The Langevin equation :: with applications to stochastic problems in physics, chemistry and electrical engineering /
This volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineer...
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| Sprache: | English |
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Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2012.
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| Ausgabe: | 3rd ed. |
| Schriftenreihe: | World Scientific series in contemporary chemical physics ;
v. 27. |
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| Online-Zugang: | Volltext |
| Zusammenfassung: | This volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineering, and so on. In order to improve the presentation, to accommodate all the new developments, and to appeal to the specialized interests of the various communities involved, the book has been extensively rewritten and a very large amount of new material has been added. This has been done in order to present a comprehensive overview of the subject emphasizing via a synergetic approach that seemingly unrelated physical problems involving random noise may be described using virtually identical mathematical methods in the spirit of the founders of the subject, viz., Einstein, Langevin, Smoluchowski, Kramers, etc. The book has been written in such a way that all the material should be accessible both to an advanced researcher and a beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of scattered research papers and review articles. |
| Beschreibung: | 1 online resource (xxii, 827 pages) : illustrations (some color). |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789814355674 9814355674 |
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| 245 | 1 | 4 | |a The Langevin equation : |b with applications to stochastic problems in physics, chemistry and electrical engineering / |c William T. Coffey, Yuri P. Kalmykov. |
| 250 | |a 3rd ed. | ||
| 260 | |a Singapore ; |a Hackensack, N.J. : |b World Scientific Pub. Co., |c ©2012. | ||
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| 490 | 1 | |a World Scientific series in contemporary chemical physics ; |v v. 27 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Ch. 1. Historical background and introductory concepts. 1.1. Brownian motion. 1.2. Einstein's explanation of Brownian movement. 1.3. The Langevin equation. 1.4. Einstein's method. 1.5. Essential concepts in 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' theory. 1.14. Applications to 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 Néel relaxation. 1.18. Asymptotic expressions for the Néel relaxation. 1.19. Ferrofluids. 1.20. Depletion effect in a biased bistable potential. 1.21. Stochastic resonance. 1.22. Anomalous diffusion -- ch. 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: Itô and Stratonovich rules. 2.4. Derivation of differential-recurrence relations from the one-dimensional Langevin equation. 2.5. Nonlinear Langevin equation in several dimensions. 2.6. Average of the multiplicative noise term in the Langevin equation. 2.7. Methods of solution of differential-recurrence relations arising from the nonlinear Langevin equation. 2.8. Linear response theory. 2.9. Integral relaxation theory. 2.10. Linear response theory for systems with dynamics governed by single-variable Fokker-Planck equations. 2.11. Smallest non-vanishing eigenvalue: continued-fraction approach. 2.12. Effective relaxation time. 2.13. Evaluation of the dynamic susceptibility using [symbol], [symbol] and [symbol]. 2.14. Nonlinear transient response of a Brownian particle -- ch. 3. Brownian motion of a free particle and a harmonic oscillator. 3.1. Introduction. 3.2. Ornstein-Uhlenbeck theory of Brownian motion. 3.3. Stationary solution of the Langevin equation: the Wiener-Khinchin theorem. 3.4. Application to phase diffusion in MRI. 3.5. Rotational Brownian motion of a fixed-axis rotator. 3.7. Torsional oscillator model: example of the use of the Wiener integral -- ch. 4. Rotational Brownian motion about a fixed axis in N-fold cosine potentials. 4.1. Introduction. 4.2. Langevin equation for rotation about a fixed axis. 4.3. Longitudinal and transverse effective relaxation times. 4.4. Polarizabilities and relaxation times of a fixed-axis rotator with two equivalent sites. 4.5. Effect of a d.c. bias field on the orientational relaxation of a fixed-axis rotator with two equivalent sites. | |
