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The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems [[electronic resource] /] / Ian Snook
The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems [[electronic resource] /] / Ian Snook
Autore Snook Ian
Pubbl/distr/stampa Boston, : Elsevier, 2006
Descrizione fisica 1 online resource (321 p.)
Disciplina 530.14/4
Soggetto topico Langevin equations
Brownian movements
Random dynamical systems
Physics
Soggetto genere / forma Electronic books.
ISBN 1-280-74716-1
9786610747160
0-08-046792-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Cover; The Langevin and Generalised Langevin Approach to the Dynamics of Atomic, Polymeric and Colloidal Systems; Copyright page; Contents; Preface; Notation; A. Potential Energy Functions; B. Symbols Used; C. Operations; Chapter 1. Background, Mechanics and Statistical Mechanics; 1.1 Background; 1.2 The Mechanical Description of a System of Particles; 1.3 Summary; 1.4. Conclusions; References; Chapter 2. The Equation of Motion for a Typical Particle at Equilibrium:The Mori-Zwanzig Approach; 2.1 The Projection Operator; 2.2 The Generalised Langevin Equation
2.3 The Generalised Langevin Equation in Terms of the Velocity2.4 Equation of Motion for the Velocity Autocorrelation Function; 2.5 The Langevin Equation Derived from the Mori Approach: The Brownian Limit; 2.6 Generalisation to any Set of Dynamical Variables; 2.7 Memory Functions Derivation of Expressions for Linear Transport Coefficients; 2.8 Correlation Function Expression for the Coefficient of Newtonian Viscosity; 2.9 Summary; 2.10 Conclusions; References; Chapter 3. Approximate Methods to Calculate Correlation Functions and Mori-Zwanzig Memory Functions; 3.1 Taylor Series Expansion
3.2 Spectra3.3 Mori ́s Continued Fraction Method; 3.4 Use of Information Theory; 3.5 Perturbation Theories; 3.6 Mode Coupling Theory; 3.7 Macroscopic Hydrodynamic Theory; 3.8 Memory Functions Calculated by the Molecular-Dynamics Method; 3.9 Conclusions; References; Chapter 4. The Generalised Langevin Equation in Non-Equilibrium; 4.1 Derivation of Generalised Langevin Equation in Non-Equilibrium; 4.2 Langevin Equation for a Single Brownian Particle in a Shearing Fluid; 4.3 Conclusions; References; Chapter 5. The Langevin Equation and the Brownian Limit
5.1 A Dilute Suspension - One Large Particle in a Background5.2 Many-Body Langevin Equation; 5.3 Generalisation to Non-Equilibrium; 5.4 The Fokker-Planck Equation and the Diffusive Limit; 5.5 Approach to the Brownian Limit and Limitations; 5.6 Summary; 5.7 Conclusions; References; Chapter 6. Langevin and Generalised Langevin Dynamics; 6.1 Extensions of the GLE to Collections of Particles; 6.2 Numerical Solution of the Langevin Equation; 6.3 Higher-Order BD Schemes for the Langevin Equation; 6.4 Generalised Langevin Equation; 6.5 Systems in an External Field
6.6 Boundary Conditions in Simulations6.7 Conclusions; References; Chapter 7. Brownian Dynamics; 7.1 Fundamentals; 7.2 Calculation of Hydrodynamic Interactions; 7.3 Alternative Approaches to Treat Hydrodynamic Interactions; 7.4 Brownian Dynamics Algorithms; 7.5 Brownian Dynamics in a Shear Field; 7.6 Limitations of the BD Method; 7.7 Alternatives to BD Simulations; 7.8 Conclusions; References; Chapter 8. Polymer Dynamics; 8.1 Toxvaerd Approach; 8.2 Direct Use of Brownian Dynamics; 8.3 Rigid Systems; 8.4 Conclusions; References
Chapter 9. Theories Based on Distribution Functions, Master Equations and Stochastic Equations
Record Nr. UNINA-9910457244703321
Snook Ian  
Boston, : Elsevier, 2006
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems [[electronic resource] /] / Ian Snook
The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems [[electronic resource] /] / Ian Snook
Autore Snook Ian
Pubbl/distr/stampa Boston, : Elsevier, 2006
Descrizione fisica 1 online resource (321 p.)
