Related papers: Shadow and percolation I: discrete landscapes with…
We investigate level-set percolation of the Gaussian free field on transient trees, for instance on super-critical Galton-Watson trees conditioned on non-extinction. Recently developed Dynkin-type isomorphism theorems provide a comparison…
We prove the existence of non-trivial phase transitions for the intersection of two independent random interlacements and the complement of the intersection. Some asymptotic results about the phase curves are also obtained. Moreover, we…
The consensus of opinion in cosmology is that the Universe is currently undergoing a period of accelerated expansion. With current and proposed high precision experiments it offers the hope of being able to discriminate between the two…
Atmospheric refraction is responsible for the bending of light-rays in the atmosphere. It is a result of the continuous decrease in the refractive index of the air as a function of altitude. A well-known consequence of this phenomenon is…
Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a…
We propose a 3D latent representation that jointly models object geometry and view-dependent appearance. Most prior works focus on either reconstructing 3D geometry or predicting view-independent diffuse appearance, and thus struggle to…
Suppose each site independently and randomly chooses some sites around it, and it is weakly (strongly) connected with them (if there choose each other). What is the probability that the weak (strong) connected cluster is infinite? We…
Equations to investigate fluctuations in cosmic X-ray background radiation due to point-like sources at high-redshift are formulated in a systematic way. The angular power spectrum of X-ray background fluctuations is investigated from…
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…
Occultation and microlensing are different limits of the same phenomena of one body passing in front of another body. We derive a general exact analytic expression which describes both microlensing and occultation in the case of spherical…
In the seventies, scientists observed discrepancies of the bending of light around the Sun based on Einstein's prediction of the curvature of star light due to the mass of the Sun. We claim that the interior electromagnetic properties of…
We consider a general five-dimensional sigma-model coupled to gravity, with any number of scalars and general sigma-model metric and potential. We discuss in detail the problem of the boundary conditions for the scalar fluctuations, in the…
We investigate the null geodesic flow and in particular the light rings (LRs), fundamental photon orbits (FPOs) and shadows of a black hole (BH) immersed in a strong, uniform magnetic field, described by the Schwarzschilld-Melvin…
Let $f \colon X \to X$ be a continuous map on a compact metric space $X$ and let $\alpha_f$, $\omega_f$ and $ICT_f$ denote the set of $\alpha$-limit sets, $\omega$-limit sets and nonempty closed internally chain transitive sets…
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
In the current article we discuss an illumination problem proposed by Urrutia and Zaks. The focus is on configurations of finitely many two-sided mirrors in the plane together with a source of light placed at an arbitrary point. In this…
Most networks of interest do not live in isolation. Instead they form components of larger systems in which multiple networks with distinct topologies coexist and where elements distributed amongst different networks may interact directly.…
We introduce a new set of flow parameters to describe the time dependence of the equation of state and the speed of sound in single field cosmological models. A scale invariant power spectrum is produced if these flow parameters satisfy…
We study reflection and transmission of light at the interface between different phases of a U(1) x U(1) gauge theory. On each side of the interface, one can choose a basis so that one generator is free (allowing propagation of light), and…
The light pollution levels experienced at any given site generally depend on a wide number of artificial light sources distributed throughout the surrounding territory. Since photons can travel long distances before being scattered by the…