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Author Nelson, David R
Title Statistical Mechanics of Membranes and Surfaces
Imprint Singapore : World Scientific Publishing Co Pte Ltd, 2004
©2004
book jacket
Edition 2nd ed
Descript 1 online resource (443 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Series On Innovation And Knowledge Management
Series On Innovation And Knowledge Management
Note Intro -- Preface to the First Edition -- Preface to the Second Edition -- CONTENTS -- Chapter 1 The Statistical Mechanics of Membranes and Interfaces David R. Nelson -- 1. Flat Surfaces -- 1.1. The Roughening Transition -- 1.2. Wetting Transitions -- 2. Crumpled Membranes -- 2.1. Experimental Realizations -- 2.2. Plaquette Surfaces -- 2.3. Perturbation Theory for Tethered Surfaces -- References -- Chapter 2 Interfaces: Fluctuations, Interactions and Related Transitions Michael E. Fisher -- Introduction -- 1. Interface Models, Mean Field Theory, and Wetting -- 1.1. Levels of Theory -- 1.2. Mean Field Theory for Order Parameters -- 1.3. Derivation of Interface Models -- 1.4. External Forces -- 1.5. The Complete Wetting Transition -- 1.6. Wall Effects and the Interface Hamiltonian -- 1.7. Wetting Transitions with Short-range Forces: Mean Field Theory -- 2. Fluctuations and Steric Repulsions -- 2.1. The Wandering Exponent -- 2.2. Interfaces in Two-dimensions: Random Walks -- 2.3. Correlations and Correlation Lengths -- 2.4. The Stiffening or Roughening Transition -- 2.5. Random Media -- 2.6. Fluctuations at Complete Wetting under Long-range Forces -- 2.7. Constrained Interfaces and the Wall-interface Potential -- 2.8. Membranes -- 2.9. Checks of the Wall-interface Potential -- 2.10. Complete Wetting Revisited -- 2.11. Many Walls and the Shape of a Vicinal Crystal Face -- 3. Critical Wetting and Renormalization Groups for Interfaces -- 3.1. Critical Wetting in d = 2 Dimensions -- 3.2. Renormalization Groups for Critical Wetting -- 3.3. The Linearized Functional Renormalization Group -- 3.4. Critical Wetting in d = 3 Dimensions -- 3.5. Test of the d = 3 Critical Wetting Predictions -- 3.6. Approximate Nonlinear Renormalization Group -- 3.7. Numerical Studies -- 3.8. Approach to d = 3: Anomalous Bifurcation -- 3.9. Concluding Remarks -- References
Chapter 3 Equilibrium Statistical Mechanics of Fluctuating Films and Membranes Stanislas Leibler -- Introduction -- 1. Cell Membranes as an Inspiration for Physics -- 1.1. A History of the Discovery of Membrane Structure: A Few Basic Facts about Membranes -- 1.2. Some Physical Properties of Membranes and Amphiphilic Films -- (1) The amphiphilic nature of the constituents. -- (ii) Fluidity of the membranes. -- (iii) The possibility of topology variations -- 2. The Elastic Properties of Fluid Membranes and the Shapes of Vesicles -- 2.1. Curvature Energy and a Simple Elastic Model -- 2.2. Shapes and Fluctuations of Vesicles -- 2.3. Measuring of Elastic Constants -- 3. The Role of Thermal Fluctuations in the Behavior of (Fluid) Membranes and Films -- 3.1. Fluctuations of a Single Fluid Membrane -- 3.2. Perturbation Calculations and the Concept of Crumpling Transition -- 3.3. The Thermodynamic Behavior of an Ensemble of Fluid Membranes -- 4. Unbinding Transitions and the Swelling of Lamellar Phases -- 4.1. Molecular Forces between Membranes -- 4.2. Fluctuations-Induced Interactions -- 4.3. The Competition between Molecular and Fluctuation-Induced Interactions: Functional Renormalization -- 4.4. Complete versus Incomplete Unbinding and the Swelling of Lamellar Phases -- 4.5. The Critical Unbinding Transition -- 