Disciplina 530.14/4
Soggetto topico Langevin equations
Brownian movements
Random dynamical systems
Physics
ISBN 1-280-74716-1
9786610747160
0-08-046792-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Cover; The Langevin and Generalised Langevin Approach to the Dynamics of Atomic, Polymeric and Colloidal Systems; Copyright page; Contents; Preface; Notation; A. Potential Energy Functions; B. Symbols Used; C. Operations; Chapter 1. Background, Mechanics and Statistical Mechanics; 1.1 Background; 1.2 The Mechanical Description of a System of Particles; 1.3 Summary; 1.4. Conclusions; References; Chapter 2. The Equation of Motion for a Typical Particle at Equilibrium:The Mori-Zwanzig Approach; 2.1 The Projection Operator; 2.2 The Generalised Langevin Equation
2.3 The Generalised Langevin Equation in Terms of the Velocity2.4 Equation of Motion for the Velocity Autocorrelation Function; 2.5 The Langevin Equation Derived from the Mori Approach: The Brownian Limit; 2.6 Generalisation to any Set of Dynamical Variables; 2.7 Memory Functions Derivation of Expressions for Linear Transport Coefficients; 2.8 Correlation Function Expression for the Coefficient of Newtonian Viscosity; 2.9 Summary; 2.10 Conclusions; References; Chapter 3. Approximate Methods to Calculate Correlation Functions and Mori-Zwanzig Memory Functions; 3.1 Taylor Series Expansion
3.2 Spectra3.3 Mori ́s Continued Fraction Method; 3.4 Use of Information Theory; 3.5 Perturbation Theories; 3.6 Mode Coupling Theory; 3.7 Macroscopic Hydrodynamic Theory; 3.8 Memory Functions Calculated by the Molecular-Dynamics Method; 3.9 Conclusions; References; Chapter 4. The Generalised Langevin Equation in Non-Equilibrium; 4.1 Derivation of Generalised Langevin Equation in Non-Equilibrium; 4.2 Langevin Equation for a Single Brownian Particle in a Shearing Fluid; 4.3 Conclusions; References; Chapter 5. The Langevin Equation and the Brownian Limit
5.1 A Dilute Suspension - One Large Particle in a Background5.2 Many-Body Langevin Equation; 5.3 Generalisation to Non-Equilibrium; 5.4 The Fokker-Planck Equation and the Diffusive Limit; 5.5 Approach to the Brownian Limit and Limitations; 5.6 Summary; 5.7 Conclusions; References; Chapter 6. Langevin and Generalised Langevin Dynamics; 6.1 Extensions of the GLE to Collections of Particles; 6.2 Numerical Solution of the Langevin Equation; 6.3 Higher-Order BD Schemes for the Langevin Equation; 6.4 Generalised Langevin Equation; 6.5 Systems in an External Field
6.6 Boundary Conditions in Simulations6.7 Conclusions; References; Chapter 7. Brownian Dynamics; 7.1 Fundamentals; 7.2 Calculation of Hydrodynamic Interactions; 7.3 Alternative Approaches to Treat Hydrodynamic Interactions; 7.4 Brownian Dynamics Algorithms; 7.5 Brownian Dynamics in a Shear Field; 7.6 Limitations of the BD Method; 7.7 Alternatives to BD Simulations; 7.8 Conclusions; References; Chapter 8. Polymer Dynamics; 8.1 Toxvaerd Approach; 8.2 Direct Use of Brownian Dynamics; 8.3 Rigid Systems; 8.4 Conclusions; References
Chapter 9. Theories Based on Distribution Functions, Master Equations and Stochastic Equations
Record Nr. UNINA-9910784596303321
Snook Ian  
Boston, : Elsevier, 2006
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems / / Ian Snook
The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems / / Ian Snook
Autore Snook Ian
Edizione [1st ed.]
