Normal and anomalous diffusion of Brownian particles on disordered potentials

Salgado-García, R.

doi:10.1016/j.physa.2016.02.042

Cited by 10 publications

(13 citation statements)

References 18 publications

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“…As a particular limit, the dynamics with = 2 is ballistic motion in which a particle moves at a constant velocity. Apart from this classification, recently interest has been shown in whether a diffusive motion is homogeneous or spatiotemporally heterogeneous [72][73][74][75][76][77][78][79][80]. In soft complex systems, some processes have been found to show the Fickian, but non-Gaussian, diffusion originating from spatiotemporal heterogeneity [81][82][83][84][85][86][87][88][89].…”

Section: Diffusion Processes and Mathematical Modelsmentioning

confidence: 99%

A mini-review of the diffusion dynamics of DNA-binding proteins: experiments and models

Park

Lee

Durang

2021

J. Korean Phys. Soc.

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In the course of various biological processes, specific DNA-binding proteins must efficiently find a particular target sequence/ protein or a damaged site on the DNA. DNA-binding proteins perform this task based on diffusion. Nevertheless, investigations over recent decades have found that the diffusion dynamics of DNA-binding proteins are generally complicated and, further, protein specific. In this review, we collect experimental and theoretical studies that quantify the diffusion dynamics of DNA-binding proteins and review them from the viewpoint of diffusion processes.

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Section: Diffusion Processes and Mathematical Modelsmentioning

confidence: 99%

A mini-review of the diffusion dynamics of DNA-binding proteins: experiments and models

Park

Lee

Durang

2021

J. Korean Phys. Soc.

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“…This difference is attributed to spatial correlations: their presence brings about a smoothing of the potential energy landscape, removes the deep "Three Site Traps," and thereby leads to the reduction to Zwanzig's result [18]. The case of diffusion in a one-dimensional piecewise-defined energy landscape made up of triangular sections with Gaussian-distributed heights was studied and agreement with Zwanzig's result was obtained in the limit of large thermal energies [19]. In this regime the effect of the presence of three site traps upon the motion will not be significant.…”

Section: Introductionmentioning

confidence: 72%

Effective diffusion in one-dimensional rough potential-energy landscapes

Gray

Yong

2020

Phys. Rev. E

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Diffusion in spatially rough, confining, one-dimensional continuous energy landscapes is treated using Zwanzig's proposal, which is based on the Smoluchowski equation. We show that Zwanzig's conjecture agrees with Brownian dynamics simulations only in the regime of small roughness. Our correction of Zwanzig's framework corroborates well with numerical results. A numerical simulation scheme based on our coarse-grained Langevin dynamics offers significant reductions in computational time. The mean first-passage time problem in the case of random roughness is treated. Finally, we address the validity of the separation of length scales assumption for the case of polynomial backgrounds and cosine-based roughness. Our results are applicable to hierarchical energy landscapes such as that of a protein's folding and transport processes in disordered media, where there is clear separation of length scale between smooth underlying potential and its rough perturbation.

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“…Now we shall present some calculations for obtaining an analytical expression for the effective diffusion coefficient. To this end we will made use of the central limit theorem in order to obtain the asymptotic statistical properties of the net displacement |r(t) − r(0)| for large t. This procedure is similar to the one used for obtaining the transport properties (such as the diffusion coefficient and the effective particle current) in one-dimensional disordered systems [24][25][26][27].…”

Section: Normal Diffusionmentioning

confidence: 99%

Active particles in reactive disordered media: how does adsorption affects diffusion?

Salgado-García

2021

Preprint

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In this work we study analytically and numerically the transport properties of non-interacting active particles moving on a d-dimensional disordered media. The disorder in the space is modeled by means of a set of non-overlapping spherical obstacles. We assume that obstacles are reactive in the sense that they react in the presence of the particles in an attractive manner: when the particle collides with an obstacle, it is attached during a random time (adsorption time), i.e., it gets adsorbed by an obstacle; thereafter the particle is detached from the obstacle and continues its motion in a random direction. We give an analytical formula for the effective diffusion coefficient when the mean adsorption time is finite. When the mean adsorption time is infinite, we show that the system undergoes a transition from a normal to anomalous diffusion regime. We also show that another transition takes place in the mean number of adsorbed particles: in the anomalous diffusion phase all the particles become adsorbed in the average. We show that the fraction of adsorbed particles, seen as an order parameter of the system, undergoes a second-order-like phase transition, because the fraction of adsorbed particles is not differentiable but changes continuously as a function of a parameter of the model.

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Normal and anomalous diffusion of Brownian particles on disordered potentials

Cited by 10 publications

References 18 publications

A mini-review of the diffusion dynamics of DNA-binding proteins: experiments and models

A mini-review of the diffusion dynamics of DNA-binding proteins: experiments and models

Effective diffusion in one-dimensional rough potential-energy landscapes

Active particles in reactive disordered media: how does adsorption affects diffusion?

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