Trapping reactions with subdiffusive traps and particles (Invited Paper)

  title={Trapping reactions with subdiffusive traps and particles (Invited Paper)},
  author={Santos B. Yuste and Katja Lindenberg},
  booktitle={SPIE International Symposium on Fluctuations and Noise},
Reaction dynamics involving subdiffusive species is an interesting topic with only few known results, especially when the motion of different species is characterized by different anomalous diffusion exponents. Here we study the reaction dynamics of a (sub)diffusive particle surrounded by a sea of (sub)diffusive traps in one dimension. Under some reasonable assumptions we find rigorous results for the asymptotic survival probability of the particle in most cases, but have not succeeded in doing… 
1 Citations



From subdiffusion to superdiffusion of particles on solid surfaces.

A numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two-dimensional potential that observes superdiffusion, large-step diffusion, diffusion, and subdiffusion.

Exact asymptotics for one-dimensional diffusion with mobile traps.

It is shown that the asymptotic behavior of the survival probability of the diffusing particle, P(t), satisfies lim([-ln(P(t)]/sqrt[rho2Dt]=4/ sqrt[pi], independent of D'.

Formal solution of a class of reaction-diffusion models: reduction to a single-particle problem.

By formally eliminating the B particles from the problem, an effective dynamics for the A particles is derived from which the survival probability of a given A particle and the statistics of its spatial fluctuations can be calculated in a rather general way.

Time decay of excitations in the one-dimensional trapping problem

An exact solution is obtained for the survival fraction in the one-dimensional diffusion problem with randomly distributed deep traps. The time decay is studied both with and without a bias field.

Pascal Principle for Diffusion-Controlled Trapping Reactions

In this paper we analyse the long-time behavior of the survival probability P A ( t ) of an A particle, which performs lattice random walk in the presence of randomly moving traps B . We show that

Fractional dynamics approach to diffusion-assisted reactions in disordered media

We present a theory for describing nonclassical dynamics of reactions occurring in disordered media based on the fractional diffusion equation. An exact expression is derived for the Green’s function

Subdiffusion and localization in the one-dimensional trap model.

  • E. BertinJ. Bouchaud
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
A one-dimensional generalization of the exponential trap model is studied, which finds the dynamical participation ratios to be finite, but different from their equilibrium counterparts, and obtains the asymptotic shape of the average diffusion front in the subdiffusive phase.

Diffusion on a solid surface: anomalous is normal.

A numerical study of classical particles diffusing on a solid surface shows that this anomalous behavior is controlled by the friction coefficient and stress that it emerges naturally in a system described by ordinary canonical Maxwell-Boltzmann statistics.