相关论文: Numerical Methods for Handlebody Phases
In the paper we study some numerical solutions to Volterra equations which interpolate heat and wave equations. We present a scheme for construction of approximate numerical solutions for one and two spatial dimensions. Some solutions to…
We calculate the Hilbert action for the Bondi-Sachs metrics. It yields the Einstein vacuum equations in a closed form. Following the Dirac approach to constrained systems we investigate the related Hamiltonian formulation.
In this letter we present the first multiparticle solutions to Einstein's field equations in the presence of matter. These solutions are iteratively obtained via the perturbiner method, which can circumvent gravity's infinite number of…
We propose a method for computing upper bounds for the Heilbronn problem for triangles.
In this paper, we develop a new method to find the exact solutions of the Einstein's field equations by using which we construct time-periodic solutions. The singularities of the time-periodic solutions are investigated and some new…
The third del Pezzo surface admits a unique Kaehler-Einstein metric, which is not known in closed form. The manifold's toric structure reduces the Einstein equation to a single Monge-Ampere equation in two real dimensions. We numerically…
A procedure to find static axially symmetric solutions to the Einstein field equations is presented. We obtained two general solutions and five particular solutions, which depend on the existence conditions for circular and $z$ direction…
In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalisation error for a class of penalty terms, and we…
Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite…
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each…
The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily…
We formulate three-dimensional equations for the finite temperature in-matter three-body problem. Our approach takes into account the full infinite series for the effective pair-interaction kernel, so that all possible two-body…
In this paper we propose a Hamiltonian approach to gapped topological phases on an open surface with boundary. Our setting is an extension of the Levin-Wen model to a 2d graph on the open surface, whose boundary is part of the graph. We…
In this paper we propose an approach to the problem of two body motion in classical electrodynamics that takes into account the electromagnetic radiation and the radiation reaction forces. The resulting differential equations are solved…
We analyse the mathematical underpinnings of a mixed hyperbolic-elliptic form of the Einstein equations of motion in which the lapse function is determined by specified mean curvature and the shift is arbitrary. We also examine a new…
In this paper we derive homogeneous vacuum plane-wave solutions to Einstein's field equations in 4+1 dimensions. The solutions come in five different types of which three generalise the vacuum plane-wave solutions in 3+1 dimensions to the…
In this article, we present a numerical approach to ensure the preservation of physical bounds on the solutions to linear and nonlinear hyperbolic convection-reaction problems at the discrete level. We provide a rigorous framework for error…
A key issue in the solution of partial differential equations via integral equation methods is the evaluation of possibly singular integrals involving the Green's function and its derivatives multiplied by simple functions over discretized…
he Singular Manifold Method is presented as an excellent tool to study a 2+1 dimensional equation in despite of the fact that the same method presents several problems when applied to 1+1 reductions of the same equation. Nevertheless these…