Multiscale Models in Mechano and Tumor Biology

Multiscale Models in Mechano and Tumor Biology

Author: Alf Gerisch

Publisher: Springer

Published: 2018-03-16

Total Pages: 205

ISBN-13: 3319733710

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This book presents and discusses the state of the art and future perspectives in mathematical modeling and homogenization techniques with the focus on addressing key physiological issues in the context of multiphase healthy and malignant biological materials. The highly interdisciplinary content brings together contributions from scientists with complementary areas of expertise, such as pure and applied mathematicians, engineers, and biophysicists. The book also features the lecture notes from a half-day introductory course on asymptotic homogenization. These notes are suitable for undergraduate mathematics or physics students, while the other chapters are aimed at graduate students and researchers.


Multiscale Modeling in Biomechanics and Mechanobiology

Multiscale Modeling in Biomechanics and Mechanobiology

Author: Suvranu De

Publisher: Springer

Published: 2014-10-10

Total Pages: 287

ISBN-13: 1447165993

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Presenting a state-of-the-art overview of theoretical and computational models that link characteristic biomechanical phenomena, this book provides guidelines and examples for creating multiscale models in representative systems and organisms. It develops the reader's understanding of and intuition for multiscale phenomena in biomechanics and mechanobiology, and introduces a mathematical framework and computational techniques paramount to creating predictive multiscale models. Biomechanics involves the study of the interactions of physical forces with biological systems at all scales – including molecular, cellular, tissue and organ scales. The emerging field of mechanobiology focuses on the way that cells produce and respond to mechanical forces – bridging the science of mechanics with the disciplines of genetics and molecular biology. Linking disparate spatial and temporal scales using computational techniques is emerging as a key concept in investigating some of the complex problems underlying these disciplines. Providing an invaluable field manual for graduate students and researchers of theoretical and computational modelling in biology, this book is also intended for readers interested in biomedical engineering, applied mechanics and mathematical biology.


The Mathematics of Mechanobiology

The Mathematics of Mechanobiology

Author: Antonio DeSimone

Publisher: Springer Nature

Published: 2020-06-29

Total Pages: 217

ISBN-13: 3030451976

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This book presents the state of the art in mathematical research on modelling the mechanics of biological systems – a science at the intersection between biology, mechanics and mathematics known as mechanobiology. The book gathers comprehensive surveys of the most significant areas of mechanobiology: cell motility and locomotion by shape control (Antonio DeSimone); models of cell motion and tissue growth (Benoît Perthame); numerical simulation of cardiac electromechanics (Alfio Quarteroni); and power-stroke-driven muscle contraction (Lev Truskinovsky). Each section is self-contained in terms of the biomechanical background, and the content is accessible to all readers with a basic understanding of differential equations and numerical analysis. The book disentangles the phenomenological complexity of the biomechanical problems, while at the same time addressing the mathematical complexity with invaluable clarity. The book is intended for a wide audience, in particular graduate students and applied mathematicians interested in entering this fascinating field.


Constitutive Modelling of Solid Continua

Constitutive Modelling of Solid Continua

Author: José Merodio

Publisher: Springer Nature

Published: 2019-11-14

Total Pages: 397

ISBN-13: 3030315479

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This volume consists of a collection of chapters by recognized experts to provide a comprehensive fundamental theoretical continuum treatment of constitutive laws used for modelling the mechanical and coupled-field properties of various types of solid materials. It covers the main types of solid material behaviour, including isotropic and anisotropic nonlinear elasticity, implicit theories, viscoelasticity, plasticity, electro- and magneto-mechanical interactions, growth, damage, thermomechanics, poroelasticity, composites and homogenization. The volume provides a general framework for research in a wide range of applications involving the deformation of solid materials. It will be of considerable benefit to both established and early career researchers concerned with fundamental theory in solid mechanics and its applications by collecting diverse material in a single volume. The readership ranges from beginning graduate students to senior researchers in academia and industry.


