Note: Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden. - Auch als gedr. Ausg. vorhanden , Systemvoraussetzungen: Acrobat reader.

Note: Intro -- Preface -- Contents -- About the Editors -- Relaxation of p-Growth Integral Functionals Under Space-Dependent Differential Constraints -- 1 Introduction -- 2 Preliminary Results -- 3 Proof of Theorem 1 -- References -- Weak Lower Semicontinuity by Means of Anisotropic Parametrized Measures -- 1 Introduction -- 1.1 Basic Notation -- 1.2 Quasiconvex Functions -- 1.3 Young Measures -- 1.4 DiPerna-Majda Measures -- 1.4.1 Definition and Basic Properties -- 2 Anisotropic Parametrized Measures Generated by Pairs of Sequences -- 2.1 Representation of Limits Using Parametrized Measures -- 2.2 Analysis for Couples { (uk,uk)} -- 2.3 Examples -- 3 Applications to Weak Lower Semicontinuity in Sobolev Spaces -- 4 Concluding Remarks -- References -- What Does Rank-One Convexity Have to Do with Viscosity Solutions? -- 1 Introduction -- 2 Non-Negative Polynomials -- 2.1 Hilbert's Theorem -- 3 The Fundamental Lemma -- 4 Some Consequences for Rank-One Convexity -- 5 Proof of Theorem 1 -- References -- On Friedrichs Inequality, Helmholtz Decomposition, Vector Potentials, and the div-curl Lemma -- 1 Introduction -- 1.1 Disclaimer -- 1.2 Applications -- 1.3 An Observation -- 2 Notation -- 3 Friedrichs Inequality -- 4 Helmholtz Decomposition -- 5 Construction of Vector Potentials -- 6 Global div-curl Lemma -- 7 Comments and Generalizations -- References -- Variational Analysis of Nematic Shells -- 1 Introduction: The Model and the Role of the Topology -- 2 Shells of Zero Euler Characteristic -- 2.1 Existence of Minimizers -- 2.2 Existence of Solutions of the Gradient Flow of (1) -- 2.3 Justification of the Energy (1): A Discrete to Continuum Approach -- 3 Shells of Non-Zero Euler Characteristic: Emergence of Defects -- References -- Modeling of Microstructures in a Cosserat Continuum Using Relaxed Energies -- 1 Introduction. , 2 Intergranular Interactions and Counter Rotations -- 3 A Relaxed Variational Model for Granular Materials -- 3.1 Variational Model -- 3.2 Computation of Relaxed Energy Envelope -- 3.2.1 Stationarity Conditions -- 3.2.2 Material Phase with Microstructure in Microrotational Motions (Micromotions) (Phase 1) -- 3.2.3 Material Phase with No Microstructure (Phase 2) -- 3.2.4 Material Phase with Microstructure in Translational Motions (Phase 3) -- 3.2.5 Relaxed Energy -- 3.2.6 Nonlinear Constitutive Relations -- 4 Numerical Results -- 4.1 A Simple Shear Test -- 4.2 A Tension-Compression Test -- 5 Conclusion -- References -- From Nonlinear to Linear Elasticity in a Coupled Rate-Dependent/Independent System for Brittle Delamination -- 1 Introduction -- 2 Our Main Result: Motivation and Statement -- 2.1 The Brittle Delamination System, Its Adhesive Contact Approximation, and the Adhesive-to-Brittle Limit -- 2.2 Our Main Result -- 3 Proof of Theorem 3 -- 3.1 Preliminary Definitions and Results -- 3.2 Construction of the Recovery Sequence and Proof of the Γ-limsup Inequality -- 4 Applications -- 4.1 From Nonlinear to Linear Elasticity in the Brittle Delamination System -- 4.2 The Joint Discrete-to-Continuous and Adhesive-to-Brittle Limit in the Mechanical Force Balance of the Thermoviscoelastic System -- References -- Three Examples Concerning the Interaction of Dry Friction and Oscillations -- 1 Introduction -- 2 Prescribed Oscillatory Friction -- 2.1 Evolutionary Variational Inequalities -- 2.2 A Scalar Hysteresis Operator -- 2.3 The Averaging Result for Oscillatory Friction -- 3 Self-Induced Oscillations in State-Dependent Friction -- 4 A Model for the Rocking Toy Animal -- 4.1 Description of the Mechanical Toy -- 4.2 A Model with Inertia -- 4.3 A Simplified Model Without Translational Inertia -- 4.4 Restriction to Simple Period Motions -- References. , Numerical Approach to a Model for Quasistatic Damage with Spatial BV-Regularization -- 1 The Damage Model, Its Solution Concept, and Our Results -- 2 Setup and Notation -- 3 Numerical Method -- 3.1 Minimization with Respect to z in (5b) -- 3.2 Alternate Minimization (5) -- 4 Existence Result on a Discrete Level -- 5 Numerical Experiments -- 5.1 Membrane with Hole -- 5.2 Notched Square -- 6 Conclusion -- References -- Rigidity Effects for Antiferromagnetic Thin Films: A Prototypical Example -- 1 Introduction -- 2 Analysis of the Thin-Film Limit -- 3 Conclusions -- References -- Limiting Problems for a Nonstandard Viscous Cahn-Hilliard System with Dynamic Boundary Conditions -- 1 Introduction -- 2 Statement of the Problem and Results -- 3 Well-Posedness -- 4 Long-Time Behavior -- References -- On a Cahn-Hilliard-Darcy System for Tumour Growth with Solution Dependent Source Terms -- 1 Introduction -- 2 Assumptions and Main Results -- 3 Dirichlet Boundary Conditions for the Pressure -- 4 Robin Boundary Conditions for the Pressure -- 5 Neumann Boundary Conditions for the Chemical Potential -- References -- Molecular Extended Thermodynamics of a Rarefied Polyatomic Gas -- 1 Continuum and Kinetic Approaches of a Non-Equilibrium Gas -- 2 Extended Thermodynamics of Rarefied Monatomic Gases -- 3 Closure via the Maximum Entropy Principle and Molecular Extended Thermodynamics of Monatomic Gases -- 4 Convergence Problem and Approximation Near an Equilibrium State -- 5 ET Beyond the Monatomic Gas: Polyatomic Gas -- 5.1 ET of Polyatomic Rarefied Gases with Many Moments -- 6 The 6-Moment Case and Non-Linear Closure -- 6.1 Molecular ET6 for a Polytropic Gas -- 6.2 Molecular ET6 for a Non-Polytropic Gas -- 6.3 Closure and Field Equations -- 6.4 Entropy Density and Main Field -- 7 Comparison Between the ET6 Theory and Meixner's Theory -- 8 Qualitative Analysis. , 9 Shock Wave Structure in a Rarefied Polyatomic Gas -- References -- A Comparison of Two Settings for Stochastic Integration with Respect to Lévy Processes in Infinite Dimensions -- 1 Introduction -- 2 Probabilistic Preliminaries -- 2.1 Lévy Processes -- 2.2 Martingales and Quadratic Variation -- 3 Stochastic Integration with Respect to Square-Integrable Lévy Martingales -- 3.1 Square-Integrable Lévy Martingales -- 3.2 Integration with Respect to Square-Integrable Lévy Martingales -- 4 Stochastic Integration with Respect to Poisson Random Measures -- 4.1 Poisson Point Processes -- 4.2 Integration with Respect to Poisson Random Measures -- 5 Comparing Lévy Noise: The Square-Integrable Case -- 5.1 The Lévy-Khinchin Decomposition -- 5.2 Integration with Respect to Compensated Compound Poisson Processes -- 5.3 Summary of the Square-Integrable Case -- 5.4 An Application to Markov Properties -- 6 Comparing Lévy Noise: The Non-Square-Integrable Case -- 6.1 Integration with Respect to a Square-Integrable Compound Poisson Process -- 6.2 Integration with Respect to a Compound Poisson Process -- 6.3 Comparing Two Integrals with Respect to a Compound Poisson Process -- 6.4 Summary of the Non-Square-Integrable Case -- References.

