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catalog contributor b12589452.
catalog created "c2002.".
catalog date "2002".
catalog date "c2002.".
catalog dateCopyrighted "c2002.".
catalog description "1 Historical Background 1 -- 1.1 Robert Brown 1 -- 1.2 Between Brown and Einstein 3 -- 1.3 Albert Einstein 5 -- 1.4 Marian von Smoluchowski 7 -- 1.5 Molecular Reality 8 -- 1.6 The Scope of this Book 10 -- 2 Probability Theory 11 -- 2.1 Probability 11 -- 2.2 Conditional Probability and Independence 14 -- 2.3 Random Variables and Probability Distributions 16 -- 2.4 Expectations and Particular Distributions 18 -- 2.5 Characteristic Function; Sums of Random Variables 23 -- 3 Stochastic Processes 26 -- 3.1 Stochastic Processes 26 -- 3.2 Distribution Functions 27 -- 3.3 Classification of Stochastic Processes 29 -- 3.4 The Fokker-Planck Equation 33 -- 3.5 Some Special Processes 35 -- 3.6 Calculus of Stochastic Processes 37 -- 3.7 Fourier Analysis of Random Processes 40 -- 3.8 White Noise 43 -- 4 Einstein-Smoluchowski Theory 46 -- 4.1".
catalog description "187 -- 14.4 The Coagulation of Colloids 191 -- 14.5 Taylor Diffusion 192 -- 15 Rotational Diffusion 197 -- 15.1 Rotational Diffusion 197 -- 15.2 Fluorescence Depolarization 201 -- 15.3 Non-Spherical Brownian Particles 204 -- 16 Polymer Solutions 208 -- 16.1 A Model for Dilute Solutions of Polymers 208 -- 16.2 Hydrodynamic Interaction 210 -- 16.3 The Equation of Motion 212 -- 16.4 Diffusion and Intrinsic Viscosity 214 -- 16.5 Historical Remarks and Additional Reading 219 -- 17 Interacting Brownian Particles 222 -- 17.1 Effects of Concentration 222 -- 17.2 The Fokker-Planck Equation 223 -- 17.3 The Multiparticle Smoluchowski Equation 226 -- 17.4 The Diffusion Coefficient 228 -- 17.5 The Viscosity 235 -- 18 Dynamics, Fractals, and Chaos 240 -- 18.1 Brownian Dynamics 240 -- 18.2 Brownian Paths as Fractals 246 -- 18.3 Brownian Motion and Chaos 251 --".
catalog description "A The Applicability of Stokes' Law 258 -- B Functional Calculus 260 -- C An Operator Identity 263 -- D Euler Angles 264 -- E The Oseen Tensor 266 -- F Mutual Diffusion and Self-Diffusion 268 -- F.1 Mutual Diffusion 268 -- F.2 Self-Diffusion 269 -- F.3 Relation between D[subscript m] and D[subscript s] 269.".
catalog description "Includes bibliographical references (p. 271-284) and index.".
catalog description "Projection Operators -- The Mori Equation 133 -- 11 Stochastic Equations from a Statistical Mechanical Viewpoint 138 -- 11.1 The Langevin Equation A Heuristic View 138 -- 11.2 The Fokker-Planck Equation -- A Heuristic View 141 -- 11.3 What is Wrong with these Derivations? 144 -- 11.4 Eliminating Fast Processes 146 -- 11.5 The Distribution Function 153 -- 12 Two Exactly Treatable Models 159 -- 12.1 Two Illustrative Examples 159 -- 12.2 Brownian Motion in a Dilute Gas 159 -- 12.4 The Particle Bound to a Lattice 163 -- 12.5 The One-Dimensional Case 167 -- 13 Brownian Motion and Noise 170 -- 13.1 Limits on Measurement 170 -- 13.2 Oscillations of a Fiber 171 -- 13.3 A Pneumatic Example 174 -- 13.4 Electrical Systems 178 -- 14 Diffusion Phenomena 183 -- 14.1 Brownian Motion in Configuration Space 183 -- 14.2 Diffusion Controlled Reactions 183 -- 14.3 The Effect of Forces".
