The contributions gathered here provide an overview of current research projects and selected software products of the Fraunhofer Institute for Algorithms and Scientific Computing SCAI. They show the wide range of challenges that scientific computing currently faces, the solutions it offers, and its important role in developing applications for industry. Given the exciting field of applied collaborative research and development it discusses, the book will appeal to scientists, practitioners, and students alike. The Fraunhofer Institute for Algorithms and Scientific Computing SCAI combines excellent research and application-oriented development to provide added value for our partners. SCAI develops numerical techniques, parallel algorithms and specialized software tools to support and optimize industrial simulations. Moreover, it implements custom software solutions for production and logistics, and offers calculations on high-performance computers. Its services and products are based on state-of-the-art methods from applied mathematics and information technology.

Density Functional Theory (DFT) has firmly established itself as the workhorse for atomic-level simulations of condensed phases, pure or composite materials and quantum chemical systems. This work offers a rigorous and detailed introduction to the foundations of this theory, up to and including such advanced topics as orbital-dependent functionals as well as both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, the text concentrates on the self-contained presentation of the basics of the most widely used DFT variants: this implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating the strengths and weaknesses of particular approaches or functionals. The structure and content of this book allow a tutorial and modular self-study approach: the reader will find that all concepts of many-body theory which are indispensable for the discussion of DFT - such as the single-particle Green's function or response functions - are introduced step by step, along with the actual DFT material. The same applies to basic notions of solid state theory, such as the Fermi surface of inhomogeneous, interacting systems. In fact, even the language of second quantization is introduced systematically in an Appendix for readers without formal training in many-body theory.

This thesis presents a study of the scalar sector in the standard model (SM), as well as various searches for an extended scalar sector in theories beyond the SM (BSM). The first part of the thesis details the search for an SM Higgs boson decaying to taus, and produced by gluon fusion, vector boson fusion, or associated production with a vector boson, leading to evidence for decays of the Higgs boson to taus. In turn, the second part highlights several searches for an extended scalar sector, with scalar boson decays to taus. In all of the analyses presented, at least one scalar boson decays to a pair of taus. The results draw on data collected by the Compact Muon Solenoid (CMS) detector during proton-proton collisions with a center-of-mass energy of 7 or 8 TeV.

Since the early eighties, Ali Suleyman Ustunelhas beenone of the main contributors to the field of Malliavin calculus. In a workshop held in Paris, June 2010 several prominent researchers gave exciting talks in honor of his 60th birthday. The present volume includes scientific contributions from this workshop.
Probability theory is first and foremost aimed at solving real-life problems containing randomness. Markov processes are one of the key tools for modeling that plays a vital part concerning such problems. Contributions on inventory control, mutation-selection in genetics and public-private partnerships illustrate several applications in this volume. Stochastic differential equations, be they partial or ordinary, also play a key role in stochastic modeling. Two of the contributions analyze examples that share a focus on probabilistic tools, namely stochastic analysis and stochastic calculus. Three other papers are devoted more to the theoretical development of these aspects. The volume addresses graduate students and researchers interested in stochastic analysis and its applications."

This volume contains the proceedings from two closely related workshops: Computational Diffusion MRI (CDMRI 13) and Mathematical Methods from Brain Connectivity (MMBC 13), held under the auspices of the 16th International Conference on Medical Image Computing and Computer Assisted Intervention, which took place in Nagoya, Japan, September 2013.

Inside, readers will find contributions ranging from mathematical foundations and novel methods for the validation of inferring large-scale connectivity from neuroimaging data to the statistical analysis of the data, accelerated methods for data acquisition, and the most recent developments on mathematical diffusion modeling.

This volume offers a valuable starting point for anyone interested in learning computational diffusion MRI and mathematical methods for brain connectivity as well as offers new perspectives and insights on current research challenges for those currently in the field. It will be of interest to researchers and practitioners in computer science, MR physics, and applied mathematics.

"

By the dawn of the new millennium, robotics has undergone a major transformation in scope and dimensions. This expansion has been brought about by the maturity of the field and the advances in its related technologies. From a largely dominant industrial focus, robotics has been rapidly expanding into the challenges of the human world. The new generation of robots is expected to safely and dependably co-habitat with humans in homes, workplaces, and communities, providing support in services, entertainment, education, healthcare, manufacturing, and assistance. Beyond its impact on physical robots, the body of knowledge robotics has produced is revealing a much wider range of applications reaching across diverse research areas and scientific disciplines, such as: biomechanics, haptics, neuros- ences, virtual simulation, animation, surgery, and sensor networks among others. In return, the challenges of the new emerging areas are proving an abundant source of stimulation and insights for the field of robotics. It is indeed at the intersection of disciplines that the most striking advances happen. The goal of the series of Springer Tracts in Advanced Robotics (STAR) is to bring, in a timely fashion, the latest advances and developments in robotics on the basis of their significance and quality. It is our hope that the wider dissemination of research developments will stimulate more exchanges and collaborations among the research community and contribute to further advancement of this rapidly growing field.