| 505 | 8 | |a Ch. 5. Brownian motion in a tilted periodic potential: application to the Josephson tunneling junction. 5.1. Introduction. 5.2. Langevin equations. 5.3. Josephson junction: dynamic model. 5.4. Reduction of the averaged Langevin equation for the junction to a set of differential-recurrence relations. 5.5. Current-voltage characteristics. 5.6. Linear response to an applied alternating current. 5.7. Effective eigenvalues for the Josephson junction. 5.8. Linear impedance. 5.9. Spectrum of the Josephson radiation. 5.10. Nonlinear effects in d.c. and a.c. current-voltage characteristics. 5.11. Concluding remarks -- ch. 6. Translational Brownian motion in a double-well potential. 6.1. Introduction. 6.2. Characteristic times of the position correlation function. 6.3. Converging continued fractions for the correlation functions. 6.4. Two-mode approximation. 6.5. Stochastic resonance. 6.6. Concluding remarks -- ch. 7. Non-inertial rotational diffusion in axially symmetric external potentials: applications to orientational relaxation of molecules in fluids and liquid crystals. 7.1. Introduction. 7.2. Rotational diffusion in a potential: Langevin equation approach. 7.3. Brownian rotation in a uniaxial potential. 7.4. Brownian rotation in a uniform d.c. external field. 7.5. Nonlinear transient responses in dielectric and Kerr-effect relaxation. 7.6. Nonlinear dielectric relaxation of polar molecules in a strong a.c. electric field: steady-state response. 7.7. Concluding remarks -- ch. 8. Anisotropic non-inertial rotational diffusion in an external potential: application to linear and nonlinear dielectric relaxation and the dynamic Kerr effect. 8.1. Introduction. 8.2. Anisotropic non-inertial rotational diffusion of an asymmetric top in an external potential. 8.3. Application to dielectric relaxation. 8.4. Kerr-effect relaxation. 8.5. Concluding remarks -- ch. 9. Brownian motion of classical spins: application to magnetization relaxation in superparamagnets. 9.1. Introduction. 9.2. Brown's model: Langevin equation approach. 9.3. Magnetization relaxation in uniaxial superparamagnets. 9.4. Reversal time of the magnetization in superparamagnets with nonaxially symmetric potentials: escape-rate theory approach. 9.5. Magnetization relaxation in superparamagnets with non-axially symmetric anisotropy: matrix continued-fraction approach. 9.6. Nonlinear a.c. stationary response of superparamagnets. 9.7. Concluding remarks -- ch. 10. Inertial effects in rotational and translational Brownian motion for a single degree of freedom. 10.1. Introduction. 10.2. Inertial effects in nonlinear dielectric response. 10.3. Brownian motion of a fixed-axis rotator in a double-well potential. 10.4. Brownian motion of a fixed-axis rotator in an asymmetric double-well potential. 10.5. Brownian motion in a tilted periodic potential. 10.6. Translational Brownian motion in a double-well potential. 10.7. Concluding remarks. | |
| 505 | 8 | |a Ch. 11. Inertial effects in rotational diffusion in space: application to orientational relaxation in molecular liquids and ferrofluids. 11.1. Introduction. 11.2. Inertial rotational Brownian motion of a thin rod in space. 11.3. Rotational Brownian motion of a symmetrical top. 11.4. Inertial rotational Brownian motion of a rigid dipolar rotator in a uniaxial biased potential. 11.5. Itinerant oscillator model of rotational motion in liquids. 11.6. Application of the cage model to ferrofluids -- ch. 12. Anomalous diffusion and relaxation. 12.1. Discrete- and continuous-time random walks. 12.2. Fractional diffusion equation for the continuous-time random walk model. 12.3. Solution of fractional diffusion equations. 12.4. Characteristic times of anomalous diffusion. 12.5. Inertial effects in anomalous relaxation. 12.6. Barkai and Silbey's fractional kinetic equation. 12.7. Anomalous diffusion in a periodic potential. 12.8. Fractional Langevin equation. 12.9. Concluding remarks. | |
| 520 | |a This volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineering, and so on. In order to improve the presentation, to accommodate all the new developments, and to appeal to the specialized interests of the various communities involved, the book has been extensively rewritten and a very large amount of new material has been added. This has been done in order to present a comprehensive overview of the subject emphasizing via a synergetic approach that seemingly unrelated physical problems involving random noise may be described using virtually identical mathematical methods in the spirit of the founders of the subject, viz., Einstein, Langevin, Smoluchowski, Kramers, etc. The book has been written in such a way that all the material should be accessible both to an advanced researcher and a beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of scattered research papers and review articles. | ||
| 650 | 0 | |a Langevin equations. |0 http://id.loc.gov/authorities/subjects/sh96010212 | |
| 650 | 0 | |a Brownian motion processes. |0 http://id.loc.gov/authorities/subjects/sh85017265 | |
| 650 | 6 | |a Équations de Langevin. | |
| 650 | 6 | |a Processus de mouvement brownien. | |
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| 650 | 7 | |a Brownian motion processes |2 fast | |
| 650 | 7 | |a Langevin equations |2 fast | |
| 700 | 1 | |a Kalmykov, Yu. P. | |
