• Mathematics

From Hyperbolic Systems to Kinetic Theory

A Personalized Quest
Author: Luc Tartar
Publisher: Springer Science & Business Media
ISBN: 9783540775621
Category: Mathematics
Page: 282
View: 3359
This fascinating book, penned by Luc Tartar of America’s Carnegie Mellon University, starts from the premise that equations of state are not always effective in continuum mechanics. Tartar relies on H-measures, a tool created for homogenization, to explain some of the weaknesses in the theory. These include looking at the subject from the point of view of quantum mechanics. Here, there are no "particles", so the Boltzmann equation and the second principle, can’t apply.

    • Science

The General Theory of Homogenization

A Personalized Introduction
Author: Luc Tartar
Publisher: Springer Science & Business Media
ISBN: 9783642051951
Category: Science
Page: 471
View: 4910
Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.

    • Mathematics

Numerical Methods for Eulerian and Lagrangian Conservation Laws


Author: Bruno Després
Publisher: Birkhäuser
ISBN: 3319503553
Category: Mathematics
Page: 349
View: 8017
This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems. The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.

    • Mathematics

An Introduction to Sobolev Spaces and Interpolation Spaces


Author: Luc Tartar
Publisher: Springer Science & Business Media
ISBN: 3540714839
Category: Mathematics
Page: 219
View: 7764
After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.

    • Mathematics

An Introduction to Navier-Stokes Equation and Oceanography


Author: Luc Tartar
Publisher: Springer Science & Business Media
ISBN: 3540365451
Category: Mathematics
Page: 247
View: 2908
This text corresponds to a graduate mathematics course taught at Carnegie Mellon University in the spring of 1999. Included are comments added to the lecture notes, a bibliography containing 23 items, and brief biographical information for all scientists mentioned in the text, thus showing that the creation of scientific knowledge is an international enterprise.

    • Mathematics

Numerical Methods for Singularly Perturbed Differential Equations

Convection-Diffusion and Flow Problems
Author: Hans-G. Roos,Martin Stynes,Lutz Tobiska
Publisher: Springer Science & Business Media
ISBN: 3662032066
Category: Mathematics
Page: 352
View: 3909
The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.

    • Computers

Automata, Languages and Programming

29th International Colloquium, ICALP 2002, Malaga, Spain, July 8-13, 2002. Proceedings
Author: Peter Widmayer,Francisco Triguero,Rafael Morales,Matthew Hennessy,Stephan Eidenbenz,Ricardo Conejo
Publisher: Springer
ISBN: 3540454659
Category: Computers
Page: 1072
View: 859

    • Technology & Engineering

Semiconductor Nanocrystal Quantum Dots

Synthesis, Assembly, Spectroscopy and Applications
Author: Andrey Rogach
Publisher: Springer Science & Business Media
ISBN: 3211752374
Category: Technology & Engineering
Page: 372
View: 8828
This is the first book to specifically focus on semiconductor nanocrystals, and address their synthesis and assembly, optical properties and spectroscopy, and potential areas of nanocrystal-based devices. The enormous potential of nanoscience to impact on industrial output is now clear. Over the next two decades, much of the science will transfer into new products and processes. One emerging area where this challenge will be very successfully met is the field of semiconductor nanocrystals. Also known as colloidal quantum dots, their unique properties have attracted much attention in the last twenty years.

    • Mathematics

Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47)


Author: William G. Faris
Publisher: Princeton University Press
ISBN: 1400865255
Category: Mathematics
Page: 256
View: 7333
Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

    • Science

Synchronization

From Simple to Complex
Author: Alexander Balanov,Natalia Janson,Dmitry Postnov,Olga Sosnovtseva
Publisher: Springer Science & Business Media
ISBN: 3540721282
Category: Science
Page: 426
View: 7441
This fascinating work is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from the human heart to neural networks. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating systems can be described in the framework of the general approach, and the authors study this phenomenon as applied to oscillations of different types, such as those with periodic, chaotic, noisy and noise-induced nature.

    • Mathematics

Survival and Event History Analysis

A Process Point of View
Author: Odd Aalen,Ornulf Borgan,Hakon Gjessing
Publisher: Springer Science & Business Media
ISBN: 038768560X
Category: Mathematics
Page: 540
View: 8896
The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics.

    • Science

Mathematical Problems in Semiconductor Physics


Author: P A Marcati,P A Markowich,Roberto Natalini
Publisher: CRC Press
ISBN: 9780582287044
Category: Science
Page: 224
View: 1079
This collection of papers arises from a workshop held at the Istituto per le Applicazioni del Calcolo of the Italian CNR. The first part of the book includes the material covered by three mini-series of lectures at graduate level on some advanced mathematical topics in semiconductor physics. The second part of the book includes more specialized topics, covered by invited speakers in their individual lectures.

    • Mathematics

Partial Differential Relations


Author: Misha Gromov
Publisher: Springer Science & Business Media
ISBN: 3662022672
Category: Mathematics
Page: 363
View: 7338
The classical theory of partial differential equations is rooted in physics, where equations (are assumed to) describe the laws of nature. Law abiding functions, which satisfy such an equation, are very rare in the space of all admissible functions (regardless of a particular topology in a function space). Moreover, some additional (like initial or boundary) conditions often insure the uniqueness of solutions. The existence of these is usually established with some apriori estimates which locate a possible solution in a given function space. We deal in this book with a completely different class of partial differential equations (and more general relations) which arise in differential geometry rather than in physics. Our equations are, for the most part, undetermined (or, at least, behave like those) and their solutions are rather dense in spaces of functions. We solve and classify solutions of these equations by means of direct (and not so direct) geometric constructions. Our exposition is elementary and the proofs of the basic results are selfcontained. However, there is a number of examples and exercises (of variable difficulty), where the treatment of a particular equation requires a certain knowledge of pertinent facts in the surrounding field. The techniques we employ, though quite general, do not cover all geometrically interesting equations. The border of the unexplored territory is marked by a number of open questions throughout the book.