Leveraging Distortions

Leveraging Distortions

Author: Collin Rice

Publisher: MIT Press

Published: 2021-08-17

Total Pages: 367

ISBN-13: 0262542617

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An examination of how scientists deliberately and justifiably use pervasive distortions of relevant features to explain and understand natural phenomena. A fundamental rule of logic is that in order for an argument to provide good reasons for its conclusion, the premises of the argument must be true. In this book, Collin Rice shows how the practice of science repeatedly, pervasively, and deliberately violates this principle. Rice argues that scientists strategically use distortions that misrepresent relevant features of natural phenomena in order to explain and understand--and that they use these distortions deliberately and justifiably in order to discover truths that would be otherwise inaccessible. Countering the standard emphasis on causation, accurate representation, and decomposition of science into its accurate and inaccurate parts, Rice shows that science's epistemic achievements can still be factive despite their being produced through the use of holistically distorted scientific representations. Indeed, he argues, this distortion is one of the most widely employed and fruitful tools used in scientific theorizing. Marshalling a range of case studies, Rice contends that many explanations in science are noncausal, and he presents an alternate view of explanation that captures the variety of noncausal explanations found across the sciences. He proposes an alternative holistic distortion view of idealized models, connecting it to physicists' concept of a universality class; shows how universality classes can overcome some of the challenges of multiscale modeling; and offers accounts of explanation, idealization, modeling, and understanding.


Multiscale Modeling of Cancer

Multiscale Modeling of Cancer

Author: Vittorio Cristini

Publisher: Cambridge University Press

Published: 2010-09-09

Total Pages: 299

ISBN-13: 1139491504

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Mathematical modeling, analysis and simulation are set to play crucial roles in explaining tumor behavior, and the uncontrolled growth of cancer cells over multiple time and spatial scales. This book, the first to integrate state-of-the-art numerical techniques with experimental data, provides an in-depth assessment of tumor cell modeling at multiple scales. The first part of the text presents a detailed biological background with an examination of single-phase and multi-phase continuum tumor modeling, discrete cell modeling, and hybrid continuum-discrete modeling. In the final two chapters, the authors guide the reader through problem-based illustrations and case studies of brain and breast cancer, to demonstrate the future potential of modeling in cancer research. This book has wide interdisciplinary appeal and is a valuable resource for mathematical biologists, biomedical engineers and clinical cancer research communities wishing to understand this emerging field.


DUNE — The Distributed and Unified Numerics Environment

DUNE — The Distributed and Unified Numerics Environment

Author: Oliver Sander

Publisher: Springer Nature

Published: 2020-12-07

Total Pages: 616

ISBN-13: 3030597024

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The Distributed and Unified Numerics Environment (Dune) is a set of open-source C++ libraries for the implementation of finite element and finite volume methods. Over the last 15 years it has become one of the most commonly used libraries for the implementation of new, efficient simulation methods in science and engineering. Describing the main Dune libraries in detail, this book covers access to core features like grids, shape functions, and linear algebra, but also higher-level topics like function space bases and assemblers. It includes extensive information on programmer interfaces, together with a wealth of completed examples that illustrate how these interfaces are used in practice. After having read the book, readers will be prepared to write their own advanced finite element simulators, tapping the power of Dune to do so.


An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases

An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases

Author: Francis X. Giraldo

Publisher: Springer Nature

Published: 2020-10-30

Total Pages: 572

ISBN-13: 3030550699

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This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.


Exercises in Numerical Linear Algebra and Matrix Factorizations

Exercises in Numerical Linear Algebra and Matrix Factorizations

Author: Tom Lyche

Publisher: Springer Nature

Published: 2020-11-02

Total Pages: 273

ISBN-13: 303059789X

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To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory by solving many exercises, thus obtaining a firmer grasp of its diverse applications. Similarly, from a theoretical perspective, diving into the literature on advanced linear algebra often reveals more and more topics that are deferred to exercises instead of being treated in the main text. As exercises grow more complex and numerous, it becomes increasingly important to provide supporting material and guidelines on how to solve them, supporting students’ learning process. This book provides precisely this type of supporting material for the textbook “Numerical Linear Algebra and Matrix Factorizations,” published as Vol. 22 of Springer’s Texts in Computational Science and Engineering series. Instead of omitting details or merely providing rough outlines, this book offers detailed proofs, and connects the solutions to the corresponding results in the textbook. For the algorithmic exercises the utmost level of detail is provided in the form of MATLAB implementations. Both the textbook and solutions are self-contained. This book and the textbook are of similar length, demonstrating that solutions should not be considered a minor aspect when learning at advanced levels.


BEM-based Finite Element Approaches on Polytopal Meshes

BEM-based Finite Element Approaches on Polytopal Meshes

Author: Steffen Weißer

Publisher: Springer

Published: 2019-07-18

Total Pages: 258

ISBN-13: 303020961X

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This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes. The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments. Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.