相关论文: The constraints as evolution equations for numeric…

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised…

We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…

We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…

Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the non-linearity of Einstein's equations. The latter of these ensures that smoothing spacetime over cosmological scales does not…

The Einstein initial-value equations in the extrinsic curvature (Hamiltonian) representation and conformal thin sandwich (Lagrangian) representation are brought into complete conformity by the use of a decomposition of symmetric tensors…

A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…

A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…

In order to obtain stable and accurate general relativistic simulations, re-formulations of the Einstein equations are necessary. In a series of our works, we have proposed using eigenvalue analysis of constraint propagation equations for…

An extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional…

A new class of the constrained Monte Carlo (CMC) algorithms for the QCD evolution equation was recently discovered. The constraint is imposed on the type and the total longitudinal energy of the parton exiting QCD evolution and entering a…

In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…

I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…

The effectiveness of the hyperbolic relaxation method for solving the Einstein constraint equations numerically is studied here on a variety of compact orientable three-manifolds. Convergent numerical solutions are found using this method…

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…

One possibility for avoiding constraint violation in numerical relativity simulations adopting free-evolution schemes is to modify the continuum evolution equations so that constraint violations are damped away. Gundlach et. al.…

One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where…

In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…

We derive a theory-independent version of the momentum constraint equation for use in cosmology, as a part of the Parameterised Post-Newtonian Cosmology (PPNC) framework. Our equations are constructed by adapting the corresponding…

Uniqueness problems in the elliptic sector of constrained formulations of Einstein equations have a dramatic effect on the physical validity of some numerical solutions, for instance when calculating the spacetime of very compact stars or…

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…