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Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…
This paper presents the approximate analytical solutions to the longitudinal space charge (LSC) impedances of a round beam with uniform transverse distribution and sinusoidal line density modulations under two boundary conditions: (a)…
This study presents a spiral-based complete coverage strategy for ball-end milling on freeform surfaces, utilizing conformal slit mapping to generate milling trajectories that are more compact, smoother, and evenly distributed when…
The point at which two random rough surfaces make contact takes place at the contact of the highest asperities. The distance upon contact d_0 in the limit of zero load has crucial importance for determination of dispersive forces. Using…
We consider the reflection of non-polarized radiation from the point-like sources above the accretion discs both the optically thick and optically thin. We investigate the dependence of the polarization of reflected radiation on the…
We study by numerical simulations the scattering of $s$-polarized light from a rough dielectric film deposited on the planar surface of a semi-infinite perfect conductor. The dielectric film is allowed to be either active or passive,…
Various methods for calculating the capacitance of unloaded rolling elements are compared to improve the electric characterization of rolling element bearings. Semi-analytical approximations and finite element simulations are applied and a…
The long wavelength diffusion coefficient of a critical fluid confined between two parallel plates separated by a distance L is strongly affected by the finite size. Finite size scaling leads us to expect that the vanishing of the diffusion…
Dimensional analysis, superposition principle, and continuity of electric potential are used to study electric potential of a uniformly charged square sheet at its plane. It is shown that knowing the electric potential on the diagonal and…
Using particle-in-cell (PIC) numerical simulations with electron-positron pair plasma, we study how the efficiencies of magnetic dissipation and particle acceleration scale with the initial coherence length $\lambda_0$ in relation to the…
We have recently shown that critical Anderson electron in $D=3$ dimensions effectively occupies a spatial region of infrared (IR) scaling dimension $d_\text{IR} \approx 8/3$. Here we inquire about the dimensional substructure involved. We…
The percolation threshold and wrapping probability $R_{\infty}$ for the two-dimensional problem of continuum percolation on the surface of a Klein bottle have been calculated by the Monte Carlo method with the Newman--Ziff algorithm for…
The scaling of coherent and non-coherent channel capacity is studied in a single-input multiple-output (SIMO) block Rayleigh fading channel as both the bandwidth and the number of receiver antennas go to infinity jointly with the transmit…
We study the dynamics of a twisted tilted disc under the influence of an external radiation field. Assuming the effect of absorption and reemission/scattering is that a pressure is applied to the disc surface where the local optical depth…
Recently there have been discussions about which complex metrics should be allowable in quantum gravity. These discussions assumed that the matter fields were real valued. We make the observation that for compactified solutions it makes…
We numerically investigate the electric potential distribution over a two-dimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal…
Polymers confined to a narrow channel are subject to strong entropic forces that tend to drive the molecules apart. In this study, we use Monte Carlo computer simulations to study the segregation behavior of two flexible hard-sphere…
The physical background of scaling laws of disk galaxies is reviewed. The match between analytically derived and observed scaling laws is briefly discussed. Accurate modeling of the fraction of baryons that end populating a disk, and the…
The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly…
Two-dimensional (2D) materials have great potential for use in future electronics due to their atomically thin nature which withstands short channel effects and thus enables better scalability. Device scaling is the process of reducing all…