Clas Blomberg - Physics of life-Elsevier Science (2007)

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Chapter 23. Brownian motion and continuation 247In a stationary situation without periodic force, the probability is 1/2. Now use the expressionfor r and look for a contribution, proportional to the periodic force. Again, ax 0 /kT isconsidered small. We may put W 1/2 W 1 sin(t w), and get:avW1 cos( vtw) r0 sin( vt) r0W1sin( vt−w)2kTIdentification of coefficients of cos and sin terms then yields the result:vtanw ;r0ax bP1kTBr 0vv2r0 2(23.25)w is a phase shift of the stochastic oscillations, W 1 is the amplitude of the oscillating contributionof the probability. This is usually compared to the spectral function of the noise,in this case, the Brownian motion in the potential at the frequency . This spectral functionis in this case primarily given by the Fourier transform of the slowly decaying probabilitywith the exponential decay function exp(r 0 t) which is 1/( 2 R 2 0). Thus, that quotient,the signal–noise ratio, becomes proportional to v r 0 . As a function of the friction (whichalso determines the strength of the irregular term, and what is called noise), it will have thesame maximum as found in the Kramers’ problem.
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PHYSICS OF LIFEThe Physicist’s Ro
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PHYSICS OF LIFEThe Physicist’s Ro
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ContentsPrefaceixPart I General int
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Contentsvii20E Birth-death process
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PrefaceFor me, the journey to the p
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Part IGeneral introduction§ 1 INTR
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Chapter 1. Introduction: the aim an
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Chapter 2. The physics of life: phy
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Part IIThe physics basis§ 3 CONCEP
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Chapter 4. Basics of classical (New
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Chapter 5. Electricity: the core of
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Chapter 6. Quantum mechanics 45(I h
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Chapter 6. Quantum mechanics 47The
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Chapter 6. Quantum mechanics 49prin
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Chapter 6. Quantum mechanics 51that
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Chapter 6. Quantum mechanics 53“v
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Chapter 6. Quantum mechanics 55The
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Chapter 6. Quantum mechanics 57If w
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Chapter 6. Quantum mechanics 59On t
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Chapter 6. Quantum mechanics 61than
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Chapter 7. Basic thermodynamics: in
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Chapter 8. Statistical thermodynami
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Part IIIThe general trends and obje
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Chapter 9. Some trends in 20th cent
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Chapter 10. From the simple equilib
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Chapter 11. Theoretical physics mod
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Chapter 11. Theoretical physics mod
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Chapter 12. The biological molecule
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Chapter 13. What is life? 113Figure
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Chapter 13. What is life? 115after
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Part IVGoing further with thermodyn
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Chapter 14. Thermodynamics formalis
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Chapter 15. Examples of entropy and
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Chapter 16. Statistical thermodynam
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Part VStochastic dynamics§ 17 PROB
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Chapter 17. Probability concepts 17
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Chapter 17. Probability concepts 17
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Chapter 18. Stochastic processes 17
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Chapter 18. Stochastic processes 18
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Chapter 19. Random walk 183The tota
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Chapter 19. Random walk 185r in the
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Chapter 19. Random walk 187boundary
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Chapter 19. Random walk 189The sum
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Chapter 20. Step processes: master
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Page 228 and 229: Chapter 21. Brownian motion: first
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Page 260 and 261: Part VIMacromolecular applications
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Page 268 and 269: Chapter 25. Enzyme kinetics 257and
Page 270 and 271: Chapter 25. Enzyme kinetics 259long
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Page 278 and 279: Part VIINon-linearity§ 26 WHAT DOE
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Chapter 28. Deterministic chaos 297
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Chapter 29. Noise and non-linear ph
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Part VIIIApplications§ 30 RECOGNIT
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Chapter 30. Recognition and selecti
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Chapter 31. Brownian ratchet: unidi
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Chapter 32. The neural system 343Fi
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Chapter 32. The neural system 345ev
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Chapter 32. The neural system 347Th
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Chapter 32. The neural system 34932
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Chapter 33. Origin of life 351once
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Chapter 33. Origin of life 353It is
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Chapter 33. Origin of life 355as am
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Chapter 33. Origin of life 357What
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Chapter 33. Origin of life 359world
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Chapter 33. Origin of life 361This
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Chapter 33. Origin of life 363its l
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Chapter 33. Origin of life 365k is
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Chapter 33. Origin of life 367We al
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Chapter 33. Origin of life 369As a
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Chapter 33. Origin of life 371Eithe
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Chapter 33. Origin of life 373loops
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Chapter 33. Origin of life 375itsel
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Part IXGoing further§ 34 PHYSICS A
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Chapter 34. Physics aspects of evol
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Chapter 34. Physics aspects of evol
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Chapter 35. Determinism and randomn
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Chapter 36. Higher functions of lif
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Chapter 37. About the direction of
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Chapter 38. We live in the best of
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Chapter 38. We live in the best of
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ReferencesAbramowitz, M. and Stegun
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References 413Decroly, D. and Goldb
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References 415Hammerhoff, S. R., 19
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References 417Mosekilde, E., 1996.
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References 419Tsong, T. Y. and Chan
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Indexa-helix, 99s-bond, 50-51, 99d-
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Index 423Fibonacci series, 289, 291
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Index 425polar, 32, 97, 100, 102-10
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Clas Blomberg - Physics of life-Elsevier Science (2007)

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