The goal of the Entropy and the Quantum schools has been to introduce young researchers to some of the exciting current topics in mathematical physics. These topics often involve analytic techniques ...that can easily be understood with a dose of physical intuition. In March of 2010, four beautiful lectures were delivered on the campus of the University of Arizona. They included Isoperimetric Inequalities for Eigenvalues of the Laplacian by Rafael Benguria, Universality of Wigner Random Matrices by Laszlo Erdos, Kinetic Theory and the Kac Master Equation by Michael Loss, and Localization in Disordered Media by Gunter Stolz. Additionally, there were talks by other senior scientists and a number of interesting presentations by junior participants. The range of the subjects and the enthusiasm of the young speakers are testimony to the great vitality of this field, and the lecture notes in this volume reflect well the diversity of this school.
The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial ...data of size $\epsilon \leq c_0\mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t \rightarrow \infty $. For times $t \gtrsim \mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of "2.5 dimensional" streamwise-independent solutions referred to as streaks.
Engineering Damage Mechanics is deliberately oriented toward applications of Continuum Damage Mechanics to failures of mechanical and civil engineering components in ductile, creep, fatigue and ...brittle conditions depending upon the thermomechanical loading and the materials: metals and alloys, polymers, elastomers, composites, concretes. Nevertheless, to help engineers, researchers, beginners or not, the first two chapters are devoted to the main concepts of damage mechanics and to the associated computational tools.
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This monograph covers all important issues of terminal ballistics in a comprehensive way combining experimental data, numerical simulations and analytical modeling. It uses a unique approach to ...numerical simulations as sensitivity measure for the major physical parameters.In the first chapter, the book includes necessary details about the experimental equipment which are used for ballistic tests. The second chapter covers essential features of the codes which are used in recent years all over the world, the Euler vs. Lagrange schemes, meshing techniques etc. The third chapter, devoted to the penetration mechanics of rigid rods, brings the update of modeling in this field. The fourth chapter deals with plate perforation and the fifth chapter deals with the penetration of shaped charge jets and eroding long rods. The last chapter includes several techniques for the disruption and defeating of the main threats in armor design. Throughout the book the authors demonstrate the advantages of the simulation approach in understanding the basis physics behind the investigated phenomena.
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This volume describes the fundamentals and techniques necessary for Lamb-wave-based damage identification. This damage assessment method offers efficient structural failure detection which lowers ...maintenance costs and increases safety benefits.
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This open access book contains a structured collection of the complete solutions of all essential axisymmetric contact problems. Based on a systematic distinction regarding the type of contact, the ...regime of friction and the contact geometry, a multitude of technically relevant contact problems from mechanical engineering, the automotive industry and medical engineering are discussed. In addition to contact problems between isotropic elastic and viscoelastic media, contact problems between transversal-isotropic elastic materials and functionally graded materials are addressed, too. The optimization of the latter is a focus of current research especially in the fields of actuator technology and biomechanics. The book takes into account adhesive effects which allow access to contact-mechanical questions about micro- and nano-electromechanical systems. Solutions of the contact problems include both the relationships between the macroscopic force, displacement and contact length, as well as the stress and displacement fields at the surface and, if appropriate, within the half-space medium. Solutions are always obtained with the simplest available method - usually with the method of dimensionality reduction (MDR) or approaches which use the solution of the non-adhesive normal contact problem to solve the respective contact problem.
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We have grown accustomed to the idea that scientific theories are embedded in their place and time. But in the case of the development of mathematical physics in eighteenth-century France, the ...relationship was extremely close. In Before Voltaire, J.B. Shank shows that although the publication of Isaac Newton's Principia in 1687 exerted strong influence, the development of calculus-based physics is better understood as an outcome that grew from French culture in general. Before Voltaire explores how Newton's ideas made their way not just through the realm of French science, but into the larger world of society and culture of which Principia was an intertwined part. Shank also details a history of the beginnings of calculus-based mathematical physics that integrates it into the larger intellectual currents in France at the time, including the Battle of the Ancients and the Moderns, the emergence of wider audiences for science, and the role of the newly reorganized Royal Academy of Sciences. The resulting book offers an unprecedented cultural history of one the most important and influential elements of Enlightenment science.
This is the second edition of the valuable reference source for numerical simulations of contact mechanics suitable for many fields. These include civil engineering, car design, aeronautics, metal ...forming, or biomechanics. For this second edition, illustrative simplified examples and new discretisation schemes and adaptive procedures for coupled problems are added. This book is at the cutting edge of an area of significant and growing interest in computational mechanics.
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Topics of this book span the range from spatial and temporal discretization techniques for contact and impact problems with small and finite deformations over investigations on the reliability of ...micromechanical contact models over emerging techniques for rolling contact mechanics to homogenization methods and multi-scale approaches in contact problems. Furthermore, solution algorithms for single- and multi-processor computing environments, enabling methods that span from multi-contact to multi-scale approaches are discussed together with numerical experiments related to soil mechanics using discontinuous deformation analysis.
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This application-oriented book introduces the associations between contact mechanics and friction and with it offers a deeper understanding of tribology. It deals with the associated phenomena of ...contact, adhesion, capillary forces, friction, lubrication, and wear from one consistent viewpoint. The author goes into (1) methods of rough estimation of tribological quantities, (2) methods for analytical calculations which attempt to minimize the necessary complexity, (3) the crossover into numerical simulation methods. With these methods the author conveys a consistent view of tribological processes in various scales of magnitude (from nanotribology to earthquake research).Also, system dynamic aspects of tribological systems, such as squeal and its suppression as well as other types of instabilities and spatial patterns are investigated.This book contains problems and worked solutions for individual chapters in which the reader can apply the theory to practical situations and deepen the understanding of the material.
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