Pubbl/distr/stampa Boston, : Elsevier, 2006
Descrizione fisica 1 online resource (321 p.)
Disciplina 530.14/4
530.144
Soggetto topico Langevin equations
Brownian movements
Random dynamical systems
Physics
ISBN 1-280-74716-1
9786610747160
0-08-046792-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Cover; The Langevin and Generalised Langevin Approach to the Dynamics of Atomic, Polymeric and Colloidal Systems; Copyright page; Contents; Preface; Notation; A. Potential Energy Functions; B. Symbols Used; C. Operations; Chapter 1. Background, Mechanics and Statistical Mechanics; 1.1 Background; 1.2 The Mechanical Description of a System of Particles; 1.3 Summary; 1.4. Conclusions; References; Chapter 2. The Equation of Motion for a Typical Particle at Equilibrium:The Mori-Zwanzig Approach; 2.1 The Projection Operator; 2.2 The Generalised Langevin Equation
2.3 The Generalised Langevin Equation in Terms of the Velocity2.4 Equation of Motion for the Velocity Autocorrelation Function; 2.5 The Langevin Equation Derived from the Mori Approach: The Brownian Limit; 2.6 Generalisation to any Set of Dynamical Variables; 2.7 Memory Functions Derivation of Expressions for Linear Transport Coefficients; 2.8 Correlation Function Expression for the Coefficient of Newtonian Viscosity; 2.9 Summary; 2.10 Conclusions; References; Chapter 3. Approximate Methods to Calculate Correlation Functions and Mori-Zwanzig Memory Functions; 3.1 Taylor Series Expansion
3.2 Spectra3.3 Mori ́s Continued Fraction Method; 3.4 Use of Information Theory; 3.5 Perturbation Theories; 3.6 Mode Coupling Theory; 3.7 Macroscopic Hydrodynamic Theory; 3.8 Memory Functions Calculated by the Molecular-Dynamics Method; 3.9 Conclusions; References; Chapter 4. The Generalised Langevin Equation in Non-Equilibrium; 4.1 Derivation of Generalised Langevin Equation in Non-Equilibrium; 4.2 Langevin Equation for a Single Brownian Particle in a Shearing Fluid; 4.3 Conclusions; References; Chapter 5. The Langevin Equation and the Brownian Limit
5.1 A Dilute Suspension - One Large Particle in a Background5.2 Many-Body Langevin Equation; 5.3 Generalisation to Non-Equilibrium; 5.4 The Fokker-Planck Equation and the Diffusive Limit; 5.5 Approach to the Brownian Limit and Limitations; 5.6 Summary; 5.7 Conclusions; References; Chapter 6. Langevin and Generalised Langevin Dynamics; 6.1 Extensions of the GLE to Collections of Particles; 6.2 Numerical Solution of the Langevin Equation; 6.3 Higher-Order BD Schemes for the Langevin Equation; 6.4 Generalised Langevin Equation; 6.5 Systems in an External Field
6.6 Boundary Conditions in Simulations6.7 Conclusions; References; Chapter 7. Brownian Dynamics; 7.1 Fundamentals; 7.2 Calculation of Hydrodynamic Interactions; 7.3 Alternative Approaches to Treat Hydrodynamic Interactions; 7.4 Brownian Dynamics Algorithms; 7.5 Brownian Dynamics in a Shear Field; 7.6 Limitations of the BD Method; 7.7 Alternatives to BD Simulations; 7.8 Conclusions; References; Chapter 8. Polymer Dynamics; 8.1 Toxvaerd Approach; 8.2 Direct Use of Brownian Dynamics; 8.3 Rigid Systems; 8.4 Conclusions; References
Chapter 9. Theories Based on Distribution Functions, Master Equations and Stochastic Equations
Record Nr. UNINA-9910823047403321
Snook Ian  
Boston, : Elsevier, 2006
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov
The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov
Autore Coffey William <1948->
Edizione [3rd ed.]
