Lorenzo Magnea Curriculum Vitae
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Faceting Space(Time): Regge's View of Geometry
Faceting space(time): Regge’s view of geometry Annalisa Marzuoli, Dipartimento di Matematica, Pavia University Curved surfaces as ‘simple’ models of curved spacetimes in Einstein’s General Relativity (Gauss geometries) The curvature of a generic smooth surface is perceived through its embedding into the 3D Euclidean space Looking at different regions three types of Gauss model geometries can be recognized The saddle surface (negative Gauss curvature) The surface of a sphere The Euclidean plane (positive Gauss is flat, i.e. its curvature) curvature is zero Principal curvatures are defined through ‘extrinsic properties’ of the surface, which is bent as seen in the ambient 3D space Glimpse definition In every point consider the tangent plane and the normal vector to the surface. (Any pair of) normal planes intersect the surface in curved lines. By resorting to the notion of osculating circle, the curvature of these embedded curves is evaluated (in the point). CASES: • > 0 and equal to 1/r • < 0 and equal to -1/r • = 0 r: radius of the osculating circle (Th.) There are only two distinct and mutually ortogonal principal directions in each point of an embedded surface, or: every direction is principal Principal Saddle surface: the principal curvatures curvatures have opposite sign (modulus) K1 = + 1/r1 K2 = - 1/r2 K1 = 1/r1 Sphere of radius r: K2 = 1/r2 K1 = K2 = 1/r > 0 (r1, r2 :radii of the All principal osculating circles) curvatures are equal in each Plane: limiting case point of the sphere r → ∞ (K1 = K2 = 0) Gauss curvature & the theorema -
Regge Finite Elements with Applications in Solid Mechanics and Relativity
Regge Finite Elements with Applications in Solid Mechanics and Relativity A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Lizao Li IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy Advisor: Prof. Douglas N. Arnold May 2018 © Lizao Li 2018 ALL RIGHTS RESERVED Acknowledgements I would like to express my sincere gratitude to my advisor Prof. Douglas Arnold, who taught me how to be a mathematician: diligence in thought and clarity in communication (I am still struggling with both). I am also grateful for his continuous guidance, help, support, and encouragement throughout my graduate study and the writing of this thesis. i Abstract This thesis proposes a new family of finite elements, called generalized Regge finite el- ements, for discretizing symmetric matrix-valued functions and symmetric 2-tensor fields. We demonstrate its effectiveness for applications in computational geometry, mathemati- cal physics, and solid mechanics. Generalized Regge finite elements are inspired by Tullio Regge’s pioneering work on discretizing Einstein’s theory of general relativity. We analyze why current discretization schemes based on Regge’s original ideas fail and point out new directions which combine Regge’s geometric insight with the successful framework of finite element analysis. In particular, we derive well-posed linear model problems from general relativity and propose discretizations based on generalized Regge finite elements. While the first part of the thesis generalizes Regge’s initial proposal and enlarges its scope to many other applications outside relativity, the second part of this thesis represents the initial steps towards a stable structure-preserving discretization of the Einstein’s field equation. -
*Impaginazione OK
Ministero per i Beni e le Attività Culturali Direzione Generale per i Beni Librari e gli Istituti Culturali Comitato Nazionale per le celebrazioni del centenario della nascita di Enrico Fermi Proceedings of the International Conference “Enrico Fermi and the Universe of Physics” Rome, September 29 – October 2, 2001 Accademia Nazionale dei Lincei Istituto Nazionale di Fisica Nucleare SIPS Proceedings of the International Conference “Enrico Fermi and the Universe of Physics” Rome, September 29 – October 2, 2001 2003 ENEA Ente per le Nuove tecnologie, l’Energia e l’Ambiente Lungotevere Thaon di Revel, 76 00196 - Roma ISBN 88-8286-032-9 Honour Committee Rettore dell’Università di Roma “La Sapienza” Rettore dell’Università degli Studi di Roma “Tor Vergata” Rettore della Terza Università degli Studi di Roma Presidente del Consiglio Nazionale delle Ricerche (CNR) Presidente dell’Ente per le Nuove tecnologie, l’Energia e l’Ambiente (ENEA) Presidente dell’Istituto Nazionale di Fisica Nucleare (INFN) Direttore Generale del Consiglio Europeo di Ricerche Nucleari (CERN) Presidente dell’Istituto Nazionale di Fisica della Materia (INFM) Presidente dell’Agenzia Italiana Nucleare (AIN) Presidente della European Physical Society (EPS) Presidente dell’Accademia Nazionale dei Lincei Presidente dell’Accademia Nazionale delle Scienze detta dei XL Presidente della Società Italiana di Fisica (SIF) Presidente della Società Italiana per il Progresso delle Scienze (SIPS) Direttore del Dipartimento di Fisica dell’Università di Roma “La Sapienza” Index 009 A Short -
