Target problem with evanescent subdiffusive traps.

  title={Target problem with evanescent subdiffusive traps.},
  author={Santos B. Yuste and Juan Jesus Ruiz-Lorenzo and Katja Lindenberg},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={74 4 Pt 2},
We calculate the survival probability of a stationary target in one dimension surrounded by diffusive or subdiffusive traps of time-dependent density. The survival probability of a target in the presence of traps of constant density is known to go to zero as a stretched exponential whose specific power is determined by the exponent that characterizes the motion of the traps. A density of traps that grows in time always leads to an asymptotically vanishing survival probability. Trap evanescence… 

Figures from this paper

Elucidating the Role of Subdiffusion and Evanescence in the Target Problem: Some Recent Results

We present an overview of recent results for the classic problem of the survival probability of an immobile target in the presence of a single mobile trap or of a collection of uncorrelated mobile

The survival probability of a diffusing particle constrained by two moving, absorbing boundaries

We calculate the exact asymptotic survival probability, Q, of a one-dimensional Brownian particle, initially located at the point x ∊ (−L, L), in the presence of two moving, absorbing boundaries

Evanescent continuous-time random walks.

This work studies how an evanescence process affects the number of distinct sites visited by a continuous-time random walker in one dimension by considering three different forms of the waiting time distribution between jumps, namely, exponential, long tailed, and ultraslow.

Optimal search strategies of space-time coupled random walkers with finite lifetimes.

Analytic results confirmed by numerical results show that there is an ω(m)-dependent optimal frequency ω=ω(opt) that maximizes the probability of eventual target detection, and suggests that the observed effects are robust to changes in dimensionality.

First-encounter time of two diffusing particles in confinement.

The results highlight the great impact of boundary effects in diffusion-controlled kinetics even for simple one-dimensional settings, as well as the difficulty of obtaining analytic results as soon as the translational invariance of such systems is broken.

Divergent series and memory of the initial condition in the long-time solution of some anomalous diffusion problems.

This work considers various anomalous d -dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry, finding that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single decay mode in the long-time regime.

Efficient search by optimized intermittent random walks

It is shown that a number of very efficient search strategies can lead to a decrease of PN by orders of magnitude upon appropriate choices of α and L, and that such optimal intermittent strategies are much more efficient than Brownian searches and are as efficient as search algorithms based on random walks with heavy-tailed Cauchy jump-length distributions.

Exact asymptotics for nonradiative migration-accelerated energy transfer in one-dimensional systems.

  • G. OshaninM. Tachiya
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
This work determines exactly long-time asymptotics of the donor decay function in one-dimensional systems.

Poissonian renormalizations, exponentials, and power laws.

  • I. Eliazar
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2013
A Poissonian explanation to the omnipresence of white and 1/f noises is established and is shown to be governed by uniform and harmonic intensities.

Topography of chance.

A model of multiplicative Langevin dynamics that is based on two foundations: the Langevin equation and the notion of multiplier evolution is presented, and probability distributions with power-law tails are shown to be universally and robustly generated by controls on the "edge of convexity".



Diffusion and Reactions in Fractals and Disordered Systems

Preface Part I. Basic Concepts: 1. Fractals 2. Percolation 3. Random walks and diffusion 4. Beyond random walks Part II. Anomalous Diffusion: 5. Diffusion in the Sierpinski gasket 6. Diffusion in

Aspects and Applications of the Random Walk

Introductory comments the ubiquitous characteristic function asymptotic properties and the diffusion limit lattice walks boundaries and constraints multistate random walks selected applications.

Diffusion and Reactions in Fractals and Disordered Systems

行 わ れ た 1段審査 を尊重 して 配分 した. 審査 の 印象 と して は次 の 点 が 挙げ られ る. 1) ボ ー ダ ー ラ イ ン で は 1段審査 員 の コ メ ン トが 必要で あ るが,それ に 欠 け る もの が 多 い. 2) 申請書 の 書 き方 と して ,2 段審査 委員 は も ち ろん ,点数をっ け る 1段 審査員 で も,決して 自分の 分野の 専


  • Rev. Lett. 89, 150601 (2002); R. A. Blythe and J. Bray, Phys. Rev. E 67, 041101
  • 2003


  • Rev. E 72, 061103
  • 2005

Aspects and applications of the random walk

Integral and Differential Equations of Fractional Order Integral and Differential Equations of Fractional Order

In these lectures we introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is


  • 79, 5131 (1983); J. Klafter, A. Blumen, and G. Zumofen, J. Stat. Phys. 36, 561
  • 1984