Analysis of Confined Random Walkers with Applications to Processes Occurring in Molecular Aggregates and Immunological Systems

Chase, Matthew; Spendier, Kathrin; Kenkre, V. M.

doi:10.1021/acs.jpcb.5b12548

Cited by 17 publications

(20 citation statements)

References 33 publications

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“…In the case of the drift model, the bias is represented by a constant drift towards the focal point that is present at all times, while in the case of the stochastic resetting model, the bias is represented through a long jump (an infinitely fast movement) to the focal point at random times. The former is an example of a Smoluchowski-type model that has been used in various contexts, e.g., to model Brownian particles subject to dry friction [7] and motion of excitons in doped molecular crystals and signal receptor clusters on the surface of T-cells during immunological synapse formation [8]. It has also appeared in the animal movement literature to represent movement within a home range, and is called the Holgate-Okubo model [9,10,11].…”

Section: Focal Point Modelsmentioning

confidence: 99%

“…The values of the dynamical parameters of the two models are chosen so as to have the steady-state characteristic spatial scale in the two models the same, by setting v/D = r/D = α, see Eqs. (8) and (13). The temporal scale is on the other hand set to rt = T for the drift model and v 2 t/D = T for the resetting model.…”

Section: Focal Point Modelsmentioning

confidence: 99%

“…A separation of variable allows to map the problem to an eigenvalue problem of the Sturm-Liouville type [7]. Another way is to solve the equation in the Laplace variable , that is, to find P (x, |x 0 , 0) ≡ ∞ 0 dt e − t P (x, t|x 0 , 0) in the region to the left and to the right of x 0 , and then match the two solutions at x 0 to obtain [8]…”

Section: The Drift Modelmentioning

confidence: 99%

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Comparison of two models of tethered motion

Giuggioli¹,

Gupta²,

Chase³

2019

J. Phys. A: Math. Theor.

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We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic bias towards the focal point, while in the other case, it resets its position to the focal point at random times. The deterministic tendency of the biased walker makes the forays away from the focal point more unlikely when compared to the random nature of the returns of the resetting walker. This difference has consequences on the spatio-temporal dynamics at intermediate times. To show the differences in the two models, we analyze their probability distribution and their dynamics in presence and absence of partially or fully absorbing traps. We derive analytically various quantities: (i) mean first-passage times to one target, where we recover results obtained earlier by a different technique, (ii) splitting probabilities to either of two targets as well as survival probabilities when one or either target is partially absorbing. The interplay between confinement, diffusion and absorbing traps produces interesting non-monotonic effects in various quantities, all potentially accessible in experiments. The formalism developed here may have a diverse range of applications, from study of animals roaming within home ranges and of electronic excitations moving in organic crystals to developing efficient search algorithms for locating targets in a crowded environment.

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Section: Focal Point Modelsmentioning

confidence: 99%

Section: Focal Point Modelsmentioning

confidence: 99%

Section: The Drift Modelmentioning

confidence: 99%

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Comparison of two models of tethered motion

Giuggioli¹,

Gupta²,

Chase³

2019

J. Phys. A: Math. Theor.

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“…x . By using proper boundary condition, the Green's function for the linear or V shaped potential will be [17] G 0 (x, s+k r |x 0 ) = e −(|x|−|x0|)/2l…”

Section: Linear Potentialmentioning

confidence: 99%

A new approach in an analytical method for diffusion dynamics for the presence of delocalized sink in a potential well: Application to different potential curves

Samanta

2020

Chemical Physics Letters

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We provide a new approach to solve one dimension Fokker-Planck equation in the Laplace domain for the case where a particle is evolving in a potential energy curve in the presence of general delocalized sink. We also calculate rate constants in the presence of non-localized sink on different potential energy curves. In the previous method, we need to solve matrix equations to calculate rate constant but in our method it is not required. We also calculate the rate constant by using the method to some known potential curve, viz, flat potential, linear potential and parabolic potential.

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“…Following on from ref. [30], an FP representation for the one-time and two-time PDF has been developed to construct the conditional PDF for a DLE [31].…”

Section: Introductionmentioning

confidence: 99%

Fokker–Planck representations of non-Markov Langevin equations: application to delayed systems

Giuggioli

Neu

2019

Phil. Trans. R. Soc. A.

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Noise and time delays, or history-dependent processes, play an integral part in many natural and man-made systems. The resulting interplay between random fluctuations and time non-locality are essential features of the emerging complex dynamics in non-Markov systems. While stochastic differential equations in the form of Langevin equations with additive noise for such systems exist, the corresponding probabilistic formalism is yet to be developed. Here we introduce such a framework via an infinite hierarchy of coupled Fokker–Planck equations for the n -time probability distribution. When the non-Markov Langevin equation is linear, we show how the hierarchy can be truncated at n = 2 by converting the time non-local Langevin equation to a time-local one with additive coloured noise. We compare the resulting Fokker–Planck equations to an earlier version, solve them analytically and analyse the temporal features of the probability distributions that would allow to distinguish between Markov and non-Markov features. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

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Analysis of Confined Random Walkers with Applications to Processes Occurring in Molecular Aggregates and Immunological Systems

Cited by 17 publications

References 33 publications

Comparison of two models of tethered motion

Comparison of two models of tethered motion

A new approach in an analytical method for diffusion dynamics for the presence of delocalized sink in a potential well: Application to different potential curves

Fokker–Planck representations of non-Markov Langevin equations: application to delayed systems

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