The Center for Theoretical Physics: the First 50 Years
CTP50 The Center for Theoretical Physics: The First 50 Years Saturday, March 24, 2018 50 SPEAKERS Andrew Childs, Co-Director of the Joint Center for Quantum Information and Computer CTPScience and Professor of Computer Science, University of Maryland Will Detmold, Associate Professor of Physics, Center for Theoretical Physics Henriette Elvang, Professor of Physics, University of Michigan, Ann Arbor Alan Guth, Victor Weisskopf Professor of Physics, Center for Theoretical Physics Daniel Harlow, Assistant Professor of Physics, Center for Theoretical Physics Aram Harrow, Associate Professor of Physics, Center for Theoretical Physics David Kaiser, Germeshausen Professor of the History of Science and Professor of Physics Chung-Pei Ma, J. C. Webb Professor of Astronomy and Physics, University of California, Berkeley Lisa Randall, Frank B. Baird, Jr. Professor of Science, Harvard University Sanjay Reddy, Professor of Physics, Institute for Nuclear Theory, University of Washington Tracy Slatyer, Jerrold Zacharias CD Assistant Professor of Physics, Center for Theoretical Physics Dam Son, University Professor, University of Chicago Jesse Thaler, Associate Professor, Center for Theoretical Physics David Tong, Professor of Theoretical Physics, University of Cambridge, England and Trinity College Fellow Frank Wilczek, Herman Feshbach Professor of Physics, Center for Theoretical Physics and 2004 Nobel Laureate The Center for Theoretical Physics: The First 50 Years 3 50 SCHEDULE 9:00 Introductions and Welcomes: Michael Sipser, Dean of Science; CTP Peter -
Regge Calculus As a Numerical Approach to General Relativity By
Regge Calculus as a Numerical Approach to General Relativity by Parandis Khavari A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Department of Astronomy and Astrophysics University of Toronto Copyright c 2009 by Parandis Khavari Abstract Regge Calculus as a Numerical Approach to General Relativity Parandis Khavari Doctor of Philosophy Department of Astronomy and Astrophysics University of Toronto 2009 A (3+1)-evolutionary method in the framework of Regge Calculus, known as “Paral- lelisable Implicit Evolutionary Scheme”, is analysed and revised so that it accounts for causality. Furthermore, the ambiguities associated with the notion of time in this evolu- tionary scheme are addressed and a solution to resolving such ambiguities is presented. The revised algorithm is then numerically tested and shown to produce the desirable results and indeed to resolve a problem previously faced upon implementing this scheme. An important issue that has been overlooked in “Parallelisable Implicit Evolutionary Scheme” was the restrictions on the choice of edge lengths used to build the space-time lattice as it evolves in time. It is essential to know what inequalities must hold between the edges of a 4-dimensional simplex, used to construct a space-time, so that the geom- etry inside the simplex is Minkowskian. The only known inequality on the Minkowski plane is the “Reverse Triangle Inequality” which holds between the edges of a triangle constructed only from space-like edges. However, a triangle, on the Minkowski plane, can be built from a combination of time-like, space-like or null edges. Part of this thesis is concerned with deriving a number of inequalities that must hold between the edges of mixed triangles. -
The Sums Over Histories Which Specify the Guantum State of the Differ:Ent
Proceedings of the Fourth MARCEL GBOSSTWANN lviEETtNG ON GENERAL RELATIVITY, R. Ruffini (ed') 85 O Elsevier Science Publishers 8.V., l9Bo t : SI}IPLICIAL QUANTUM GRAVITY AND UNRTILY TOPOLOGY JATTTCS B. HARTLE Department of Physics, University of California' Santa Barbara, CA 93106 USA The sums over histories which specify the guantum state of the universe may be given concrete meaning with the methods of the Regge calculus. Sums over geometries may include sums over differ:ent topologies as u'ell as sums cver different metrics oil a given topology. In a simplicial approximation to such a sum, a sum over topologies is a sum over different ways of putting simplices together to make a simplicial geometry while a sum otrer rretrics becOmes an integral