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| contents | Ch. 1. Historical background and introductory concepts. 1.1. Brownian motion. 1.2. Einstein's explanation of Brownian movement. 1.3. The Langevin equation. 1.4. Einstein's method. 1.5. Essential concepts in 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' theory. 1.14. Applications to 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 Néel relaxation. 1.18. Asymptotic expressions for the Néel relaxation. 1.19. Ferrofluids. 1.20. Depletion effect in a biased bistable potential. 1.21. Stochastic resonance. 1.22. Anomalous diffusion -- ch. 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: Itô and Stratonovich rules. 2.4. Derivation of differential-recurrence relations from the one-dimensional Langevin equation. 2.5. Nonlinear Langevin equation in several dimensions. 2.6. Average of the multiplicative noise term in the Langevin equation. 2.7. Methods of solution of differential-recurrence relations arising from the nonlinear Langevin equation. 2.8. Linear response theory. 2.9. Integral relaxation theory. 2.10. Linear response theory for systems with dynamics governed by single-variable Fokker-Planck equations. 2.11. Smallest non-vanishing eigenvalue: continued-fraction approach. 2.12. Effective relaxation time. 2.13. Evaluation of the dynamic susceptibility using [symbol], [symbol] and [symbol]. 2.14. Nonlinear transient response of a Brownian particle -- ch. 3. Brownian motion of a free particle and a harmonic oscillator. 3.1. Introduction. 3.2. Ornstein-Uhlenbeck theory of Brownian motion. 3.3. Stationary solution of the Langevin equation: the Wiener-Khinchin theorem. 3.4. Application to phase diffusion in MRI. 3.5. Rotational Brownian motion of a fixed-axis rotator. 3.7. Torsional oscillator model: example of the use of the Wiener integral -- ch. 4. Rotational Brownian motion about a fixed axis in N-fold cosine potentials. 4.1. Introduction. 4.2. Langevin equation for rotation about a fixed axis. 4.3. Longitudinal and transverse effective relaxation times. 4.4. Polarizabilities and relaxation times of a fixed-axis rotator with two equivalent sites. 4.5. Effect of a d.c. bias field on the orientational relaxation of a fixed-axis rotator with two equivalent sites. Ch. 5. Brownian motion in a tilted periodic potential: application to the Josephson tunneling junction. 5.1. Introduction. 5.2. Langevin equations. 5.3. Josephson junction: dynamic model. 5.4. Reduction of the averaged Langevin equation for the junction to a set of differential-recurrence relations. 5.5. Current-voltage characteristics. 5.6. Linear response to an applied alternating current. 5.7. Effective eigenvalues for the Josephson junction. 5.8. Linear impedance. 5.9. Spectrum of the Josephson radiation. 5.10. Nonlinear effects in d.c. and a.c. current-voltage characteristics. 5.11. Concluding remarks -- ch. 6. Translational Brownian motion in a double-well potential. 6.1. Introduction. 6.2. Characteristic times of the position correlation function. 6.3. Converging continued fractions for the correlation functions. 6.4. Two-mode approximation. 6.5. Stochastic resonance. 6.6. Concluding remarks -- ch. 7. Non-inertial rotational diffusion in axially symmetric external potentials: applications to orientational relaxation of molecules in fluids and liquid crystals. 7.1. Introduction. 7.2. Rotational diffusion in a potential: Langevin equation approach. 7.3. Brownian rotation in a uniaxial potential. 7.4. Brownian rotation in a uniform d.c. external field. 7.5. Nonlinear transient responses in dielectric and Kerr-effect relaxation. 7.6. Nonlinear dielectric relaxation of polar molecules in a strong a.c. electric field: steady-state response. 7.7. Concluding remarks -- ch. 8. Anisotropic non-inertial rotational diffusion in an external potential: application to linear and nonlinear dielectric relaxation and the dynamic Kerr effect. 8.1. Introduction. 8.2. Anisotropic non-inertial rotational diffusion of an asymmetric top in an external potential. 8.3. Application to dielectric relaxation. 8.4. Kerr-effect relaxation. 8.5. Concluding remarks -- ch. 9. Brownian motion of classical spins: application to magnetization relaxation in superparamagnets. 9.1. Introduction. 9.2. Brown's model: Langevin equation approach. 9.3. Magnetization relaxation in uniaxial superparamagnets. 9.4. Reversal time of the magnetization in superparamagnets with nonaxially symmetric potentials: escape-rate theory approach. 9.5. Magnetization relaxation in superparamagnets with non-axially symmetric anisotropy: matrix continued-fraction approach. 9.6. Nonlinear a.c. stationary response of superparamagnets. 9.7. Concluding remarks -- ch. 10. Inertial effects in rotational and translational Brownian motion for a single degree of freedom. 10.1. Introduction. 10.2. Inertial effects in nonlinear dielectric response. 10.3. Brownian motion of a fixed-axis rotator in a double-well potential. 10.4. Brownian motion of a fixed-axis rotator in an asymmetric double-well potential. 10.5. Brownian motion in a tilted periodic potential. 10.6. Translational Brownian motion in a double-well potential. 10.7. Concluding remarks. Ch. 11. Inertial effects in rotational diffusion in space: application to orientational relaxation in molecular liquids and ferrofluids. 11.1. Introduction. 11.2. Inertial rotational Brownian motion of a thin rod in space. 11.3. Rotational Brownian motion of a symmetrical top. 11.4. Inertial rotational Brownian motion of a rigid dipolar rotator in a uniaxial biased potential. 11.5. Itinerant oscillator model of rotational motion in liquids. 11.6. Application of the cage model to ferrofluids -- ch. 12. Anomalous diffusion and relaxation. 12.1. Discrete- and continuous-time random walks. 12.2. Fractional diffusion equation for the continuous-time random walk model. 12.3. Solution of fractional diffusion equations. 12.4. Characteristic times of anomalous diffusion. 12.5. Inertial effects in anomalous relaxation. 12.6. Barkai and Silbey's fractional kinetic equation. 12.7. Anomalous diffusion in a periodic potential. 12.8. Fractional Langevin equation. 12.9. Concluding remarks. |
