A fast iterative algorithm for near-diagonal eigenvalue problems

We introduce a novel iterative eigenvalue algorithm for near-diagonal matrices termed iterative perturbative theory (IPT). Built upon a "perturbative" partitioning of the matrix into diagonal and off-diagonal parts, IPT computes one or all eigenpairs with a complexity per iteration of one matrix-vector or one matrix-matrix multiplication respectively. Thanks to the high parallelism of these basic linear algebra operations, we obtain excellent performance on multi-core processors and GPUs, with large speed-ups over standard methods (up to $\sim50$x with respect to LAPACK and ARPACK). For matrices which are not close to being diagonal but have well-separated eigenvalues, IPT can be be used to refine low-precision eigenpairs obtained by other methods. We give sufficient conditions for linear convergence and demonstrate performance on dense and sparse test matrices. In a real-world application from quantum chemistry, we find that IPT performs similarly to the Davidson algorithm.Comment: Based on arXiv:2002.1287

Rifting continental : Causes, effets, évolution - Exemple du rift Baïkal

This report for ‘Habilitation à Diriger des Recherches’ presents a summary of my research activity about the Baikal rift which has began ten years ago, when I obtained my present position as Assistant Professor at Villefranche-sur-Mer Observatory (UPMC). Activities concerning the geodynamics of the Ligurian Sea and previous studies in theAndes (Ph. Thesis) are not developped in this report. What I have tried to perform, together with several colleagues, is a multidisciplinary study of the Baikal rift system. This was done in the framework of a collaboration between the Institute of the Earth’s Crust (Irkutsk) and Géosciences Azur (CNRS-UPMC, Nice, France). We attempt to gather several geophysical and geological data (either revised or new) and to interpret them with some caution, in order to determine a realistic picture of the on-going deformation pattern in the Baikal area, and more widely, to better understand the dynamics of the lithospheric deformation in an intracontinental setting. Our main objectives were the following : (1) describe the geometry and rate of active faulting using satellite imagery, field investigations, and seismicity, (2) directly measure crustal deformation and fault motion using GPS geodesy, (3) determine the stress field using earthquake source data, and (4) understand the physical mechanisms at work through numerical modeling. A number of funding agencies made this project possible : INTAS, NATO, the Siberian Branch of the Russian Academy of Science, the Mongolian Academy of Science, the FrenchMinistry for Foreign Affairs, the French National Center for Scientific Research (CNRS), and University Pierre and MarieCurie.Chapter I gives a brief review of the problems that are currently debated about continental rifts and the way I have used and complemented ‘seismo -geology’ for the analysis of causes and effects of continental deformation under extension. Chapter II is a critical review of the deformation pattern in Asia during Tertiary, which aims at situating the Baikal rift in this important tectonic context. Chapter III is an overview of the main results obtained concerning thestructure, evolution and dynamics of the Baikal rift, and puts in perspective the 11 publications reproduced in Annex 2.Finally, Chapter IV briefly opens some perspectives of work.Ce rapport d’Habilitation à Diriger des Recherches présente, outre un compte-rendu détaillé d’activité, un résumé de mon activité de recherche sur le rift Baïkal qui a commencé il y a 10 ans, lors de ma nomination comme Maître de Conférence de l’Université Pierre et Marie Curie à l’Observatoire de Villefranche-sur-Mer. Comme pendant ma thèse, un fil directeur thématique a relié mes différentes activités de recherches : l’extension continentale et ses effets, qu’elle se produise au sein d’une chaîne de montagne liminaire (la Cordillère Blanche au Pérou), dans un paléorift maintenant immergé, le bassin Ligure et ses marges, en contexte d’arrière-arc, ou au cœur d’un continent, le rift Baïkal. Si j’ai choisi de ne présenter que ce dernier, c’est à la fois pour des raisons de temps, et pour éviter une ‘gymnastique’ intellectuelle un peu artificielle : la comparaison entre ces deux derniers objets, par la différence de contexte tectonique et de méthodes d’investigation qu’elle implique, ne me paraît pour l’instant pas assez fructueuse. J’ai voulu plutôt tirer parti du fait qu’un cycle d’étude s’achevait en domaine intracontinental asiatique, avec une confrontation utile entre plusieurs résultats récents (modélisations gravimétriques, mesures GPS et modélisations numériques) et l’analyse plus spécifiquement ‘sismo-géologique’ que j’ai menée. Enfin une autre circonstance m’a incité à agir de la sorte : la soutenance proche de la thèse de doctorat de Nadège Rollet sur le bassin Ligure.Le chapitre I fournit un bref aperçu des problèmes couramment débattus à propos des rifts continentaux actuels, et justifie la démarche générale que j’ai choisie afin de mieux comprendre les causes et les effets de la déformation active en extension en domaine intracontinental : l’utilisation de la « sismo-géologie », au cœur de mon domaine de compétence, dans un cadre élargi par l’apport d’autres approches complémentaires (gravimétrie, géodésie, modélisations numériques). Le Chapitre II est un examen critique du comportement de la lithosphère asiatique au cours du Tertaire, d’après la bibliographie. Cette partie peut surprendre le lecteur dans le cadre de cette Habilitation : elle m’a paru nécessaire pour renforcer la compréhension des processus de déformation observée à l’échelle du rift Baïkal, car le contexte de la collision Inde-Asie et des subductions le long de l’océan Pacifique y joue à l’évidence un rôle primordial. Le Chapitre III donne et discute les principaux résultats obtenus concernant la structure, le comportement thermo-mécanique, l’évolution et la dynamique actuelle du rift Baïkal, en se référant aux 11 publications reproduites en Annexe 2. Finalement, le Chapitre IV ouvre brièvement quelques perspectives d’étude à la suite de ces travaux

