron beams or other prescribed classical current…
Assume that A is a bounded selfadjoint operator in a Hilbert space H. Then, the variational principle is obtained for some functional. As an application of this principle, a variational principle for the electrical capacitance of a…
Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman-von Neumann-Sudarshan prescription for classical mechanics on Hilbert spaces {\em sans} the…
The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on…
The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…
In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.
An $\hbar$-expansion is presented for the ensemble-averaged spectral function of noninteracting matter waves in random potentials. We obtain the leading quantum corrections to the deep classical limit at high energies by the Wigner-Weyl…
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…
{The problem of laser beam concentration in a focal spot via wavefront variations is formulated as a maximization of the $beam$ $propagation$ $functional$ defined as the light power passing through aperture of an arbitrary shape located in…
We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time regularizations of gradient flows by combining the…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
Given a positive definite, bounded linear operator $A$ on the Hilbert space $\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space $\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any countable set and…
Consider a rowwise independent triangular array of gamma random variables with varying parameters. Under several different conditions on the shape parameter, we show that the sequence of row-maximums converges weakly after linear or power…
Analytical solutions are presented for the electromagnetic radiation by an arbitrary pulsed source into a homogeneous time-varying background medium. In the constant-impedance case an explicit radiation formula is obtained for the…
The first order quantum correction to the power of spontaneous radiation of electrons in an arbitrary two-component periodic magnetic field was obtained. The phenomenon of selfpolarization of the spin of electrons in a process of…
In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…
A simultaneous variational principle is introduced that offers a novel avenue to the description of the equilibrium configurations, and at the same time of the elementary excitations, or undulations, of fluid lipid membranes, described by a…
A general method is presented for determining the maximum electric energy in a bounded region of optical fields with given time-averaged flux of electromagnetic energy. Time-harmonic fields are considered whose plane wave expansion consists…
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…
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…