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We introduce a non-standard model for percolation on the integer lattice $\mathbb Z^2$. Randomly assign to each vertex $a \in \mathbb Z^2$ a potential, denoted $\phi_a$, chosen independently and uniformly from the interval $[0, 1]$. For…
We formulate the inverse scattering transform for the scalar Maxwell-Bloch system of equations describing the resonant interaction of light and active optical media in the case when the light intensity does not vanish at infinity. We show…
We consider Bernoulli bond percolation on a large scale-free tree in the supercritical regime, meaning informally that there exists a giant cluster with high probability. We obtain a weak limit theorem for the sizes of the next largest…
It is speculated that the correct theory of fundamental physics includes a large landscape of states, which can be described as a potential which is a function of N scalar fields and some number of discrete variables. The properties of such…
The concept of potential energy landscapes is applied in many areas of science. We experimentally realize a random potential energy landscape (rPEL) to which colloids are exposed. This is achieved exploiting the interaction of matter with…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
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…
The capability of color encoding the continuous sequence of views from a scene was demonstrated previously by the author (1990). In the present work, the scheme for this process is shown where white light from a black and white object is…
We study the percolative properties of random interlacements on the product of G with the integer line Z, when G is a weighted graph satisfying certain sub-Gaussian estimates attached to the parameters alpha > 1, measuring the volume growth…
The atmosphere of the Sun is characterized by a complex interplay of competing physical processes: convection, radiation, conduction, and magnetic fields. The most obvious imprint of the solar convection and its overshooting in the low…
We examine the possibility of "soft cosmology", namely small deviations from the usual framework due to the effective appearance of soft-matter properties in the Universe sectors. One effect of such a case would be the dark energy to…
We consider the task of detecting a salient cluster in a sensor network, that is, an undirected graph with a random variable attached to each node. Motivated by recent research in environmental statistics and the drive to compete with the…
We investigate the static and spherically symmetric solutions of Einstein's equations for a scalar field with non-canonical kinetic term, assumed to provide both the dark matter and dark energy components of the Universe. In particular, we…
Data on the variability of the continuum optical emission are used for the first time to estimate the degree of spotting in stars similar to that of the sun. It is sown that the amount of spotting increases gradually from the sun to the…
Diverse cosmological and astrophysical observations strongly hint at the presence of dark matter and dark energy in the Universe. One of the main goals of Cosmology is to explain the nature of these two components. It may well be that both…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
The direction angle of twilight sky background polarization in the celestial sphere points far from solar vertical is found to depend on the ratio of single and multiple scattering contributions. The polarization direction behavior during…
We image with cameras entangled photon light transmitted through a random medium. Near-field and far-field spatial quantum correlations show that entangled photon pairs (bi-photons) generated by spontaneous optical parametric…
We study non-uniform percolation in a two-dimensional cluster growth model with multiple seeds. With increasing concentration of seeds, the percolation threshold is found to increase monotonically, while the exponents for correlation…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…