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BL
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| Record Number
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864471
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| Main Entry
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International Workshop "Multiscale Models in Mechano and Tumor Biology: Modeling, Homogenization and Applications"(2015 :, Darmstadt, Germany)
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| Title & Author
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Multiscale models in mechano and tumor biology : : modeling, homogenization, and applications /\ Alf Gerisch, Raimondo Penta, Jens Lang, editors.
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| Publication Statement
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Cham, Switzerland :: Springer,, 2018.
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| Series Statement
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Lecture notes in computational science and engineering,; 122
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| Page. NO
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1 online resource
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| ISBN
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3319733710
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: 9783319733715
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9783319733708
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Preface; Contents; List of Contributors; 1 An Introduction to Asymptotic Homogenization; 1.1 Introduction; 1.2 One Dimensional Diffusion Problem; 1.2.1 Basic Set of Assumptions; 1.2.2 The Homogenized Problem; (Sf (B0; (Sf (B1; (Sf (B2; 1.3 Multidimensional Diffusion Problem; (Sf (B0; (Sf (B1; (Sf (B2; 1.4 Porous Media Flow: Homogenization of the Stokes' Problem; 1.4.1 Non-Dimensionalisation; 1.4.2 The Homogenized Problem; (Sf (B0; (Sf (B1; 1.5 Concluding Remarks; References; 2 Asymptotic Homogenization with a Macroscale Variation in the Microscale; 2.1 Introduction; 2.1.1 Literature Review; 2.1.2 Chapter Outline
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2.2 Model Set-Up2.3 Homogenization; 2.3.1 Transforming the Normal; 2.3.2 Homogenization Procedure; 2.3.2.1 The O(1) Problem; 2.3.2.2 The O((Sf (B) Problem; 2.3.2.3 The O((Sf (B2) Problem; 2.3.2.4 The Homogenized Equations; 2.4 Interpreting the Homogenized Problem; Appendix 1; Appendix 2; References; 3 Mathematical Models for Acid-Mediated Tumor Invasion: From Deterministic to Stochastic Approaches; 3.1 Introduction; 3.2 Continuum Mathematical Models: A Synopsis; 3.2.1 Deterministic Approaches; 3.2.2 Stochastic Approaches; 3.3 Multiscale Stochastic Models for Acid-Mediated Tumor Invasion
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3.3.1 Description of the Models3.3.1.1 Microscopic Dynamics: The Intracellular Proton Concentration; 3.3.1.2 Extracellular Proton Concentration; 3.3.1.3 Cell Dynamics on the Macroscale; 3.3.2 Analytical Results; 3.3.3 Simulation Results; 3.3.3.1 Simulations for the SMAMCI Model; 3.3.3.2 Simulations for the SAIG Model; 3.4 Discussion; Appendix; References; 4 Numerical Simulation of a Contractivity Based Multiscale Cancer Invasion Model; 4.1 Introduction; 4.2 Mathematical Model; 4.3 Numerical Method; 4.3.1 Space Discretization; 4.3.2 Time Discretization; 4.3.3 Treatment of the Delay Term
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4.3.4 Choice of the Time Step4.4 Experimental Results; 4.4.1 Description of Experiments; 4.5 Conclusions; References; 5 Modelling Tissue Self-Organization: From Micro to Macro Models; 5.1 Introduction; 5.2 Individual Based Model for Fibers Interacting Through Alignment Interactions; 5.3 Derivation of a Kinetic Model; 5.4 Scaling and Macroscopic Model; 5.5 Conclusion; References; 6 A Multiscale Modeling Approach to Transport of Nano-Constructs in Biological Tissues; 6.1 Biophysics of Cancer; 6.1.1 An Overview of Transport Phenomena in Tumors
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6.2 A Microscale Approach to Transport of Nano-Constructs6.2.1 Microscopic Model; 6.2.1.1 Hydrodynamic Retardations; 6.2.1.2 Driving Forces; 6.2.1.3 Microscopic Geometry; 6.2.2 Upscaling Method; 6.2.3 Numerical Methods; 6.2.4 Numerical Results; 6.2.4.1 Sensitivity Analysis of Microscopic Effects; 6.2.4.2 Nanofluid Motion Around a Cell; 6.2.4.3 Nanofluid Motion into a Pore/Layer; 6.3 A Macroscale Approach to Transport in Vascularized Tissues; 6.3.1 Governing Equations of Flow at the Macroscale; 6.3.2 Governing Equations of Mass Transport at the Macroscale; 6.3.3 Computational Solver
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| Subject
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Multiscale modeling, Congresses.
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| Subject
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Applied mathematics.
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Differential calculus equations.
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Multiscale modeling.
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Numerical analysis.
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SCIENCE-- System Theory.
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TECHNOLOGY ENGINEERING-- Operations Research.
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| Dewey Classification
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003/.3
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| LC Classification
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QA76.9.C65
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| Added Entry
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Gerisch, Alf
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Lang, Jens
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Penta, Raimondo
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