This book addresses dynamic modelling methodology and analyses of tree-type robotic systems. Such analyses are required to visualize the motion of a system without really building it. The book contains novel treatment of the tree-type systems using concept of kinematic modules and the corresponding Decoupled Natural Orthogonal Complements (DeNOC), unified representation of the multiple-degrees-of freedom-joints, efficient recursive dynamics algorithms, and detailed dynamic analyses of several legged robots. The book will help graduate students, researchers and practicing engineers in applying their knowledge of dynamics for analysis of complex robotic systems. The knowledge contained in the book will help one in virtual testing of robot operation, trajectory planning and control.

This proceedings provides novel concepts and techniques for air traffic management (ATM) and communications, navigation, and surveillance (CNS) systems. The volume consists of selected papers from the 5th ENRI International Workshop on ATM/CNS (EIWAC2017) held in Tokyo in November 2017, the theme of which was "Drafting Future Skies". Included are key topics to realize safer and more efficient skies in the future, linked to the integrated conference theme consisting of long-term visions based on presentations from various fields. The proceedings is dedicated not only to researchers, academicians, and university students, but also to engineers in the industry, air navigation service providers (ANSPs), and regulators of aviation.

Mortality improvements, uncertainty in future mortality trends and the relevant impact on life annuities and pension plans constitute important topics in the field of actuarial mathematics and life insurance techniques. In particular, actuarial calculations concerning pensions, life annuities and other living benefits (provided, for example, by long-term care insurance products and whole life sickness covers) are based on survival probabilities which necessarily extend over a long time horizon. In order to avoid underestimation of the related liabilities, the insurance company (or the pension plan) must adopt an appropriate forecast of future mortality.
Great attention is currently being devoted to the management of life annuity portfolios, both from a theoretical and a practical point of view, because of the growing importance of annuity benefits paid by private pension schemes. In particular, the progressive shift from defined benefit to defined contribution pension schemes has increased the interest in life annuities with a guaranteed annual amount.
This book provides a comprehensive and detailed description of methods for projecting mortality, and an extensive introduction to some important issues concerning longevity risk in the area of life annuities and pension benefits. It relies on research work carried out by the authors, as well as on a wide teaching experience and in CPD (Continuing Professional Development) initiatives. The following topics are dealt with: life annuities in the framework of post-retirement income strategies; the basic mortality model; recent mortality trends that have been experienced; general features of projection models; discussion of stochastic projection models, with numerical illustrations; measuring and managing longevity risk.

Spatial Patterns offers a study of nonlinear higher order model equations that are central to the description and analysis of spatio-temporal pattern formation in the natural sciences. Through a unique combination of results obtained by rigorous mathematical analysis and computational studies, the text exhibits the principal families of solutions, such as kinks, pulses and periodic solutions, and their dependence on critical eigenvalue parameters, and points to a rich structure, much of which still awaits exploration.

The exposition unfolds systematically, first focusing on a single equation to achieve optimal transparency, and then branching out to wider classes of equations. The presentation is based on results from real analysis and the theory of ordinary differential equations.

Key features:

* presentation of a new mathematical method specifically designed for the analysis of multi-bump solutions of reversible systems

* strong emphasis on the global structure of solution branches

* extensive numerical illustrations of complex solutions and their dependence on eigenvalue parameters

* application of the theory to well-known equations in mathematical physics and mechanics, such as the Swift--Hohenberg equation, the nonlinear SchrAdinger equation and the equation for the nonlinearly supported beam

* includes recent original results by the authors

* exercises scattered throughout the text to help illuminate the theory

* many research problems

The book is intended for mathematicians who wish to become acquainted with this new area of partial and ordinary differential equations, for mathematical physicists who wish to learn about the theory developed for aclass of well-known higher order pattern-forming model equations, and for graduate students who are looking for an exciting and promising field of research.

This volume highlights the latest advances, innovations, and applications in the field of sustainable concrete structures, as presented by scientists and engineers at the RILEM International Conference on Numerical Modeling Strategies for Sustainable Concrete Structures (SSCS), held in Marseille, France, on July 4-6, 2022. It demonstrates that numerical methods (finite elements, finite volumes, finite differences) are a relevant response to the challenge to optimize the utilization of cement in concrete constructions while checking that these constructions have a lifespan compatible with the stakes of sustainable development. They are indeed accurate tools for an optimized design of concrete constructions, and allow us to consider all types of complexities: for example, those linked to rheological, physicochemical and mechanical properties of concrete, those linked to the geometry of the structures or even to the environmental boundary conditions. This optimization must also respect constraints of time, money, security, energy, CO2 emissions, and, more generally, life cycle more reliably than the codes and analytical approaches currently used. Numerical methods are, undoubtedly, the best calculation tools at the service of concrete eco-construction. The contributions present traditional and new ideas that will open novel research directions and foster multidisciplinary collaboration between different specialists.