| ctrlnum | (OCoLC)840254741 |
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| edition | 3rd ed. |
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Historical background and introductory concepts. 1.1. Brownian motion. 1.2. Einstein's explanation of Brownian movement. 1.3. The Langevin equation. 1.4. Einstein's method. 1.5. Essential concepts in 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' theory. 1.14. Applications to 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 Néel relaxation. 1.18. Asymptotic expressions for the Néel relaxation. 1.19. Ferrofluids. 1.20. Depletion effect in a biased bistable potential. 1.21. Stochastic resonance. 1.22. Anomalous diffusion -- ch. 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: Itô and Stratonovich rules. 2.4. Derivation of differential-recurrence relations from the one-dimensional Langevin equation. 2.5. Nonlinear Langevin equation in several dimensions. 2.6. Average of the multiplicative noise term in the Langevin equation. 2.7. Methods of solution of differential-recurrence relations arising from the nonlinear Langevin equation. 2.8. Linear response theory. 2.9. Integral relaxation theory. 2.10. Linear response theory for systems with dynamics governed by single-variable Fokker-Planck equations. 2.11. Smallest non-vanishing eigenvalue: continued-fraction approach. 2.12. Effective relaxation time. 2.13. Evaluation of the dynamic susceptibility using [symbol], [symbol] and [symbol]. 2.14. Nonlinear transient response of a Brownian particle -- ch. 3. Brownian motion of a free particle and a harmonic oscillator. 3.1. Introduction. 3.2. Ornstein-Uhlenbeck theory of Brownian motion. 3.3. Stationary solution of the Langevin equation: the Wiener-Khinchin theorem. 3.4. Application to phase diffusion in MRI. 3.5. Rotational Brownian motion of a fixed-axis rotator. 3.7. Torsional oscillator model: example of the use of the Wiener integral -- ch. 4. Rotational Brownian motion about a fixed axis in N-fold cosine potentials. 4.1. Introduction. 4.2. Langevin equation for rotation about a fixed axis. 4.3. Longitudinal and transverse effective relaxation times. 4.4. Polarizabilities and relaxation times of a fixed-axis rotator with two equivalent sites. 4.5. Effect of a d.c. bias field on the orientational relaxation of a fixed-axis rotator with two equivalent sites.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Ch. 5. Brownian motion in a tilted periodic potential: application to the Josephson tunneling junction. 5.1. Introduction. 5.2. Langevin equations. 5.3. Josephson junction: dynamic model. 5.4. Reduction of the averaged Langevin equation for the junction to a set of differential-recurrence relations. 5.5. Current-voltage characteristics. 5.6. Linear response to an applied alternating current. 5.7. Effective eigenvalues for the Josephson junction. 5.8. Linear impedance. 5.9. Spectrum of the Josephson radiation. 5.10. Nonlinear effects in d.c. and a.c. current-voltage characteristics. 5.11. Concluding remarks -- ch. 6. Translational Brownian motion in a double-well potential. 6.1. Introduction. 6.2. Characteristic times of the position correlation function. 6.3. Converging continued fractions for the correlation functions. 6.4. Two-mode approximation. 6.5. Stochastic resonance. 6.6. Concluding remarks -- ch. 7. Non-inertial rotational diffusion in axially symmetric external potentials: applications to orientational relaxation of molecules in fluids and liquid crystals. 7.1. Introduction. 7.2. Rotational diffusion in a potential: Langevin equation approach. 7.3. Brownian rotation in a uniaxial potential. 7.4. Brownian rotation in a uniform d.c. external field. 7.5. Nonlinear transient responses in dielectric and Kerr-effect relaxation. 7.6. Nonlinear dielectric relaxation of polar molecules in a strong a.c. electric field: steady-state response. 7.7. Concluding remarks -- ch. 8. Anisotropic non-inertial rotational diffusion in an external potential: application to linear and nonlinear dielectric relaxation and the dynamic Kerr effect. 8.1. Introduction. 8.2. Anisotropic non-inertial rotational diffusion of an asymmetric top in an external potential. 8.3. Application to dielectric relaxation. 8.4. Kerr-effect relaxation. 8.5. Concluding remarks -- ch. 9. Brownian motion of classical spins: application to magnetization relaxation in superparamagnets. 9.1. Introduction. 9.2. Brown's model: Langevin equation approach. 9.3. Magnetization relaxation in uniaxial superparamagnets. 9.4. Reversal time of the magnetization in superparamagnets with nonaxially symmetric potentials: escape-rate theory approach. 9.5. Magnetization relaxation in superparamagnets with non-axially symmetric anisotropy: matrix continued-fraction approach. 