Related papers: Some mathematical problems in numerical relativity
It is becoming common to hear teaching advice about spending more time on the "physics of the problem" so that students will get more physical insight and develop a stronger intuition that can be very helpful when thinking about physics…
The integration of the equations of motion in gravitational dynamical systems -- either in our Solar System or for extra-solar planetary system -- being non integrable in the global case, is usually performed by means of numerical…
Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…
The precision reached by current and forthcoming strong-lensing observations requires to accurately model various perturbations to the main deflector. Hitherto, theoretical models have been developed to account for either cosmological…
In the canonical approach to quantization of gravity, one often uses relational clock variables and an interpretation in terms of conditional probabilities to overcome the problem of time. In this essay we show that these suffer from…
Identifying the relativistic multipole moments of a spacetime of an astrophysical object that has been constructed numerically is of major interest, both because the multipole moments are intimately related to the internal structure of the…
Three of the big puzzles of theoretical physics are the following: (i) There is apparently no time evolution in the dynamics of quantum general relativity, because the allowed quantum states must obey the Hamiltonian constraint. (ii) During…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
The special theory of relativity is constructed demanding the retention of the rectilinear form of a trajectory and invariance of the wave equation under linear transformations of space and time coordinates. The usual approach to relativity…
Linear systems under the influence of nonlinear and random linear perturbations, and with random initial and boundary conditions, are discussed. The notion of states of a system is substituted by the notion of the generating vectors for…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
In this paper we sum up our works on multiscale programs, mainly simulations. We first start with describing what multiscaling is about, how it helps perceiving signal from a background noise in a ?ow of data for example, for a direct…
We discuss the application of computer algebra to problems commonly arising in numerical relativity, such as the derivation of 3+1-splits, manipulation of evolution equations and automatic code generation. Particular emphasis is put on…
We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and…
Loop quantum gravity is a mature theory. To proceed to explicit calculations in cosmology, it is necessary to make assumptions and simplifications based on the symmetries of the cosmological setting. Symmetry reduction is especially…
The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…
Our conventional understanding of space-time, as well as our notion of geometry, break down once we attempt to describe the very early stages of the evolution of our universe. The extreme physical conditions near the Big Bang necessitate an…
Quantum computing is a fascinating interdisciplinary research field that promises to revolutionize computing by efficiently solving previously intractable problems. Recent years have seen tremendous progress on both the experimental…
These lectures were addressed to nonspecialists willing to learn some basic facts, approaches, tools and observational evidence which conform modern cosmology. The aim is also to try to complement the many excellent treatises that exists on…