Related papers: Isolated and dynamical horizons from a common pers…
Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
Modified gravity theories can be used for the description of homogeneous and isotropic cosmological models through the corresponding field equations. These can be cast into systems of autonomous differential equations because of their sole…
The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential…
Non-Hermitian Hamiltonians H possess the real (i.e., observable) spectra inside certain specific domains of parameters D. In general, the determination of their observability-horizon boundaries is difficult. We list the pseudo-Hermitian…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
Boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A spacetime representing a black hole which itself is in equilibrium but whose exterior contains radiation admits such a horizon. Inspired by…
In this paper, we introduce a new method for study on backward stochastic differential equations with stopping time as time horizon. And using this, we show that some results on backward stochastic differential equations with constant time…
Predictability horizon properties of chaotic dynamical systems can be related to their spectral properties. It is shown, using this relationship, that the spectral properties of the leading large-scale climate daily indices indicate a…
We study two coupled discrete-time equations with different (asynchronous) periodic time scales. The coupling is of the type sample and hold, i.e., the state of each equation is sampled at its update times and held until it is read as an…
Based on a previously found general class of quantum improved exact solutions composed of non-interacting (dust) particles, we model the gravitational collapse of stars. As the modeled star collapses a closed apparent 3-horizon is generated…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
In the present paper, the primitive equations, which can be used to simulate the large scale motion of ocean and atmosphere, are considered in the three-dimensional domain bounded below by a fixed solid boundary and above by a free moving…
Using minimalist assumptions we develop a natural functional decomposition for the spacetime metric, and explicit tractable formulae for the surface gravities, in arbitrary stationary circular (PT symmetric) axisymmetric spacetimes. We…
This article is dedicated to establishing a novel approach to the cosmological constant, in which it is treated as an eigenvalue of a certain Sturm--Liouville problem. The key to this approach lies in the proper formulation of physically…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…
Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially…
In this paper we study the geometry of a certain class of compact dynamical horizons with a time-dependent induced metric in locally rotationally symmetric class II spacetimes. We first obtain a compactness condition for embedded…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
We simulate the gravitational dynamics of the conifold geometries (resolved and deformed) involved in the description of certain compact spacetimes. As the cycles of the conifold collapse towards a singular geometry we find that a horizon…