Related papers: Shadow and percolation II: discrete and continuous…
Let X be a planar random field on Z^2 which we interpret as a random height function describing some landscape of montains. We consider a source of light (a sun) located at infinity in a direction parallel with an axis od Z^2 and emitting…
We study some geometric properties of the excursion set of a slope field alpha associated to a smooth, planar, centered, Gaussian field f. That, is we consider the set of all points such that the value of alpha is at most l where l is a…
We study the dynamical evolution of the deposition interface using both discrete and continuous models for which shadowing effects are important. We explain why continuous and discrete models implying both only shadowing deposition do not…
Clouds cast shadows on the surface and locally enhance solar irradiance by absorbing and scattering sunlight, resulting in fast and large solar irradiance fluctuations on the surface. Typical spatiotemporal scales and driving mechanisms of…
The luminosity variation of a stellar source due to the gravitational microlensing effect can be considered also if the light rays are defocused (instead of focused) toward the observer. In this case, we should detect a gap instead of a…
We study the polarization of light emitted by spatially correlated sources. We show that in general polarization acquires nontrivial spectral dependence due to spatial correlations. The spectral dependence is found to be absent only for a…
A shadow of a geometric object $A$ in a given direction $v$ is the orthogonal projection of $A$ on the hyperplane orthogonal to $v$. We show that any topological embedding of a circle into Euclidean $d$-space can have at most two shadows…
In light of recent discussions of the string landscape, it is essential to understand the degree to which string theory is predictive. We argue that it is unlikely that the landscape as a whole will exhibit unique correlations amongst…
There has been some debate as to whether the landscape does or does not predict low energy supersymmetry. We argue that under rather mild assumptions, the landscape seems to favor such breaking, quite possibly at a very low scale. Some of…
This note was motivated by natural questions related to oriented percolation on a layered environment that introduces long range dependence. As a convenient tool, we are led to deal with questions on the strict decrease of the percolation…
We consider the reflection from a random medium of light with short coherence length. We found that the second order correlation function of light can have a peak in a direction where the reflection angle is equal to angle of incidence.…
We present the shape of the black hole shadow on the standard background screen as it is registered by the distant observer. The screen is an infinite plane, emitting the quanta uniformly distributed to a hemisphere. The source of emission…
We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…
In this paper, we study the problem of reproducing the world lighting from a single image of an object covered with random specular microfacets on the surface. We show that such reflectors can be interpreted as a randomized mapping from the…
In any CAT(k) space M, the "shadow" of a tangent vector Z at a point p is the set vectors that form an angle of \pi or more with Z. Taking logarithm maps at points approaching p along a fixed geodesic ray from p with tangent Z collapses the…
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…
We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously…
In coherent radiation sources (diffraction radiation, Smith-Purcell effect, etc.) based on relativistic electrons passing by a material radiator, the electron self-field is partly shadowed after each part of the radiator over a distance of…
Self-similarity and long-range correlations are the remarkable features of the Earth's surface topography. Here we develop an approach based on percolation theory to study the geometrical features of Earth. Our analysis is based on…
Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…