9.6. Nonlinear a.c. stationary response of superparamagnets. 9.7. Concluding remarks -- ch. 10. Inertial effects in rotational and translational Brownian motion for a single degree of freedom. 10.1. Introduction. 10.2. Inertial effects in nonlinear dielectric response. 10.3. Brownian motion of a fixed-axis rotator in a double-well potential. 10.4. Brownian motion of a fixed-axis rotator in an asymmetric double-well potential. 10.5. Brownian motion in a tilted periodic potential. 10.6. Translational Brownian motion in a double-well potential. 10.7. Concluding remarks.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Ch. 11. Inertial effects in rotational diffusion in space: application to orientational relaxation in molecular liquids and ferrofluids. 11.1. Introduction. 11.2. Inertial rotational Brownian motion of a thin rod in space. 11.3. Rotational Brownian motion of a symmetrical top. 11.4. Inertial rotational Brownian motion of a rigid dipolar rotator in a uniaxial biased potential. 11.5. Itinerant oscillator model of rotational motion in liquids. 11.6. Application of the cage model to ferrofluids -- ch. 12. Anomalous diffusion and relaxation. 12.1. Discrete- and continuous-time random walks. 12.2. Fractional diffusion equation for the continuous-time random walk model. 12.3. Solution of fractional diffusion equations. 12.4. Characteristic times of anomalous diffusion. 12.5. Inertial effects in anomalous relaxation. 12.6. Barkai and Silbey's fractional kinetic equation. 12.7. Anomalous diffusion in a periodic potential. 12.8. Fractional Langevin equation. 12.9. Concluding remarks.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineering, and so on. In order to improve the presentation, to accommodate all the new developments, and to appeal to the specialized interests of the various communities involved, the book has been extensively rewritten and a very large amount of new material has been added. This has been done in order to present a comprehensive overview of the subject emphasizing via a synergetic approach that seemingly unrelated physical problems involving random noise may be described using virtually identical mathematical methods in the spirit of the founders of the subject, viz., Einstein, Langevin, Smoluchowski, Kramers, etc. The book has been written in such a way that all the material should be accessible both to an advanced researcher and a beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of scattered research papers and review articles.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Langevin equations.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh96010212</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Brownian motion processes.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85017265</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Équations de Langevin.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Processus de mouvement brownien.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Probability & Statistics</subfield><subfield code="x">General.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Brownian motion processes</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Langevin equations</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kalmykov, Yu. 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| id | ZDB-4-EBA-ocn840254741 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:18Z |
| institution | BVB |
| institution_GND | http://id.loc.gov/authorities/names/no2001005546 |
| isbn | 9789814355674 9814355674 |
| language | English |
| oclc_num | 840254741 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxii, 827 pages) : illustrations (some color). |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific Pub. Co., |
| record_format | marc |
| series | World Scientific series in contemporary chemical physics ; |
| series2 | World Scientific series in contemporary chemical physics ; |
| spelling | Coffey, William, 1948- https://id.oclc.org/worldcat/entity/E39PCjtWmyQVhWMJymGg8dwtJC http://id.loc.gov/authorities/names/n83198177 The Langevin equation : with applications to stochastic problems in physics, chemistry and electrical engineering / William T. Coffey, Yuri P. Kalmykov. 3rd ed. Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2012. 1 online resource (xxii, 827 pages) : illustrations (some color). text txt rdacontent computer c rdamedia online resource cr rdacarrier World Scientific series in contemporary chemical physics ; v. 27 Includes bibliographical references and index. Ch. 1. Historical background and introductory concepts. 1.1. Brownian motion. 1.2. Einstein's explanation of Brownian movement. 1.3. The Langevin equation. 1.4. Einstein's method. 1.5. Essential concepts in 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' theory. 1.14. Applications to 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 Néel relaxation. 1.18. Asymptotic expressions for the Néel relaxation. 1.19. Ferrofluids. 1.20. Depletion effect in a biased bistable potential. 1.21. Stochastic resonance. 1.22. Anomalous diffusion -- ch. 