This contributed volume provides an up-to-date overview of the mechanics of granular materials, ranging from sparse media to soils. With chapters exploring state-of-the-art theoretical, experimental, and applied trends in the study of granular matter in various states, readers will be motivated to learn about the current challenges and potential avenues of exploration in this active area of research. Including a variety of perspectives, this volume will be a valuable reference for audiences in a number of fields. Specific topics covered include: X-ray tomography techniques for analyzing sand Evaluation of effective stress in unsaturated soils Hyper-plasticity Wave propagation in granular systems Partly saturated porous media Multi-scale approaches to the dynamics of sparse media Views on Microstructures in Granular Materials is an ideal resource for PhD students and researchers in applied mathematics, solid-state physics, civil engineering, and mechanical engineering.

Inspired by the Research Collaboration Workshop for Women in Mathematical Biology, this volume contains research and review articles that cover topics ranging from models of animal movement to the flow of blood cells in the embryonic heart. Hosted by the National Institute for Mathematics and Biological Synthesis (NIMBioS), the workshop brought together women working in biology and mathematics to form four research groups that encouraged multidisciplinary collaboration and lifetime connections in the STEM field. This volume introduces many of the topics from the workshop, including the aerodynamics of spider ballooning; sleep, circadian rhythms, and pain; blood flow regulation in the kidney; and the effects of antimicrobial therapy on gut microbiota and microbiota and Clostridium difficile. Perfect for students and researchers in mathematics and biology, the papers included in this volume offer an introductory glimpse at recent research in mathematical biology.

This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems). The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and stochastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8. For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.

An authoritative treatment of contaminant transport modeling now significantly revised and expanded

The challenges facing groundwater scientists and engineers today demand expertise in a wide variety of disciplines–geology, hydraulics, geochemistry, geophysics, and biology. As the number of the subdisciplines has increased and as each has become more complex and quantitative, the problem of integrating their concepts and contributions into a coherent overall interpretation has become progressively more difficult. To an increasing degree transport simulation has emerged as an answer to this problem, and the transport model has become a vehicle for integrating the vast amount of field data from a variety of sources and for understanding the relationship of various physical, chemical, and biological processes.

Applied Contaminant Transport Modeling is the first resource designed to provide coverage of the discipline’s basic principles, including the theories behind solute transport in groundwater, common numerical techniques for solving transport equations, and step-by-step guidance on the development and use of field-scale modeling.

The Second Edition incorporates recent advances in contaminant transport theory and simulation techniques, adding the following to the original text:

• An expanded discussion of the role of aquifer heterogeneity in controlling solute transport
• A new section on the dual-domain mass transfer approach as an alternative to the classical advection-dispersion model
• Additional chemical processes and reactions in the discussion of reactive transport
• A discussion of the TVD (total-variation-diminishing) approach to transport solution
• An entirely new Part III containing two chapters on simulation of flow and transport under variable water density and under variable saturation, respectively, and a third chapter on the use of the simulation-optimization approach in remediation system design

Applied Contaminant Transport Modeling, Second Edition remains the premier reference for practicing hydrogeologists, environmental scientists, engineers, and graduate students in the field. In 1998, in recognition of their work on the first edition, the authors were honored with the John Hem Excellence in Science and Engineering Award of the National Ground Water Association.

This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems - i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of "quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".

This book is placed at the interface between string theory and elementary particle physics and shows novel results in the search for a heterotic string vacuum that reproduces those matter particles and interactions observed in our universe. The author provides a systematic classification of potentially realistic heterotic covariant lattice vacua, which possess a lower number of moduli fields when compared to conventional compactification methods, by means of number theoretical methods. These methods, while well known to the mathematics community, have not yet found many applications to physics. They are introduced to the degree necessary to understand the computations carried out throughout this work. Furthermore, explicit covariant lattice models with particularly interesting properties are analyzed in detail. Finally, new light is shed on the relation between covariant lattice models and asymmetric orbifold compactifications, the result being a concrete correspondence between certain types of asymmetric orbifolds and those classified covariant lattices.