over the geome*,ry's ec{gt: lengths. The role whlch decision problems play in several appioaches to summing over topologies 1s discussed and the possibifity that geomeLries less regular than manifolds - unruly topologies - may csntribute significantly to the sum is raised. In two dimensions pseudcrnanifolds are a reasonable candidaLe for unrulY toPologies. I. INTRODUCTION The proposal that the quantum state of the universe is the analog of the ground state for closed cosmologies is a compelling candidate for a l-aw of initial conditions in cosmology.l fan Moss and Jonathan HalliwelI and Stephen Hawking have reviewed elsewhere j-n these proceedings how the correlations and fluctuations in this state can explain the large scale approximate homogeneity, isotropl' and spatial flatness of the universe as well as being consistent with the observed spectrum of density fluctuations. -
The Strong and Weak Senses of Theory-Ladenness of Experimentation: Theory-Driven Versus Exploratory Experiments in the History of High-Energy Particle Physics
[Accepted for Publication in Science in Context] The Strong and Weak Senses of Theory-Ladenness of Experimentation: Theory-Driven versus Exploratory Experiments in the History of High-Energy Particle Physics Koray Karaca University of Wuppertal Interdisciplinary Centre for Science and Technology Studies (IZWT) University of Wuppertal Gaußstr. 20 42119 Wuppertal, Germany [email protected] Argument In the theory-dominated view of scientific experimentation, all relations of theory and experiment are taken on a par; namely, that experiments are performed solely to ascertain the conclusions of scientific theories. As a result, different aspects of experimentation and of the relation of theory to experiment remain undifferentiated. This in turn fosters a notion of theory- ladenness of experimentation (TLE) that is too coarse-grained to accurately describe the relations of theory and experiment in scientific practice. By contrast, in this article, I suggest that TLE should be understood as an umbrella concept that has different senses. To this end, I introduce a three-fold distinction among the theories of high-energy particle physics (HEP) as background theories, model theories and phenomenological models. Drawing on this categorization, I contrast two types of experimentation, namely, “theory-driven” and “exploratory” experiments, and I distinguish between the “weak” and “strong” senses of TLE in the context of scattering experiments from the history of HEP. This distinction enables to identify the exploratory character of the deep-inelastic electron-proton scattering experiments— performed at the Stanford Linear Accelerator Center (SLAC) between the years 1967 and 1973—thereby shedding light on a crucial phase of the history of HEP, namely, the discovery of “scaling”, which was the decisive step towards the construction of quantum chromo-dynamics (QCD) as a gauge theory of strong interactions. -
Introduction to Regge and Wheeler “Stability of a Schwarzschild Singularity”
September 24, 2019 12:14 World Scientific Reprint - 10in x 7in 11643-main page 3 3 Introduction to Regge and Wheeler “Stability of a Schwarzschild Singularity” Kip S. Thorne Theoretical Astrophysics, California Institute of Technology, Pasadena, CA 91125 USA 1. Introduction The paper “Stability of a Schwarzschild Singularity” by Tullio Regge and John Archibald Wheeler1 was the pioneering formulation of the theory of weak (linearized) gravitational perturbations of black holes. This paper is remarkable because black holes were extremely poorly understood in 1957, when it was published, and the very name black hole would not be introduced into physics (by Wheeler) until eleven years later. Over the sixty years since the paper’s publication, it has been a foundation for an enormous edifice of ideas, insights, and quantitative results, including, for example: Proofs that black holes are stable against linear perturbations — both non-spinning • black holes (as treated in this paper) and spinning ones.1–4 Demonstrations that all vacuum perturbations of a black hole, except changes of its • mass and spin, get radiated away as gravitational waves, leaving behind a quiescent black hole described by the Schwarzschild metric (if non-spinning) or the Kerr metric (if spinning).5 This is a dynamical, evolutionary version of Wheeler’s 1970 aphorism “a black hole has no hair”; it explains how the “hair” gets lost. Formulations of the concept of quasinormal modes of a black hole with complex • eigenfrequencies,6 and extensive explorations of quasinormal-mode -
Physics and Mathematics : a Happily Evolving Marriage ?
