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.

Mathematical Modelling in Motor Neuroscience: State of the Art and Translation to the Clinic, Gaze Orienting Mechanisms and Disease, Volume 249, the latest release in the Progress in Brain Research series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of topics, including Sequential Bayesian updating, Maps and Sensorimotor Transformations for Eye-Head Gaze Shifts: Role of the Midbrain Superior Colliculus, Modeling Gaze Position-Dependent Opsoclonus, Eye Position-Dependent Opsoclonus in Mild Traumatic Brain Injury, Saccades in Parkinson's disease -- hypometric, slow, and maladaptive, Brainstem Neural Circuits for Fixation and Generation of Saccadic Eye Movements, and much more.

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.

The book is centered around the research areas of combinatorics, special functions, and computer algebra. What these research fields share is that many of their outstanding results do not only have applications in Mathematics, but also other disciplines, such as computer science, physics, chemistry, etc. A particular charm of these areas is how they interact and influence one another. For instance, combinatorial or special functions' techniques have motivated the development of new symbolic algorithms. In particular, first proofs of challenging problems in combinatorics and special functions were derived by making essential use of computer algebra. This book addresses these interdisciplinary aspects. Algorithmic aspects are emphasized and the corresponding software packages for concrete problem solving are introduced. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.

Machine learning heavily relies on optimization algorithms to solve its learning models. Constrained problems constitute a major type of optimization problem, and the alternating direction method of multipliers (ADMM) is a commonly used algorithm to solve constrained problems, especially linearly constrained ones. Written by experts in machine learning and optimization, this is the first book providing a state-of-the-art review on ADMM under various scenarios, including deterministic and convex optimization, nonconvex optimization, stochastic optimization, and distributed optimization. Offering a rich blend of ideas, theories and proofs, the book is up-to-date and self-contained. It is an excellent reference book for users who are seeking a relatively universal algorithm for constrained problems. Graduate students or researchers can read it to grasp the frontiers of ADMM in machine learning in a short period of time.

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.

Discover the subject of optimization in a new light with this modern and unique treatment. Includes a thorough exposition of applications and algorithms in sufficient detail for practical use, while providing you with all the necessary background in a self-contained manner. Features a deeper consideration of optimal control, global optimization, optimization under uncertainty, multiobjective optimization, mixed-integer programming and model predictive control. Presents a complete coverage of formulations and instances in modelling where optimization can be applied for quantitative decision-making. As a thorough grounding to the subject, covering everything from basic to advanced concepts and addressing real-life problems faced by modern industry, this is a perfect tool for advanced undergraduate and graduate courses in chemical and biochemical engineering.

This edited volume provides an essential resource for urban morphology, the study of urban forms and structures, offering a much-needed mathematical perspective. Experts on a variety of mathematical modeling techniques provide new insights into specific aspects of the field, such as street networks, sustainability, and urban growth. The chapters collected here make a clear case for the importance of tools and methods to understand, model, and simulate the formation and evolution of cities. The chapters cover a wide variety of topics in urban morphology, and are conveniently organized by their mathematical principles. The first part covers fractals and focuses on how self-similar structures sort themselves out through competition. This is followed by a section on cellular automata, and includes chapters exploring how they generate fractal forms. Networks are the focus of the third part, which includes street networks and other forms as well. Chapters that examine complexity and its relation to urban structures are in part four.The fifth part introduces a variety of other quantitative models that can be used to study urban morphology. In the book's final section, a series of multidisciplinary commentaries offers readers new ways of looking at the relationship between mathematics and urban forms. Being the first book on this topic, Mathematics of Urban Morphology will be an invaluable resource for applied mathematicians and anyone studying urban morphology. Additionally, anyone who is interested in cities from the angle of economics, sociology, architecture, or geography will also find it useful. "This book provides a useful perspective on the state of the art with respect to urban morphology in general and mathematics as tools and frames to disentangle the ideas that pervade arguments about form and function in particular. There is much to absorb in the pages that follow and there are many pointers to ways in which these ideas can be linked to related theories of cities, urban design and urban policy analysis as well as new movements such as the role of computation in cities and the idea of the smart city. Much food for thought. Read on, digest, enjoy." From the foreword by Michael Batty

Features recent trends and advances in the theory and techniques used to accurately measure and model growth Growth Curve Modeling: Theory and Applications features an accessible introduction to growth curve modeling and addresses how to monitor the change in variables over time since there is no one size fits all approach to growth measurement. A review of the requisite mathematics for growth modeling and the statistical techniques needed for estimating growth models are provided, and an overview of popular growth curves, such as linear, logarithmic, reciprocal, logistic, Gompertz, Weibull, negative exponential, and log-logistic, among others, is included. In addition, the book discusses key application areas including economic, plant, population, forest, and firm growth and is suitable as a resource for assessing recent growth modeling trends in the medical field. SAS(R) is utilized throughout to analyze and model growth curves, aiding readers in estimating specialized growth rates and curves. Including derivations of virtually all of the major growth curves and models, Growth Curve Modeling: Theory and Applications also features: Statistical distribution analysis as it pertains to growth modeling Trend estimations Dynamic site equations obtained from growth models Nonlinear regression Yield-density curves Nonlinear mixed effects models for repeated measurements data Growth Curve Modeling: Theory and Applications is an excellent resource for statisticians, public health analysts, biologists, botanists, economists, and demographers who require a modern review of statistical methods for modeling growth curves and analyzing longitudinal data. The book is also useful for upper-undergraduate and graduate courses on growth modeling.

