First-passage phenomena and their applications / editors Ralf Metzler, Gleb Oshanin, Sidney Redner.

Format:

Book

Contributor:

Metzler, Ralf, editor of compilation.

Oshanin, G. (Gleb), editor of compilation.

Redner, Sidney, 1951- editor of compilation.

Language:

English

Subjects (All):

Statistical mechanics--Study and teaching (Graduate).

Statistical mechanics.

Stochastic processes--Study and teaching (Graduate).

Stochastic processes.

Random walks (Mathematics)--Study and teaching (Graduate).

Random walks (Mathematics).

Physical Description:

1 online resource (608 p.)

Place of Publication:

Singapore : World Scientific, 2014.

Language Note:

English

Summary:

The book contains review articles on recent advances in first-passage phenomena and applications contributed by leading international experts. It is intended for graduate students and researchers who are interested in learning about this intriguing and important topic. Sample Chapter(s). Chapter 1: Arrival Statistics and Exploration Properties of Mortal Walkers (290 KB). Contents: Arrival Statistics and Exploration Properties of Mortal Walkers (S B Yuste et al.); First-Passage of a Randomly Accelerated Particle (T Burkhardt); First-Passage Problems in Anomalous Diffusion (A Rosso and A Zoia);

Contents:

Preface; Contents; 1. Arrival Statistics and Exploration Properties of Mortal Walkers; 1. Introduction; 2. Generating function formalism for mortal walkers; 2.1. Master equation for mortal walkers; 2.2. First-passage probabilities and statistics of site occupation; 2.2.1. Number of distinct sites visited by a mortal walker; 2.2.2. Expected number of sites visited at least a given number of times; 2.2.3. Repeated visits to a given lattice site; 3. Results for specific decay laws; 3.1. Exponential evanescence; 3.1.1. Number of distinct sites visited

3.1.2. Repeated visits to a given lattice site3.2. Power-law evanescence; 4. The target problem with evanescent traps; 4.1. Discrete-time problem; 4.2. Continuous space and time; 5. Conclusions and outlook; Acknowledgments; Appendix A. Derivation of a continuum reaction-diffusion equation from the master equation for mortal walkers; Appendix B. Time-discretization of the walker density; References; 2. First Passage of a Randomly Accelerated Particle; 1. Introduction; 2. Random acceleration on the half line x > 0; 2.1. First arrival at the origin; 2.2. First return to the origin

2.3. Multiple returns to the origin2.4. Solution of the Fokker-Planck equation; 2.5. Particle subject to a constant force and a random force; 2.6. Partially absorbing, inelastic boundary; 2.7. Windy cliff problem; 3. First exit from the interval 0 < x < 1; 3.1. Mean exit time; 3.2. Splitting probabilities; 3.3. Long time behavior; 4. Extreme statistics of the random acceleration process; 5. Applications; 5.1. Semi-flexible polymer in a cylindrical channel; 5.2. Spatial persistence in interface growth; 5.3. Other applications; Acknowledgments; References

3. First Passage Problems in Anomalous Diffusion1. Beyond Brownian motion: anomalous diffusion; 2. Polymer translocation and fractional Brownian motion; 2.1. The fractional Brownian motion; 2.2. First-passage properties: the hitting probability; 2.3. The effects of the boundaries: the exponent φ; 2.4. Perturbation methods; 2.5. The tagged monomer; 3. Continuous time random walks and Levy flights; 3.1. First-passage properties of Levy Flights; 4. The random acceleration model; 4.1. Extreme statistics; 4.1.1. Integral of a Brownian bridge; 4.1.2. Integral of a free Brownian motion

4.2. The convex hull of a random acceleration process5. A digression on the hitting probability; 6. Conclusions and perspectives; References; 4. First-Passage Times of Intermittent Random Walks; 1. Introduction; 2. Animals looking for food; 2.1. Model of intermittent search; 2.2. Minimizing the search time; 2.3. Should animals really perform Levy strategies?; 3. How does a protein find its target sequence on DNA?; 3.1. Definition of the model; 3.2. First-passage density; 3.3. Optimal search strategy; 4. Active intermittent transport in cells; 5. Robustness of the results; 5.1. Basic equations

5.2. Results for the diffusive mode of detection

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters.

Description based on print version record.

ISBN:

981-4590-29-0