LEADER 05262nam 2200709Ia 450 001 9910819881703321 005 20230617040914.0 010 $a1-281-93552-2 010 $a9786611935528 010 $a981-279-509-X 035 $a(CKB)1000000000537818 035 $a(EBL)1679721 035 $a(OCoLC)879074223 035 $a(SSID)ssj0000188798 035 $a(PQKBManifestationID)11939206 035 $a(PQKBTitleCode)TC0000188798 035 $a(PQKBWorkID)10154341 035 $a(PQKB)11681423 035 $a(MiAaPQ)EBC1679721 035 $a(WSP)00005343 035 $a(Au-PeEL)EBL1679721 035 $a(CaPaEBR)ebr10255379 035 $a(CaONFJC)MIL193552 035 $a(EXLCZ)991000000000537818 100 $a20040324d2004 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, J.T. Waldron 205 $a2nd ed. 210 $aSingapore ;$aRiver Edge, N.J. $cWorld Scientific$dc2004 215 $a1 online resource (704 p.) 225 1 $aSeries in contemporary chemical physics ;$vv. 14 300 $aDescription based upon print version of record. 311 $a981-238-462-6 320 $aIncludes bibliographical references and index. 327 $aContents ; 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 327 $a1.5 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 327 $a1.12 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 327 $a1.16 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 327 $aReferences 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 $a This volume is the second edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the Brownian motion in a potential, with emphasis on modern applications in the natural sciences, electrical engineering and so on. It has been substantially enlarged to cover in a succinct manner a number of new topics, such as anomalous diffusion, continuous time random walks, stochastic resonance etc, which are of major current interest in view of the large number of disparate physical systems exhibiting these phenomena. The book has been written in suc 410 0$aWorld Scientific series in contemporary chemical physics ;$vv. 14. 606 $aLangevin equations 606 $aBrownian motion processes 615 0$aLangevin equations. 615 0$aBrownian motion processes. 676 $a519.2 676 $a530.475 700 $aCoffey$b William$f1948-$0269440 701 $aKalmykov$b Yu. P$0294627 701 $aWaldron$b J. T$0300676 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910819881703321 996 $aThe Langevin equation$94116093 997 $aUNINA