For $\xi = (\xi_1, \xi_2, \ldots, \xi_d) \in \mathbb{R}^d$ let $Q(\xi) := \sum_{j=1}^d \sigma_j \xi_j^2$ be a quadratic form with signs $\sigma_j \in \{\pm1\}$ not all equal. Let $S \subset \mathbb{R}^{d+1}$ be the hyperbolic paraboloid given by $S = \big\{(\xi, \tau) \in \mathbb{R}^{d}\times \mathbb{R} \ : \ \tau = Q(\xi)\big\}$. In this note we prove…
In recent joint works of the present author with M.Prasolov and V.Shastin a new technique for distinguishing Legendrian knots has been developed. In this paper the technique is extended further to provide a tool for distinguishing transverse knots. It is shown that the equivalence problem for transverse knots with trivial orientation-preserving symmetry group is algorithmically…
Given a sequence of lattice approximations $D_N\subset\mathbb Z^2$ of a bounded continuum domain $D\subset\mathbb R^2$ with the vertices outside $D_N$ fused together into one boundary vertex $\varrho$, we consider discrete-time simple random walks in $D_N\cup\{\varrho\}$ run for a time proportional to the expected cover time and describe the scaling limit of the exceptional level sets…
The goal of this paper is to apply the method of Lagrangian descriptors to reveal the phase space mechanism by which a Caldera-type potential energy surface (PES) exhibits the dynamical matching phenomenon. Using this technique, we can easily establish that the non-existence of dynamical matching is a consequence of heteroclinic connections between the unstable manifolds…
In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical evaluation of such moments. To demonstrate their use, we tabulate means and second moments of order statistics from random vectors having some typical…
We present an analysis of electron recoils in cryogenic germanium detectors operated during the SuperCDMS Soudan experiment. The data are used to set new constraints on the axioelectric coupling of axion-like particles and the kinetic mixing parameter of dark photons, assuming the respective species constitutes all of the galactic dark matter. This study covers the…
In the article the authors present a numerical method for modelling a laminar-turbulent transition in magnetohydrodynamic flows. The equations in the small magnetic Reynolds numbers approach is considered. Speed, pressure and electrical potential are decomposed to the sum of the state values and the finite amplitude perturbations. A solver based on the Nectar++ framework is…
We propose a method to make a highly clustered complex network within the configuration model. Using this method, we generated highly clustered random regular networks and analyzed the properties of them. We show that highly clustered random regular networks with appropriate parameters satisfy all the conditions of the small-world network: connectedness, high clustering coefficient, and…
Dynamics of femtosecond pulses with the telecom carrier wavelength is investigated numerically in a subwavelength layer of an indium tin oxide (ITO) epsilon-near-zero (ENZ) material with high dispersion and high nonlinearity. Due to the subwavelength thickness of the ITO ENZ material, and the fact that the pulse’s propagation time is shorter than its temporal width,…
This article shows the importance of flow compressibility on the heat transfer in confined impinging jets, and how it is driven by both the Mach number and the wall heat-flux. Hence, we present a collection of cases at several Mach numbers with different heat-flux values applied at the impingement wall. The wall temperature scales linearly…