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This volume presents a selection of in-depth studies and state-of-the-art surveys of several challenging topics that are at the forefront of modern applied mathematics, mathematical modeling, and computational science.  These three areas represent the foundation upon which the methodology of mathematical modeling and computational experiment is built as a tool in all areas of applications of mathematics. The articles cover both fundamental and applied research, and provide the reader with state-of-the-art achievements in the development and application of new theories at the interfaces of applied mathematics, modeling, and computational science. The book can serve as a reference on several important current topics in modern applied mathematics and modeling, including random matrix theory with its innovative applications, and dynamic blocking problems. Other important areas covered include: energy stable weighted essentially non-oscillatory schemes with applications in fluid dynamics and aerospace sciences; elliptic curves over finite fields and their applications in cryptography; multiple scale methods coupling network and continuum models and their applications in various areas involving porous media; new and efficient finite difference schemes for hyperbolic equations; statistical geometric  and topological techniques and their applications in the life sciences; optimal control applications combining discrete and continuous features. The material presented in this book aims at fostering interdisciplinary collaborations required to meet the modern challenges of applied mathematics, modeling and computational science. At the same time, the contributions combine rigorous mathematical and computational procedures and examples from a variety of applications ranging from engineering to life sciences, and provide a rich source for graduate student projects.

Computer science -- Mathematics. --- Mathematical models. --- Mathematics. --- Mathematics --- Mathematical models --- Computer science --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Applied Mathematics --- Mathematical Theory --- Mathematics - General --- Computer simulation. --- Computer science. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Informatics --- Models, Mathematical --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Math --- Applied mathematics. --- Engineering mathematics. --- Biomathematics. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Mathematical and Computational Biology. --- Simulation methods --- Science --- Biology --- Engineering --- Engineering analysis --- Mathematical analysis --- Electromechanical analogies --- Model-integrated computing

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This volume gathers selected contributions from the participants of the Banff International Research Station (BIRS) workshop Coupled Mathematical Models for Physical and Biological Nanoscale Systems and their Applications, who explore various aspects of the analysis, modeling and applications of nanoscale systems, with a particular focus on low dimensional nanostructures and coupled mathematical models for their description. Due to the vastness, novelty and complexity of the interfaces between mathematical modeling and nanoscience and nanotechnology, many important areas in these disciplines remain largely unexplored. In their efforts to move forward, multidisciplinary research communities have come to a clear understanding that, along with experimental techniques, mathematical modeling and analysis have become crucial to the study, development and application of systems at the nanoscale. The conference, held at BIRS in autumn 2016, brought together experts from three different communities working in fields where coupled mathematical models for nanoscale and biosystems are especially relevant: mathematicians, physicists (both theorists and experimentalists), and computational scientists, including those dealing with biological nanostructures. Its objectives: summarize the state-of-the-art; identify and prioritize critical problems of major importance that require solutions; analyze existing methodologies; and explore promising approaches to addressing the challenges identified. The contributions offer up-to-date introductions to a range of topics in nano and biosystems, identify important challenges, assess current methodologies and explore promising approaches. As such, this book will benefit researchers in applied mathematics, as well as physicists and biologists interested in coupled mathematical models and their analysis for physical and biological nanoscale systems that concern applications in biotechnology and medicine, quantum information processing and optoelectronics.

Mathematics. --- Mathematical physics. --- Computer mathematics. --- Biomathematics. --- Mathematical Applications in the Physical Sciences. --- Computational Science and Engineering. --- Statistical Physics and Dynamical Systems. --- Physiological, Cellular and Medical Topics. --- Biotechnology --- Nanotechnology --- Mathematical models --- Molecular technology --- Nanoscale technology --- High technology --- Chemical engineering --- Genetic engineering --- Computer science. --- Statistical physics. --- Physiology --- Animal physiology --- Animals --- Biology --- Anatomy --- Physics --- Mathematical statistics --- Informatics --- Science --- Statistical methods --- Computer mathematics --- Electronic data processing --- Mathematics --- Physical mathematics

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The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26–30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics and its areas of applications.

Mathematics. --- Computational Science and Engineering. --- Applications of Mathematics. --- Appl.Mathematics/Computational Methods of Engineering. --- Math Applications in Computer Science. --- Mathematics in the Humanities and Social Sciences. --- Computer science. --- Engineering mathematics. --- Mathématiques --- Informatique --- Mathématiques de l'ingénieur --- Mathematical models -- Congresses. --- Mathematics -- Congresses. --- Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- Mathematical models --- Models, Mathematical --- Math --- Computer science --- Applied mathematics. --- Computer mathematics. --- Social sciences. --- Behavioral sciences --- Human sciences --- Sciences, Social --- Social science --- Social studies --- Civilization --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Engineering --- Engineering analysis --- Mathematical analysis --- Science --- Simulation methods --- Mathematical and Computational Engineering. --- Informatics --- Computer science—Mathematics.

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This book focuses on the recent development of methodologies and computation methods in mathematical and statistical modelling, computational science and applied mathematics. It emphasizes the development of theories and applications, and promotes interdisciplinary endeavour among mathematicians, statisticians, scientists, engineers and researchers from other disciplines. The book provides ideas, methods and tools in mathematical and statistical modelling that have been developed for a wide range of research fields, including medical, health sciences, biology, environmental science, engineering, physics and chemistry, finance, economics and social sciences. It presents original results addressing real-world problems. The contributions are products of a highly successful meeting held in August 2017 on the main campus of Wilfrid Laurier University, in Waterloo, Canada, the International Conference on Applied Mathematics, Modeling and Computational Science (AMMCS-2017). They make this book a valuable resource for readers interested not only in a broader overview of the methods, ideas and tools in mathematical and statistical approaches, but also in how they can attain valuable insights into problems arising in other disciplines.

Mathematics --- Math --- Science --- Computer science. --- Distribution (Probability theory. --- Statistics. --- Computational Science and Engineering. --- Mathematical Modeling and Industrial Mathematics. --- Probability Theory and Stochastic Processes. --- Mathematical and Computational Biology. --- Mathematics in the Humanities and Social Sciences. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Informatics --- Computer mathematics. --- Mathematical models. --- Probabilities. --- Biomathematics. --- Mathematics. --- Social sciences. --- Statistics . --- Behavioral sciences --- Human sciences --- Sciences, Social --- Social science --- Social studies --- Civilization --- Biology --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Models, Mathematical --- Simulation methods --- Computer mathematics --- Electronic data processing