    • Experimental mathematics

Experimental and Computational Mathematics

Selected Writings
Author: Jonathan M. Borwein
Publisher: PSIpress
ISBN: 193563805X
Category: Experimental mathematics
Page: 297
View: 8785
A quiet revolution in mathematical computing and scientific visualization took place in the latter half of the 20th century. These developments have dramatically enhanced modes of mathematical insight and opportunities for "exploratory" computational experimentation. This volume collects the experimental and computational contributions of Jonathan and Peter Borwein over the past quarter century.

    • Mathematics

Mathematical Lives

Protagonists of the Twentieth Century From Hilbert to Wiles
Author: CLAUDIO BARTOCCI,Renato Betti,Angelo Guerraggio,Roberto Lucchetti
Publisher: Springer Science & Business Media
ISBN: 9783642136061
Category: Mathematics
Page: 238
View: 565
Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the social and political problems of their times. What we have sought to document is mathematics’ central position in the culture of our day. Space has been made not only for the great mathematicians but also for literary texts, including contributions by two apparent interlopers, Robert Musil and Raymond Queneau, for whom mathematical concepts represented a valuable tool for resolving the struggle between ‘soul and precision.’

    • Mathematics

Zeta Functions over Zeros of Zeta Functions


Author: André Voros
Publisher: Springer
ISBN: 9783642052026
Category: Mathematics
Page: 163
View: 2214
In this text, the famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions)are analyzed through several zeta functions built over those zeros.

    • Science

The Social and Economic Roots of the Scientific Revolution

Texts by Boris Hessen and Henryk Grossmann
Author: Gideon Freudenthal,Peter McLaughlin
Publisher: Springer Science & Business Media
ISBN: 1402096046
Category: Science
Page: 273
View: 5420
The texts of Boris Hessen and Henryk Grossmann assembled in this volume are important contributions to the historiography of the Scienti?c Revolution and to the methodology of the historiography of science. They are of course also historical documents, not only testifying to Marxist discourse of the time but also illustrating typical European fates in the ?rst half of the twentieth century. Hessen was born a Jewish subject of the Russian Czar in the Ukraine, participated in the October Revolution and was executed in the Soviet Union at the beginning of the purges. Grossmann was born a Jewish subject of the Austro-Hungarian Kaiser in Poland and served as an Austrian of?cer in the First World War; afterwards he was forced to return to Poland and then because of his revolutionary political activities to emigrate to Germany; with the rise to power of the Nazis he had to ?ee to France and then Americawhilehisfamily,whichremainedinEurope,perishedinNaziconcentration camps. Our own acquaintance with the work of these two authors is also indebted to historical context (under incomparably more fortunate circumstances): the revival of Marxist scholarship in Europe in the wake of the student movement and the p- fessionalization of history of science on the Continent. We hope that under the again very different conditions of the early twenty-?rst century these texts will contribute to the further development of a philosophically informed socio-historical approach to the study of science.

    • Science

Bayesian Networks and Decision Graphs


Author: Thomas Dyhre Nielsen,FINN VERNER JENSEN
Publisher: Springer Science & Business Media
ISBN: 9780387682815
Category: Science
Page: 448
View: 4277
This is a brand new edition of an essential work on Bayesian networks and decision graphs. It is an introduction to probabilistic graphical models including Bayesian networks and influence diagrams. The reader is guided through the two types of frameworks with examples and exercises, which also give instruction on how to build these models. Structured in two parts, the first section focuses on probabilistic graphical models, while the second part deals with decision graphs, and in addition to the frameworks described in the previous edition, it also introduces Markov decision process and partially ordered decision problems.

    • Science

Exploring the Cosmic Frontier

Astrophysical Instruments for the 21st Century
Author: A.P. Lobanov,J.A. Zensus,C. Cesarsky,Ph. Diamond
Publisher: Springer Science & Business Media
ISBN: 3540397566
Category: Science
Page: 246
View: 1475
On May 18-21, 2004, the Max-Planck-Society’s Harnack-Haus in Dahlem, Berlin hosted the international symposium "Exploring the Cosmic Frontier: Astrophysical Instruments for the 21st Century". The symposium was dedicated to exploring the complementarity and synergies between different branches of astrophysical research, by presenting and discussing the fundamental scientific problems that will be addressed in the next few decades.

    • Computers

Data-Driven Process Discovery and Analysis

First International Symposium, SIMPDA 2011, Campione D’Italia, Italy, June 29 – July 1, 2011, Revised Selected Papers
Author: Karl Aberer,Ernesto Damiani,Tharam Dillon
Publisher: Springer
ISBN: 364234044X
Category: Computers
Page: 213
View: 2130
This book constitutes the thoroughly refereed proceedings of the First International Symposium on Data-Driven Process Discovery and Analysis held in Campione d'Italia, Italy, in June/July 2011. The 11 revised full papers were carefully selected from 31 submissions. In addition to the thorough review process, the lively discussions at the event itself also helped the authors to improve their papers and to foster interesting extensions. The selected papers cover a wide range of topics spanning from theoretical issues related to process representation to practical experience in process discovery and analysis.