5. Membranes with Internal Degrees of Freedom -- 5.1. The "Membranology" of f-Membrane Systems -- 5.2. Curvature Instability in Fluid Membranes -- 5.3. The Polymorphism of Lipid/Water Systems: Different Kinds of f-Membranes -- 5.4. Towards a Mean-Field Theory of Lamellar Phases -- 5.5. Cubic Phases as Crystals of f-Membranes -- References -- Chapter 4 The Physics of Microemulsions and Amphiphilic Monolayers David Andelman -- Abstract -- Acknowledgments -- References -- Chapter 5 Properties of Tethered Surfaces Yacov Kantor -- 1. Introduction
1.1. What is a "Tethered Surface"? -- 1.2. The Tethered Surface as a Polymer -- 2. Phantom Chains and Networks -- 2.1. Linear Polymers -- 2.2. Gaussian Networks and Surfaces -- 2.3. Properties of Phantom Tethered Surfaces -- 3. Excluded Volume Effects -- 3.1. Bounds on the Exponent ν -- 3.2. Analytic Estimates of ν -- 3.3. Monte Carlo Investigation of Tethered Surfaces -- 4. Crumpling Transition in Tethered Surfaces -- 4.1. Very Rigid and Very Flexible Surfaces -- 4.2. Excluded Volume Effects -- 5. Concluding Remarks -- 5.1. Summary and Discussion -- 5.2. What Next? -- References -- Chapter 6 Theory of the Crumpling Transition David R. Nelson -- 1. Normal-Normal Correlation in Liquid Membranes -- 2. Tethered Surfaces with Bending Energy -- 3. Landau Theory of the Crumpling Transition -- 4. Defects and Hexatic Order in Membranes -- References -- Chapter 7 Geometry and Field Theory of Random Surfaces and Membranes Fran¸cois David -- 1. Introduction -- 2. Differential Geometry for Surfaces -- 2.1. Surfaces, Tangent Vectors, Tensors -- 2.2. Geodesics, Parallel Transport, Covariant Derivatives -- 2.3. Integration, Stokes Formula -- 2.4. Extrinsic Curvature -- 2.5. The Riemann Curvature Tensor -- 2.6. The Gauss-Bonnet Theorem -- 2.7. Minimal Surfaces -- 2.8. Conformal (or Isothermal) Coordinates -- 3. Fields on Surfaces -- 3.1. Free Field -- 3.2. The Heat Kernel Regularization -- 3.3. The Conformal Anomaly and the Liouville Action -- 4. Fluid Membranes Models -- 4.1. Continuous Model for Fluid Membranes -- 4.2. Partition Function, Gauge Fixing -- 4.3. Effective Action and the Background Field Method -- 4.4. Renormalization of the Bending and Gaussian Rigidity -- 4.5. Renormalization of the Surface Tension -- 4.6. Effect of Tangential Flows -- 5. Fluid Membranes: Non-Perturbative Issues and the Large d Limit -- 5.1. The Large d Limit
5.2. Planar Configuration -- 5.3. Renormalization Group Behavior -- 5.4. Conformal Fluctuations and Instabilities -- 6. Effective Models for Fluid Membranes and Strings -- 6.1. The Polyakov String Model -- 6.2. The Liouville Model -- 6.3. Discretized Models for Surfaces -- 7. Hexatic Membranes -- 7.1. Hexatic Membranes: Continuous Model -- 7.2. Hexatic Membranes: Renormalization Group Behavior -- 8. Crystalline Membranes -- References -- Chapter 8 Statistical Mechanics of Self-Avoiding Crumpled Manifolds - Part I Bertrand Duplantier -- 1. Continuum Model of Self-Avoiding Manifolds -- 1.1. Edwards Model -- 1.2. Gaussian D-Dimensional Manifold -- 1.3. Dimensional Analysis -- 1.4. Higher Order Interactions -- 1.5. Analytical Continuation in Dimension and Regularization -- 1.6. Extension to Negative Dimensions -- 2. Perturbation Expansion -- 2.1. Rules -- 2.2. Divergences -- 2.2.1. End-to-end Distance -- 2.2.2. Partition Function -- 2.2.3. Dimensional Regularization -- 3. Direct Renormalization -- 3.1. Scaling Functions -- 3.2. Second Virial Coefficient -- 3.3. Critical Exponents -- 4. Contact Exponents -- 5. On the Nonuniversality of Exponent γ -- 6. Conclusion -- References -- Chapter 