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Random optical fields with two widely different correlation lengths generate far field speckle spots that are themselves highly speckled. We call such patterns speckled speckle, and study their critical points (singularities and stationary…
Splines are central objects for the interpolation of discrete data via piecewise smooth paths. Their iterated-integral signature is an infinite collection of tensors which characterizes paths almost uniquely. We study truncations of this…
We study the commutation relation for 2-radial SLE in the unit disc starting from two boundary points. We follow the framework introduced by Dub\'{e}dat. Under an additional requirement of the interchangeability of the two curves, we…
In a smooth dynamical system, a homoclinic connection is a closed orbit returning to a saddle equilibrium. Under perturbation, homoclinics are associated with bifurcations of periodic orbits, and with chaos in higher dimensions. Homoclinic…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
This paper concerns stochastic perturbations of piecewise-smooth ODE systems relevant for vibro-impacting dynamics, where impact events constitute the primary source of randomness. Such systems are characterised by the existence of…
We study striped morphologies induced by magnetic impurities in d-wave superconductors (DSCs) near optimal doping by self-consistently solving the Bogoliubov-de Gennes equations based on the $t-t^{\prime }-U-V$ model. For the single…
We investigate the scattering properties of one-dimensional, periodically and non-periodically forced oscillators. The pattern of singularities of the scattering function, in the periodic case, shows a characteristic hierarchical structure…
We find that the electronic spin rotation induced by drift transport around a closed path in a wide variety of nonmagnetic semiconductors at zero magnetic field depends solely on the physical path taken. Physical paths that produce any…
This paper continues a series reporting different aspects of the behaviour of disc galaxy simulations that support spiral instabilities. The focus in this paper is to demonstrate how linear spiral instabilities saturate and decay, and how…
We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…
To address questions about the physical nature and origin of spiral arms in galaxies, it is necessary to measure their dynamical properties, such as the angular speed, $\Omega_p$, or the corotation radius. Observations suggest that galaxies…
In this paper, we report our ongoing investigations of the inherent non-determinism in contemporary execution environments that can potentially lead to divergence in state of a multi-channel hardware/software system. Our approach involved…
We investigate by exact optimization method properties of two- and three-dimensional systems of elastic lines in presence of splayed columnar disorder. The ground state of many lines is separable both in 2d and 3d leading to a random walk…
In this paper we study a type of two singular point singular cycle where one heteroclinic orbit is the transversal intersection of the 2-dimensional stable manifold of one singular point and the 2-dimensional unstable manifold of other…
We address the problem of detecting non-locality in coupled N level systems in the language of spin. Through a number of examples, we show that non-locality can be detected via a violation of the standard Bell inequality, irrespective of…
An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…
We investigate the spin-orbit induced spin-interference pattern of ballistic electrons travelling along any regular polygon. It is found that the spin-interference depends strongly on the Rashba and Dresselhaus spin-orbit constants as well…
We show that string theory with Dirichlet boundaries is equivalent to string theory containing surfaces with certain singular points. Surface curvature is singular at these points. A singular point is resolved in conformal coordinates to a…
We investigate the Drude model of spin dynamics in two-dimensional spin-orbit coupled systems. In the absence of an applied electric field, the spin aligns with the k-dependent effective magnetic field. The influence of disorder (the…