Charles R. Doering
Timothy C. Elston
Publisher: Cambridge University Press
Print Publication Year: 1997
Online Publication Date:December 2009
Online ISBN:9780511564284
Hardback ISBN:9780521559744
Paperback ISBN:9780521018340
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511564284.024
Subjects: Statistical Physics, Condensed Matter Physics, Nanoscience and Mesoscopic Physics
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Two recent developments involving activation and transport processes in simple stochastic nonlinear systems are reviewed in this chapter. The first is the idea of ‘resonant activation’ in which the mean first-passage time for escape over a fluctuating barrier passes through a minimum as the characteristic time scale of the fluctuating barrier is varied. The other is the notion of active transport in a fluctuating environment by so-called ‘ratchet’ mechanisms. Here, nonequilibrium fluctuations combined with spatial anisotropy conspire to generate systematic motion. The fundamental principles of these phenomena are covered, and some motivations for their study are described.
Introduction
The study of the interplay of noise and nonlinear dynamics presents many challenges, and interesting phenomena and insights appear even in onedimensional (1D) systems. Examples include Kramers’ fundamental theory of the Arrhenius temperature dependence of activated rate processes, Landauer's further insights into the role of multiplicative noise, and the theory of noise-induced transitions. This chapter reviews more recent developments which go beyond those studies in that the characteristic time scale of the fluctuations plays a major role in the dynamics of the system, whereas the phenomena in are fundamentally white-noise effects. Specifically, the two effects to be described in this chapter are the phenomena of ‘resonant activation’ and transport in ‘stochastic ratchets’.
Resonant activation is a generalization of Kramers’ model of activation over a potential barrier to the situation where the barrier itself is fluctuating randomly.
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Part I - Reaction-Diffusion Systems and Models of Catalysis: Read PDF
pp. 1-2
1 - Scaling theories of diffusion-controlled and ballistically controlled bimolecular reactions: Read PDF
pp. 3-28
2 - The coalescence process, A + A → A, and the method of interparticle distribution functions: Read PDF
pp. 29-50
3 - Critical phenomena at absorbing states: Read PDF
pp. 51-70
Part II - Kinetic Ising Models: Read PDF
pp. 71-72
4 - Kinetic Ising models with competing dynamics: mappings, correlations, steady states, and phase transitions: Read PDF
pp. 73-92
5 - Glauber dynamics of the Ising model: Read PDF
pp. 93-110
6 - 1D kinetic Ising models at low temperatures—critical dynamics, domain growth, and freezing: Read PDF
pp. 111-140
Part III - Ordering, Coagulation, Phase Separation: Read PDF
pp. 141-142
7 - Phase-ordering dynamics in one dimension: Read PDF
pp. 143-166
8 - Phase separation, cluster growth, and reaction kinetics in models with synchronous dynamics: Read PDF
pp. 167-180
9 - Stochastic models of aggregation with injection: Read PDF
pp. 181-202
Part IV - Random Adsorption and Relaxation Processes: Read PDF
pp. 203-204
10 - Random and cooperative sequential adsorption: exactly solvable models on 1D lattices, continuum limits, and 2D extensions: Read PDF
pp. 205-228
11 - Lattice models of irreversible adsorption and diffusion: Read PDF
pp. 229-246
12 - Deposition-evaporation dynamics: jamming, conservation laws, and dynamical diversity: Read PDF
pp. 247-260
Part V - Fluctuations in Particle and Surface Systems: Read PDF
pp. 261-262
13 - Microscopic models of macroscopic shocks: Read PDF
pp. 263-276
14 - The asymmetric exclusion model: exact results through a matrix approach: Read PDF
pp. 277-304
15 - Nonequilibrium surface dynamics with volume conservation: Read PDF
pp. 305-328
16 - Directed-walk models of polymers and wetting: Read PDF
pp. 329-334
Part VI - Diffusion and Transport in One Dimension: Read PDF
pp. 335-336
17 - Some recent exact solutions of the Fokker-Planck equation: Read PDF
pp. 337-358
18 - Random walks, resonance, and ratchets: Read PDF
pp. 359-370
19 - One-dimensional interacting random walks in a random environment: Read PDF
pp. 371-388
Part VII - Experimental Results: Read PDF
pp. 389-390
20 - Diffusion-limited exciton kinetics in one-dimensional systems: Read PDF
pp. 391-420
21 - Experimental investigations of molecular and excitonic elementary reaction kinetics in one-dimensional systems: Read PDF
pp. 421-442
22 - Luminescence quenching as a probe of particle distribution: Read PDF
pp. 443-460
pp. 461-468
pp. 469-470