This book presents an introduction to the analysis of general movements in 3D space, especially for movements of the human body. It is based on the lecture notes of a class on 3D Kinematics, which the author has been holding in the Master Degree Program of his home institution, the University of Applied Sciences Upper Austria. The lecture introduces the mathematics underlying the measurement and analysis of 3D movements. The target audience primarily comprises research experts in the field, but the book may also be beneficial for graduate students alike.

As the first book of a three-part series, this book is offered as a tribute to pioneers in vision, such as Bela Julesz, David Marr, King-Sun Fu, Ulf Grenander, and David Mumford. The authors hope to provide foundation and, perhaps more importantly, further inspiration for continued research in vision. This book covers David Marr's paradigm and various underlying statistical models for vision. The mathematical framework herein integrates three regimes of models (low-, mid-, and high-entropy regimes) and provides foundation for research in visual coding, recognition, and cognition. Concepts are first explained for understanding and then supported by findings in psychology and neuroscience, after which they are established by statistical models and associated learning and inference algorithms. A reader will gain a unified, cross-disciplinary view of research in vision and will accrue knowledge spanning from psychology to neuroscience to statistics.

This comprehensive textbook/reference provides an in-depth overview of the key aspects of transportation analysis, with an emphasis on modeling real transportation systems and executing the models. Topics and features: presents comprehensive review questions at the end of each chapter, together with detailed case studies, useful links, references and suggestions for further reading; supplies a variety of teaching support materials at the book's webpage on Springer.com, including a complete set of lecture slides; examines the classification of models used for multimodal transportation systems, and reviews the models and evaluation methods used in transportation planning; explains traffic assignment to road networks, and describes computer simulation integration platforms and their use in the transportation systems sector; provides an overview of transportation simulation tools, and discusses the critical issues in the design, development and use of the simulation models.

Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes. Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.

Dye-Sensitized Solar Cells: Mathematical Modelling and Materials Design and Optimization presents the latest information as edited from leaders in the field. It covers advances in DSSC design, fabrication and mathematical modelling and optimization, providing a comprehensive coverage of various DSSC advances that includes different system scales, from electronic to macroscopic level, and a consolidation of the results with fundamentals. The book is extremely useful as a monograph for graduate students and researchers, but is also a comprehensive, general reference on state-of-the-art techniques in modelling, optimization and design of DSSCs.

This book introduces and develops the mathematical models used to describe crane dynamics, and explores established and emerging control methods employed for industrial cranes. It opens with a general introduction to the design and structure of various crane types including gantry cranes, rotary cranes, and mobile cranes currently being used for material handling processes. Mathematical models describing their dynamics for control purposes are developed via two different modeling approaches: lumped-mass and distributed parameter models. Control strategies applicable to real industrial problems are then discussed, including open-loop control, feedback control, boundary control, and hybrid control strategies. Finally, based on the methods covered in the book, future research directions are proposed for the advancement of crane technologies. This book can be used by graduate students, engineers, and researchers in the material handling industry including those working in warehouses, manufacturing, construction sites, ship building, seaports, container terminals, nuclear power plants, and in offshore engineering.

This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

As the role of the modern engineer is markedly different from that of even a decade ago, the theme of engineering mathematics educa tion (EME) is an important one. The need for mathematical model ling (MM) courses and consideration of the educational impact of computer-based technology environments merit special attention. This book contains the proceeding of the NATO Advanced Research Workshop held on this theme in July 1993. We have left the industrial age behind and have entered the in formation age. Computers and other emerging technologies are penetrating society in depth and gaining a strong influence in de termining how in future society will be organised, while the rapid change of information requires a more qualified work force. This work force is vital to high technology and economic competitive ness in many industrialised countries throughout the world. Within this framework, the quality of EME has become an issue. It is expected that the content of mathematics courses taught in schools of engineering today have to be re-evaluated continuously with regard to computer-based technology and the needs of mod ern information society. The main aim of the workshop was to pro vide a forum for discussion between mathematicians, engineering scientists, mathematics educationalists, and courseware develop ers in the higher education sector and to focus on the issues and problems of the design of more relevant and appropriate MM courses for engineering education."

