LEADER 05616nam 2200673Ia 450 001 9910463981803321 005 20200520144314.0 010 $a981-4355-67-4 035 $a(CKB)3280000000006436 035 $a(EBL)1193336 035 $a(OCoLC)840254741 035 $a(SSID)ssj0000915943 035 $a(PQKBManifestationID)11526306 035 $a(PQKBTitleCode)TC0000915943 035 $a(PQKBWorkID)10874572 035 $a(PQKB)11684576 035 $a(MiAaPQ)EBC1193336 035 $a(WSP)00002926 035 $a(Au-PeEL)EBL1193336 035 $a(CaPaEBR)ebr10700643 035 $a(CaONFJC)MIL486904 035 $a(EXLCZ)993280000000006436 100 $a20060524d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Langevin equation$b[electronic resource] $ewith applications to stochastic problems in physics, chemistry, and electrical engineering /$fW.T. Coffey, Yu. P. Kalmykov 205 $a3rd ed. 210 $aRiver Edge, NJ $cWorld Scientific$dc2012 215 $a1 online resource (852 p.) 225 0 $aWorld Scientific series in contemporary chemical physics ;$vv. 27 300 $aDescription based upon print version of record. 311 $a981-4355-66-6 320 $aIncludes bibliographical references and index. 327 $aPreface 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 327 $a1.5.9. 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 327 $a1.8.2. 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 327 $a1.13.7. 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 327 $a1.20. 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 327 $a2.4. Derivation of differential-recurrence relations from the one-dimensional Langevin equation 330 $aThis volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineering, and so on. In order to improve the presentation, to accommodate all the new developments, and to appeal to the specialized interests of the various communities involved, the book has been extensively rewritten and a very large amount of new material has been added. This has been done in order t 410 0$aWorld Scientific Series in Contemporary Chemical Physics 606 $aLangevin equations 606 $aBrownian motion processes 608 $aElectronic books. 615 0$aLangevin equations. 615 0$aBrownian motion processes. 676 $a519.2 700 $aCoffey$b William$f1948-$0269440 701 $aKalmykov$b Yu. P$0294627 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910463981803321 996 $aThe Langevin equation$92260084 997 $aUNINA