Pubbl/distr/stampa River Edge, NJ, : World Scientific, c2012
Descrizione fisica 1 online resource (852 p.)
Disciplina 519.2
Altri autori (Persone) KalmykovYu. P
Collana World Scientific series in contemporary chemical physics
Soggetto topico Langevin equations
Brownian motion processes
Soggetto genere / forma Electronic books.
ISBN 981-4355-67-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface to the Tllird Edition; CONTENTS; Contents; Chapter 1 Historical Background and Introductory Concepts; 1.1. Brownian motion; 1.2. Einstein's explanation of Brownian movement; 1.3. The Langevin equation; 1.3.1. Calculation of Avogadro's number; 1.4. Einstein's Method; 1.5. Essential concepts in Statistical Mechanics; 1.5.1. Ensemble of systems; 1.5.2. Phase space; 1.5.3. Representative point; 1.5.4. Ergodic hypothesis; 1.5.5. Calculation of averages; 1.5.6. Liouville equation; 1.5.7. Reduction of the Liouville equation; 1.5.8. Langevin equation for a system with one degree of freedom
1.5.9. Intuitive derivation of the Klein-Kramers equation1.5.10. Conditions under which a Maxwellian distribution in the velocities may be deemed to be attained; 1.5.11. Very-high-damping (VHD) regime; 1.5.12. Very-low-damping (VLD) regime; 1.6. Probability theory; 1.6.1. Random variables and probability distributions; 1.6.2. The Gaussian distribution; 1.6.3. Moment-generating fimctious; 1.6.4. Central limit theorem; 1.6.5. Random processes; 1.6.6. Wiener-Khinchin theorem; 1.7. Application to the Langevin equation; 1.8. Wiener process; 1.8.1. Variance of the Wiener process
1.8.2. Wiener integrals1.9. The Fokker-Planok equation; 1.10. Drift and diffusion coefficients; 1.11. Solution of the one-dimensional Fokker-Planck equation; 1.12. The Smoluchowski equation; 1.13. Escape of particles over potential barriers: Kramers' theory; 1.13.1. Escape rate in the IHD limit; 1.13.2. Kramers' calculation of the escape rate in the VLD limit; 1.13.3. Range of validity of the IHD and VLD formulas; 1.13.4. Extension of Kramers' theory to many dimensions in the IHD limit; 1.13.5. Langer's treatment of the IHD limit; 1.13.6. Kramers' formula as a special case of Langer's formula
1.13.7. Kramers' turn over problem1.14. Applications of the theory of Brownian movement in a potential; 1.15. Rotational Brownian motion: application to dielectric relaxation; 1.15.1. Breakdown of the Debye theory at high frequencies; 1.16. Superparamagnetism: magnetic after-effect; 1.17. Brown's treatment of Neel relaxation; 1.18. Asymptotic expressions for the Neel relaxation time; 1.18.1. Magnetization reversal time in a uniaxial superparamagnet: application of Kramers' method; 1.18.2. Escape rate formulas for superparamagnets; 1.19. Ferrofluids
1.20. Depletion effect in a biased bistable potential1.21. Stochastic resonance; 1.22. Anomalous diffusion; 1.22.1. Empirical formulas for the complex dielectric permittivity; 1.22.2. Theoretical justification for anomalous relaxation behavior; 1.22.3. Anomalous dielectric relaxation of an assembly of dipolar molecules; References; Chapter 2 Langevin Equations and Methods of Solution; 2.1. Criticisms of the Langevin equation; 2.2. Doob's interpretation of the Langevin equation; 2.3. Nonlinear Langevin equation with a multiplicative noise term: Ito and Stratonovich rules
2.4. Derivation of differential-recurrence relations from the one-dimensional Langevin equation
Record Nr. UNINA-9910463981803321
Coffey William <1948->  
River Edge, NJ, : World Scientific, c2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov
The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov
Autore Coffey William <1948->
Edizione [3rd ed.]
