Related papers: Consistent discretizations: the Gowdy spacetimes
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous…
The present work concerns the derivation of a numerical scheme to approximate weak solutions of the Euler equations with a gravitational source term. The designed scheme is proved to be fully well-balanced since it is able to exactly…
Using the recently proposed covariant framework of general relativistic stochastic mechanics and stochastic thermodynamics, we proved the detailed and integral fluctuation theorems in curved spacetime. The time-reversal transformation is…
We develop a new formalism for the treatment of gravitational backreaction in the cosmological setting. The approach is inspired by projective techniques in non-equilibrium statistical mechanics. We employ group-averaging with respect to…
We present a high-order space-time discretization equipped with fully-discrete entropy stability properties for general choices of volume and surface quadrature rules. The formulation uses flux reconstruction (FR) in the spatial dimension…
A method for consistent quantization of conformal gravity treating conformal symmetry in a very controllable way is presented. First, we discuss local conformal symmetry in the framework of gravitational interactions, where we view it as an…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
We study generalisations of the Einstein--Straus model in cylindrically symmetric settings by considering the matching of a static space-time to a non-static spatially homogeneous space-time, preserving the symmetry. We find that such…
The property that the velocity $\boldsymbol{u}$ belongs to $L^\infty(0,T;L^2(\Omega)^d)$ is an essential requirement in the definition of energy solutions of models for incompressible fluids. It is, therefore, highly desirable that the…
In my previous work, physics/0205011, I reported several observations on special relativity, its experimental facts and its relations to quantum mechanics and statistical mechanics. These observations made us conscious: Special relativity…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The…
Dynamical simulations are a fundamental tool for studying the secular evolution of disc galaxies. Even at their maximum resolution, they still follow a limited number of particles and typically resolve scales of the order of a few tens of…
We consider the strong solution of the 2D Navier-Stokes equations in a torus subject to an additive noise. We implement a fully implicit time numerical scheme and a finite element method in space. We prove that the rate of convergence of…
This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniques based on…
The primary emphasis of this work is the development of a finite element based space-time discretization for solving the stochastic Lagrangian averaged Navier-Stokes (LANS-$\alpha$) equations of incompressible fluid turbulence with…
We provide a gauge-invariant theory of gravitation in the context of Weyl Integrable Space-Times. After making a brief review of the theory's postulates, we carefully define the observers' proper-time and point out its relation with…
Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete quantum gravity, where dynamical spacetime…
Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…