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Preface; Contents; Mechanics and Physics of Lipid Bilayers; 1 A Model for Lipid Membranes with Tilt and Distension, Derived from Three-Dimensional Liquid Crystal Theory; 1.1 Introduction; 1.2 Liquid Crystal Theory; 1.3 Dimension Reduction; 1.4 The Optimal Two-Dimensional Model; 1.5 Euler Equations and Boundary Conditions; 1.6 Distension Without Tilt; 1.7 Surface Dilation and Its Gradient; 1.8 Equilibrium Equations and Edge Conditions; 1.9 Legendre
Hadamard Necessary Condition for Energy Minimizers; 2 The Classical Canham/Helfrich Model; 2.1 Surface Geometry and the Energy Functional.
2.2 The Shape Equation2.3 Edge Conditions; 3 Dissipative Effects: Diffusion and Viscous Flow; 3.1 Effect of a Second Chemical Species; 3.2 Equilibrium Theory; 3.3 Diffusion; 3.4 Dissipative Dynamic Evolution; 3.5 Constitutive Equations for the Dissipative Variables; 3.6 Convected Coordinates versus Surface-Fixed Coordinates; 4 A Transport Theory Without Dilation or Distension; 4.1 Energetics; 4.2 Balance Laws; 4.3 Constitutive Equations; 5 Electromechanics of Polarized Lipid Bilayers; 5.1 Energetics of Three-Dimensional Liquid Crystals in the Presence of a Stationary Applied Field.
5.2 Liquid Crystal Films5.3 Variational Problem and Equilibrium Equations; References; 2 Elasticity and Hereditariness; 1 Introduction; 2 The New Elastic Energy for Lipid Membranes; 2.1 Stretching Energy; 2.2 Thinning Transition in Flat Lipid Layers; 2.3 Line Tension Holding Zones in a Given Phase; 2.4 Elastic Properties of the Lipid Membrane; 2.5 The Onset of Change of Elastic Phase; 2.6 Unstable Region: bar'' 0; 2.8 Singular Ground States: bar'' = 0; 3 Hereditariness of Lipid Membranes; 3.1 The Physics of Hereditariness in Lipid Structures.
3.2 The Free Energy for Small Perturbations of Planar Lipid Structures3.3 Time Evolution of Phase Perturbations; 3.4 Spatial Modes for the Perturbations; 3.5 Time Evolutions of the Perturbations; 3.6 Eigenvalue Problem Governing the Time Dependence of the Perturbations; 3.7 Influence of the Initial Conditions; 4 Conclusions; References; Lipid Membranes: From Self-assembly to Elasticity; 1 Surfactant Self Assembly: Morphology and Statistical thermodynamics; 1.1 Morphology; 1.2 Statistical Thermodynamics; 2 Fluid Elastic Sheets: From Three to Two Dimensions.
2.1 The Starting Point: Thin Fluid Elastic Sheets2.2 Decomposing the Membrane Deformation into Three Stages; 2.3 The Link Between Curvature and Local Area Strain; 2.4 From Three Dimensions to Two; 2.5 Some Consequences of the Curvature-Tilt Functional; 3 Measuring the Bending Modulus; 3.1 Active Versus Passive Strategies; 3.2 Buckling for Fluid Membranes; 3.3 Buckling for Gel-Phase Membranes; References; The Geometry of Fluid Membranes: Variational Principles, Symmetries and Conservation Laws; 1 Introduction; 2 Surface Geometry: Intrinsic Versus Extrinsic Elements; 3 The Bending Energy.
Hadamard Necessary Condition for Energy Minimizers; 2 The Classical Canham/Helfrich Model; 2.1 Surface Geometry and the Energy Functional.
2.2 The Shape Equation2.3 Edge Conditions; 3 Dissipative Effects: Diffusion and Viscous Flow; 3.1 Effect of a Second Chemical Species; 3.2 Equilibrium Theory; 3.3 Diffusion; 3.4 Dissipative Dynamic Evolution; 3.5 Constitutive Equations for the Dissipative Variables; 3.6 Convected Coordinates versus Surface-Fixed Coordinates; 4 A Transport Theory Without Dilation or Distension; 4.1 Energetics; 4.2 Balance Laws; 4.3 Constitutive Equations; 5 Electromechanics of Polarized Lipid Bilayers; 5.1 Energetics of Three-Dimensional Liquid Crystals in the Presence of a Stationary Applied Field.
5.2 Liquid Crystal Films5.3 Variational Problem and Equilibrium Equations; References; 2 Elasticity and Hereditariness; 1 Introduction; 2 The New Elastic Energy for Lipid Membranes; 2.1 Stretching Energy; 2.2 Thinning Transition in Flat Lipid Layers; 2.3 Line Tension Holding Zones in a Given Phase; 2.4 Elastic Properties of the Lipid Membrane; 2.5 The Onset of Change of Elastic Phase; 2.6 Unstable Region: bar'' 0; 2.8 Singular Ground States: bar'' = 0; 3 Hereditariness of Lipid Membranes; 3.1 The Physics of Hereditariness in Lipid Structures.
3.2 The Free Energy for Small Perturbations of Planar Lipid Structures3.3 Time Evolution of Phase Perturbations; 3.4 Spatial Modes for the Perturbations; 3.5 Time Evolutions of the Perturbations; 3.6 Eigenvalue Problem Governing the Time Dependence of the Perturbations; 3.7 Influence of the Initial Conditions; 4 Conclusions; References; Lipid Membranes: From Self-assembly to Elasticity; 1 Surfactant Self Assembly: Morphology and Statistical thermodynamics; 1.1 Morphology; 1.2 Statistical Thermodynamics; 2 Fluid Elastic Sheets: From Three to Two Dimensions.
2.1 The Starting Point: Thin Fluid Elastic Sheets2.2 Decomposing the Membrane Deformation into Three Stages; 2.3 The Link Between Curvature and Local Area Strain; 2.4 From Three Dimensions to Two; 2.5 Some Consequences of the Curvature-Tilt Functional; 3 Measuring the Bending Modulus; 3.1 Active Versus Passive Strategies; 3.2 Buckling for Fluid Membranes; 3.3 Buckling for Gel-Phase Membranes; References; The Geometry of Fluid Membranes: Variational Principles, Symmetries and Conservation Laws; 1 Introduction; 2 Surface Geometry: Intrinsic Versus Extrinsic Elements; 3 The Bending Energy.