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: Itô and Stratonovich rules. 2.4. Derivation of differential-recurrence relations from the one-dimensional Langevin equation. 2.5. Nonlinear Langevin equation in several dimensions. 2.6. Average of the multiplicative noise term in the Langevin equation. 2.7. Methods of solution of differential-recurrence relations arising from the nonlinear Langevin equation. 2.8. Linear response theory. 2.9. Integral relaxation theory. 2.10. Linear response theory for systems with dynamics governed by single-variable Fokker-Planck equations. 2.11. Smallest non-vanishing eigenvalue: continued-fraction approach. 2.12. Effective relaxation time. 2.13. Evaluation of the dynamic susceptibility using [symbol], [symbol] and [symbol]. 2.14. Nonlinear transient response of a Brownian particle -- ch. 3. Brownian motion of a free particle and a harmonic oscillator. 3.1. Introduction. 3.2. Ornstein-Uhlenbeck theory of Brownian motion. 3.3. Stationary solution of the Langevin equation: the Wiener-Khinchin theorem. 3.4. Application to phase diffusion in MRI. 3.5. Rotational Brownian motion of a fixed-axis rotator. 3.7. Torsional oscillator model: example of the use of the Wiener integral -- ch. 4. Rotational Brownian motion about a fixed axis in N-fold cosine potentials. 4.1. Introduction. 4.2. Langevin equation for rotation about a fixed axis. 4.3. Longitudinal and transverse effective relaxation times. 4.4. Polarizabilities and relaxation times of a fixed-axis rotator with two equivalent sites. 4.5. Effect of a d.c. bias field on the orientational relaxation of a fixed-axis rotator with two equivalent sites. Ch. 5. Brownian motion in a tilted periodic potential: application to the Josephson tunneling junction. 5.1. Introduction. 5.2. Langevin equations. 5.3. Josephson junction: dynamic model. 5.4. Reduction of the averaged Langevin equation for the junction to a set of differential-recurrence relations. 5.5. Current-voltage characteristics. 5.6. Linear response to an applied alternating current. 5.7. Effective eigenvalues for the Josephson junction. 5.8. Linear impedance. 5.9. Spectrum of the Josephson radiation. 5.10. Nonlinear effects in d.c. and a.c. current-voltage characteristics. 5.11. Concluding remarks -- ch. 6. Translational Brownian motion in a double-well potential. 6.1. Introduction. 6.2. Characteristic times of the position correlation function. 6.3. Converging continued fractions for the correlation functions. 6.4. Two-mode approximation. 6.5. Stochastic resonance. 6.6. Concluding remarks -- ch. 7. Non-inertial rotational diffusion in axially symmetric external potentials: applications to orientational relaxation of molecules in fluids and liquid crystals. 7.1. Introduction. 7.2. Rotational diffusion in a potential: Langevin equation approach. 7.3. Brownian rotation in a uniaxial potential. 7.4. Brownian rotation in a uniform d.c. external field. 7.5. Nonlinear transient responses in dielectric and Kerr-effect relaxation. 7.6. Nonlinear dielectric relaxation of polar molecules in a strong a.c. electric field: steady-state response. 7.7. Concluding remarks -- ch. 8. Anisotropic non-inertial rotational diffusion in an external potential: application to linear and nonlinear dielectric relaxation and the dynamic Kerr effect. 8.1. Introduction. 8.2. Anisotropic non-inertial rotational diffusion of an asymmetric top in an external potential. 8.3. Application to dielectric relaxation. 8.4. Kerr-effect relaxation. 8.5. Concluding remarks -- ch. 9. Brownian motion of classical spins: application to magnetization relaxation in superparamagnets. 9.1. Introduction. 9.2. Brown's model: Langevin equation approach. 9.3. Magnetization relaxation in uniaxial superparamagnets. 9.4. Reversal time of the magnetization in superparamagnets with nonaxially symmetric potentials: escape-rate theory approach. 9.5. Magnetization relaxation in superparamagnets with non-axially symmetric anisotropy: matrix continued-fraction approach. 9.6. Nonlinear a.c. stationary response of superparamagnets. 9.7. Concluding remarks -- ch. 10. Inertial effects in rotational and translational Brownian motion for a single degree of freedom. 10.1. Introduction. 10.2. Inertial effects in nonlinear dielectric response. 10.3. Brownian motion of a fixed-axis rotator in a double-well potential. 10.4. Brownian motion of a fixed-axis rotator in an asymmetric double-well potential. 10.5. Brownian motion in a tilted periodic potential. 10.6. Translational Brownian motion in a double-well potential. 10.7. Concluding remarks. Ch. 11. Inertial effects in rotational diffusion in space: application to orientational relaxation in molecular liquids and ferrofluids. 11.1. Introduction. 11.2. Inertial rotational Brownian motion of a thin rod in space. 11.3. Rotational Brownian motion of a symmetrical top. 11.4. Inertial rotational Brownian motion of a rigid dipolar rotator in a uniaxial biased potential. 11.5. Itinerant oscillator model of rotational motion in liquids. 11.6. Application of the cage model to ferrofluids -- ch. 12. Anomalous diffusion and relaxation. 12.1. Discrete- and continuous-time random walks. 