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Multiscale Modeling and Homogenization of Reaction-Diffusion Systems Involving Biological Surfaces

Author: Isabella Graf

Publisher: Logos Verlag Berlin GmbH

Published: 2013

Total Pages: 288

ISBN-13: 3832533974

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Many complex chemical processes are responsible for the proper functioning of the human body. A prime example is the finely structured endoplasmic reticulum, which plays an important role in the metabolisms of human cells. To handle mathematical models that account for this fine structure, periodic homogenization methods are derived and applied. Previous results on homogenization of partial differential equations on finely structured manifolds are extended: Using the periodic unfolding method, diffusion terms on manifolds with different scalings with powers of the homogenization parameter, in particular in case of fast diffusion, are homogenized and are applied in three different biological systems: a linear model of carcinogenesis of cells, a nonlinear extension of the linear carcinogenesis model and a model considering T-cell signaling. Simulations and interpretations of the homogeneous T-cell signaling model give an insight into the related biological mechanisms.

Book Synopsis Multiscale Modeling and Homogenization of Reaction-Diffusion Systems Involving Biological Surfaces by : Isabella Graf

Download or read book Multiscale Modeling and Homogenization of Reaction-Diffusion Systems Involving Biological Surfaces written by Isabella Graf and published by Logos Verlag Berlin GmbH. This book was released on 2013 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many complex chemical processes are responsible for the proper functioning of the human body. A prime example is the finely structured endoplasmic reticulum, which plays an important role in the metabolisms of human cells. To handle mathematical models that account for this fine structure, periodic homogenization methods are derived and applied. Previous results on homogenization of partial differential equations on finely structured manifolds are extended: Using the periodic unfolding method, diffusion terms on manifolds with different scalings with powers of the homogenization parameter, in particular in case of fast diffusion, are homogenized and are applied in three different biological systems: a linear model of carcinogenesis of cells, a nonlinear extension of the linear carcinogenesis model and a model considering T-cell signaling. Simulations and interpretations of the homogeneous T-cell signaling model give an insight into the related biological mechanisms.

Multiscale Modeling and Homogenization of Reaction-diffusion Systems Involving Biological Surfaces

Author:

Publisher:

Published: 2014

Total Pages:

ISBN-13: 9783832591489

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Book Synopsis Multiscale Modeling and Homogenization of Reaction-diffusion Systems Involving Biological Surfaces by :

Download or read book Multiscale Modeling and Homogenization of Reaction-diffusion Systems Involving Biological Surfaces written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Global Regularity and Uniqueness of Solutions in a Surface Growth Model Using Rigorous A-Posteriori Methods

Author: Christian Nolde

Publisher: Logos Verlag Berlin GmbH

Published: 2017-04-20

Total Pages: 88

ISBN-13: 3832544534

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The use of rigorous numerical methods to approach problems which can not be solved using standard methods (yet) has increased signifiantly in recent years. In this book, riogorous a-posteriori methods are used to study the time evolution of a surface growth model, given by a fourth order semi-linear parabolic partial differential equation, where standard methods fail to verify global uniqueness and smoothness of solutions. Based on an arbitrary numerical approximation, a-posteriori error-analysis is applied in order to prevent a blow up analytically. This is a method that in a similar way also applies to the three dimensional Navier-Stokes equations. The main idea consists of energy-estimates for the error between solution and approximation that yields a scalar differential equation controlling the norm of the error with coefficients depending solely on the numerical data. This allows the solution of the differential equation to be bounded using only numerical data. A key technical tool is a rigorous eigenvalue bound for the nonlinear operator linearized around the numerical approximation. The presented method succeeds to show global uniqueness for relatively large initial conditions, which is demonstrated in many numerical examples.

Book Synopsis Global Regularity and Uniqueness of Solutions in a Surface Growth Model Using Rigorous A-Posteriori Methods by : Christian Nolde

Download or read book Global Regularity and Uniqueness of Solutions in a Surface Growth Model Using Rigorous A-Posteriori Methods written by Christian Nolde and published by Logos Verlag Berlin GmbH. This book was released on 2017-04-20 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of rigorous numerical methods to approach problems which can not be solved using standard methods (yet) has increased signifiantly in recent years. In this book, riogorous a-posteriori methods are used to study the time evolution of a surface growth model, given by a fourth order semi-linear parabolic partial differential equation, where standard methods fail to verify global uniqueness and smoothness of solutions. Based on an arbitrary numerical approximation, a-posteriori error-analysis is applied in order to prevent a blow up analytically. This is a method that in a similar way also applies to the three dimensional Navier-Stokes equations. The main idea consists of energy-estimates for the error between solution and approximation that yields a scalar differential equation controlling the norm of the error with coefficients depending solely on the numerical data. This allows the solution of the differential equation to be bounded using only numerical data. A key technical tool is a rigorous eigenvalue bound for the nonlinear operator linearized around the numerical approximation. The presented method succeeds to show global uniqueness for relatively large initial conditions, which is demonstrated in many numerical examples.