catalog description "The Harmonically Bound Particle 87 -- 7.5 A Particle in a Constant Force Field 92 -- 7.6 The Uniaxial Rotor 93 -- 7.7 An Equation for the Distribution of Displacements 94 -- 8 The Smoluchowski Equation 97 -- 8.1 The Kramers-Klein Equation 97 -- 8.2 The Smoluchowski Equation 98 -- 8.3 Elimination of Fast Variables 101 -- 8.4 The Smoluchowski Equation Continued 104 -- 8.5 Passage over Potential Barriers 105 -- 9 Random Walk 111 -- 9.1 The Random Walk 111 -- 9.2 The One-Dimensional Pearson Walk 112 -- 9.3 The Biased Random Walk 114 -- 9.4 The Persistent Walk 117 -- 9.5 Boundaries and First Passage Times 120 -- 9.6 Random Remarks on Random Walks 125 -- 10 Statistical Mechanics 127 -- 10.1 Molecular Distribution Functions 127 -- 10.2 The Liouville Equation 129 -- 10.3 Projection Operators -- The Zwanzig Equation 131 -- 10.4".
catalog description "What is Brownian Motion? 46 -- 4.2 Smoluchowski's Theory 48 -- 4.3 Smoluchowski Theory Continued 52 -- 4.4 Einstein's Theory 54 -- 4.5 Diffusion Coefficient and Friction Constant 57 -- 4.6 The Langevin Theory 59 -- 5 Stochastic Differential Equations and Integrals 62 -- 5.1 The Langevin Equation Revisited 62 -- 5.2 Stochastic Differential Equations 64 -- 5.3 Which Rule Should Be Used? 67 -- 5.4 Some Examples 69 -- 6 Functional Integrals 71 -- 6.1 Functional Integrals 71 -- 6.2 The Wiener Integral 72 -- 6.3 Wiener Measure 74 -- 6.4 The Feynman-Kac Formula 76 -- 6.5 Feynman Path Integrals 78 -- 6.6 Evaluation of Wiener Integrals 79 -- 6.7 Applications of Functional Integrals 82 -- 7 Some Important Special Cases 83 -- 7.1 Several Cases of Interest 83 -- 7.2 The Free Particle 83 -- 7.3 The Distribution of Displacements 85 -- 7.4".
catalog extent "xii, 289 p. :".
catalog identifier "0198515677 (acid-free paper)".
catalog isPartOf "International series of monographs on physics (Oxford, England) ; 112.".
catalog isPartOf "International series of monographs on physics ; 112".
catalog isPartOf "Oxford science publications".
catalog issued "2002".
catalog issued "c2002.".
catalog language "eng".
catalog publisher "Oxford : Clarendon Press ; New York : Oxford University Press,".
catalog subject "530.4/75 21".
catalog subject "Brownian motion processes.".
catalog subject "QA274.75 .M39 2002".
catalog tableOfContents "1 Historical Background 1 -- 1.1 Robert Brown 1 -- 1.2 Between Brown and Einstein 3 -- 1.3 Albert Einstein 5 -- 1.4 Marian von Smoluchowski 7 -- 1.5 Molecular Reality 8 -- 1.6 The Scope of this Book 10 -- 2 Probability Theory 11 -- 2.1 Probability 11 -- 2.2 Conditional Probability and Independence 14 -- 2.3 Random Variables and Probability Distributions 16 -- 2.4 Expectations and Particular Distributions 18 -- 2.5 Characteristic Function; Sums of Random Variables 23 -- 3 Stochastic Processes 26 -- 3.1 Stochastic Processes 26 -- 3.2 Distribution Functions 27 -- 3.3 Classification of Stochastic Processes 29 -- 3.4 The Fokker-Planck Equation 33 -- 3.5 Some Special Processes 35 -- 3.6 Calculus of Stochastic Processes 37 -- 3.7 Fourier Analysis of Random Processes 40 -- 3.8 White Noise 43 -- 4 Einstein-Smoluchowski Theory 46 -- 4.1".
catalog tableOfContents "187 -- 14.4 The Coagulation of Colloids 191 -- 14.5 Taylor Diffusion 192 -- 15 Rotational Diffusion 197 -- 15.1 Rotational Diffusion 197 -- 15.2 Fluorescence Depolarization 201 -- 15.3 Non-Spherical Brownian Particles 204 -- 16 Polymer Solutions 208 -- 16.1 A Model for Dilute Solutions of Polymers 208 -- 16.2 Hydrodynamic Interaction 210 -- 16.3 The Equation of Motion 212 -- 16.4 Diffusion and Intrinsic Viscosity 214 -- 16.5 Historical Remarks and Additional Reading 219 -- 17 Interacting Brownian Particles 222 -- 17.1 Effects of Concentration 222 -- 17.2 The Fokker-Planck Equation 223 -- 17.3 The Multiparticle Smoluchowski Equation 226 -- 17.4 The Diffusion Coefficient 228 -- 17.5 The Viscosity 235 -- 18 Dynamics, Fractals, and Chaos 240 -- 18.1 Brownian Dynamics 240 -- 18.2 Brownian Paths as Fractals 246 -- 18.3 Brownian Motion and Chaos 251 --".
