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We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…
Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known. It is known that EFT coefficients must obey certain positivity constraints if causality and unitarity…
The Gutenberg-Richter power law distribution of earthquake sizes is one of the most famous example illustrating self-similarity. It is well-known that the Gutenberg-Richter distribution has to be modified for large seismic moments, due to…
The influence of the Doppler effect in the fireball framework on the spectrum of gamma-ray bursts is investigated. The study shows that the shape of the expected spectrum of an expanding fireball remains almost the same as that of the…
We investigated the effects of the momentum spread of photon around incoming electrons during nonlinear Compton scattering of an elliptically polarized laser off an ultrarelativistic electron beam. It has been assumed to be a good…
We study the finite-size scaling of the roughness of signals in systems displaying Gaussian 1/f power spectra. It is found that one of the extreme value distributions (Gumbel distribution) emerges as the scaling function when the boundary…
We evaluate numerically the velocity field distributions produced by a bounded, two-dimensional fluid model consisting of a collection of parallel ideal line vortices. We sample at many spatial points inside a rigid circular boundary. We…
Given a sequence of $n$ identically distributed random variables with common distribution $F$, the \emph{fragility distribution of order $m$}, represented by $\FD$, is the limit conditional distribution of the number of exceedances given…
Probability distributions and densities are derived for the excess and deficiency of the intensity or instantaneous energy (quasi-static power) associated with a $p$-dimensional random vector field. Explicit expressions for the exact…
Modern electron linear accelerators are often designed to produce smooth bunch distributions characterized by their macroscopic ensemble-average moments. However, an increasing number of accelerator applications call for finer control over…
We consider a relativistically moving blob consisting of an isotropic electron distribution that Compton-scatters photons from an external isotropic radiation field. We compute the resulting beaming pattern, i.e. the distribution of the…
The elastic scattering amplitude (ESA) is obtained in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) for planar charged fermions in an external constant magnetic field. We obtain the elastic…
Five methods of calculating electrical field distributions in one dimensional wave-guide arrays are reviewed. We analytically solve the scalar Helmholtz Equation and, based on the computed Bloch functions and associated bands of propagation…
This work continues the development of the raytracing method of [1] for computing the scattered fields from metasurfaces characterized by locally periodic reflection and transmission coefficients. In this work, instead of describing the…
Using a TE/TM decomposition for an angular plane-wave spectrum of free random electromagnetic waves and matched boundary conditions, we derive the probability density function for the energy density of the vector electric field in the…
The distribution of the electric microfield at a charged particle moving in a two-component plasma is calculated. The theoretical approximations are obtained via the parameter integration technique and using the screened pair approximation…
We fit the exponent of the Pareto distribution, that is equivalent or can approximate the continuous power law distribution given a cutoff point, using linear regression (LR). We use LR on the logged variables of the empirical tail (one…
We study analytically and numerically the winding of a flux line around a columnar defect. Reflecting and absorbing boundary conditions apply to marginal or repulsive defects, respectively. In both cases, the winding angle distribution…
Magnetic guiding fields in combination with energy dispersive semiconductor detectors have been employed already more than 50 years ago for in-beam internal conversion electron spectroscopy. Even then it was recognized that efficiency…
Direct observation of electric potential and field variation near local scatterers like grain boundaries, triple points and voids in thin platinum films studied by scanning tunneling potentiometry is presented. The field is highest at a…