Commutability of Gamma-limits in problems with multiple scales

Author: Martin Jesenko

Publisher: Logos Verlag Berlin GmbH

Published: 2017-05-15

Total Pages: 145

ISBN-13: 383254478X

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In the calculus of variations, the goal is to explore extrema of a given integral functional. From origins of the problem, it might be expected that the functional can be adequately simplified by neglecting some small quantities. A way to rigorously justify such an approximation is the Γ-convergence that ensures convergence of corresponding (global) extrema. The main motivation of this work is to investigate properties of doubly indexed integral functionals that Γ-converge for one index fixed. In other words, for two possible approximations we would like to determine whether we may perform them consecutively and if they commute. Our examples are taken from material science with homogenization being one of these two processes. In the first part we are considering a setting related to the elastic regime. However, our assumptions are fairly general and allow for applications in different areas. The second part is devoted to problems in the Hencky plasticity. They are considerably different due to special growth properties of the density.

Book Synopsis Commutability of Gamma-limits in problems with multiple scales by : Martin Jesenko

Download or read book Commutability of Gamma-limits in problems with multiple scales written by Martin Jesenko and published by Logos Verlag Berlin GmbH. This book was released on 2017-05-15 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the calculus of variations, the goal is to explore extrema of a given integral functional. From origins of the problem, it might be expected that the functional can be adequately simplified by neglecting some small quantities. A way to rigorously justify such an approximation is the Γ-convergence that ensures convergence of corresponding (global) extrema. The main motivation of this work is to investigate properties of doubly indexed integral functionals that Γ-converge for one index fixed. In other words, for two possible approximations we would like to determine whether we may perform them consecutively and if they commute. Our examples are taken from material science with homogenization being one of these two processes. In the first part we are considering a setting related to the elastic regime. However, our assumptions are fairly general and allow for applications in different areas. The second part is devoted to problems in the Hencky plasticity. They are considerably different due to special growth properties of the density.

Multiscale Models in Mechano and Tumor Biology

Author: Alf Gerisch

Publisher: Springer

Published: 2018-03-16

Total Pages: 195

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.

Book Synopsis Multiscale Models in Mechano and Tumor Biology by : Alf Gerisch

Download or read book Multiscale Models in Mechano and Tumor Biology written by Alf Gerisch and published by Springer. This book was released on 2018-03-16 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 of Particle Interactions

Author: Michael King

Publisher: John Wiley & Sons

Published: 2010-03-30

Total Pages: 398

ISBN-13: 047057982X

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Discover how the latest computational tools are building our understanding of particle interactions and leading to new applications With this book as their guide, readers will gain a new appreciation of the critical role that particle interactions play in advancing research and developing new applications in the biological sciences, chemical engineering, toxicology, medicine, and manufacturing technology The book explores particles ranging in size from cations to whole cells to tissues and processed materials. A focus on recreating complex, real-world dynamical systems helps readers gain a deeper understanding of cell and tissue mechanics, theoretical aspects of multiscale modeling, and the latest applications in biology and nanotechnology. Following an introductory chapter, Multiscale Modeling of Particle Interactions is divided into two parts: Part I, Applications in Nanotechnology, covers: Multiscale modeling of nanoscale aggregation phenomena: applications in semiconductor materials processing Multiscale modeling of rare events in self-assembled systems Continuum description of atomic sheets Coulombic dragging and mechanical propelling of molecules in nanofluidic systems Molecular dynamics modeling of nanodroplets and nanoparticles Modeling the interactions between compliant microcapsules and patterned surfaces Part II, Applications in Biology, covers: Coarse-grained and multiscale simulations of lipid bilayers Stochastic approach to biochemical kinetics In silico modeling of angiogenesis at multiple scales Large-scale simulation of blood flow in microvessels Molecular to multicellular deformation during adhesion of immune cells under flow Each article was contributed by one or more leading experts and pioneers in the field. All readers, from chemists and biologists to engineers and students, will gain new insights into how the latest tools in computational science can improve our understanding of particle interactions and support the development of novel applications across the broad spectrum of disciplines in biology and nanotechnology.