Pubbl/distr/stampa River Edge, NJ, : World Scientific, c2012
Descrizione fisica 1 online resource (852 p.)
Disciplina 519.2
Altri autori (Persone) KalmykovYu. P
Collana World Scientific series in contemporary chemical physics
Soggetto topico Langevin equations
Brownian motion processes
ISBN 981-4355-67-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface to the Tllird Edition; CONTENTS; Contents; Chapter 1 Historical Background and Introductory Concepts; 1.1. Brownian motion; 1.2. Einstein's explanation of Brownian movement; 1.3. The Langevin equation; 1.3.1. Calculation of Avogadro's number; 1.4. Einstein's Method; 1.5. Essential concepts in Statistical Mechanics; 1.5.1. Ensemble of systems; 1.5.2. Phase space; 1.5.3. Representative point; 1.5.4. Ergodic hypothesis; 1.5.5. Calculation of averages; 1.5.6. Liouville equation; 1.5.7. Reduction of the Liouville equation; 1.5.8. Langevin equation for a system with one degree of freedom
1.5.9. Intuitive derivation of the Klein-Kramers equation1.5.10. Conditions under which a Maxwellian distribution in the velocities may be deemed to be attained; 1.5.11. Very-high-damping (VHD) regime; 1.5.12. Very-low-damping (VLD) regime; 1.6. Probability theory; 1.6.1. Random variables and probability distributions; 1.6.2. The Gaussian distribution; 1.6.3. Moment-generating fimctious; 1.6.4. Central limit theorem; 1.6.5. Random processes; 1.6.6. Wiener-Khinchin theorem; 1.7. Application to the Langevin equation; 1.8. Wiener process; 1.8.1. Variance of the Wiener process
1.8.2. Wiener integrals1.9. The Fokker-Planok equation; 1.10. Drift and diffusion coefficients; 1.11. Solution of the one-dimensional Fokker-Planck equation; 1.12. The Smoluchowski equation; 1.13. Escape of particles over potential barriers: Kramers' theory; 1.13.1. Escape rate in the IHD limit; 1.13.2. Kramers' calculation of the escape rate in the VLD limit; 1.13.3. Range of validity of the IHD and VLD formulas; 1.13.4. Extension of Kramers' theory to many dimensions in the IHD limit; 1.13.5. Langer's treatment of the IHD limit; 1.13.6. Kramers' formula as a special case of Langer's formula
1.13.7. Kramers' turn over problem1.14. Applications of the theory of Brownian movement in a potential; 1.15. Rotational Brownian motion: application to dielectric relaxation; 1.15.1. Breakdown of the Debye theory at high frequencies; 1.16. Superparamagnetism: magnetic after-effect; 1.17. Brown's treatment of Neel relaxation; 1.18. Asymptotic expressions for the Neel relaxation time; 1.18.1. Magnetization reversal time in a uniaxial superparamagnet: application of Kramers' method; 1.18.2. Escape rate formulas for superparamagnets; 1.19. Ferrofluids
1.20. Depletion effect in a biased bistable potential1.21. Stochastic resonance; 1.22. Anomalous diffusion; 1.22.1. Empirical formulas for the complex dielectric permittivity; 1.22.2. Theoretical justification for anomalous relaxation behavior; 1.22.3. Anomalous dielectric relaxation of an assembly of dipolar molecules; References; Chapter 2 Langevin Equations and Methods of Solution; 2.1. Criticisms of the Langevin equation; 2.2. Doob's interpretation of the Langevin equation; 2.3. Nonlinear Langevin equation with a multiplicative noise term: Ito and Stratonovich rules
2.4. Derivation of differential-recurrence relations from the one-dimensional Langevin equation
Record Nr. UNINA-9910788450903321
Coffey William <1948->  
River Edge, NJ, : World Scientific, c2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov
The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov
Autore Coffey William <1948->
Edizione [3rd ed.]
