Related papers: A review of the variational methods for solving DC…
We generalize Wheeler-Feynman electrodynamics with a variational boundary-value problem with past and future boundary segments that can include velocity discontinuity points. Critical-point trajectories must satisfy the Euler-Lagrange…
In this article we show that Einstein covariance principle provides a wide opportunity in the solutions of different problems of theoretical physics. Here we apply covariance principle in some problems of classical electrodynamics and…
We develop a variational calculus for entropy solutions of the Generalized Riemann Problem (GRP) for strictly hyperbolic systems of conservation laws where the control is the initial state. The GRP has a discontinuous initial state with…
We explore the possibility of obtaining unidirectional current in a symmetric (periodic) potential system without the application of any obvious (apparent) externally applied bias. There are many physical models proposed to accomplish this…
We present a novel generic framework to approximate the non-equilibrium steady states of dissipative quantum many-body systems. It is based on the variational minimization of a suitable norm of the quantum master equation describing the…
We consider newtonian dynamics of $N$ charged particles on the circle with nearest neigbour interaction with Coulomb repulsive potential $r^{-1}$ . Also there is an external accelerating force which is nonzero only on a small part of the…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the…
The electrostatic field magnitude can play a role in a variational principle similar to the role of the index of refraction in geometrical optics, allowing the determination of the electric field lines. This was identified in the context of…
The self-energy-functional approach (SFA) is discussed in the context of different variational principles for strongly correlated electron systems. Formal analogies between static and dynamical variational approaches, different types of…
The goal of the paper is to develop a method that will combine the use of variational techniques with regularization methods in order to study existence and multiplicity results for the periodic and the Dirichlet problem associated to the…
Real world water waves often propagate on current. And, the measurement of waves and current is an important task for coastal and marine engineers. Modern marine measurement technologies (i.e. unmanned autonomous vehicles, drones) often…
A framework for defining stochastic currents associated with diffusion processes on curved Riemannian manifolds is presented. This is achieved by introducing an overdamped Stratonovich-Langevin equation that remains fully covariant under…
Achieving robust and scalable convergence for simulation of realistic power flow cases can be challenging. One specific issue relates to the disconnected solution space that is created by the use of piecewise-discontinuous models of power…
In Maxwell's classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency…
A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for…
The AC power flow equations are fundamental in all aspects of power systems planning and operations. They are routinely solved using Newton-Raphson like methods. However, there is little theoretical understanding of when these algorithms…
We study a series array of nonlinear electrical circuit elements that possess negative differential resistance and find that \emph{heterogeneity} in the element properties leads to the presence of multiple branches in current-voltage curves…
The classical energy minimization principles of Dirichlet and Thompson are extended as minimization principles to acoustics, elastodynamics and electromagnetism in lossy inhomogeneous bodies at fixed frequency. This is done by building upon…
We give a simple proof of the well known fact that the approximate eigenvalues provided by the Rayleigh-Ritz variational method are increasingly accurate upper bounds to the exact ones. To this end, we resort to the variational principle,…