Related papers: How to detect Wada Basins
The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the generalized Hill problem. The parametric variation of the position and the linear stability of the equilibrium points is…
In this paper a Complex Network approach is taken to understand the salient features of Indian Water Dam Networks. Detailed analysis of 15 river basin networks have been carried out. The data has been taken from "River Basin Atlas of India"…
The double-well potential is a good example, where we can compute the splitting in the bound state energy of the system due to the tunneling effect with various methods, namely WKB or instanton calculations. All these methods are…
We give sufficient conditions under which the set of eventually periodic points in the intersection of immediate attracting basins boundaries is non-empty. We give other conditions under which this set is dense in the intersection.
This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…
The multi-modal nature of neural loss landscapes is often considered to be the main driver behind the empirical success of deep ensembles. In this work, we probe this belief by constructing various "connected" ensembles which are restricted…
Drainage basins are essential to Geohydrology and Biodiversity. Defining those regions in a simple, robust and efficient way is a constant challenge in Earth Science. Here, we introduce a model to delineate multiple drainage basins through…
Feature identification is an important task in many fluid dynamics applications and diverse methods have been developed for this purpose. These methods are based on a physical understanding of the underlying behavior of the flow in the…
The circular Sitnikov problem, where the two primary bodies are prolate or oblate spheroids, is numerically investigated. In particular, the basins of convergence on the complex plane are revealed by using a large collection of numerical…
We study the porosity properties of fractal percolation sets $E\subset\mathbb{R}^d$. Among other things, for all $0<\varepsilon<\tfrac12$, we obtain dimension bounds for the set of exceptional points where the upper porosity of $E$ is less…
In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our method is to establish some graph structures on fractal squares to reveal the…
Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape…
Consider a Brownian particle in three dimensions which is attracted by a plane with a strength proportional to some dimensionless parameter $\alpha$. We investigate the fractal spatial structure of the visited lattice sites in a cubic…
Ward identities for charge-density and spin-density fluctuations are discussed in comparison with those for superconducting fluctuations.
We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of NK landscapes as an example. In our case the inherent…
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or…
We show that a known condition for having rough basin boundaries in bistable 2D maps holds for high-dimensional bistable systems that possess a unique nonattracting chaotic set embedded in their basin boundaries. The condition for roughness…
We propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid, and apply it to the Bader charge partitioning for the electron charge density. Starting with the…
We invent the notion of a derived and fluid variety. Fluid variety has no proper derived variety as its subvariety. We examine some properties of fluid and derived varieties. Examples of such varieties of bands are presented.
Recently, new insights in the relation between the geometry of the vessel that confines a fluid and its thermodynamic properties were traced through the study of cluster integrals for inhomogeneous fluids. In this work I analyze the…