Search results for "Singularity"

I. Glass Transition. Theoretical concepts on the glass transition of polymers and their test by computer simulation

1996

Various organic molecules, in particular polymers, are extremely good glass formers and allow the study of supercooled melts near the glass transition in metastable equilibrium. Theories of the glass transition imply such an equilibrium (e.g. mode-coupling theory, or Gibbs-di Marzio theory) and can hence be tested in these systems. Simplified lattice models for polymer melts (e.g. the bond fluctuation model) have been developed that can very efficiently be studied by Monte-Carlo simulation, and although they fail to accurately describe the local structure, they describe many features of the experiments very well. In this model, the mechanism of the glass transition is a competition between …

Temperature dependence of the static structure factor of ortho-terphenyl in the supercooled liquid regime close to the glass transition

1993

Abstract Studying the temperature dependence of the static structure factor of ortho-terphenyl from the liquid state down to the glass we find that the main peak of S ( Q ) is split into two maxima which behave quite differently. While the maximum at Q =1.4 A −1 is not much affected by the temperature variation the one at 1.9 A −1 is significantly enhanced. This effect is connected with a change of the short range order, i.e. of the intermolecular distances, but evolves continuously. Thus the dynamic anomalies that have been observed in this system around a characteristic temperature T c ≈290 K are not simply due to a discontinuous change in S ( Q ) but can be attributed to the existence of…

Black Holes, Geons, and Singularities in Metric-Affine Gravity

2016

Uno de los problemas abiertos en la descripción de la gravedad es la existencia de singularidades. Las geometrías singulares se caracterizan por geodésicas incompletas, lo que físicamente se corresponde con observadores que desaparecen del espacio-tiempo, o que aparecen de la nada. Múltiples extensiones de la Relatividad General tratan de resolver este problema de algún modo. Por ello, en esta tesis estudio modificaciones al Lagrangiano de Relatividad General, tales como gravedad cuadrática y gravedad de Born-Infeld, en el formalismo Métrico-Afín. En este formalismo, la conexión (de la cual se derivan los tensores de curvatura) se considera independiente de la métrica, y permitimos que sea …

Up-wind difference approximation and singularity formation for a slow erosion model

2020

We consider a model for a granular flow in the slow erosion limit introduced in [31]. We propose an up-wind numerical scheme for this problem and show that the approximate solutions generated by the scheme converge to the unique entropy solution. Numerical examples are also presented showing the reliability of the scheme. We study also the finite time singularity formation for the model with the singularity tracking method, and we characterize the singularities as shocks in the solution.

Olemisen ainutkertaisuudesta ainutkertaisuuden politiikkaan : Parmenides, Heidegger, Nancy

2013

Dynamical Hadrons: Case Studies of Meson-Meson and Meson-Baryon Molecules and Triangle Singularities

2020

In this thesis we use various methods to study the interaction of hadrons. We focus on topics related to exotic hadrons, such as tetraquarks from meson-meson interaction, pentaquarks from meson-baryon, and also triangular singularities. We show how experimental data can be explained with our theoretical models, and make predictions that can be compared with future experiments. In chapter 1 we show our method to describe meson-meson interactions, known as chiral unitary approach, showing how the interaction of pseudoscalars generates the f0(500), f0(980) and a0(980), which appear in the two articles discussed in this chapter: that of the eta_c -> eta pi+ pi- decay, and that of the a0(980)-f0…

The Calderón problem for the fractional Schrödinger equation with drift

2020

We investigate the Calder\'on problem for the fractional Schr\"odinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does \emph{not} enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many \emph{generic} measurements is discussed. Here the genericity is obtained through \emph{singularity theory} which might also be interesting in the context of hybrid inverse pro…

A Complete, Exact and Efficient Implementation for Computing the Edge-Adjacency Graph of an Arrangement of Quadrics

2011

International audience; We present a complete, exact and efficient implementation to compute the edge-adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the edge-adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always comp…

Lenses on very curved zones of a singular line field of ${\mathbb C}^2$ or of a singular plane field of ${\mathbb C}^3$

2020

We renormalize, using suitable lenses, small domains of a singular holomorphic line field of ${\mathbb C}^2$ or plane field of ${\mathbb C}^3$ where the curvature of a plane-field is concentrated. At a proper scale the field is almost invariant by translations. When the field is integrable, the leaves are locally almost translates of a surface that we will call {\it profile}. When the singular rays of the tangent cone (a generalization to a plane-field of the tangent cone of a singular surface is defined) are isolated, we obtain more precise results. We also generalize a result of Merle (\cite{Me}) concerning the contact order of generic polar curves with the singular level $f=0$ when $\ome…

Lebesgue-type decomposition for sesquilinear forms via differences

2022

Definitions of regularity and singularity are proposed for sesquilinear forms with respect to a non-negative one and a correspondent Lebesgue-type decomposition is proved. In contrast to other Lebesgue-type decompositions established in the literature for sesquilinear forms with generic sign, the underlying idea in this paper is to write symmetric forms as the difference of non-negative sesquilinear forms.