Related papers: A review of the variational methods for solving DC…
Two of the most influential ideas developed by Richard Feynman are the Feynman diagram technique and his variational approach. The former provides a powerful tool to construct a systematic expansion for a generic interacting system, while…
The DC Power Flow approximation has been widely used for decades in both industry and academia due to its computational speed and simplicity, but suffers from inaccuracy, in part due to the assumption of a lossless network. Here we present…
During the last decade, possibilities to realize new phenomena and create new applications by varying system properties in time have gained increasing attention in many research fields, spanning a wide range from acoustics to optics. While…
Continuous-time Markov chains have been successful in modelling systems across numerous fields, with currents being fundamental entities that describe the flows of energy, particles, individuals, chemical species, information, or other…
Exact multicentered solutions to the governing equations of the Born--Infeld nonlinear theory of electrodynamics describing distributions of electric, magnetic, and dyonic point charge sources are constructed explicitly for the first time.…
Understanding DC electrical conductivity is crucial for the study of materials. Macroscopic DC conductivity can be calculated from first principles using the Kubo-Greenwood equation. The procedure involves finding the thermodynamic limit of…
Almost all theories of physics have expressed physical laws by means of differential equations. One can ask: why differential equations? What is special about them? This article addresses these questions and is presented as an inquiry-based…
We study the global dynamics of isothermal fluids evolving in the domain of outer communication of a Schwarzschild black hole. We first formulate the initial value problem within a class of weak solutions with bounded variation (BV),…
A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features of the formulation are discussed.
The Lagrange, Euler, and Euler-Poincar\'{e} variational principles for the guiding-center Vlasov-Maxwell equations are presented. Each variational principle presents a different approach to deriving guiding-center polarization and…
Numerical solutions to the 1D steady-state Vlasov-Poisson system are used to develop a straightforward empirical formula for the electric current density transmitted through a vacuum diode (voltage gap) as a function of gap distance, gap…
We study the non-equilibrium steady state arising from the interplay between coherent and dissipative dynamics in strongly interacting Rydberg gases using a recently introduced variational method [H. Weimer, Phys. Rev. Lett. 114, 040402…
In 1931, Onsager proposed a variational principle which has become the base of many kinetic equations for non-equilibrium systems. We have been showing that this principle is useful in obtaining approximate solutions for the kinetic…
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.…
Secure operation of electric power grids fundamentally relies on their dynamical stability properties. For the third order model, a paradigmatic model that captures voltage dynamics, three routes to instability are established in the…
The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…
A rigorous method for introducing the variational principle describing relativistic ideal hydrodynamic flows with all possible types of discontinuities (including shocks) is presented in the framework of an exact Clebsch type representation…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
The Ampere-Maxwell's law and the displacement current constitute one of the most difficult aspects of electromagnetic theory for students in introductory electromagnetics courses. Here we present a set of examples that go beyond the…
We present a new algorithm for computing the electromagnetic fields of currents inside and outside of finite current sources, for arbitrary time variations in the currents. Unexpectedly, we find that our solutions for these fields are free…