These are the proceedings of the 20th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linearor nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems in mind. This is essential for approaching peak floating point performance. There is an increasingly well developed theory whichis having a direct impact on the development and improvements of these algorithms.

This book is based upon lectures presented in the summer of 2009 at the INFN-Laboratori Nazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci. The symposium included such prestigious lecturers as S. Ferrara, G. Dall'Agata, J.F. Morales, J. Simon and M. Trigiante. All lectures were given at a pedagogical, introductory level, which is reflected in the specific "flavor" of this volume. The book also benefits from extensive discussions about, and the related reworking of, the various contributions. It is the fifth volume in a series of books on the general topics of supersymmetry, supergravity, black holes and the attractor mechanism.

This new Handbook addresses the state of the art in the application of operations research models to problems in preventing terrorist attacks, planning and preparing for emergencies, and responding to and recovering from disasters. The purpose of the book is to enlighten policy makers and decision makers about the power of operations research to help organizations plan for and respond to terrorist attacks, natural disasters, and public health emergencies, while at the same time providing researchers with one single source of up-to-date research and applications. The Handbook consists of nine separate chapters: Using Operations Research Methods for Homeland Security Problems Operations Research and Homeland Security: Overview and Case Study of Pandemic Influenza Deployed Security Games for Patrol Planning Interdiction Models and Applications Time Discrepant Shipments in Manifest Data Achieving Realistic Levels of Defensive Hedging Mitigating the Risk of an Anthrax Attack with Medical Countermeasures Service Networks for Public Health Preparedness and Large-scale Disaster Relief Efforts Disaster Response Planning in the Private Sector

The production of heavy quarks in high-energy experiments offers a rich field to study, both experimentally and theoretically. Due to the additional quark mass, the description of these processes in the framework of perturbative QCD is much more demanding than it is for those involving only massless partons. In the last two decades, a large amount of precision data has been collected by the deep inelastic HERA experiment. In order to make full use of these data, a more precise theoretical description of charm quark production in deep inelastic scattering is needed. This work deals with the first calculation of fixed moments of the NNLO heavy flavor corrections to the proton structure function F2 in the limit of a small charm-quark mass. The correct treatment of these terms will allow not only a more precise analysis of the HERA data, but starting from there also a more precise determination of the parton distribution functions and the strong coupling constant, which is an essential input for LHC physics. The complexity of this calculation requires the application and development of technical and mathematical methods, which are also explained here in detail.

Aerobic granular sludge technology will play an important role as an innovative technology alternative to the present activated sludge process in industrial and municipal wastewater treatment in the near future. Intended to fill the gaps in the studies of aerobic granular sludge, this thesis comprehensively investigates the formation, characterization and mathematical modeling of aerobic granular sludge, through integrating the process engineering tools and advanced molecular microbiology. The research results of this thesis contributed significantly to the advance of understanding and optimization of the bacterial granulation processes, the next generation of technology for cost-effective biological wastewater treatment. Dr. Bing-Jie Ni works at Advanced Water Management Centre (AWMC) of The University of Queensland, Australia.

This book is the first monograph providing an introduction to and an overview of numerical methods for the simulation of two-phase incompressible flows. The Navier-Stokes equations describing the fluid dynamics are examined in combination with models for mass and surfactant transport. The book pursues a comprehensive approach: important modeling issues are treated, appropriate weak formulations are derived, level set and finite element discretization techniques are analyzed, efficient iterative solvers are investigated, implementational aspects are considered and the results of numerical experiments are presented. The book is aimed at M Sc and PhD students and other researchers in the fields of Numerical Analysis and Computational Engineering Science interested in the numerical treatment of two-phase incompressible flows.

This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincare, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?, or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories are different in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition. In the second case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds. "

This book is aimed at those readers who already have some knowledge of mathematical methods and have also been introduced to the basic ideas of quantum optics. It should be attractive to students who have already explored one of the more introductory texts such as Loudon's The quantum theory of light (2/e, 1983, OUP) and are seeking to acquire the mathematical skills used in real problems. This book is not primarily about the physics of quantum optics but rather presents the mathematical methods widely used by workers in this field. There is no comparable book which covers either the range or the depth of mathematical techniques.

Mathematical inequalities are essential tools in mathematics, natural science and engineering. This book gives an overview on recent advances. Some generalizations and improvements for the classical and well-known inequalities are described. They will be applied and further developed in many fields. Applications of the inequalities to entropy theory and quantum physics are also included.

A billiard is a dynamical system in which a point particle alternates between free motion and specular reflections fromthe boundaryof a domain."Exterior Billiards" presents billiards in the complement of domains and their applications in aerodynamics and geometrical optics.