Note: Intro -- Preface -- Abstract -- Contents -- 1 Cell Motility and Locomotion by Shape Control -- 1.1 Introduction -- 1.2 Swimming at Low Reynolds Numbers -- 1.3 Locomotion Principles and Minimal Swimmers -- 1.3.1 Looping in the Space of Shapes: No Looping? No Party! -- 1.3.2 Minimal Swimmers With or Without Directional Control -- 1.3.3 Steering by Modulation of the Actuation Speed -- 1.3.4 Swimming by Lateral Undulations: Optimality of Traveling Waves of Bending -- 1.4 Biological Swimmers -- 1.4.1 Chlamydomonas' Breaststroke -- 1.4.2 Sperm Cells and Flagellar Beat -- 1.5 Euglena Gracilis: A Case Study in Biophysics and a Journey from Biology to Technology -- 1.5.1 Metaboly and Mechanisms for Shape Change, Embodied Intelligence -- 1.5.2 Flagellar Swimming, Helical Trajectories and a Principle for Self-Assembly -- 1.6 Shape Control and Gaussian Morphing -- 1.6.1 Controlling the Shape of Surfaces by Prescribing Their Metric -- 1.6.2 Axisymmetric Surfaces -- 1.6.3 Cylinders from Cylinders -- 1.6.4 Axisymmetric Surfaces with Non-constant Metric -- 1.6.5 Protruding Necks and Localized Bulges -- 1.7 Discussion and Outlook -- References -- 2 Models of Cell Motion and Tissue Growth -- 2.1 Introduction -- 2.2 Bacterial Movement by Run and Tumble -- 2.2.1 Modeling Run and Tumble -- 2.2.2 Existence of Solutions -- 2.2.3 Derivation of the Patlak/Keller-Segel System -- 2.2.4 Modulation Along the Path -- 2.3 Macroscopic Models of Chemotactic Movement -- 2.3.1 Elementary Properties -- 2.3.2 Blow-Up in the Keller-Segel System -- 2.3.3 Keller-Segel System with Prevention of Overcrowding -- 2.3.4 The Flux Limited Keller-Segel System -- 2.3.5 Traveling Bands -- 2.3.6 Instabilities -- 2.4 Compressible Models of Tissue Growth -- 2.4.1 A Simple Model with a Single Type of Cells -- 2.4.1.1 Supersolution with Bounded Support. , 2.4.1.2 Existence of Solutions and a Priori Bounds -- 2.4.1.3 A Variant of Aronson-Bénilan Estimate -- 2.4.2 Single Cell Type Population Model with Nutrient -- 2.4.3 Models with Two Cell Types -- 2.4.4 Two Cell Type Model with Different Mobilities -- 2.4.5 Surface Tension and the Degenerate Cahn-Hilliard Model -- 2.5 Incompressible Models of Tissue Growth -- 2.5.1 Single Cell Type Free Boundary Problem -- 2.5.2 Single Cell Type Model with Nutrient and Free Boundary -- 2.5.3 Two Cell Types Incompressible Model -- 2.5.4 Multiphase Models -- 2.5.4.1 The One Phase Closure -- 2.5.4.2 The Darcy/Stokes Closure -- 2.5.4.3 The Single Pressure Closure -- 2.6 The Incompressible Limit and Stiff Pressure Law -- 2.6.1 Single Cell Type Model, Incompressible Limit -- 2.6.1.1 Weak Formulation of the Hele-Shaw Problem -- 2.6.1.2 The Complementary Relation -- 2.6.1.3 From the Weak Formulation to the Free Boundary Statement -- 2.6.2 Single Cell Type with Nutrient, Incompressible Limit -- 2.6.3 Open Problems -- References -- 3 Segregated Algorithms for the Numerical Simulation of Cardiac Electromechanics in the Left Human Ventricle -- 3.1 Introduction -- 3.2 Mathematical Models -- 3.2.1 Ionic Model and Monodomain Equation -- 3.2.2 Mechanical Activation -- 3.2.3 Passive and Active Mechanics -- 3.2.3.1 Prestress -- 3.2.4 Cardiac Cycle -- 3.3 Space and Time Discretizations -- 3.3.1 Space Discretization -- 3.3.2 Time Discretization -- 3.3.2.1 Discretization of the 0D Fluid Model -- 3.4 Numerical Coupling: Segregated Strategies -- 3.4.1 Fully Monolithic Strategy (IIEIAIMI) -- 3.4.2 Partially Segregated Strategy (IIEIAI)-(MI) -- 3.4.3 Partially Segregated Strategy (ISIESIASI)-(MI) -- 3.4.4 Fully Segregated Strategy (ISI)-(ESI)-(ASI)-(MI) -- 3.5 Numerical Results -- 3.5.1 Preprocessing -- 3.5.2 Benchmark Problem with Idealized Geometry. , 3.5.3 Subject-Specific LV: The Full Heartbeat -- 3.6 Conclusions -- References -- 4 Power-Stroke-Driven Muscle Contraction -- 4.1 Introduction -- 4.2 General Ratchet Model -- 4.3 X-Tilted Ratchet -- 4.3.1 Typical Cycles -- 4.3.2 Force-Velocity Relations and Stochastic Energetics -- 4.4 Y-Tilted Ratchet -- 4.4.1 Typical Cycles -- 4.4.2 Force-Velocity Relations and Stochastic Energetics -- 4.5 XY-Tilted Ratchet -- 4.5.1 Motor Cycles -- 4.5.2 Force-Velocity Relations and Stochastic Energetics -- 4.6 Comparison of the Three Models -- 4.6.1 Soft Device -- 4.6.2 Hard Device -- 4.6.3 Stochastic Energetics -- 4.7 XY-Tilted Ratchet with a Steric Feedback -- 4.7.1 The Model -- 4.7.2 Hysteretic Coupling -- 4.7.3 Non-potential Models -- 4.8 Active Rigidity -- 4.8.1 Macroscopic Problem -- 4.8.2 Mean Field Model -- 4.8.3 Non-dimensionalization -- 4.8.4 Phase Diagrams -- 4.8.5 Zero Temperature Limit -- 4.9 Conclusions -- References.