Related papers: A review of the variational methods for solving DC…
This paper proposes a novel method rooted in differential geometry to approximate the voltage stability boundary of power systems under high variability of renewable generation. We extract intrinsic geometric information of the power flow…
This work introduces a novel data-driven modified nodal analysis (MNA) circuit solver. The solver is capable of handling circuit problems featuring elements for which solely measurement data are available. Rather than utilizing hard-coded…
The analytic continuation from the Euclidean domain to real space of the one-particle irreducible quantum effective action is discussed in the context of generalized local equilibrium states. Discontinuous terms associated with dissipative…
Unlike many deterministic PDEs, stochastic equations are not amenable to the classical variational theory of Euler-Lagrange. In this paper, we show how self-dual variational calculus leads to solutions of various stochastic partial…
Discontinuous Galerkin (DG) methods are considered for solving a plate contact problem, which is a 4th-order elliptic variational inequality of second kind. Numerous $C^0$ DG schemes for the Kirchhoff plate bending problem are extended to…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
The equations governing one-dimensional, steady-state electrodiffusion are considered when there are arbitrarily many mobile ionic species present, in any number of valence classes, possibly also with a uniform distribution of fixed…
In solving the problem of finding a temperature distribution which, at zero temperature, corresponds to superfluidity, i.e., to nonzero energy, the author tried to quantize free energy. This was done on the basis of supersecondary…
Robust simulation is essential for reliable operation and planning of transmission and distribution power grids. At present, disparate methods exist for steady-state analysis of the transmission (power flow) and distribution power grid…
The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when…
To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…
A review of old inconsistencies of Classical Electrodynamics (CED) and of some new ideas that solve them is presented. Problems with causality violating solutions of the wave equation and of the electron equation of motion, and problems…
Exact finite-energy solutions to the nonlinear governing equations of the Born-Infeld theory of electrodynamics, describing continuous distributions of electric, magnetic, and dyonic charge sources, in both classical and generalized…
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…
This paper investigates an induction heating problem in a multi-component system containing a moving non-magnetic conductor. The electromagnetic process is described by the eddy current model, and the heat transfer process is governed by…
Motivated by the possibility of electrochemical control of phase separation, a variational theory of thermodynamic stability is developed for driven reactive mixtures, based on a nonlinear generalization of the Cahn-Hilliard and Allen-Cahn…
The main purpose of this paper is mathematical analysis on time-periodic flows of electrons and holes in semiconductors. The flows appear in a situation that alternating-current voltages are applied to devices. In this paper, we study the…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
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…
We consider a one-dimensional XX spin chain in a nonequilibrium setting with a Lindblad-type boundary driving. By calculating large deviation rate function in the thermodynamic limit, being a generalization of free energy to a…