First passage time distribution in stochastic processes with moving and static absorbing boundaries with application to biological rupture experiments

The non-static generalized Langevin equation and its corresponding Fokker-Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external force was obtained analytically. The non-Markovian stochastic differential equation, associated to the dynamics of the position under a colored noise, was then applied to the description of the dynamics and persistence time of particles constrained within absorbing barriers. Comparisons with molecular dynamics were very satisfactory.

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“…with a time dependent diffusion term D z (t) given by Eq. (34). According to this, it is identical to D(t) only for zero external force.…”

Section: Solution Of Position Gfpementioning

confidence: 89%

The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

Olivares-Rivas

Colmenares

2016

Physica A: Statistical Mechanics and its Applications

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“…Instead, with the general formalism derived in Section II, we can first study the system without resets and introduce the results to the formulas derived above. Then, we start from the Langevin equation for the Brownian particle in an harmonic potential ( [37]):…”

Section: Brownian Motion In a Biased Harmonic Potentialmentioning

confidence: 99%

“…Let us now study its MFAT for this system. The first arrival distribution q x0 (t) at the minimum of the potential for this motion process has been found to be ( [37]) from which the survival probability can be found as…”

Section: Brownian Motion In a Biased Harmonic Potentialmentioning

confidence: 99%

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

2019

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Stochastic resets have lately emerged as a mechanism able to generate finite equilibrium mean square displacement (MSD) when they are applied to diffusive motion. Furthermore, walkers with an infinite mean first arrival time (MFAT) to a given position x, may reach it in a finite time when they reset their position. In this work we study these emerging phenomena from a unified perspective. On one hand we study the existence of a finite equilibrium MSD when resets are applied to random motion with x 2 (t) m ∼ t p for 0 < p ≤ 2. For exponentially distributed reset times, a compact formula is derived for the equilibrium MSD of the overall process in terms of the mean reset time and the motion MSD. On the other hand, we also test the robustness of the finiteness of the MFAT for different motion dynamics which are subject to stochastic resets. Finally, we study a biased Brownian oscillator with resets with the general formulas derived in this work, finding its equilibrium first moment and MSD, and its MFAT to the minimum of the harmonic potential.PACS numbers:

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“…Moreover, if we treat the problem discretely, one expects the particle to return with a time distribution given approximately by 22 where q d is the discrete return time distribution function, τ is the discrete time step, and t is time. Introducing a more continuous model, we can use the fact that the particle has an MFP, l , and assuming the particle moves approximately that far upon reflecting from the surface, we can calculate the continuous return time distribution through first passage time theories as 23 where D is the diffusion constant. The long-time functional form of eqs 3 and 4 are equivalent (∼ t –3/2 ).…”

Section: Resultsmentioning

confidence: 99%

Explaining the Transition from Diffusion Limited to Reaction Limited Surface Assembly of Molecular Species through Spatial Variations

et al. 2017

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Surface assembly is often decomposed into two classes: diffusion and reaction limited processes. The transition between the two cases is complex because the dynamics are so different. In this article, we simulate, explain, and experimentally discuss the evolution of the spatial distribution for surface assemblies with diffusion limited and reaction limited processes. Explicitly, we demonstrate that diffusion limited and reaction limited processes show some temporal differences, but more importantly, we show that the spatial arrangements are different enough to discriminate between the two cases. Using fundamental properties, such as the diffusion constant, we calculate the evolution of the spatial profile and derive from physical, heuristic models the assembly rate for reaction and diffusion limited processes based on the individual particle’s interactions with the surface. Finally, we confirm the spatial profile differences between diffusion and reaction limited cases by experimentally measuring the surface assembly between two molecules of similar size, but having different assembly routes. Unique to our description is that we have derived and simulated everything through the particle picture in place of ensemble descriptions such as the diffusion equation, and we show the equivalence between our heuristic formulas and those derived from the diffusion equation.

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First passage time distribution in stochastic processes with moving and static absorbing boundaries with application to biological rupture experiments

Cited by 36 publications

References 24 publications

The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

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

Explaining the Transition from Diffusion Limited to Reaction Limited Surface Assembly of Molecular Species through Spatial Variations

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