Related papers: Junctions and thin shells in general relativity us…
This thesis studies general relativity (GR) using chiral formulations, which take advantage of the decomposition of the four-dimensional Lorentz group into self-dual and anti-self-dual sectors. Within this framework, GR can be expressed…
A generalized boundary integral method is developed to investigate the rheology of multiple emulsions with orderly structures up to n layers and up to mi droplets in the i-th layer in microchannels with various geometries. Recently, as fine…
Algebraic computing in relativity and gravitation dates back more than thirty years, but only relatively recently has hardware of sufficient power to tackle large scale calculations become commonplace. Whereas it is generally understood…
This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial…
We report on a package of routines for the computer algebra system Maple which supports the explicit determination of the geometric quantities, field equations, equations of motion, and conserved quantities of General Relativity in the…
The Israel equations for thin shells in General Relativity are derived directly from the least action principle. The method is elaborated for obtaining the equations for double layers in quadratic gravity from the least action principle.
The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface -termed as…
In this article we propose some Maple procedures, for teaching purposes, to study the basics of General Relativity (GR) and Cosmology. After presenting some features of GRTensorII, a package specially built to deal with GR, we give two…
A new approach to large-scale nuclear structure calculations, based on the Density Matrix Renormalization Group (DMRG), is described. The method is tested in the context of a problem involving many identical nucleons constrained to move in…
The purpose of this paper is to construct spherical thin-shell wormhole solutions through cut and paste technique and investigate the stability of these solutions in the vicinity of modified Chaplygin gas. The Darmois-Israel formalism is…
The generalized Swiss - cheese model, consisting of a Lema\^itre - Tolman (inhomogeneous dust) region matched, by way of a comoving boundary surface, onto a Robertson-Walker background of homogeneous dust, has become a standard construction…
The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. This year, GRworkbench has been significantly extended to facilitate numerical experimentation. The numerical…
This paper presents a general non-linear computational formulation for rotation-free thin shells based on isogeometric finite elements. It is a displacement-based formulation that admits general material models. The formulation allows for a…
Systems of Y-junctions are interesting both from a fundamental viewpoint and because of their potential use in nanoscale devices. These systems can be studied numerically with the density matrix renormalization group(DMRG), but existing…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
We present a generic technique, automated by computer-algebra systems and available as open-source software \cite{scuff-em}, for efficient numerical evaluation of a large family of singular and nonsingular 4-dimensional integrals over…
This paper combines the post-Minkowskian expansion of general relativity with the language of intersection theory. Because of the nature of the soft limit inherent to the post-Minkowskian expansion, the intersection-based approach is of…
Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations.…
We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…