Related papers: Evolutionary constraints: Gluing in a toy model
This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution…
A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the…
We solve the Einstein constraint equations for a 3 + 1 dimensional vacuum spacetime with a space-like translational Killing field in the asymptotically flat case.. The presence of a space-like translational Killing field allows for a…
We investigate a number of simple toy models to explore interesting relationships between dynamics and typicality. We start with an infinite model that has been proposed as an illustration of how non-ergodic dynamics can produce interesting…
We consider numerically dynamics of a flat anisotropic Universe in Einstein-Gauss-Bonnet gravity with positive $\Lambda$ in dimensionalities 5+1 and 6+1. We identify three possible outcomes of the evolution, one singular and two…
In this note we construct self-dual cosmic strings from a gauge field theory with a generalized linear formation of potential energy density. By integrating the Einstein equation, we obtain a nonlinear elliptic equation which is equal with…
We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously…
We present our numerical comparisons between the BSSN formulation widely used in numerical relativity today and its adjusted versions using constraints. We performed three testbeds: gauge-wave, linear wave, and Gowdy-wave tests, proposed by…
We investigate, in a model-independent way, the conditions required to obtain a satisfactory model of extended inflation in which inflation is brought to an end by a first-order phase transition. The constraints are that the correct present…
The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic…
There exists the "entropy problem" of the early universe, that is, why did the universe begin with an extremely low entropy and how did it evolve into such high entropy at late times? It has been long believed that inflation cannot be the…
A class of evolutionary operator equations is studied. As an application the equations of linear acoustics are considered with complex material laws. A dynamic boundary condition is imposed which in the time-harmonic case corresponds to an…
The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric…
A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
Trapped surfaces are studied as inner boundary for the Einstein vacuum constraint equations. The trapped surface condition can be written as a non linear boundary condition for these equations. Under appropriate assumptions, we prove…
We construct a toy model of a nucleon, in which three static quarks interact via a SU(3) gauge field on a planar honeycomb lattice. The dynamics of the gauge field is described by the Kogut-Susskind Hamiltonian, truncated to the lowest…
The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is presented. The spacelike section of the class of metrics under consideration is a warped product of the real line with a nontrivial…
A class of evolution quasistatic systems which leads, after a suitable time discretization, to recursive nonlinear programs, is considered and optimal control or identification problems governed by such systems are investigated. The…
Understanding how evolutionary algorithms perform on constrained problems has gained increasing attention in recent years. In this paper, we study how evolutionary algorithms optimize constrained versions of the classical LeadingOnes…