Pubbl/distr/stampa River Edge, NJ, : World Scientific, c2012
Descrizione fisica 1 online resource (852 p.)
Disciplina 519.2
Altri autori (Persone) KalmykovYu. P
Collana World Scientific series in contemporary chemical physics
Soggetto topico Langevin equations
Brownian motion processes
ISBN 981-4355-67-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface to the Tllird Edition; CONTENTS; Contents; Chapter 1 Historical Background and Introductory Concepts; 1.1. Brownian motion; 1.2. Einstein's explanation of Brownian movement; 1.3. The Langevin equation; 1.3.1. Calculation of Avogadro's number; 1.4. Einstein's Method; 1.5. Essential concepts in Statistical Mechanics; 1.5.1. Ensemble of systems; 1.5.2. Phase space; 1.5.3. Representative point; 1.5.4. Ergodic hypothesis; 1.5.5. Calculation of averages; 1.5.6. Liouville equation; 1.5.7. Reduction of the Liouville equation; 1.5.8. Langevin equation for a system with one degree of freedom
1.5.9. Intuitive derivation of the Klein-Kramers equation1.5.10. Conditions under which a Maxwellian distribution in the velocities may be deemed to be attained; 1.5.11. Very-high-damping (VHD) regime; 1.5.12. Very-low-damping (VLD) regime; 1.6. Probability theory; 1.6.1. Random variables and probability distributions; 1.6.2. The Gaussian distribution; 1.6.3. Moment-generating fimctious; 1.6.4. Central limit theorem; 1.6.5. Random processes; 1.6.6. Wiener-Khinchin theorem; 1.7. Application to the Langevin equation; 1.8. Wiener process; 1.8.1. Variance of the Wiener process
1.8.2. Wiener integrals1.9. The Fokker-Planok equation; 1.10. Drift and diffusion coefficients; 1.11. Solution of the one-dimensional Fokker-Planck equation; 1.12. The Smoluchowski equation; 1.13. Escape of particles over potential barriers: Kramers' theory; 1.13.1. Escape rate in the IHD limit; 1.13.2. Kramers' calculation of the escape rate in the VLD limit; 1.13.3. Range of validity of the IHD and VLD formulas; 1.13.4. Extension of Kramers' theory to many dimensions in the IHD limit; 1.13.5. Langer's treatment of the IHD limit; 1.13.6. Kramers' formula as a special case of Langer's formula
1.13.7. Kramers' turn over problem1.14. Applications of the theory of Brownian movement in a potential; 1.15. Rotational Brownian motion: application to dielectric relaxation; 1.15.1. Breakdown of the Debye theory at high frequencies; 1.16. Superparamagnetism: magnetic after-effect; 1.17. Brown's treatment of Neel relaxation; 1.18. Asymptotic expressions for the Neel relaxation time; 1.18.1. Magnetization reversal time in a uniaxial superparamagnet: application of Kramers' method; 1.18.2. Escape rate formulas for superparamagnets; 1.19. Ferrofluids
1.20. Depletion effect in a biased bistable potential1.21. Stochastic resonance; 1.22. Anomalous diffusion; 1.22.1. Empirical formulas for the complex dielectric permittivity; 1.22.2. Theoretical justification for anomalous relaxation behavior; 1.22.3. Anomalous dielectric relaxation of an assembly of dipolar molecules; References; Chapter 2 Langevin Equations and Methods of Solution; 2.1. Criticisms of the Langevin equation; 2.2. Doob's interpretation of the Langevin equation; 2.3. Nonlinear Langevin equation with a multiplicative noise term: Ito and Stratonovich rules
2.4. Derivation of differential-recurrence relations from the one-dimensional Langevin equation
Record Nr. UNINA-9910826070503321
Coffey William <1948->  
River Edge, NJ, : World Scientific, c2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov, J.T. Waldron
The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov, J.T. Waldron
Autore Coffey William <1948->
Edizione [2nd ed.]
