Related papers: Topics in coarsening phenomena
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
The changes of main paradigms on the structure and evolution of the Universe are reviewed. Two puzzles of the modern cosmology, the mean density of matter and the regularity of the Universe on large scales, as well as the possibility to…
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
This paper analyses the convergence and degeneration of sequences of metrics on a 3-manifold, and relations of such with Thurston's geometrization conjecture. The sequences are minimizing sequences for a certain (optimal) scalar-curvature…
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \geq 3$ dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model…
These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is…
This study presents a simplified approach to studying the dynamics of global texture collapse. We derive equations of motion for a spherically symmetric field configuration using a two parameter ansatz. Then we analyse the effective…
Recent developments in theory and phenomenology relevant to deep inelastic lepton scattering are reviewed, concentrating on the following topics: Predicted behaviour of non-singlet and polarized structure functions at small $x$; Theoretical…
This is a pedagogical introduction to the basics of the cosmic string theory and also a review of the recent progress made with respect to the macrophysical predictions of the theory. Topics covered include, string formation and evolution,…
In this pedagogical introduction, I discuss theoretical aspects of superfluidity and superconductivity, mostly using a field-theoretical formalism. While the emphasis is on general concepts and mechanisms behind superfluidity, I also…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
The concept of torsion in geometry, although known for a long time, has not gained considerable attention by the physics community until relatively recently, due to its diverse and potentially important applications to a plethora of…
In this introductory chapter of the Special Issue entitled `The Structure and Evolution of Stars', we highlight the recent major progress made in our understanding in the physics that governs stellar interiors. In so doing, we combine…
These are the author's lectures at the 1992 Les Houches Summer School, "Gravitation and Quantizations". They develop a generalized sum-over-histories quantum mechanics for quantum cosmology that does not require either a preferred notion of…
A brief overview of the current state of the problem of electromagnetic field singularities arising from the refraction and scattering of light by material objects is given. The discussion begins with caustics arising from ray tracing in…
The subject of the paper is the geometry and topology of cosmological spacetimes and vector bundles thereon, which are used to model physical fields propagating in the universe. Global hyperbolicity and factorization properties of the…
These lecture notes review the theoretical problems associated with coarse-graining the observed inhomogeneous structure of the universe at late epochs, of describing average cosmic evolution in the presence of growing inhomogeneity, and of…
In this report of the workshop on `Physics of the Very Early Universe' held at GR14, the recent status and open problems in a selected number of major areas of interest are reviewed, focusing on attempts to develop a superstring cosmology…
This article gives an overview of many of the recent developments in understanding the structure of relativistic scattering amplitudes in gauge theories ranging from QCD to N=4 super-Yang-Mills theory, as well as (super)gravity. I also…
This set of lecture notes first gives an introduction to the geometry of principal bundles. Next, it demonstrates how they can be used to formalize the concept of gauge theories arising in physics. A basic familiarity with the differential…