Multilevel Modeling Methods with Introductory and Advanced Applications provides a cogent and comprehensive introduction to the area of multilevel modeling for methodological and applied researchers as well as advanced graduate students. The book is designed to be able to serve as a textbook for a one or two semester course in multilevel modeling. The topics of the seventeen chapters range from basic to advanced, yet each chapter is designed to be able to stand alone as an instructional unit on its respective topic, with an emphasis on application and interpretation. In addition to covering foundational topics on the use of multilevel models for organizational and longitudinal research, the book includes chapters on more advanced extensions and applications, such as cross-classified random effects models, non-linear growth models, mixed effects location scale models, logistic, ordinal, and Poisson models, and multilevel mediation. In addition, the volume includes chapters addressing some of the most important design and analytic issues including missing data, power analyses, causal inference, model fit, and measurement issues. Finally, the volume includes chapters addressing special topics such as using large-scale complex sample datasets, and reporting the results of multilevel designs. Each chapter contains a section called Try This!, which poses a structured data problem for the reader. We have linked our book to a website (http://modeling.uconn.edu) containing data for the Try This! section, creating an opportunity for readers to learn by doing. The inclusion of the Try This! problems, data, and sample code eases the burden for instructors, who must continually search for class examples and homework problems. In addition, each chapter provides recommendations for additional methodological and applied readings.

The theory of dynamic games is very rich in nature and very much alive If the reader does not already agree with this statement, I hope he/she will surely do so after having consulted the contents of the current volume. The activities which fall under the heading of 'dynamic games' cannot easily be put into one scientific discipline. On the theoretical side one deals with differential games, difference games (the underlying models are described by differential, respec tively difference equations) and games based on Markov chains, with determin istic and stochastic games, zero-sum and nonzero-sum games, two-player and many-player games - all under various forms of equilibria. On the practical side, one sees applications to economics (stimulated by the recent Nobel prize for economics which went to three prominent scientists in game theory), biology, management science, and engineering. The contents of this volume are primarily based on selected presentations made at the Sixth International Symposium on Dynamic Games and Applica tions, held in St Jovite, Quebec, Canada, 13-15 July 1994. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival technical journals. This conference, as well as its predecessor which was held in Grimentz, 1992, took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. One of the activities of the ISDG is the publication of these Annals. The contributions in this volume have been grouped around five themes."

This book is one of the first to include an extensive discussion of integrated public transport planning. In times of growing urban populations and increasing environmental awareness, the importance of optimizing public transport systems is ever-developing. Three different aspects are presented: line planning, timetabling, and vehicle scheduling. Classically, challenges concerning these three aspects of planning are solved sequentially. Due to their high interdependence, the author presents a clear and detailed analysis of innovative, integrated models with accompanied numerical experiments performed to assess, and often support, the benefits of integration. The book will appeal to a wide readership ranging from graduate students to researchers.

This textbook provides the tools for a modern post-graduate introductory course on system reliability theory. It focuses on probabilistic aspects of the theory, including recent results based on signatures, stochastic orders, aging classes, copulas and distortion (or aggregation) functions. The reader requires on an introductory knowledge on probability theory and mathematics. The book serves both for graduate students in mathematics and for engineering students in various disciplines as well as students learning survival analysis, network reliability or simple game theory. Included also are brief introductions to the basic aspects of lifetime modelling, stochastic comparisons, aging classes, mixtures and copula theory. The book develops this knowledge with worked examples and supplies code for the program R so that students can explore its lessons and techniques.

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master's-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schroedinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

This book presents the latest advances in photometric 3D reconstruction. It provides the reader with an overview of the state of the art in the field, and of the latest research into both the theoretical foundations of photometric 3D reconstruction and its practical application in several fields (including security, medicine, cultural heritage and archiving, and engineering). These techniques play a crucial role within such emerging technologies as 3D printing, since they permit the direct conversion of an image into a solid object. The book covers both theoretical analysis and real-world applications, highlighting the importance of deepening interdisciplinary skills, and as such will be of interest to both academic researchers and practitioners from the computer vision and mathematical 3D modeling communities, as well as engineers involved in 3D printing. No prior background is required beyond a general knowledge of classical computer vision models, numerical methods for optimization, and partial differential equations.

