相关论文: Regularization of spherical and axisymmetric evolu…
We point out some criteria that imply regularity of axisymmetric solutions to Navier-Stokes equations. We show that boundedness of $\|{v_{r}}/{\sqrt{r^3}}\|_{L_2({\rm R}^3\times (0,T))}$ as well as boundedness of…
The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the KST representation of the Einstein evolution equations. The basic "Mexico City Tests" widely adopted by the numerical relativity community are…
B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. Based on this fact is our method of group classification of potential symmetries of systems of…
We describe an implicit general relativistic hydrodynamics code. The evolution equations are formulated in comoving coordinates. A conservative finite differencing of the Einstein equations is outlined, and artificial viscosity and…
We describe a method to analyze causal geodesics in static and spherically symmetric spacetimes of Kerr-Schild form which, in particular, allows for a detailed study of the geodesics in the vicinity of the central singularity by means of a…
Motion of curves and surfaces in $\R^3$ lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through…
For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
There is an abundance of empirical evidence in the numerical relativity literature that the form in which the Einstein evolution equations are written plays a significant role in the lifetime of numerical simulations. This paper attempts to…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
The dynamical systems methods are used to study evolution of the polymerised scalar field cosmologies with the cosmological constant. We have found all evolutional paths admissible for all initial conditions on the two-dimensional phase…
This is the first in a series of papers on the construction and validation of a three-dimensional code for general relativistic hydrodynamics, and its application to general relativistic astrophysics. This paper studies the consistency and…
A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements.…
We study the regularization of the codimension-2 singularities in six-dimensional Einstein-Maxwell axisymmetric models with warping. These singularities are replaced by codimension-1 branes of a ring form, situated around the axis of…
We describe efforts over the last six years to implement regularization methods suitable for studying one or more interacting black holes by direct N-body simulations. Three different methods have been adapted to large-N systems: (i)…
We derive a differential equation that is regular at the collision of two equal-mass bodies with attractive interaction in the relativistic action-at-a-distance electrodynamics. Our method uses the energy constant related to the…
The Einstein equations have proven surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be…
Recently, various evolutionary partial differential equations (PDEs) with a mixed derivative have been emerged and drawn much attention. Nonetheless, their PDE-theoretical and numerical studies are still in their early stage. In this paper,…