12.2. Fractional diffusion equation for the continuous-time random walk model. 12.3. Solution of fractional diffusion equations. 12.4. Characteristic times of anomalous diffusion. 12.5. Inertial effects in anomalous relaxation. 12.6. Barkai and Silbey's fractional kinetic equation. 12.7. Anomalous diffusion in a periodic potential. 12.8. Fractional Langevin equation. 12.9. Concluding remarks. This volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineering, and so on. In order to improve the presentation, to accommodate all the new developments, and to appeal to the specialized interests of the various communities involved, the book has been extensively rewritten and a very large amount of new material has been added. This has been done in order to present a comprehensive overview of the subject emphasizing via a synergetic approach that seemingly unrelated physical problems involving random noise may be described using virtually identical mathematical methods in the spirit of the founders of the subject, viz., Einstein, Langevin, Smoluchowski, Kramers, etc. The book has been written in such a way that all the material should be accessible both to an advanced researcher and a beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of scattered research papers and review articles. Langevin equations. http://id.loc.gov/authorities/subjects/sh96010212 Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Équations de Langevin. Processus de mouvement brownien. MATHEMATICS Probability & Statistics General. bisacsh Brownian motion processes fast Langevin equations fast Kalmykov, Yu. P. World Scientific (Firm) http://id.loc.gov/authorities/names/no2001005546 Print version: 9789814355667 World Scientific series in contemporary chemical physics ; v. 27. http://id.loc.gov/authorities/names/no93025701 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=575426 Volltext |
| spellingShingle | Coffey, William, 1948- The Langevin equation : with applications to stochastic problems in physics, chemistry and electrical engineering / World Scientific series in contemporary chemical physics ; Ch. 1. Historical background and introductory concepts. 1.1. Brownian motion. 1.2. Einstein's explanation of Brownian movement. 1.3. The Langevin equation. 1.4. Einstein's method. 1.5. Essential concepts in 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' theory. 1.14. Applications to 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 Néel relaxation. 1.18. Asymptotic expressions for the Néel relaxation. 1.19. Ferrofluids. 1.20. Depletion effect in a biased bistable potential. 1.21. Stochastic resonance. 1.22. Anomalous diffusion -- ch. 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: Itô and Stratonovich rules. 2.4. Derivation of differential-recurrence relations from the one-dimensional Langevin equation. 2.5. Nonlinear Langevin equation in several dimensions. 2.6. Average of the multiplicative noise term in the Langevin equation. 2.7. Methods of solution of differential-recurrence relations arising from the nonlinear Langevin equation. 2.8. Linear response theory. 2.9. Integral relaxation theory. 2.10. Linear response theory for systems with dynamics governed by single-variable Fokker-Planck equations. 2.11. Smallest non-vanishing eigenvalue: continued-fraction approach. 2.12. Effective relaxation time. 2.13. Evaluation of the dynamic susceptibility using [symbol], [symbol] and [symbol]. 2.14. Nonlinear transient response of a Brownian particle -- ch. 3. Brownian motion of a free particle and a harmonic oscillator. 3.1. Introduction. 3.2. Ornstein-Uhlenbeck theory of Brownian motion. 3.3. Stationary solution of the Langevin equation: the Wiener-Khinchin theorem. 3.4. Application to phase diffusion in MRI. 3.5. Rotational Brownian motion of a fixed-axis rotator. 3.7. Torsional oscillator model: example of the use of the Wiener integral -- ch. 4. Rotational Brownian motion about a fixed axis in N-fold cosine potentials. 4.1. Introduction. 4.2. Langevin equation for rotation about a fixed axis. 4.3. Longitudinal and transverse effective relaxation times. 4.4. Polarizabilities and relaxation times of a fixed-axis rotator with two equivalent sites. 4.5. Effect of a d.c. bias field on the orientational relaxation of a fixed-axis rotator with two equivalent sites. Ch. 5. Brownian motion in a tilted periodic potential: application to the Josephson tunneling junction. 5.1. Introduction. 5.2. Langevin equations. 5.3. Josephson junction: dynamic model. 5.4. Reduction of the averaged Langevin equation for the junction to a set of differential-recurrence relations. 5.5. Current-voltage characteristics. 5.6. Linear response to an applied alternating current. 5.7. Effective eigenvalues for the Josephson junction. 5.8. Linear impedance. 5.9. Spectrum of the Josephson radiation. 5.10. Nonlinear effects in d.c. and a.c. current-voltage characteristics. 5.11. Concluding remarks -- ch. 6. Translational Brownian motion in a double-well potential. 6.1. Introduction. 6.2. Characteristic times of the position correlation function. 6.3. Converging continued fractions for the correlation functions. 6.4. Two-mode approximation. 6.5. Stochastic resonance. 