PUBLICATIONS MATHÉMATIQUES DE L’I.H.É.S. GABRIELE VENEZIANO Physics and mathematics : a happily evolving marriage ? Publications mathématiques de l’I.H.É.S., tome S88 (1998), p. 183-189 <http://www.numdam.org/item?id=PMIHES_1998__S88__183_0> © Publications mathématiques de l’I.H.É.S., 1998, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions géné- rales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou im- pression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ PHYSICS AND MATHEMATICS: A HAPPILY EVOLVING MARRIAGE? by GABRIELE VENEZIANO Abstract. - The interplay of physics and mathematics started affecting my student life some forty years ago, and has remained a personal struggle since. 1. High School Days Forty years ago, when the IHÉS was created, I was in my third year as a high school student in Florence. 1 was doing well in most subjects, typically through hard work, and, with almost no effort, 1 was doing particularly well in maths and physics. These two subjects were taught, in Italian high schools, by the same Professor. Very luckily, my class had been assigned to an excellent teacher whose name 1 still remember: Prof. Liverani. 1 recall very well how he gave me the feeling he loved those two subjects and how he could transmit this love to (some of) us. -
The Birth of String Theory
THE BIRTH OF STRING THEORY String theory is currently the best candidate for a unified theory of all forces and all forms of matter in nature. As such, it has become a focal point for physical and philosophical dis- cussions. This unique book explores the history of the theory’s early stages of development, as told by its main protagonists. The book journeys from the first version of the theory (the so-called Dual Resonance Model) in the late 1960s, as an attempt to describe the physics of strong interactions outside the framework of quantum field theory, to its reinterpretation around the mid-1970s as a quantum theory of gravity unified with the other forces, and its successive developments up to the superstring revolution in 1984. Providing important background information to current debates on the theory, this book is essential reading for students and researchers in physics, as well as for historians and philosophers of science. andrea cappelli is a Director of Research at the Istituto Nazionale di Fisica Nucleare, Florence. His research in theoretical physics deals with exact solutions of quantum field theory in low dimensions and their application to condensed matter and statistical physics. elena castellani is an Associate Professor at the Department of Philosophy, Uni- versity of Florence. Her research work has focussed on such issues as symmetry, physical objects, reductionism and emergence, structuralism and realism. filippo colomo is a Researcher at the Istituto Nazionale di Fisica Nucleare, Florence. His research interests lie in integrable models in statistical mechanics and quantum field theory. paolo di vecchia is a Professor of Theoretical Physics at Nordita, Stockholm, and at the Niels Bohr Institute, Copenhagen. -
Pos(HRMS)078 ∗ [email protected] Speaker
Two unforgettable years with Hector PoS(HRMS)078 Gabriele Veneziano∗ Collège de France, Paris, France and Theory Division, CERN, CH-1211 Geneva 23, Switzerland E-mail: [email protected] .......................... ........................... Quarks, Strings and the Cosmos - Hector Rubinstein Memorial Symposium August 09-11, 2010 AlbaNova (Stockholm) Sweden ∗Speaker. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ Two unforgettable years Gabriele Veneziano 1. Another lucky coincidence As a high school student in Florence I had the luck of being taught by some excellent teachers: Professor Tebaldo Liverani, in particular, was the one who initiated me to loving maths and physics. His preference, he once confessed, went to the former. However, after some hesitation, mine went to the latter as I entered the local University in 1960. Three years later I had to make another choice, this time about which branch of physics to go for. I was about to be "recruited" by the local high-energy experimental group when, just in time, Professor Raoul Gatto moved from Cagliari to Florence and "rescued" me to theoretical physics. PoS(HRMS)078 At the end of 1965 I received my "Laurea" in physics defending a thesis on some applications of the group SU(6)W . Only later I learned that the W in there apparently stood for Weizmann . Working in Florence as one of Gatto’s "gattini" was very stimulating. However, having always lived at home in my family in Florence, I felt the need to enlarge my horizons, both in physics and in life in general. -
Jan/Feb 2015
I NTERNATIONAL J OURNAL OF H IGH -E NERGY P HYSICS CERNCOURIER WELCOME V OLUME 5 5 N UMBER 1 J ANUARY /F EBRUARY 2 0 1 5 CERN Courier – digital edition Welcome to the digital edition of the January/February 2015 issue of CERN Courier. CMS and the The coming year at CERN will see the restart of the LHC for Run 2. As the meticulous preparations for running the machine at a new high energy near their end on all fronts, the LHC experiment collaborations continue LHC Run 1 legacy to glean as much new knowledge as possible from the Run 1 data. Other labs are also working towards a bright future, for example at TRIUMF in Canada, where a new flagship facility for research with rare isotopes is taking shape. To sign up to the new-issue alert, please visit: http://cerncourier.com/cws/sign-up. To subscribe to the magazine, the e-mail new-issue alert, please visit: http://cerncourier.com/cws/how-to-subscribe. TRIUMF TRIBUTE CERN & Canada’s new Emilio Picasso and research facility his enthusiasm SOCIETY EDITOR: CHRISTINE SUTTON, CERN for rare isotopes for physics The thinking behind DIGITAL EDITION CREATED BY JESSE KARJALAINEN/IOP PUBLISHING, UK p26 p19 a new foundation p50 CERNCOURIER www. V OLUME 5 5 N UMBER 1 J AARYN U /F EBRUARY 2 0 1 5 CERN Courier January/February 2015 Contents 4 COMPLETE SOLUTIONS Covering current developments in high-energy Which do you want to engage? physics and related fi elds worldwide CERN Courier is distributed to member-state governments, institutes and laboratories affi liated with CERN, and to their personnel.