A Proposal for a Three Detector Short-Baseline Neutrino Oscillation Program in the Fermilab Booster Neutrino Beam

A Short-Baseline Neutrino (SBN) physics program of three LAr-TPC detectors located along the Booster Neutrino Beam (BNB) at Fermilab is presented. This new SBN Program will deliver a rich and compelling physics opportunity, including the ability to resolve a class of experimental anomalies in neutrino physics and to perform the most sensitive search to date for sterile neutrinos at the eV mass-scale through both appearance and disappearance oscillation channels. Using data sets of 6.6e20 protons on target (P.O.T.) in the LAr1-ND and ICARUS T600 detectors plus 13.2e20 P.O.T. in the MicroBooNE detector, we estimate that a search for muon neutrino to electron neutrino appearance can be performed with ~5 sigma sensitivity for the LSND allowed (99% C.L.) parameter region. In this proposal for the SBN Program, we describe the physics analysis, the conceptual design of the LAr1-ND detector, the design and refurbishment of the T600 detector, the necessary infrastructure required to execute the program, and a possible reconfiguration of the BNB target and horn system to improve its performance for oscillation searches.Comment: 209 pages, 129 figure

Vibration, Control and Stability of Dynamical Systems

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

On some eigenvalue problems for elastic instabilities in tension

It is well known that buckling instabilities occur when elastic solids are subject to compressive stresses. However, this does not preclude the occurrence of instabilities in systems subject to global tensile loads. Such tensile instabilities may be caused by certain discontinuities (geometrical or material) which re-distribute the stresses applied on its boundary, generating local compressive stresses inside the solid. This research deals with the tensile instabilities in elastic solids by using linear bifurcation analysis, which leads to eigenvalue problems. Then the links between mechanics and mathematics in these tensile instabilities/eigen-systems are demonstrated by using a combination of both numerical and asymptotic analyses. Three main problems have been investigated: a hybrid energy method on edge-buckling, the tensile wrinkling of a stretched bi-annular plate, and the tensile instabilities developed in a radially stretched thick cylindrical tube. We start by recording a coordinate-free derivation for Föppl–von Kármán equations and the corresponding bifurcation equations (both weak forms and strong forms with their boundary conditions) based on minimum energy principle. This set of equations is applicable to anisotropic elastic thin plates in any planar geometries, which is then specialised for the bifurcation problem of isotropic elastic plates, and a further case under in-plane loading. In the first main problem, we propose a hybrid energy method which provides an accurate and computationally efficient algorithm for the instability analysis of a class of edge-buckling problems. This algorithm is based on the existing simplest asymptotic approximations and an energy principle (weak form for bifurcation). Fairly accurate and robust approximations can be achieved for both the critical buckling load and mode number even though the simplest asymptotic ansatz is employed. We also explore a number of additional mathematical features that have an intrinsic interest in the context of multi-parameter eigenvalue problems. Then we consider the wrinkling instabilities of a stretched bi-annular plate, which consists of two fully bonded concentric annuli with different mechanical properties. The effects of the mechanical and geometrical parameters on critical wrinkling are studied, using both numerical and asymptotic techniques. It is found that the critical external buckling loading, the wrinkle numbers and the wrinkled-shape can behave completely differently compared with the single-annular case. The influence of discontinuities (the interface between these two annuli) on localised instabilities is also illustrated thoroughly. Finally, a WKB analysis is conducted which provides accurate approximations. In the third problem, we consider the bifurcation of an infinite thick cylindrical tube made of St. Venant–Kirchhoff elastic material, subject to radial tensile loading on both inner and outer walls. In particular, linear Lamé solutions in plane-strain are taken for the pre-bifurcation state, and the bifurcation equations are obtained by using Biot’s incremental bifurcation theory. The bifurcation of this plane-strain problem is completely different from the corresponding plane-stress case. Numerical investigations reveal two main bifurcation modes: a long-wave local deformation around the central hole of the domain, or a material wrinkling-type instability along the same boundary. Strictly speaking, the latter scenario is related to the violation of the Shapiro-Lopatinskij condition in an appropriate traction boundary-value problem. It is further shown that the main features of this material instability mode can be found by using a singular-perturbation strategy