Transport properties and first-arrival statistics of random motion with stochastic reset times

Masó-Puigdellosas, Axel; Campos, Daniel; Méndez, Vicenç

doi:10.1103/physreve.99.012141

Cited by 64 publications

(84 citation statements)

References 37 publications

(49 reference statements)

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“…We have two different contributions to the PDF at the NESS: the first term in the numerator accounts for the propagation of the stochastic motion, while the second term accounts for the walkers returning to the origin at a finite velocity, after suffering a reset at a position |z| > |x|. In fact, taking the limit v → ∞, corresponding to instantaneous resets, one recovers the result recently found in [20] for Markovian resetting applied to a general propagator P (x, t).…”

Section: Markovian Resettingsupporting

confidence: 73%

“…In [20], the asymptotic behavior of the overall MSD is studied for a stochastic motion process which resets its position at times distributed according to a resetting PDF, after which remains at the origin during a period determined by a residence time PDF. There, the scaling of the overall MSD is shown to strongly depend on the resetting and the residence time PDFs.…”

Section: B Returning Time Pdfmentioning

confidence: 99%

“…(2.20) Therefore, a finite returning velocity makes the overall asymptotic MSD depend explicitly on the first and third absolute-value moments of the propagator, in addition to the second moment. Crucially, this dependence disappears when the limit v → ∞ is taken to recover the equivalent expression for instantaneous resetting [20].…”

Section: Introductionmentioning

confidence: 97%

“…The existence of a NESS has been further studied for different types of motion and resetting mechanisms [5][6][7][8][9][10][11][12][13][14][15][16][17][18], showing that they are not exclusive of diffusion with Markovian resets. Aside from these, other works have shown that the resetting does not always generate a NESS but transport is also possible when the resetting probability density function (PDF) is long-tailed [19][20][21][22] or when the resetting process is subordinated to the motion [10,12]. However, the above cited stochastic resetting models lack some realism as long as resetting is treated as an instantaneous process.…”

Section: Introductionmentioning

confidence: 99%

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Transport properties of random walks under stochastic noninstantaneous resetting

2019

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Random walks with stochastic resetting provides a treatable framework to study interesting features about central-place motion. In this work, we introduce non-instantaneous resetting as a twostate model being a combination of an exploring state where the walker moves randomly according to a propagator and a returning state where the walker performs a ballistic motion with constant velocity towards the origin. We study the emerging transport properties for two types of reset time probability density functions (PDFs): exponential and Pareto. In the first case, we find the stationary distribution and a general expression for the stationary mean square displacement (MSD) in terms of the propagator. We find that the stationary MSD may increase, decrease or remain constant with the returning velocity. This depends on the moments of the propagator. Regarding the Pareto resetting PDF we also study the stationary distribution and the asymptotic scaling of the MSD for diffusive motion. In this case, we see that the resetting modifies the transport regime, making the overall transport sub-diffusive and even reaching a stationary MSD., i.e., a stochastic localization. This phenomena is also observed in diffusion under instantaneous Pareto resetting. We check the main results with stochastic simulations of the process.PACS numbers:

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Section: Markovian Resettingsupporting

confidence: 73%

Section: B Returning Time Pdfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Transport properties of random walks under stochastic noninstantaneous resetting

2019

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“…Several variations and extensions of this simple model have been explored in recent years [16][17][18][19][20][21][22]. Specific examples include: resetting in presence of an external potential [23,24], in a confinement [25,26] or to an extended region [27], and resetting to already excursed positions [28,29].…”

Section: Introductionmentioning

confidence: 99%

Symmetric exclusion process under stochastic resetting

2019

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We study the behaviour of a Symmetric Exclusion Process (SEP) in presence of stochastic resetting where the configuration of the system is reset to a step-like profile with a fixed rate r. We show that the presence of resetting affects both the stationary and dynamical properties of SEP strongly. We compute the exact time-dependent density profile and show that the stationary state is characterized by a non-trivial inhomogeneous profile in contrast to the flat one for r = 0. We also show that for r > 0 the average diffusive current grows linearly with time t, in stark contrast to the √ t growth for r = 0. In addition to the underlying diffusive current, we also identify the resetting current in the system which emerges due to the sudden relocation of the particles to the step-like configuration. We compute the probability distributions of the diffusive current and the total current (comprising of the diffusive and the resetting current) using the renewal approach. We demonstrate that while the typical fluctuations of the diffusive current around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behaviour. arXiv:1906.11801v1 [cond-mat.stat-mech]

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Experimental and molecular dynamics simulation study on the delivery of some common drugs by ZIF‐67, ZIF‐90, and ZIF‐8 zeolitic imidazolate frameworks

Sun

Keywanlu

Tayebee

2021

Applied Organom Chemis

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Anti‐seizures have been frequently used for a long time. Most of these antiepileptic drugs, which are used on a daily basis, are central nervous system depressants, and their excessive use damages the respiratory system. Therefore, in order to achieve the desired therapeutic goals, avoiding side effects and drug interactions, it is very important to use targeted medications. Among the metal–organic frameworks (MOFs), ZIF nanoparticles have several advantages such as smooth capillary flow and the slow release of drugs, circulating and preventing increased drug concentrations in plasma. Gabapentin, levetiracetam, phenytoin, and valproate are effective drugs in the treatment of epilepsy. In this investigation, the zeolitic imidazolate frameworks ZIF‐67, ZIF‐90, and ZIF‐8 are used as carriers for the above drugs, and their loading processes are evaluated. Among these MOFs, the highest loading values are attained in the case of ZIF‐8. Therefore, the latter MOF is synthesized via a new simple method and characterized by X‐ray diffraction (XRD), Fourier transform infrared (FT‐IR), scanning electron microscopy (SEM), and X‐ray photoelectron spectroscopy (XPS) techniques. Also, the release of these drugs was measured from the pores of ZIF‐8, and the slow release of these drugs indicated that the framework could be used as a suitable carrier for a wide range of antiepileptic drugs. Finally, the in vitro cytotoxicity of gabapentin‐ZIF‐8 against Hep‐G2 liver cancer cells was investigated by MTT assay. This study confirmed a significant decrease in the MTT signal compared with the untreated cells, so the drug‐loaded ZIF‐8 could reduce the metabolic activity of cancer cells. Therefore, this nanoparticle can be used as a carrier for the delivery of the studied drugs.

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Transport properties and first-arrival statistics of random motion with stochastic reset times

Cited by 64 publications

References 37 publications

Transport properties of random walks under stochastic noninstantaneous resetting

Transport properties of random walks under stochastic noninstantaneous resetting

Symmetric exclusion process under stochastic resetting

Experimental and molecular dynamics simulation study on the delivery of some common drugs by ZIF‐67, ZIF‐90, and ZIF‐8 zeolitic imidazolate frameworks

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