Classical String Dynamics in Curved Backgrounds

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2014, Tutor: Jorge G. RussoIn this bachelor thesis, we study a rotating classical string embedded in the 5- dimensional Anti-de-Sitter spacetime (AdS5), through the analysis of the dynamics of the Polyakov action. We compute its energy E and spin S and discuss the dependence E(S). The function E(S) is explicitly derived in two limiting cases: the short string case (in which the length of the string is considerably smaller than the characteristic length of AdS5) and the long string case (in which it is considerably greater). In the former case, the dependence E(S) previously derived for a at space is recovered

Manifolds with bounded integral curvature and no positive eigenvalue lower bounds

We provide an explicit construction of a sequence of closed surfaces with uniform bounds on the diameter and on $L^p$ norms of the curvature, but without a positive lower bound on the first non-zero eigenvalue of the Laplacian $\lambda_1$. This example shows that the assumption of smallness of the $L^p$ norm of the curvature is a necessary condition to derive Lichnerowicz and Zhong-Yang type estimates under integral curvature conditions

Psychosocial and biological predictors of resident physician burnout

Background A high proportion of health professionals in training suffer from work-related stress and may develop a burnout syndrome. Objectives To study the incidence of burnout after the first year of residency in a teaching hospital and to identify baseline psychological, psychosocial work conditions, and biological risk factors. Methodology We assessed the following in a prospective cohort of residents at baseline (first month residence) and after 1 year: background factors (socio-demographics, psychiatric history), perceived stress score (Perceived Stress Scale), Maslach Burnout Inventory score, and psychosocial factors (Job Content Questionnaire). Blood samples were obtained to study serum cortisol, IL-6, and TNF-a concentrations. The cumulative incidence was modelled by multivariate log-binomial regression analysis. Results We included 71 participants with a female majority (64.8%), age 26.4 (2.65) years, psychiatric history in 20%, and burnout in 13%. Among those without burnout initially (N = 59), it had developed by 1 year in 22% of residents. Increased job demand (RR = 1.259, 95%CI = 1.019–1.556, p = 0.033) and decreased cortisol levels (RR = 0.877, 95%CI = 0.778–0.989, p = 0.032) predicted burnout after 1 year of residency among medical trainees. Conclusion Burnout syndrome develops in 22% of residents by 1 year of training and can be predicted by increased work demands and decreased cortisol levels.This research was carried out, in part, thanks to grants from PREVENT XI (DN040611; VO and RN)Peer ReviewedPostprint (author's final draft

Una Introducción a la relatividad general

This bachelor's degree thesis is an introduction to the Theory of General Relativity (GR), a relativistic theory of gravity, from the point of view of a recently graduated mathematitian. The principles of GR are stated and some motivation on the formulation of the theory is provided. It is shown that freely-falling particles move along geodesics of spacetime and Einstein's equations are derived as a generalization of Newton's gravity. The uniqueness of Einstein's equations and the presence of the cosmological constant are discussed. The thesis concludes finding Schwarzschild solution by assuming that there exists a spherically symmetric metric that is a solution to Einstein's equations in vacuum and seeing what properties should this metric have. The boundary conditions imposed are the existence of a punctual uncharged mass at the origin and flatness of the metric at infinity. The result is a particular solution that can be applied in many contexts, such as in the Solar System.Se trata de hacer una presentación de los fundamentos, ecuaciones y algunos aspectos fenomenológicos de la Teoría General de la Relatividad, desde un punto de vista matemático formal. En particular:- Repasar algunos conceptos básicos de geometría diferencial.- Analizar los antecedentes y los postulados de la Relatividad General.- Obtener las ecuaciones de Einstein y estudiar su formulación variacional (lagrangiana de Hilbert).- Describir algunas consecuencias fenomenológicas y cosmológicas de la teoría