9 Statistical Mechanics of Self-Avoiding Crumpled Manifolds - Part II Bertrand Duplantier -- 1. Interacting Manifold Renormalization: A Brief History -- 2. Manifold Model with Local δ Interaction -- 2.1. Perturbative Expansion -- 2.2. Second Virial Coefficient -- 2.3. Resummation of Leading Divergences -- 2.4. Comparison to One-Loop Renormalization -- 2.5. Analytic Continuation in D of the Euclidean Measure -- 2.6. Analysis of Divergences -- 2.7. Factorizations -- 2.8. Renormalization -- 3. Self-Avoiding Manifolds and Edwards Models -- 3.1. Introduction -- 3.2. Renormalizability to First Order -- 3.3. Renormalizability to All Orders
3.4. Perturbation Theory and Dipole Representation -- 3.5. Singular Configurations and Electrostatics in RD -- 3.6. Multi-local Operator Product Expansion -- 3.7. Power Counting and Renormalization -- 3.8. Finite Size Scaling and Direct Renormalization -- 3.9. Hyperscaling -- 3.10. Θ-Point and Long-Range Interactions -- Acknowledgments -- References -- Chapter 10 Anisotropic and Heterogeneous Polymerized Membranes Leo Radzihovsky -- 1. Preamble -- 2. Anisotropic Polymerized Membranes -- 2.1. Motivation and Introduction -- 2.2. Model -- 2.3. Mean-field theory -- 2.4. Fluctuations and Self-avoidance in the Crumpled and Flat Phases -- 2.4.1. Anomalous Elasticity of the Flat Phase -- 2.4.2. SCSA of the Flat Phase -- 2.5. Fluctuations in "Phantom" Tubules -- 2.5.1. Anomalous Elasticity of the Tubule Phase -- 2.5.2. Zero-modes and Tubule Shape Correlation -- 2.6. Self-avoidance in the Tubule Phase -- 2.6.1. Flory Theory -- 2.6.2. Renormalization Group and Scaling Relations -- 2.7. Phase Transitions -- 2.7.1. Renormalization Group Analysis of Crumpled-To-Tubule Transition -- 2.7.2. Scaling Theory of Crumpled-To-Tubule and Tubule-To-Flat Transitions -- 3. Random Heterogeneity in Polymerized Membranes -- 3.1. Motivation -- 3.2. Model of a Heterogeneous Polymerized Membrane -- 3.3. Weak Quenched Disorder: "Flat-glass" -- 3.3.1. Short-range Disorder -- 3.3.2. Long-range Disorder -- 3.4. Strong Quenched Disorder: "Crumpled-glass" -- 4. Interplay of Anisotropy and Heterogeneity: Nematic Elastomer Membranes -- 5. Summary -- 6. Acknowledgments -- References -- Chapter 11 Fixed-Connectivity Membranes Mark J. Bowick -- 1. Introduction -- 2. Physical Examples of Membranes -- 3. Phase Diagrams -- 3.1. Phantom Membranes -- 3.1.1. The Crumpled Phase -- 3.1.2. The Crumpling Transition -- 3.1.3. The Flat Phase -- 3.1.4. The Properties of the Flat Phase
3.2. Self-avoiding Membranes
This invaluable book explores the delicate interplay between geometry and statistical mechanics in materials such as microemulsions, wetting and growth interfaces, bulk lyotropic liquid crystals, chalcogenide glasses and sheet polymers, using tools from the fields of polymer physics, differential geometry, field theory and critical phenomena. Several chapters have been updated relative to the classic 1989 edition. Moreover, there are now three entirely new chapters on effects of anisotropy and heterogeneity, on fixed connectivity membranes and on triangulated surface models of fluctuating membranes
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Nelson, David R Statistical Mechanics of Membranes and Surfaces Singapore : World Scientific Publishing Co Pte Ltd,c2004 9789812387608
Subject Surfaces (Physics) -- Statistical methods.;Membranes (Technology) -- Statistical methods.;Interfaces (Physical sciences) -- Statistical methods.;Statistical mechanics
Electronic books
Alt Author Piran, Tsvi
Weinberg, Steven
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