Related papers: Shadow and percolation II: discrete and continuous…
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)…
In these proceedings we illustrate that light, very weakly interacting particles can arise naturally from physics which is fundamentally connected to very high energy scales. Searching for them therefore may give us interesting new insights…
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…
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…
In this paper we explore how light propagates from thin elements into a volume for viewing. In particular, devices that are typically connected with geometric optics, like parallax barriers, differ in treatment with those that obey physical…
Galaxy clustering on very large scales can be probed via the 2-point correlation function in the general case of wide and deep separations, including all the lightcone and relativistic effects. Using our recently developed formalism, we…
The possibilities that, in the realm of the detection of the so--called deformed dispersion relation, a light source with a continuous distribution of frequencies offers is discussed. It will be proved that the presence of finite coherence…
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…
In this work, we explore the analogy between entanglement and secret classical correlations in the context of large networks, more precisely the question of percolation of secret correlations in a network. It is known that entanglement…
We describe a numerical model for the interaction of light with large raindrops using realistic nonspherical drop shapes. We apply geometrical optics and a Monte Carlo technique to perform ray traces through the drops. We solve the problem…
We consider a static, axially symmetric spacetime describing the superposition of a Schwarzschild black hole (BH) with a thin and heavy accretion disk. The BH-disk configuration is a solution of the Einstein field equations within the Weyl…
Optics naturally provides us with some powerful mathematical operations. Here we experimentally demonstrate that during reflection or refraction at a single optical planar interface, the optical computing of spatial differentiation can be…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
General relativity provides an appropriate framework for addressing the issue of sub- or superluminality as an apparent effect. Even though a massless particle travels on the light cone, its average velocity over a finite path measured by…
We provide an alternative view of some results in [1, 3, 11]. In particular, we prove that (1) if a continuous self-map of a compact metric space has the shadowing, then the union of the basins of terminal chain components is a dense…
The zodiacal light is a night-glow mostly visible along the plane of the ecliptic. It represents the background radiation associated with solar light scattered by the tenuous flattened interplanetary cloud of dust particles surrounding the…
We consider the effect on the propagation of light of inhomogeneities with sizes of order 10 Mpc or larger. The Universe is approximated through a variation of the Swiss-cheese model. The spherical inhomogeneities are void-like, with…
We present a novel approach to construct cosmological models endowed with a particular scalar field, the stealth. The model is constructed by studying a scalar field no-minimally coupled to the gravitational field with sources; as sources,…
We present a method to capture the 7-dimensional light field structure, and translate it into perceptually-relevant information. Our spectral cubic illumination method quantifies objective correlates of perceptually relevant diffuse and…
We consider the problem of shadowing for differential equations with grow-up. We introduce so-called nonuniform shadowing properties (in which size of the error depends on the point of the phase space) and prove for them analogs of…