Book Synopsis Multiscale Modeling of Particle Interactions by : Michael King

Download or read book Multiscale Modeling of Particle Interactions written by Michael King and published by John Wiley & Sons. This book was released on 2010-03-30 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover how the latest computational tools are building our understanding of particle interactions and leading to new applications With this book as their guide, readers will gain a new appreciation of the critical role that particle interactions play in advancing research and developing new applications in the biological sciences, chemical engineering, toxicology, medicine, and manufacturing technology The book explores particles ranging in size from cations to whole cells to tissues and processed materials. A focus on recreating complex, real-world dynamical systems helps readers gain a deeper understanding of cell and tissue mechanics, theoretical aspects of multiscale modeling, and the latest applications in biology and nanotechnology. Following an introductory chapter, Multiscale Modeling of Particle Interactions is divided into two parts: Part I, Applications in Nanotechnology, covers: Multiscale modeling of nanoscale aggregation phenomena: applications in semiconductor materials processing Multiscale modeling of rare events in self-assembled systems Continuum description of atomic sheets Coulombic dragging and mechanical propelling of molecules in nanofluidic systems Molecular dynamics modeling of nanodroplets and nanoparticles Modeling the interactions between compliant microcapsules and patterned surfaces Part II, Applications in Biology, covers: Coarse-grained and multiscale simulations of lipid bilayers Stochastic approach to biochemical kinetics In silico modeling of angiogenesis at multiple scales Large-scale simulation of blood flow in microvessels Molecular to multicellular deformation during adhesion of immune cells under flow Each article was contributed by one or more leading experts and pioneers in the field. All readers, from chemists and biologists to engineers and students, will gain new insights into how the latest tools in computational science can improve our understanding of particle interactions and support the development of novel applications across the broad spectrum of disciplines in biology and nanotechnology.

Multiscale Modeling From Macromolecules to Cell: Opportunities and Challenges of Biomolecular Simulations

Author: Valentina Tozzini

Publisher: Frontiers Media SA

Published: 2020-10-27

Total Pages: 235

ISBN-13: 2889661091

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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.

Book Synopsis Multiscale Modeling From Macromolecules to Cell: Opportunities and Challenges of Biomolecular Simulations by : Valentina Tozzini

Download or read book Multiscale Modeling From Macromolecules to Cell: Opportunities and Challenges of Biomolecular Simulations written by Valentina Tozzini and published by Frontiers Media SA. This book was released on 2020-10-27 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.

Multiscale Modeling of Particle Interactions

Author: Michael King

Publisher: Wiley

Published: 2010-03-22

Total Pages: 388

ISBN-13: 9780470242353

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Book Synopsis Multiscale Modeling of Particle Interactions by : Michael King

Download or read book Multiscale Modeling of Particle Interactions written by Michael King and published by Wiley. This book was released on 2010-03-22 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover how the latest computational tools are building our understanding of particle interactions and leading to new applications With this book as their guide, readers will gain a new appreciation of the critical role that particle interactions play in advancing research and developing new applications in the biological sciences, chemical engineering, toxicology, medicine, and manufacturing technology The book explores particles ranging in size from cations to whole cells to tissues and processed materials. A focus on recreating complex, real-world dynamical systems helps readers gain a deeper understanding of cell and tissue mechanics, theoretical aspects of multiscale modeling, and the latest applications in biology and nanotechnology. Following an introductory chapter, Multiscale Modeling of Particle Interactions is divided into two parts: Part I, Applications in Nanotechnology, covers: Multiscale modeling of nanoscale aggregation phenomena: applications in semiconductor materials processing Multiscale modeling of rare events in self-assembled systems Continuum description of atomic sheets Coulombic dragging and mechanical propelling of molecules in nanofluidic systems Molecular dynamics modeling of nanodroplets and nanoparticles Modeling the interactions between compliant microcapsules and patterned surfaces Part II, Applications in Biology, covers: Coarse-grained and multiscale simulations of lipid bilayers Stochastic approach to biochemical kinetics In silico modeling of angiogenesis at multiple scales Large-scale simulation of blood flow in microvessels Molecular to multicellular deformation during adhesion of immune cells under flow Each article was contributed by one or more leading experts and pioneers in the field. All readers, from chemists and biologists to engineers and students, will gain new insights into how the latest tools in computational science can improve our understanding of particle interactions and support the development of novel applications across the broad spectrum of disciplines in biology and nanotechnology.

Principles of Multiscale Modeling

Author: Weinan E

Publisher: Cambridge University Press

Published: 2011-07-07

Total Pages: 485

ISBN-13: 1107096545

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A systematic discussion of the fundamental principles, written by a leading contributor to the field.

Book Synopsis Principles of Multiscale Modeling by : Weinan E

Download or read book Principles of Multiscale Modeling written by Weinan E and published by Cambridge University Press. This book was released on 2011-07-07 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic discussion of the fundamental principles, written by a leading contributor to the field.

Nonlinear Reaction-Diffusion Systems

Author: Roman Cherniha

Publisher: Springer

Published: 2017-09-19

Total Pages: 160

ISBN-13: 9783319654652

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This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master’s level mathematical biology courses.

Book Synopsis Nonlinear Reaction-Diffusion Systems by : Roman Cherniha

Download or read book Nonlinear Reaction-Diffusion Systems written by Roman Cherniha and published by Springer. This book was released on 2017-09-19 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master’s level mathematical biology courses.