catalog tableOfContents "A The Applicability of Stokes' Law 258 -- B Functional Calculus 260 -- C An Operator Identity 263 -- D Euler Angles 264 -- E The Oseen Tensor 266 -- F Mutual Diffusion and Self-Diffusion 268 -- F.1 Mutual Diffusion 268 -- F.2 Self-Diffusion 269 -- F.3 Relation between D[subscript m] and D[subscript s] 269.".
catalog tableOfContents "Projection Operators -- The Mori Equation 133 -- 11 Stochastic Equations from a Statistical Mechanical Viewpoint 138 -- 11.1 The Langevin Equation A Heuristic View 138 -- 11.2 The Fokker-Planck Equation -- A Heuristic View 141 -- 11.3 What is Wrong with these Derivations? 144 -- 11.4 Eliminating Fast Processes 146 -- 11.5 The Distribution Function 153 -- 12 Two Exactly Treatable Models 159 -- 12.1 Two Illustrative Examples 159 -- 12.2 Brownian Motion in a Dilute Gas 159 -- 12.4 The Particle Bound to a Lattice 163 -- 12.5 The One-Dimensional Case 167 -- 13 Brownian Motion and Noise 170 -- 13.1 Limits on Measurement 170 -- 13.2 Oscillations of a Fiber 171 -- 13.3 A Pneumatic Example 174 -- 13.4 Electrical Systems 178 -- 14 Diffusion Phenomena 183 -- 14.1 Brownian Motion in Configuration Space 183 -- 14.2 Diffusion Controlled Reactions 183 -- 14.3 The Effect of Forces".
catalog tableOfContents "The Harmonically Bound Particle 87 -- 7.5 A Particle in a Constant Force Field 92 -- 7.6 The Uniaxial Rotor 93 -- 7.7 An Equation for the Distribution of Displacements 94 -- 8 The Smoluchowski Equation 97 -- 8.1 The Kramers-Klein Equation 97 -- 8.2 The Smoluchowski Equation 98 -- 8.3 Elimination of Fast Variables 101 -- 8.4 The Smoluchowski Equation Continued 104 -- 8.5 Passage over Potential Barriers 105 -- 9 Random Walk 111 -- 9.1 The Random Walk 111 -- 9.2 The One-Dimensional Pearson Walk 112 -- 9.3 The Biased Random Walk 114 -- 9.4 The Persistent Walk 117 -- 9.5 Boundaries and First Passage Times 120 -- 9.6 Random Remarks on Random Walks 125 -- 10 Statistical Mechanics 127 -- 10.1 Molecular Distribution Functions 127 -- 10.2 The Liouville Equation 129 -- 10.3 Projection Operators -- The Zwanzig Equation 131 -- 10.4".
catalog tableOfContents "What is Brownian Motion? 46 -- 4.2 Smoluchowski's Theory 48 -- 4.3 Smoluchowski Theory Continued 52 -- 4.4 Einstein's Theory 54 -- 4.5 Diffusion Coefficient and Friction Constant 57 -- 4.6 The Langevin Theory 59 -- 5 Stochastic Differential Equations and Integrals 62 -- 5.1 The Langevin Equation Revisited 62 -- 5.2 Stochastic Differential Equations 64 -- 5.3 Which Rule Should Be Used? 67 -- 5.4 Some Examples 69 -- 6 Functional Integrals 71 -- 6.1 Functional Integrals 71 -- 6.2 The Wiener Integral 72 -- 6.3 Wiener Measure 74 -- 6.4 The Feynman-Kac Formula 76 -- 6.5 Feynman Path Integrals 78 -- 6.6 Evaluation of Wiener Integrals 79 -- 6.7 Applications of Functional Integrals 82 -- 7 Some Important Special Cases 83 -- 7.1 Several Cases of Interest 83 -- 7.2 The Free Particle 83 -- 7.3 The Distribution of Displacements 85 -- 7.4".
catalog title "Brownian motion : fluctuations, dynamics, and applications / Robert M. Mazo.".
catalog type "text".