Search results for "singularity."

Minimum Time Control of the Restricted Three-Body Problem

2012

The minimum time control of the circular restricted three-body problem is considered. Controllability is proved on an adequate submanifold. Singularities of the extremal flow are studied by means of a stratification of the switching surface. Properties of homotopy maps in optimal control are framed in a simple case. The analysis is used to perform continuations on the two parameters of the problem: The ratio of the masses, and the magnitude of the control.

On some Riemannian aspects of two and three-body controlled problems

2009

The flow of the Kepler problem (motion of two mutually attracting bodies) is known to be geodesic after the work of Moser [20], extended by Belbruno and Osipov [2, 21]: Trajectories are reparameterizations of minimum length curves for some Riemannian metric. This is not true anymore in the case of the three-body problem, and there are topological obstructions as observed by McCord et al. [19]. The controlled formulations of these two problems are considered so as to model the motion of a spacecraft within the influence of one or two planets. The averaged flow of the (energy minimum) controlled Kepler problem with two controls is shown to remain geodesic. The same holds true in the case of o…

Parabolic equations with nonlinear singularities

2011

Abstract We show the existence of positive solutions u ∈ L 2 ( 0 , T ; H 0 1 ( Ω ) ) for nonlinear parabolic problems with singular lower order terms of the asymptote-type. More precisely, we shall consider both semilinear problems whose model is { u t − Δ u + u 1 − u = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , and quasilinear problems having natural growth with respect to the gradient, whose model is { u t − Δ u + ∣ ∇ u ∣ 2 u γ = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , with γ > 0 . Moreover, we prove a comparison principle and, as an application, we study the asymptotic behav…

Airy-function approach to binary black hole merger waveforms: The fold-caustic diffraction model

2022

From numerical simulations of the Einstein equations, and also from gravitational wave observations, the gravitational wave signal from a binary black hole merger is seen to be simple and to possess certain universal features. The simplicity is somewhat surprising given that non-linearities of general relativity are thought to play an important role at the merger. The universal features include an increasing amplitude as we approach the merger, where transition from an oscillatory to a damped regime occurs in a pattern apparently oblivious to the initial conditions. We propose an Airy-function pattern to model the binary black hole (BBH) merger waveform, focusing on accounting for its simpl…

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…