Related papers: Shadow and percolation I: discrete landscapes with…
Artificial light at night has affected most of the natural nocturnal landscapes worldwide and the subsequent light pollution has diverse effects on flora, fauna and human well-being. To evaluate the environmental impacts of light pollution,…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
Estimating the number of vertices of a two dimensional projection, called a shadow, of a polytope is a fundamental tool for understanding the performance of the shadow simplex method for linear programming among other applications. We prove…
Theories of monochromatic high-frequency electromagnetic fields have been designed by Felsen, Kravtsov, Ludwig and others with a view to portraying features that are ignored by geometrical optics. These theories have recourse to eikonals…
Light displays particle and wave properties within the bounds of the inequality, K^2+V^2<=1, where K represents particle information and V represents corresponding wave information. Using two laser beams that cross and then diverge from…
The composite galaxy luminosity function (hereafter LF) of 39 Abell clusters of galaxies is derived by computing the statistical excess of galaxy counts in the cluster direction with respect to control fields. Due to the wide field coverage…
A search for discontinuity in the sky twilight brightness at different wavelengths and different solar depressions for altitudes 0, 5, 10, 30, 50 & 70 degrees is done. It is found that the logarithmic of difference in the brightness log…
A method is presented for estimating the background at a given location on a sky map by interpolating the estimated background from a set of concentric annuli which surround this location. If the background is nonuniform but smoothly…
We study families of dependent site percolation models on the triangular lattice ${\mathbb T}$ and hexagonal lattice ${\mathbb H}$ that arise by applying certain cellular automata to independent percolation configurations. We analyze the…
Consider a singularly perturbed system $$\epsilon u_t=\epsilon^2 u_{xx} + f(u,x,\epsilon),\quad u\in {\Bbb R}^n,x\in{\Bbb R},t\geq 0. $$ Assume that the system has a sequence of regular and internal layers occurring alternatively along the…
We study the accessibility percolation model on infinite trees. The model is defined by associating an absolute continuous random variable $X_v$ to each vertex $v$ of the tree. The main question to be considered is the existence or not of…
Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.
We formulate and study a model for inhomogeneous long-range percolation on $\Zbold^d$. Each vertex $x\in\Zbold^d$ is assigned a non-negative weight $W_x$, where $(W_x)_{x\in\Zbold^d}$ are i.i.d.\ random variables. Conditionally on the…
This paper examines the relationship between shadowing phenomena and the continuity properties of $\omega$-limit sets in dynamical systems. We give a necessary and sufficient condition for a shadowable point to be an upper (resp. a lower)…
This paper presents a Monte-Carlo study of percolation in a distorted square lattice, in which, the adjacent sites are not equidistant. Starting with an undistorted lattice, the position of the lattice sites are shifted through a tunable…
Earthshine observations offer a unique opportunity to study Earth as an exoplanet seen from the Moon. As the Sun-Earth-Moon geometry changes, Earth can be observed as a spatially unresolved exoplanet at different phase angles, providing…
Large and well defined variations exist between the distribution of mass and the light of stars on extragalactic scales. Mass concentrations in the range 10^12 - 10^13 M_sun manifest the most light per unit mass. Group halos in this range…
We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases, goes through a minimum and…
In radiation processes such as a transition radiation, diffraction radiation, etc. based on relativistic electrons passing through or near an opaque screen, the electron self-field is partly shadowed after the screen over a distance of the…