Related papers: Multipole Moments of Fractal Distribution of Charg…
The inverse problem for electromagnetic field produced by arbitrary altered charge distribution in dipole approximation is solved. The charge distribution is represented by its dipole moment. It is assumed that the spectral properties of…
This paper presents a review of the fractal approach for describing the large scale distribution of galaxies. We start by presenting a brief, but general, introduction to fractals, which emphasizes their empirical side and applications…
Dipole and higher moments are physical quantities used to describe a charge distribution. In analogy with electromagnetism, it is possible to define the dipole moments for a gray-scale image, according to the single aspect of a gray-tone…
Ratio of electron charge radius and Compton wavelength of electron is known to be equal to the dimensionless electromagnetic coupling constant $e^2 /\hbar c$. It is pointed out that the coupling constant has two alternative interpretations:…
Natural optical activity is the paradigmatic example of an effect originating in the weak spatial inhomogeneity of the electromagnetic field on the atomic scale. In molecules, such effects are well described by the multipole theory of…
First-passage probability estimation of high-dimensional nonlinear stochastic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
Anomalous short- and long-time self-diffusion of non-overlapping fractal particles on a percolation cluster with spreading dimension $1.67(2)$ is studied by dynamic Monte Carlo simulations. As reported in Phys. Rev. Lett. 115, 097801…
It is shown that conserved charges associated with a specific subclass of gauge symmetries of Maxwell electrodynamics are proportional to the well known electric multipole moments. The symmetries are residual gauge transformations surviving…
This paper formalizes the use of integral and differential cumulants for measurements of multi-particle event-by-event transverse momentum fluctuations, rapidity fluctuations, as well as net charge fluctuations. This enables the…
One of the most well known random fractals is the so-called Fractal percolation set. This is defined as follows: we divide the unique cube in $\mathbb{R}^d$ into $M^d$ congruent sub-cubes. For each of these cubes a certain retention…
The multipole moments of stationary axially symmetric vacuum or electrovacuum spacetimes can be expressed in terms of the power series expansion coefficients of the Ernst potential on the axis. In this paper we present a simpler, more…
This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…
A global analysis of proton electric form factor experimental data from Rosenbluth separation and low squared four-momentum transfer experiments is discussed for the evaluation of the spatial moments of the proton charge density based on…
Multipoles provide a systematic framework for describing the electronic structures of quantum materials from a symmetry perspective. Thermodynamic multipole moments in crystalline solids exhibit direct microscopic connections to certain…
Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…
Aggregates immersed in a plasma or radiative environment will have charge distributed over their extended surface. Previous studies have modeled the aggregate charge using the monopole and dipole terms of a multipole expansion, with results…
Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by…
We set up the framework for the calculation of electric dipole moments (EDMs) of light nuclei using the systematic expansion provided by chiral effective field theory (EFT). We take into account parity (P) and time-reversal (T) violation…