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Meshfree Methods for Partial Differential Equations VI
Meshfree methods are a modern alternative to classical mesh-based discretization techniques such as finite differences or finite element methods. Especially in a time-dependent setting or in the treatment of problems with strongly singular solutions their independence of a mesh makes these methods highly attractive. This volume collects selected papers presented at the Sixth International Workshop on Meshfree Methods held in Bonn, Germany in October 2011. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering.
The Brain-bladder Axis in Tissue Growth and Remodelling
Applying the general deterministic approach of systems computational biology, the monograph considers questions related to the biomechanics of the human urinary bladder in conjunction with the peripheral and central nervous systems. The step-by-step development of mathematical models of separate structural elements and their assembly into a unique self-regulatory system offers, for the first time, a holistic overview and allows the investigation of the dynamics of the lower urinary tract system at its hierarchical levels. This book provides a coherent description and explanation for intertwined intracellular pathways in terms of spatiotemporal, whole body, tractable representations which are supported by numerous computational simulations.
Handbook of Peridynamic Modeling
This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a reformulation of continuum mechanics based on integration of interactions rather than spatial differentiation of displacements. The book extends the classical theory of continuum mechanics to allow unguided modeling of crack propagation/fracture in brittle, quasi-brittle, and ductile materials; autonomous transition from continuous damage/fragmentation to fracture; modeling of long-range forces within a continuous body; and multiscale coupling in a consistent mathematical framework.
The Mathematics and Mechanics of Biological Growth
This monograph presents a general mathematical theory for biological growth. It provides both a conceptual and a technical foundation for the understanding and analysis of problems arising in biology and physiology. The theory and methods are illustrated on a wide range of examples and applications. A process of extreme complexity, growth plays a fundamental role in many biological processes and is considered to be the hallmark of life itself. Its description has been one of the fundamental problems of life sciences, but until recently, it has not attracted much attention from mathematicians, physicists, and engineers. The author herein presents the first major technical monograph on the pro...
Biomechanics of the Aorta
Biomechanics of the Aorta: Modelling for Patient Care is a holistic analysis of the aorta towards its biomechanical description. The book addresses topics such as physiology, clinical imaging, tissue and blood flow modeling, along with knowledge that is needed in diagnostics, aortic rupture prediction, assist surgical planning, and more. It encompasses a wide range of topics from the basic sciences (Vascular biology, Continuum mechanics, Image analysis) to clinical applications, as well as describing and presenting computational studies and experimental benches to mimic, understand and propose the best treatment of aortic pathologies. The book begins with an introduction to the fundamental a...
Computer Methods in Biomechanics and Biomedical Engineering
These papers are concerned with new advances and novel solutions in the areas of biofluids, image-guided surgery, tissue engineering and cardovascular mechanics, implant analysis, soft tissue mechanics, bone remodeling and motion analysis. The contents also feature a special section on dental materials, dental adhesives and orthodontic mechanics. This edition contains many examples, tables and figures, and together with the many references, provides the reader with invaluable information on the latest theoretical developments and applications.