Mathematical methods and theories with interdisciplinary applications are presented in this book. The eighteen contributions presented in this Work have been written by eminent scientists; a few papers are based on talks which took place at the International Conference at the Hellenic Artillery School in May 2015. Each paper evaluates possible solutions to long-standing problems such as the solvability of the direct electromagnetic scattering problem, geometric approaches to cyber security, ellipsoid targeting with overlap, non-equilibrium solutions of dynamic networks, measuring ballistic dispersion, elliptic regularity theory for the numerical solution of variational problems, approximation theory for polynomials on the real line and the unit circle, complementarity and variational inequalities in electronics, new two-slope parameterized achievement scalarizing functions for nonlinear multiobjective optimization, and strong and weak convexity of closed sets in a Hilbert space. Graduate students, scientists, engineers and researchers in pure and applied mathematical sciences, operations research, engineering, and cyber security will find the interdisciplinary scientific perspectives useful to their overall understanding and further research.

The book describes currently applied and newly developed advanced numerical methods for wave-induced ship motions and loads. Besides well-established computational methods based on strip theory, panel methods and finite volume methods for unsteady Reynolds-averaged Navier-Stokes equations (URANS), recent advances like a fully nonlinear Rankine panel method, URANS calculations including elastic hull deformations, and an improved method to predict added resistance in waves are explained in detail. Furthermore, statistical methods to assess extreme motions and loads are described both for linear and nonlinear responses in a stationary seaway as well as during long-term ship operations. Results of motions and loads, computed using the various methods, are compared with each other and with results of model experiments. Introductory chapters on fluid dynamics, motions of rigid and elastic ship hulls, numerical methods to compute fluid flows associated with wind waves, and the development and simulation of seaways complement the volume. The book will be of interest to post-graduate students, PhD candidates, as well as engineers in the field of naval architecture, ocean, and marine engineering.

This book is a practical guide to the uncertainty analysis of computer model applications. Used in many areas, such as engineering, ecology and economics, computer models are subject to various uncertainties at the level of model formulations, parameter values and input data. Naturally, it would be advantageous to know the combined effect of these uncertainties on the model results as well as whether the state of knowledge should be improved in order to reduce the uncertainty of the results most effectively. The book supports decision-makers, model developers and users in their argumentation for an uncertainty analysis and assists them in the interpretation of the analysis results.

Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games. The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book. Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available

This text, based on the author's teaching at Ecole Polytechnique, introduces the reader to the world of mathematical modelling and numerical simulation. Covering the finite difference method; variational formulation of elliptic problems; Sobolev spaces; elliptical problems; the finite element method; Eigenvalue problems; evolution problems; optimality conditions and algorithms and methods of operational research, and including a several exercises throughout, this is an ideal text for advanced undergraduate students and graduates in applied mathematics, engineering, computer science, and the physical sciences.

This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. In light of the recent COVID-19 pandemic, special consideration is given to applications of crowd dynamics to the prevention of the spreading of contagious diseases. Some of the specific topics covered in this volume include: - Impact of physical distancing on the evacuation of crowds- Generalized solutions of opinion dynamics models- Crowd dynamics coupled with models for infectious disease spreading- Optimized strategies for leaders in controlling the dynamics of a crowd Crowd Dynamics, Volume 3 is ideal for mathematicians, engineers, physicists, and other researchers working in the rapidly growing field of modeling and simulation of human crowds.

This book reviews the theory and applications of the normal-mode functions in numerical weather prediction and weather and climate dynamics. The normal-mode functions, the eigensolutions of the linearized primitive equations describing the evolution of atmospheric winds and mass variables, have been used for a long time. They have played an important role in the development of data assimilation schemes and the initialization of numerical weather prediction models. Chapters also present how the normal modes can be applied to many theoretical and numerical problems in the atmospheric sciences, such as equatorial wave dynamics, baroclinic instability, energy transfers, and predictability across scales.

This book provides general guidelines for solving thermal problems in the fields of engineering and natural sciences. Written for a wide audience, from beginner to senior engineers and physicists, it provides a comprehensive framework covering theory and practice and including numerous fundamental and real-world examples. Based on the thermodynamics of various material laws, it focuses on the mathematical structure of the continuum models and their experimental validation. In addition to several examples in renewable energy, it also presents thermal processes in space, and summarizes size-dependent, non-Fourier, and non-Fickian problems, which have increasing practical relevance in, e.g., the semiconductor industry. Lastly, the book discusses the key aspects of numerical methods, particularly highlighting the role of boundary conditions in the modeling process. The book provides readers with a comprehensive toolbox, addressing a wide variety of topics in thermal modeling, from constructing material laws to designing advanced power plants and engineering systems.