Search

Applied mathematics

This open access volume presents a novel computational framework for understanding how collections of excitable cells work. The key approach in the text is to model excitable tissue by representing the individual cells constituting the tissue. This is in stark contrast to the common approach where homogenization is used to develop models where the cells are not explicitly present. The approach allows for very detailed analysis of small collections of excitable cells, but computational challenges limit the applicability in the presence of large collections of cells.

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.

Dieses Open Access Buch widmet sich dem Problem der Mechanik des Zusammenstoßes zweier makroskopischer Körper. Falls die Dynamik der Körper als Ganzes dies erlaubt, ohne in unüberschaubare Komplexität zu verfallen (in der Regel ist das nur für das reine Normalstoßproblem der Fall), werden allgemeine axialsymmetrische Stoßpartner betrachtet. Für das allgemeine räumliche Stoßproblem wird sich auf den Kontakt von Kugeln beschränkt. Zunächst werden im Buch sehr ausführlich die kontaktmechanischen Grundlagen (Elastizität, Plastizität, Viskoelastizität, Adhäsion, Gradientenmedien) dargestellt und anschließend auf das Stoßproblem übertragen. Mit der Methode der Dimensionsreduktion, der ein eigenes Kapitel gewidmet ist, steht außerdem seit wenigen Jahren ein Werkzeug zu Verfügung, das die sehr effiziente analytische und numerische Behandlung von dynamischen Kontaktproblemen (wie z.B. Stößen) ermöglicht. Den Abschluss des Buch bilden Anwendungsfälle aus verschiedenen Gebieten.

This open access book offers the first comprehensive account of the pan-genome concept and its manifold implications. The realization that the genetic repertoire of a biological species always encompasses more than the genome of each individual is one of the earliest examples of big data in biology that opened biology to the unbounded. The study of genetic variation observed within a species challenges existing views and has profound consequences for our understanding of the fundamental mechanisms underpinning bacterial biology and evolution. The underlying rationale extends well beyond the initial prokaryotic focus to all kingdoms of life and evolves into similar concepts for metagenomes, phenomes and epigenomes. The book’s respective chapters address a range of topics, from the serendipitous emergence of the pan-genome concept and its impacts on the fields of microbiology, vaccinology and antimicrobial resistance, to the study of microbial communities, bioinformatic applications and mathematical models that tie in with complex systems and economic theory. Given its scope, the book will appeal to a broad readership interested in population dynamics, evolutionary biology and genomics.

This open access book contains a structured collection of the complete solutions of all essential axisymmetric contact problems. Based on a systematic distinction regarding the type of contact, the regime of friction and the contact geometry, a multitude of technically relevant contact problems from mechanical engineering, the automotive industry and medical engineering are discussed. In addition to contact problems between isotropic elastic and viscoelastic media, contact problems between transversal-isotropic elastic materials and functionally graded materials are addressed, too. The optimization of the latter is a focus of current research especially in the fields of actuator technology and biomechanics. The book takes into account adhesive effects which allow access to contact-mechanical questions about micro- and nano-electromechanical systems. Solutions of the contact problems include both the relationships between the macroscopic force, displacement and contact length, as well as the stress and displacement fields at the surface and, if appropriate, within the half-space medium. Solutions are always obtained with the simplest available method - usually with the method of dimensionality reduction (MDR) or approaches which use the solution of the non-adhesive normal contact problem to solve the respective contact problem.

Urbanization is a global phenomenon and the book emphasizes that this is not just a social-technological process. It is also a social-ecological process where cities are places for nature, and where cities also are dependent on, and have impacts on, the biosphere at different scales from local to global. The book is a global assessment and delivers four main conclusions: Urban areas are expanding faster than urban populations. Half the increase in urban land across the world over the next 20 years will occur in Asia, with the most extensive change expected to take place in India and China Urban areas modify their local and regional climate through the urban heat island effect and by altering precipitation patterns, which together will have significant impacts on net primary production, ecosystem health, and biodiversity Urban expansion will heavily draw on natural resources, including water, on a global scale, and will often consume prime agricultural land, with knock-on effects on biodiversity and ecosystem services elsewhere Future urban expansion will often occur in areas where the capacity for formal governance is restricted, which will constrain the protection of biodiversity and management of ecosystem services