This book presents the theory and computation of open channel flows, using detailed analytical, numerical and experimental results. The fundamental equations of open channel flows are derived by means of a rigorous vertical integration of the RANS equations for turbulent flow. In turn, the hydrostatic pressure hypothesis, which forms the core of many shallow water hydraulic models, is scrutinized by analyzing its underlying assumptions. The book's main focus is on one-dimensional models, including detailed treatments of unsteady and steady flows. The use of modern shock capturing finite difference and finite volume methods is described in detail, and the quality of solutions is carefully assessed on the basis of analytical and experimental results. The book's unique features include: * Rigorous derivation of the hydrostatic-based shallow water hydraulic models * Detailed treatment of steady open channel flows, including the computation of transcritical flow profiles * General analysis of gate maneuvers as the solution of a Riemann problem * Presents modern shock capturing finite volume methods for the computation of unsteady free surface flows * Introduces readers to movable bed and sediment transport in shallow water models* Includes numerical solutions of shallow water hydraulic models for non-hydrostatic steady and unsteady free surface flows This book is suitable for both undergraduate and graduate level students, given that the theory and numerical methods are progressively introduced starting with the basics. As supporting material, a collection of source codes written in Visual Basic and inserted as macros in Microsoft Excel (R) is available. The theory is implemented step-by-step in the codes, and the resulting programs are used throughout the book to produce the respective solutions.

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.

Introduction to Modeling in Physiology and Medicine, Second Edition, develops a clear understanding of the fundamental principles of good modeling methodology. Sections show how to create valid mathematical models that are fit for a range of purposes. These models are supported by detailed explanation, extensive case studies, examples and applications. This updated edition includes clearer guidance on the mathematical prerequisites needed to achieve the maximum benefit from the material, a greater detail regarding basic approaches to modeling, and discussions on non-linear and stochastic modeling. The range of case study material has been substantially extended, with examples drawn from recent research experience. Key examples include a cellular model of insulin secretion and its extension to the whole-body level, a model of insulin action during a meal/oral glucose tolerance test, a large-scale simulation model of type 1 diabetes and its use in in silico clinical trials and drug trials.

Mathematical Models and Algorithms for Power System Optimization helps readers build a thorough understanding of new technologies and world-class practices developed by the State Grid Corporation of China, the organization responsible for the world's largest power distribution network. This reference covers three areas: power operation planning, electric grid investment and operational planning and power system control. It introduces economic dispatching, generator maintenance scheduling, power flow, optimal load flow, reactive power planning, load frequency control and transient stability, using mathematic models including optimization, dynamic, differential and difference equations.

Amid recent interest in Clifford algebra for dual quaternions as a more suitable method for Computer Graphics than standard matrix algebra, this book presents dual quaternions and their associated Clifford algebras in a new light, accessible to and geared towards the Computer Graphics community. Collating all the associated formulas and theorems in one place, this book provides an extensive and rigorous treatment of dual quaternions, as well as showing how two models of Clifford algebras emerge naturally from the theory of dual quaternions. Each chapter comes complete with a set of exercises to help readers sharpen and practice their knowledge. This book is accessible to anyone with a basic knowledge of quaternion algebra and is of particular use to forward-thinking members of the Computer Graphics community. .

This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.

This book introduces new models based on R-calculus and theories of belief revision for dealing with large and changing data. It extends R-calculus from first-order logic to propositional logic, description logics, modal logic and logic programming, and from minimal change semantics to subset minimal change, pseudo-subformula minimal change and deduction-based minimal change (the last two minimal changes are newly defined). And it proves soundness and completeness theorems with respect to the minimal changes in these logics. To make R-calculus computable, an approximate R-calculus is given which uses finite injury priority method in recursion theory. Moreover, two applications of R-calculus are given to default theory and semantic inheritance networks. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. Also it is very useful for all those who are interested in data, digitization and correctness and consistency of information, in modal logics, non monotonic logics, decidable/undecidable logics, logic programming, description logics, default logics and semantic inheritance networks.

This book presents the best papers from the 2nd International Conference on Mathematical Research for Blockchain Economy (MARBLE) 2020, held in Vilamoura, Portugal. While most blockchain conferences and forums are dedicated to business applications, product development or Initial Coin Offering (ICO) launches, this conference focused on the mathematics behind blockchain to bridge the gap between practice and theory. Blockchain Technology has been considered as the most fundamental and revolutionising invention since the Internet. Every year, thousands of blockchain projects are launched and circulated in the market, and there is a tremendous wealth of blockchain applications, from finance to healthcare, education, media, logistics and more. However, due to theoretical and technical barriers, most of these applications are impractical for use in a real-world business context. The papers in this book reveal the challenges and limitations, such as scalability, latency, privacy and security, and showcase solutions and developments to overcome them.