Related papers: Equivalence between Geometric Frequency and Lagran…
Gauge invariance, a core principle in electrodynamics, has two separate meanings. One concept treats the photon as the gauge particle for electrodynamics. It is based on symmetries of the Lagrangian, and requires no mention of electric or…
An approach is presented to calculate characteristic current vs voltage curves for isolated molecules without explicit description of leads. The Hamiltonian for current-carrying molecules is defined by making resort to Lagrange multipliers,…
In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the metafluid dynamics, is extended in order to reformulate the metafluid dynamics as a gauge field theory. That analogy opens up the possibility to…
This letter extends the concept of graph-frequency to graph signals that evolve with time. Our goal is to generalize and, in fact, unify the familiar concepts from time- and graph-frequency analysis. To this end, we study a joint temporal…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
Discovery of electron hydrodynamics in graphene system has opened a new scope of analytic calculations in condensed matter physics, which was traditionally well cultivated in science and engineering as a non-relativistic hydrodynamics and…
The use of gyrokinetics, wherein phase-space coordinate transformations result in a phase-space dimensionality reduction as well as the removal of fast time scales, has enabled the simulation of microturbulence in fusion devices. The…
Teleparallel Gravity is a gauge theory where gravity is a manifestation of the torsion of space-time and its success relies on being a possible solution to some problems of General Relativity. In this essay we introduce the construction of…
A new molecular dynamics model in which the point charges on atomic sites are allowed to fluctuate in response to the environment is developed and applied to water. The idea for treating charges as variables is based on the concept of…
The goal of this paper is to encode equivalently the fractional Lagrange dynamics as a nonholonomic almost Kahler geometry. We use the fractional Caputo derivative generalized for nontrivial nonlinear connections (N-connections) originally…
The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional…
This work represents an application of constant mean curvature graphs (as solutions of the mean curvature PDE) to non-linear non-Darcy flows in porous media. It relates time invariant pressure distribution graphs to graphs of constant mean…
We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context…
The free energy balance equation for gyrokinetic fluctuations is derived and applied to instabilities. An additional term due to electromagnetic sources is included. This can provide a simpler way to compute the free energy balance in…
The formalism of the reduced density matrix is pursued in both length and velocity gauges of the perturbation to the crystal Hamiltonian. The covariant derivative is introduced as a convenient representation of the position operator. This…
The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…
Accurate electricity demand forecasting is essential for several reasons, especially as the integration of renewable energy sources and the transition to a decentralized network paradigm introduce greater complexity and uncertainty. The…
We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an…