Validity of the mean-field approximation for diffusion on a random comb

Revathi, S.; Balakrishnan, V.; Lakshmibala, S.; Murthy, K. P. N.

doi:10.1103/physreve.54.2298

Cited by 12 publications

(7 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper we prove this result which shows that mean field theory is exact in this case. Mean field theory was shown to be exact in a special case in [13]. We will also show that the spectral dimension of random combs whose teeth may be infinitely long is always 3/2.…”

Section: Introductionmentioning

confidence: 99%

Random walks on combs

Durhuus

Jónsson

Wheater

2006

J. Phys. A: Math. Gen.

115

View full text Add to dashboard Cite

Abstract. We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length. We also calculate exactly the spectral dimension of some fixed non-translationally invariant combs. We relate the spectral dimension to the critical exponent of the mass of the two-point function for random walks on random combs, and compute mean displacements as a function of walk duration. We prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension.1 durhuus@math.ku.dk 2 thjons@raunvis.hi.is

show abstract

Section: Introductionmentioning

confidence: 99%

Random walks on combs

Durhuus

Jónsson

Wheater

2006

J. Phys. A: Math. Gen.

115

View full text Add to dashboard Cite

show abstract

“…An understanding of escape time properties in such systems could open the door for understanding new stochastically driven phenomena. To our knowledge there has yet been little work done along these lines, although we are aware of some studies relating the anomalous transport properties on a random comb to the distribution of mean first passage times [6].…”

Section: Introductionmentioning

confidence: 99%

Escape time in anomalous diffusive media

2001

View full text Add to dashboard Cite

We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation ∂tρ = ∂x[∂xU ρ] + D∂ 2 x ρ ν , where the potential of the drift, U (x), presents a double-well and D, ν are real parameters. For systems close to the steady state we obtain an analytical expression of the mean first passage time, yielding a generalization of Arrhenius law. Analytical predictions are in very good agreement with numerical experiments performed through integration of the associated Ito-Langevin equation. For ν = 1 important anomalies are detected in comparison to the standard Brownian case. These results are compared to those obtained numerically for initial conditions far from the steady state.

show abstract

“…Here, it is well known that normal diffusion takes place regardless of the value of α, i.e., γ = 1 [7,26]. The diffusion coefficient for this case has already been calculated with a variety of different methods [30,45]. For the sake of completeness, a simple alternative derivation is given below.…”

Section: Case α >mentioning

confidence: 99%

Anomalous diffusion and FRAP dynamics in the random comb model

Yuste,

Abad,

Baumgaertner

2016

Preprint

View full text Add to dashboard Cite

We address the problem of diffusion on a comb whose teeth display a varying length. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying the large-ℓ behavior P (ℓ) ∼ ℓ −(1+α) (α > 0). Our method is based on the mean-field description provided by the well-tested CTRW approach for the random comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations. We subsequently incorporate retardation effects arising from binding/unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, our results for the diffusion coefficient are used as an input to compute concentration recovery curves mimicking FRAP experiments in comb-like geometries such as spiny dendrites. We show that such curves cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comb-like systems.

show abstract

Validity of the mean-field approximation for diffusion on a random comb

Cited by 12 publications

References 23 publications

Random walks on combs

Random walks on combs

Escape time in anomalous diffusive media

Anomalous diffusion and FRAP dynamics in the random comb model

Contact Info

Product

Resources

About