This book distinguishes itself from existing literature by presenting billiard dynamics "outside" bounded domains, including scattering, resistance, invisibility and retro-reflection. It begins with an overview of the mathematical notations used throughout the book and a brief review of the main results. Chapters 2 and 3 are focused on problems of minimal resistance and Newton s problem in media with positive temperature. In chapters 4 and 5, scattering of billiards bynonconvex and rough domains is characterized and some related special problems of optimal mass transportation are studied. Applications in aerodynamics are addressed next and problems of invisibility and retro-reflection within the framework of geometric optics conclude the text.

The book will appeal to mathematicians working in dynamical systems and calculus of variations. Specialists working in the areas of applications discussed will also find it useful."

This unique book describes, analyses, and improves various approaches and techniques for the numerical solution of delay differential equations. It includes a list of available codes and also aids the reader in writing his or her own.

This volume reflects "New Trends in Shape Optimization" and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nurnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.

This monograph presents the state of the art in aeroservoelastic (ASE) modeling and analysis and develops a systematic theoretical and computational framework for use by researchers and practicing engineers. It is the first book to focus on the mathematical modeling of structural dynamics, unsteady aerodynamics, and control systems to evolve a generic procedure to be applied for ASE synthesis. Existing robust, nonlinear, and adaptive control methodology is applied and extended to some interesting ASE problems, such as transonic flutter and buffet, post-stall buffet and maneuvers, and flapping flexible wing. The author derives a general aeroservoelastic plant via the finite-element structural dynamic model, unsteady aerodynamic models for various regimes in the frequency domain, and the associated state-space model by rational function approximations. For more advanced models, the full-potential, Euler, and Navier-Stokes methods for treating transonic and separated flows are also briefly addressed. Essential ASE controller design and analysis techniques are introduced to the reader, and an introduction to robust control-law design methods of LQG/LTR and H2/H synthesis is followed by a brief coverage of nonlinear control techniques of describing functions and Lyapunov functions. Practical and realistic aeroservoelastic application examples derived from actual experiments are included throughout. Aeroservoelasiticity fills an important gap in the aerospace engineering literature and will be a valuable guide for graduate students and advanced researchers in aerospace engineering, as well as professional engineers, technicians, and test pilots in the aircraft industry and laboratories.

A partnership between SIAM and COMAP, Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) enables the modeling process to be understood as part of STEM studies and research, and taught as a basic tool for problem solving and logical thinking. GAIMME helps define core competencies to include in student experiences, and provides direction to enhance math modeling education at all levels. A mix of professionals wrote and reviewed to present various levels and perspectives. The GAIMME report is a freely downloadable report from both SIAM and COMAP's websites.

This book gives a general view of sequence analysis, the statistical study of successions of states, events or actions, one of the most promising venues of social science methodology.It includesinnovative contributions on life course studies, transitions into and out of work, contemporaneous and historical careers, time use, residential trajectories and political careers. The approach presented in this book is now central to the life-course perspective and the study of other social processes.

This book promotes the dialogue between approaches to sequence analysis that developed separately, within traditions contrasted in space and disciplines. It includes the latest developments about sequential concepts, coding, atypical datasets and time patterns, optimal matching and alternative algorithms, survey optimization and visualization. Field studies include original sequential material related to parenting in 19th-century Belgium, higher education and work in Finland and Italy, family formation before and after German reunification, French Jews persecuted in occupied France, long-term trends in electoral participation and regime democratization.

Overall the book reassesses the classical uses of sequences as well as it promotes new ways of collecting, formatting, representing and processing them. The introduction provides basic sequential concepts and tools, as well as a history of the method. Chapters are presented in a way that is both accessible to the beginner and informative to the expert."

This book contains selected papers of the 11th OpenFOAM (R) Workshop that was held in Guimaraes, Portugal, June 26 - 30, 2016. The 11th OpenFOAM (R) Workshop had more than 140 technical/scientific presentations and 30 courses, and was attended by circa 300 individuals, representing 180 institutions and 30 countries, from all continents. The OpenFOAM (R) Workshop provided a forum for researchers, industrial users, software developers, consultants and academics working with OpenFOAM (R) technology. The central part of the Workshop was the two-day conference, where presentations and posters on industrial applications and academic research were shown. OpenFOAM (R) (Open Source Field Operation and Manipulation) is a free, open source computational toolbox that has a larger user base across most areas of engineering and science, from both commercial and academic organizations. As a technology, OpenFOAM (R) provides an extensive range of features to solve anything from complex fluid flows involving chemical reactions, turbulence and heat transfer, to solid dynamics and electromagnetics, among several others. Additionally, the OpenFOAM technology offers complete freedom to customize and extend its functionalities.

This work is dedicated to Wassiliy Leontief's concepts of Input-Output Analysis and to the algebraic properties of Piero Sraffa's seminal models described consequently by matrix algebra and the Perron-Frobenius Theorem. Detailed examples and visualizing graphs are presented for applications of various mathematical methods.