Related papers: Shadow and percolation II: discrete and continuous…
We examine the shadow of a rotating Kaluza-Klein black hole in Einstein gravity coupled to a Maxwell field and a dilaton. The size and the shape of the shadow depend on the mass, the charge, and the angular momentum of the compact object.…
The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…
Speckle patterns are inherent features of coherent light propagation through complex media. As a result of interference, they are sensitive to multiple experimental parameters such as the configuration of disorder or the propagating…
On large telescopes trails of MegaConstellation's satellites will appears significantly defocused because of their relatively short distance. Because of such effect their apparent surface brightness will be, under a range of conditions,…
Important open questions in cosmology require a better understanding of the Big Bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be…
When a luminous source is extended, its distortions by weak gravitational lensing are richer than a mere combination of magnification and shear. In a recent work, we proposed an elegant formalism based on complex analysis to describe and…
We consider inhomogeneous percolation on a hierarchical configuration model with a heavy-tailed degree distribution. This graph is the configuration model where all the half-edges are colored either black or white, and edges are formed by…
We present a novel approach of modelling surface light scattering in the context of freeform optical design. The model relies on energy conservation and optimal transport theory. For isotropic scattering in cylindrically or rotationally…
We analyze the redshift suffered by photons originating from an external source, traversing a collapsing dust cloud and finally being received by an asymptotic observer. In addition, we study the shadow that the collapsing cloud casts on…
Approximate distance estimation can be used to determine fundamental landscape properties including complexity and openness. We show that variations in the skyline of landscape photos can be used to estimate distances to trees on the…
A brief overview of the current state of the problem of electromagnetic field singularities arising from the refraction and scattering of light by material objects is given. The discussion begins with caustics arising from ray tracing in…
We consider rotating charged black holes with a scalar dilaton field and surrounded by plasma, with the purpose of studying their shadows. The corresponding metric has been previously obtained in the literature from the static solution by…
The Sun shrinks during solar maximum and regrows during solar minimum by a few kilometers. Here, we observe, for the first time, that the solar radius variation shows planetary relationship. This suggests that some remote planetary links…
We consider the random walk loop soup on the discrete half-plane and study the percolation problem, i.e. the existence of an infinite cluster of loops. We show that the critical value of the intensity is equal to 1/2. The absence of…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
The absolute value of the transition probability of the Rayleigh scattering is computed for the first time and applied to the scattering of solar light with molecules in the atmosphere and to the laser scattering with nanopartilces. The…
If a component of dark matter has dissipative interactions, it can cool to form compact astrophysical objects with higher density than that of conventional cold dark matter (sub)haloes. Dark matter annihilations might then appear as point…
We present a space-time diagram that displays in true values the space- time coordinates of events associated with the apparent and actual positions of a point like source moving with constant velocity. We use it in order to construct the…
Shape from shading is a classical inverse problem in computer vision. This shape reconstruction problem is inherently ill-defined; it depends on the assumed light source direction. We introduce a novel mathematical formulation for…
We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence…