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Cet ouvrage présente différents modèles discrets en dynamique pour la modélisation de phénomènes mécaniques non linéaires liés au frottement ou à l’impact. Les sollicitations sont exposées dans un cadre déterministe et stochastique. Pour ce dernier, le cas de variétés de configuration euclidienne ou riemannienne est abordé. La difficulté réside dans le type d’équations différentielles non linéaires particulières utilisées. Le cadre théorique ainsi que des schémas numériques sont détaillés pour chaque équation. Trois types de problèmes sont d’abord étudiés dans le cas particulier d’un solide à un degré de liberté : la force de frottement, la loi d’impact en déterministe et le frottement dans un cadre stochastique. Ensuite, de nombreux exemples sont commentés et fournissent, dans un cadre théorique ou applicatif, de nombreux modèles accompagnés de leurs schémas numériques. Des rappels théoriques fondamentaux sont proposés ainsi que deux preuves complètes de convergence de schémas numériques dans le cas du frottement déterministe ou stochastique.
Des systèmes dynamiques avec petit nombre de degrés de liberté et non-linéarité irrégulière sont étudiés. Les possibilités, mais surtout les limites, d'une superposition modale pour des problèmes linéaires de vibro-impact sont mises en évidence et illustrées sur le choc entre solides rigides. L'effet sur la dynamique d'un système de la présence de discontinuités de type impact ou friction dans les équations du mouvement est discuté à partir de méthodes analytiques, et en particulier la stabilité de réponses périodiques singulières est examinée dans un cadre général à un degré de liberté. D'autre part, les propriétés de convergence de schémas numériques adaptés aux systèmes mécaniques avec contrainte unilatérale sont comparées à la fois par des résultats théoriques donnant des estimations de l'erreur commise, et par des simulations numériques sur un exemple pour lequel une solution de référence est connue. L'étude se focalise notamment sur le comportement de ces différentes méthodes en présence de solutions possédant des suites infinies de chocs. Enfin, deux applications d'ingénierie pouvant être représentées par des modèles à non-linéarité irrégulières sont traitées : la première consiste en l'identification d'un grésillement parasite dans une boîte de vitesses à partir de la prise en compte de jeux mécaniques, et la seconde est consacrée à la mise en place d'une nouvelle modélisation du contact entre un solide indéformable et un sol, intégrant des phénomènes plastiques, destinée à être utilisée pour des simulations déboulements rocheux.
Time series data analysis is increasingly important due to the massive production of such data through the internet of things, the digitalization of healthcare, and the rise of smart cities. As continuous monitoring and data collection become more common, the need for competent time series analysis with both statistical and machine learning techniques will increase. Covering innovations in time series data analysis and use cases from the real world, this practical guide will help you solve the most common data engineering and analysis challengesin time series, using both traditional statistical and modern machine learning techniques. Author Aileen Nielsen offers an accessible, well-rounded introduction to time series in both R and Python that will have data scientists, software engineers, and researchers up and running quickly. You’ll get the guidance you need to confidently: Find and wrangle time series data Undertake exploratory time series data analysis Store temporal data Simulate time series data Generate and select features for a time series Measure error Forecast and classify time series with machine or deep learning Evaluate accuracy and performance
Notes and Reports in Mathematics in Science and Engineering, Volume 3: On the Cauchy Problem focuses on the processes, methodologies, and mathematical approaches to Cauchy problems. The publication first elaborates on evolution equations, Lax-Mizohata theorem, and Cauchy problems in Gevrey class. Discussions focus on fundamental proposition, proof of theorem 4, Gevrey property in t of solutions, basic facts on pseudo-differential, and proof of theorem 3. The book then takes a look at micro-local analysis in Gevrey class, including proof and consequences of theorem 1. The manuscript examines Schrödinger type equations, as well as general view-points on evolution equations. Numerical representations and analyses are provided in the explanation of these type of equations. The book is a valuable reference for mathematicians and researchers interested in the Cauchy problem.
This new, third volume of Cohen-Tannoudji's groundbreaking textbook covers advanced topics of quantum mechanics such as uncorrelated and correlated identical particles, the quantum theory of the electromagnetic field, absorption, emission and scattering of photons by atoms, and quantum entanglement. Written in a didactically unrivalled manner, the textbook explains the fundamental concepts in seven chapters which are elaborated in accompanying complements that provide more detailed discussions, examples and applications. * Completing the success story: the third and final volume of the quantum mechanics textbook written by 1997 Nobel laureate Claude Cohen-Tannoudji and his colleagues Bernard Diu and Franck Laloë * As easily comprehensible as possible: all steps of the physical background and its mathematical representation are spelled out explicitly * Comprehensive: in addition to the fundamentals themselves, the books comes with a wealth of elaborately explained examples and applications Claude Cohen-Tannoudji was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris where he also studied and received his PhD in 1962. In 1973 he became Professor of atomic and molecular physics at the Collège des France. His main research interests were optical pumping, quantum optics and atom-photon interactions. In 1997, Claude Cohen-Tannoudji, together with Steven Chu and William D. Phillips, was awarded the Nobel Prize in Physics for his research on laser cooling and trapping of neutral atoms. Bernard Diu was Professor at the Denis Diderot University (Paris VII). He was engaged in research at the Laboratory of Theoretical Physics and High Energy where his focus was on strong interactions physics and statistical mechanics. Franck Laloë was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris. His first assignment was with the University of Paris VI before he was appointed to the CNRS, the French National Research Center. His research was focused on optical pumping, statistical mechanics of quantum gases, musical acoustics and the foundations of quantum mechanics.
A collection of scholarly essays, Complexity Theory and thePhilosophy of Education provides an accessible theoreticalintroduction to the topic of complexity theory while consideringits broader implications for educational change. Explains the contributions of complexity theory to philosophyof education, curriculum, and educational research Brings together new research by an international team ofcontributors Debates issues ranging from the culture of curriculum, to theimplications of work of key philosophers such as Foucault and JohnDewey for educational change Demonstrates how social scientists and social and educationpolicy makers are drawing on complexity theory to answer questionssuch as: why is it that education decision-makers are so resistantto change; how does change in education happen; and what does ittake to make these changes sustainable? Considers changes in use of complexity theory; developedprincipally in the fields of physics, biology, chemistry, andeconomics, and now being applied more broadly to the socialsciences and to the study of education
Provides a thorough review of properties, durability and use of high performance concrete, derived from recent research and experience. This book contains contributions from the leading French, Canadian and Swiss researchers, designers and material specialists, translated into English for the first time.
Policy concepts; Identification of policy issues; Production systems, supply and demand; Market, price and trade policies; Marketing and distribution systems; Budget and manpower planning; Land tenure police for the livestock sector; Policy analysis report writing and communication; Livestock production and marketing in alphabeta - a case study.