Pubbl/distr/stampa Singapore ; ; River Edge, N.J., : World Scientific, c2004
Descrizione fisica 1 online resource (704 p.)
Disciplina 519.2
530.475
Altri autori (Persone) KalmykovYu. P
WaldronJ. T
Collana Series in contemporary chemical physics
Soggetto topico Langevin equations
Brownian motion processes
Soggetto genere / forma Electronic books.
ISBN 1-281-93552-2
9786611935528
981-279-509-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents ; Preface to the Second Edition ; Preface to the First Edition ; Chapter 1 Historical Background and Introductory Concepts ; 1.1 Brownian Motion ; 1.2 Einstein's Explanation of the Brownian Movement ; 1.3 The Langevin Equation ; 1.4 Einstein's Method
1.5 Necessary Concepts of Statistical Mechanics 1.6 Probability Theory ; 1.7 Application to the Langevin Equation ; 1.8 Wiener Process ; 1.9 The Fokker-Planck Equation ; 1.10 Drift and Diffusion Coefficients ; 1.11 Solution of the One-Dimensional Fokker-Planck Equation
1.12 The Smoluchowski Equation 1.13 Escape of Particles over Potential Barriers - Kramers' Escape Rate Theory ; 1.14 Applications of the Theory of Brownian Movement in a Potential ; 1.15 Rotational Brownian Motion - Application to Dielectric Relaxation
1.16 Superparamagnetism - Magnetic After-Effect 1.17 Brown's Treatment of Neel Relaxation ; 1.18 Asymptotic Expressions for the Neel Relaxation Time ; 1.19 Ferrofluids ; 1.20 Depletion Effect in a Biased Bistable Potential ; 1.21 Stochastic Resonance ; 1.22 Anomalous Diffusion
References Chapter 2 Langevin Equations and Methods of Solution ; 2.1 Criticisms of the Langevin Equation ; 2.2 Doob's Interpretation of the Langevin Equation ; 2.3 Nonlinear Langevin Equation with a Multiplicative Noise Term: Ito and Stratonovich Rules
2.4 Derivation of Differential-Recurrence Relations from the One-Dimensional Langevin Equation
Record Nr. UNINA-9910454310403321
Coffey William <1948->  
Singapore ; ; River Edge, N.J., : World Scientific, c2004
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov, J.T. Waldron
The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov, J.T. Waldron
Autore Coffey William <1948->
Edizione [2nd ed.]
Pubbl/distr/stampa Singapore ; ; River Edge, N.J., : World Scientific, c2004
Descrizione fisica 1 online resource (704 p.)