Gradient Estimates Under Integral Curvature Conditions

This thesis contains two main results: a Li-Yau type gradient estimate 3.3.1, anda Zhong-Yang type eigenvalue estimate 4.3.1. The classical version of these results is formulated in the setting of manifolds with nonnegative Ricci curvature. Here we presentproofs of analogous results under integral curvature assumptions, which are more generaland apply in many more settings than pointwise lower bounds. Although the totality of thiswork has not been published, part of it was published in [RO19] or appears in the preprint[ROSWZ18].The Li-Yau gradient estimate that we prove is an inequality satisfied by the gradient of the Neumann heat kernel. We restrict our attention to compact domains withinan ambient space manifold, and assume that the amount of negative Ricci curvature of themanifold is small in an Lp average sense. The domains are not necessarily convex, but mustsatisfy an interior rolling R-ball condition 1.3.4. As a corollary of this theorem, we derivea parabolic Harnack inequality 3.4.1 and a mean value inequality 3.4.2, as well as a lowerbound for the first nontrivial Neumann eigenvalue on this class of domains 3.4.3.The Zhong-Yang type estimate that we present is a lower bound for the firstnonzero eigenvalue of the drift Laplacian in the setting of closed smooth metric measurespaces. It is derived assuming that the amount of negative Bakry-Émery Ricci curvatureof the manifold is small in an Lp average sense. The estimate is sharp, since it recovers theclassical result in the limit where the Ricci tensor is nonnegative. Moreover, we show thatthe smallness of the curvature assumption is necessary in example 4.4.2

Una Introducción a la relatividad general

This bachelor's degree thesis is an introduction to the Theory of General Relativity (GR), a relativistic theory of gravity, from the point of view of a recently graduated mathematitian. The principles of GR are stated and some motivation on the formulation of the theory is provided. It is shown that freely-falling particles move along geodesics of spacetime and Einstein's equations are derived as a generalization of Newton's gravity. The uniqueness of Einstein's equations and the presence of the cosmological constant are discussed. The thesis concludes finding Schwarzschild solution by assuming that there exists a spherically symmetric metric that is a solution to Einstein's equations in vacuum and seeing what properties should this metric have. The boundary conditions imposed are the existence of a punctual uncharged mass at the origin and flatness of the metric at infinity. The result is a particular solution that can be applied in many contexts, such as in the Solar System.Se trata de hacer una presentación de los fundamentos, ecuaciones y algunos aspectos fenomenológicos de la Teoría General de la Relatividad, desde un punto de vista matemático formal. En particular:- Repasar algunos conceptos básicos de geometría diferencial.- Analizar los antecedentes y los postulados de la Relatividad General.- Obtener las ecuaciones de Einstein y estudiar su formulación variacional (lagrangiana de Hilbert).- Describir algunas consecuencias fenomenológicas y cosmológicas de la teoría

Una Introducción a la relatividad general

This bachelor's degree thesis is an introduction to the Theory of General Relativity (GR), a relativistic theory of gravity, from the point of view of a recently graduated mathematitian. The principles of GR are stated and some motivation on the formulation of the theory is provided. It is shown that freely-falling particles move along geodesics of spacetime and Einstein's equations are derived as a generalization of Newton's gravity. The uniqueness of Einstein's equations and the presence of the cosmological constant are discussed. The thesis concludes finding Schwarzschild solution by assuming that there exists a spherically symmetric metric that is a solution to Einstein's equations in vacuum and seeing what properties should this metric have. The boundary conditions imposed are the existence of a punctual uncharged mass at the origin and flatness of the metric at infinity. The result is a particular solution that can be applied in many contexts, such as in the Solar System.Se trata de hacer una presentación de los fundamentos, ecuaciones y algunos aspectos fenomenológicos de la Teoría General de la Relatividad, desde un punto de vista matemático formal. En particular:- Repasar algunos conceptos básicos de geometría diferencial.- Analizar los antecedentes y los postulados de la Relatividad General.- Obtener las ecuaciones de Einstein y estudiar su formulación variacional (lagrangiana de Hilbert).- Describir algunas consecuencias fenomenológicas y cosmológicas de la teoría

Classical String Dynamics in Curved Backgrounds

Abstract: In this bachelor thesis, we study a rotating classical string embedded in the 5-dimensional Anti-de-Sitter spacetime (AdS5), through the analysis of the dynamics of the Polyakov action. We compute its energy E and spin S and discuss the dependence E(S). The function E(S) is explicitly derived in two limiting cases: the short string case (in which the length of the string is considerably smaller than the characteristic length of AdS5) and the long string case (in which it is considerably greater). In the former case, the dependence E(S) previously derived for a flat space is recovered