6.6. Concluding remarks -- ch. 7. Non-inertial rotational diffusion in axially symmetric external potentials: applications to orientational relaxation of molecules in fluids and liquid crystals. 7.1. Introduction. 7.2. Rotational diffusion in a potential: Langevin equation approach. 7.3. Brownian rotation in a uniaxial potential. 7.4. Brownian rotation in a uniform d.c. external field. 7.5. Nonlinear transient responses in dielectric and Kerr-effect relaxation. 7.6. Nonlinear dielectric relaxation of polar molecules in a strong a.c. electric field: steady-state response. 7.7. Concluding remarks -- ch. 8. Anisotropic non-inertial rotational diffusion in an external potential: application to linear and nonlinear dielectric relaxation and the dynamic Kerr effect. 8.1. Introduction. 8.2. Anisotropic non-inertial rotational diffusion of an asymmetric top in an external potential. 8.3. Application to dielectric relaxation. 8.4. Kerr-effect relaxation. 8.5. Concluding remarks -- ch. 9. Brownian motion of classical spins: application to magnetization relaxation in superparamagnets. 9.1. Introduction. 9.2. Brown's model: Langevin equation approach. 9.3. Magnetization relaxation in uniaxial superparamagnets. 9.4. Reversal time of the magnetization in superparamagnets with nonaxially symmetric potentials: escape-rate theory approach. 9.5. Magnetization relaxation in superparamagnets with non-axially symmetric anisotropy: matrix continued-fraction approach. 9.6. Nonlinear a.c. stationary response of superparamagnets. 9.7. Concluding remarks -- ch. 10. Inertial effects in rotational and translational Brownian motion for a single degree of freedom. 10.1. Introduction. 10.2. Inertial effects in nonlinear dielectric response. 10.3. Brownian motion of a fixed-axis rotator in a double-well potential. 10.4. Brownian motion of a fixed-axis rotator in an asymmetric double-well potential. 10.5. Brownian motion in a tilted periodic potential. 10.6. Translational Brownian motion in a double-well potential. 10.7. Concluding remarks. Ch. 11. Inertial effects in rotational diffusion in space: application to orientational relaxation in molecular liquids and ferrofluids. 11.1. Introduction. 11.2. Inertial rotational Brownian motion of a thin rod in space. 11.3. Rotational Brownian motion of a symmetrical top. 11.4. Inertial rotational Brownian motion of a rigid dipolar rotator in a uniaxial biased potential. 11.5. Itinerant oscillator model of rotational motion in liquids. 11.6. Application of the cage model to ferrofluids -- ch. 12. Anomalous diffusion and relaxation. 12.1. Discrete- and continuous-time random walks. 12.2. Fractional diffusion equation for the continuous-time random walk model. 12.3. Solution of fractional diffusion equations. 12.4. Characteristic times of anomalous diffusion. 12.5. Inertial effects in anomalous relaxation. 12.6. Barkai and Silbey's fractional kinetic equation. 12.7. Anomalous diffusion in a periodic potential. 12.8. Fractional Langevin equation. 12.9. Concluding remarks. Langevin equations. http://id.loc.gov/authorities/subjects/sh96010212 Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Équations de Langevin. Processus de mouvement brownien. MATHEMATICS Probability & Statistics General. bisacsh Brownian motion processes fast Langevin equations fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh96010212 http://id.loc.gov/authorities/subjects/sh85017265 |
| title | The Langevin equation : with applications to stochastic problems in physics, chemistry and electrical engineering / |
| title_auth | The Langevin equation : with applications to stochastic problems in physics, chemistry and electrical engineering / |
| title_exact_search | The Langevin equation : with applications to stochastic problems in physics, chemistry and electrical engineering / |
| title_full | The Langevin equation : with applications to stochastic problems in physics, chemistry and electrical engineering / William T. Coffey, Yuri P. Kalmykov. |
| title_fullStr | The Langevin equation : with applications to stochastic problems in physics, chemistry and electrical engineering / William T. Coffey, Yuri P. Kalmykov. |
| title_full_unstemmed | The Langevin equation : with applications to stochastic problems in physics, chemistry and electrical engineering / William T. Coffey, Yuri P. Kalmykov. |
| title_short | The Langevin equation : |
| title_sort | langevin equation with applications to stochastic problems in physics chemistry and electrical engineering |
| title_sub | with applications to stochastic problems in physics, chemistry and electrical engineering / |
| topic | Langevin equations. http://id.loc.gov/authorities/subjects/sh96010212 Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Équations de Langevin. Processus de mouvement brownien. MATHEMATICS Probability & Statistics General. bisacsh Brownian motion processes fast Langevin equations fast |
| topic_facet | Langevin equations. Brownian motion processes. Équations de Langevin. Processus de mouvement brownien. MATHEMATICS Probability & Statistics General. Brownian motion processes Langevin equations |
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