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We deal with the orbit determination problem for a class of maps of the cylinder generalizing the Chirikov standard map. The problem consists of determining the initial conditions and other parameters of an orbit from some observations. A…
The propagation of surface (Rayleigh) waves over a rotating orthorhombic crystal is studied. The crystal possesses three crystallographic axes, normal to the symmetry planes: the half-space is cut along a plane normal to one of these axes,…
It is well known that the orbit of a lattice in hyperbolic $n$-space is uniformly distributed when projected radially onto the unit sphere. In the present work, we consider the fine-scale statistics of the projected lattice points, and…
To understand how well galaxies, gas and intracluster stars trace dark matter in and around galaxy clusters, we use the IllustrisTNG cosmological hydrodynamical simulation and compare the spatial distribution of dark matter with those of…
The Grover walk is one of the most well-studied quantum walks on graphs. In this paper, we investigate its periodicity to reveal the relationship between the quantum walk and the underlying graph, focusing particularly on the…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
In quantum spin liquid states, the fractionalized spinon excitations can carry fractional crystal symmetry quantum numbers, and this symmetry fractionalization distinguishes different topologically ordered spin liquid states. In this work…
We address the impact of asymmetric nonlocal diffusion nonlinearity on the properties of gap solitons supported by photorefractive crystal with an imprinted optical lattice. We reveal how the asymmetric nonlocal response alters the domains…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in…
We introduce a lattice model of glass transition in polymer globules. This model exhibits a novel scenario of ergodicity breaking in which the disjoint regions of phase space do not arise uniformly, but as small chambers whose number…
Simulating curvature due to gravity through warped surfaces is a common visualization aid in Physics education. We reprise a recent experiment exploring orbital trajectories on a precise 3D-printed surface to mimic Newtonian gravity, and…
We have constructed the geometric phases emerging from the non-trivial topology of a space-dependent magnetic field, interacting with the spin magnetic moment of a neutral particle. Our basic tool is the local unitary transformation which…
The motion, settling, and dispersion of microplastics in the ocean are determined by their rotational dynamics. We present experiments on elongated, large aspect ratio, and mildly curved plastic fibers slightly longer than the Kolmogorov…
We consider walks on a triangular domain that is a subset of the triangular lattice. We then specialise this by dividing the lattice into two directed sublattices with different weights. Our central result is an explicit formula for the…
Phase diagram of a two-dimensional system with a potential which stabilizes Kagome lattice is calculated. It is shown that this system demonstrate a set of crystalline and the regions of stability of these phases are calculated. The…
The rotor-router model is a popular deterministic analogue of random walk. In this paper we prove that all orbits of the rotor-router operation have the same size on a strongly connected directed graph (digraph) and give a formula for the…
The compact Abelian Higgs model is simulated on a cubic lattice where it possesses vortex lines and pointlike magnetic monopoles as topological defects. The focus of this high-precision Monte Carlo study is on the vortex network, which is…
We investigate the velocity distribution of elliptical galaxies in the framework of Non-local Gravity. According to this approach, it is possible to recover the fundamental plane of elliptical galaxies without the dark matter hypothesis.…