Disciplina 519.2
530.475
Altri autori (Persone) KalmykovYu. P
WaldronJ. T
Collana Series in contemporary chemical physics
Soggetto topico Langevin equations
Brownian motion processes
ISBN 1-281-93552-2
9786611935528
981-279-509-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents ; Preface to the Second Edition ; Preface to the First Edition ; Chapter 1 Historical Background and Introductory Concepts ; 1.1 Brownian Motion ; 1.2 Einstein's Explanation of the Brownian Movement ; 1.3 The Langevin Equation ; 1.4 Einstein's Method
1.5 Necessary Concepts of Statistical Mechanics 1.6 Probability Theory ; 1.7 Application to the Langevin Equation ; 1.8 Wiener Process ; 1.9 The Fokker-Planck Equation ; 1.10 Drift and Diffusion Coefficients ; 1.11 Solution of the One-Dimensional Fokker-Planck Equation
1.12 The Smoluchowski Equation 1.13 Escape of Particles over Potential Barriers - Kramers' Escape Rate Theory ; 1.14 Applications of the Theory of Brownian Movement in a Potential ; 1.15 Rotational Brownian Motion - Application to Dielectric Relaxation
1.16 Superparamagnetism - Magnetic After-Effect 1.17 Brown's Treatment of Neel Relaxation ; 1.18 Asymptotic Expressions for the Neel Relaxation Time ; 1.19 Ferrofluids ; 1.20 Depletion Effect in a Biased Bistable Potential ; 1.21 Stochastic Resonance ; 1.22 Anomalous Diffusion
References Chapter 2 Langevin Equations and Methods of Solution ; 2.1 Criticisms of the Langevin Equation ; 2.2 Doob's Interpretation of the Langevin Equation ; 2.3 Nonlinear Langevin Equation with a Multiplicative Noise Term: Ito and Stratonovich Rules
2.4 Derivation of Differential-Recurrence Relations from the One-Dimensional Langevin Equation
Record Nr. UNINA-9910782118003321
Coffey William <1948->  
Singapore ; ; River Edge, N.J., : World Scientific, c2004
Materiale a stampa
Lo trovi qui: Univ. Federico II
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The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov, J.T. Waldron
The Langevin equation [[electronic resource] ] : with applications to stochastic problems in physics, chemistry, and electrical engineering / / W.T. Coffey, Yu. P. Kalmykov, J.T. Waldron
Autore Coffey William <1948->
Edizione [2nd ed.]
Pubbl/distr/stampa Singapore ; ; River Edge, N.J., : World Scientific, c2004
Descrizione fisica 1 online resource (704 p.)
Disciplina 519.2
530.475
Altri autori (Persone) KalmykovYu. P
WaldronJ. T
Collana Series in contemporary chemical physics
Soggetto topico Langevin equations
Brownian motion processes
ISBN 1-281-93552-2
9786611935528
981-279-509-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents ; Preface to the Second Edition ; Preface to the First Edition ; Chapter 1 Historical Background and Introductory Concepts ; 1.1 Brownian Motion ; 1.2 Einstein's Explanation of the Brownian Movement ; 1.3 The Langevin Equation ; 1.4 Einstein's Method
1.5 Necessary Concepts of Statistical Mechanics 1.6 Probability Theory ; 1.7 Application to the Langevin Equation ; 1.8 Wiener Process ; 1.9 The Fokker-Planck Equation ; 1.10 Drift and Diffusion Coefficients ; 1.11 Solution of the One-Dimensional Fokker-Planck Equation
1.12 The Smoluchowski Equation 1.13 Escape of Particles over Potential Barriers - Kramers' Escape Rate Theory ; 1.14 Applications of the Theory of Brownian Movement in a Potential ; 1.15 Rotational Brownian Motion - Application to Dielectric Relaxation
1.16 Superparamagnetism - Magnetic After-Effect 1.17 Brown's Treatment of Neel Relaxation ; 1.18 Asymptotic Expressions for the Neel Relaxation Time ; 1.19 Ferrofluids ; 1.20 Depletion Effect in a Biased Bistable Potential ; 1.21 Stochastic Resonance ; 1.22 Anomalous Diffusion
References Chapter 2 Langevin Equations and Methods of Solution ; 2.1 Criticisms of the Langevin Equation ; 2.2 Doob's Interpretation of the Langevin Equation ; 2.3 Nonlinear Langevin Equation with a Multiplicative Noise Term: Ito and Stratonovich Rules
2.4 Derivation of Differential-Recurrence Relations from the One-Dimensional Langevin Equation
Record Nr. UNINA-9910819881703321
Coffey William <1948->  
Singapore ; ; River Edge, N.J., : World Scientific, c2004
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui