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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
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
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-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