LEADER 06394nam 2201009Ia 450 001 9910960525703321 005 20251116233810.0 010 $a9786611998790 010 $a9781281998798 010 $a1281998796 010 $a9780191565083 010 $a0191565083 010 $a9780199556441 010 $a019955644X 035 $a(CKB)2560000000298393 035 $a(EBL)431105 035 $a(OCoLC)320958687 035 $a(SSID)ssj0000115304 035 $a(PQKBManifestationID)11132045 035 $a(PQKBTitleCode)TC0000115304 035 $a(PQKBWorkID)10008345 035 $a(PQKB)10853492 035 $a(StDuBDS)EDZ0000076462 035 $a(MiAaPQ)EBC431105 035 $a(Au-PeEL)EBL431105 035 $a(CaPaEBR)ebr10358346 035 $a(CaONFJC)MIL199879 035 $a(MiAaPQ)EBC7036444 035 $a(Au-PeEL)EBL7036444 035 $a(OCoLC)967258696 035 $a(EXLCZ)992560000000298393 100 $a20020107d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBrownian motion $efluctuations, dynamics, and applications /$fRobert M. Mazo 205 $a1st ed. 210 $aOxford $cClarendon Press$d2002 215 $a1 online resource (302 p.) 225 1 $aOxford science publications 225 1 $aInternational series of monographs on physics ;$v112 300 $aDescription based upon print version of record. 311 08$a9780198515678 311 08$a0198515677 311 08$a9780191705625 311 08$a0191705624 320 $aIncludes bibliographical references (p. 271-284) and index. 327 $aContents; 1 Historical Background; 1.1 Robert Brown; 1.2 Between Brown and Einstein; 1.3 Albert Einstein; 1.4 Marian von Smoluchowski; 1.5 Molecular Reality; 1.6 The Scope of this Book; 2 Probability Theory; 2.1 Probability; 2.2 Conditional Probability and Independence; 2.3 Random Variables and Probability Distributions; 2.4 Expectations and Particular Distributions; 2.5 Characteristic Function; Sums of Random Variables; 2.6 Conclusion; 3 Stochastic Processes; 3.1 Stochastic Processes; 3.2 Distribution Functions; 3.3 Classification of Stochastic Processes; 3.4 The Fokker-Planck Equation 327 $a3.5 Some Special Processes3.6 Calculus of Stochastic Processes; 3.7 Fourier Analysis of Random Processes; 3.8 White Noise; 3.9 Conclusion; 4 Einstein-Smoluchowski Theory; 4.1 What is Brownian Motion?; 4.2 Smoluchowski's Theory; 4.3 Smoluchowski Theory Continued; 4.4 Einstein's Theory; 4.5 Diffusion Coefficient and Friction Constant; 4.6 The Langevin Theory; 5 Stochastic Differential Equations and Integrals; 5.1 The Langevin Equation Revisited; 5.2 Stochastic Differential Equations; 5.3 Which Rule Should Be Used?; 5.4 Some Examples; 6 Functional Integrals; 6.1 Functional Integrals 327 $a6.2 The Wiener Integral6.3 Wiener Measure; 6.4 The Feynman-Kac Formula; 6.5 Feynman Path Integrals; 6.6 Evaluation of Wiener Integrals; 6.7 Applications of Functional Integrals; 7 Some Important Special Cases; 7.1 Several Cases of Interest; 7.2 The Free Particle; 7.3 The Distribution of Displacements; 7.4 The Harmonically Bound Particle; 7.5 A Particle in a Constant Force Field; 7.6 The Uniaxial Rotor; 7.7 An Equation for the Distribution of Displacements; 7.8 Discussion; 8 The Smoluchowski Equation; 8.1 The Kramers-Klein Equation; 8.2 The Smoluchowski Equation 327 $a8.3 Elimination of Fast Variables8.4 The Smoluchowski Equation Continued; 8.5 Passage over Potential Barriers; 8.6 Concluding Remarks; 9 Random Walk; 9.1 The Random Walk; 9.2 The One-Dimensional Pearson Walk; 9.3 The Biased Random Walk; 9.4 The Persistent Walk; 9.5 Boundaries and First Passage Times; 9.6 Random Remarks on Random Walks; 10 Statistical Mechanics; 10.1 Molecular Distribution Functions; 10.2 The Liouville Equation; 10.3 Projection Operators-The Zwanzig Equation; 10.4 Projection Operators-The Mori Equation; 10.5 Concluding Remarks 327 $a11 Stochastic Equations from a Statistical Mechanical Viewpoint11.1 The Langevin Equation A Heuristic View; 11.2 The Fokker-Planck Equation-A Heuristic View; 11.3 What is Wrong with these Derivations?; 11.4 Eliminating Fast Processes; 11.5 The Distribution Function; 11.6 Discussion; 12 Two Exactly Treatable Models; 12.1 Two Illustrative Examples; 12.2 Brownian Motion in a Dilute Gas; 12.3 Discussion; 12.4 The Particle Bound to a Lattice; 12.5 The One-Dimensional Case; 12.6 Discussion; 13 Brownian Motion and Noise; 13.1 Limits on Measurement; 13.2 Oscillations of a Fiber 327 $a13.3 A Pneumatic Example 330 $aBrownian motion- the incessant motion of small particles suspended in a fluid- is an important topic in statistical physics and physical chemistry. This book studies its origin in molecular scale fluctuations, its description in terms of random process theory and also in terms of statistical mechanics. - ;Brownian motion - the incessant motion of small particles suspended in a fluid - is an important topic in statistical physics and physical chemistry. This book studies its origin in molecular scale fluctuations, its description in terms of random process theory and also in terms of statistica 410 0$aInternational series of monographs on physics (Oxford, England) ;$v112. 410 0$aOxford science publications. 606 $aBrownian motion processes 606 $aMarkov processes 606 $aProcessos de moviment brownià$2thub 606 $aProcessos estocàstics$2thub 606 $aProcessos de Markov$2thub 606 $aMecànica estadística$2thub 606 $aDifusió$2thub 606 $aPolímers$2thub 606 $aFluctuacions (Física)$2thub 608 $aLlibres electrònics$2thub 615 0$aBrownian motion processes. 615 0$aMarkov processes. 615 7$aProcessos de moviment brownià 615 7$aProcessos estocàstics 615 7$aProcessos de Markov 615 7$aMecànica estadística 615 7$aDifusió 615 7$aPolímers 615 7$aFluctuacions (Física) 676 $a530.42 676 $a530.475 700 $aMazo$b Robert M$066678 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910960525703321 996 $aBrownian motion$9377517 997 $aUNINA