Study of Brownian functionals for a Brownian process model of snow melt dynamics with purely time dependent drift and diffusion

Dubey, Ashutosh Kumar; Bandyopadhyay, Malay

doi:10.1140/epjb/e2018-90222-6

Cited by 4 publications

(4 citation statements)

References 55 publications

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“…The study of first passage functionals of Brownian motion [2] is an important subdiscipline and one which finds many applications. This includes the analysis of lattice polygons and queueing systems [3,4], snowmelt dynamics [5], DNA breathing [6],…”

Section: Introductionmentioning

confidence: 99%

“…The study of first passage functionals of Brownian motion [2] is an important sub-discipline and one which finds many applications. This includes the analysis of lattice polygons and queueing systems [3,4], snowmelt dynamics [5], DNA breathing [6], polymer translocation [7] and barrierless reaction kinetics [8]. Conditioning on a fixed first passage time provides insight into interface fluctuations [9], laser cooling of atoms [10] and colloidal suspensions [11]; the associated techniques being developed explicitly in [12,13], along with studies of functional correlations in [14,15].…”

Section: Introductionmentioning

confidence: 99%

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Statistics of the first passage area functional for an Ornstein–Uhlenbeck process

Kearney

Martin

2021

J. Phys. A: Math. Theor.

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We consider the area functional defined by the integral of an Ornstein–Uhlenbeck process which starts from a given value and ends at the time it first reaches zero (its equilibrium level). Exact results are presented for the mean, variance, skewness and kurtosis of the underlying area probability distribution, together with the covariance and correlation between the area and the first passage time. Among other things, the analysis demonstrates that the area distribution is asymptotically normal in the weak noise limit, which stands in contrast to the first passage time distribution. Various applications are indicated.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Statistics of the first passage area functional for an Ornstein–Uhlenbeck process

Kearney

Martin

2021

J. Phys. A: Math. Theor.

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“…The other important FPBFs studied in the literature are area and extreme maximum which have applications in statistical physics and queuing theory [29][30][31]. The FPBF has also been calculated in the context of snowmelt dynamics [32], biopolymer translocation dynamics [33], DNA breathing dynamics [34] and barrierless reactions [35]. There has been a renewed interest for studying functionals in the presence of stochastic resetting.…”

Section: Introductionmentioning

confidence: 99%

First-passage functionals for Ornstein–Uhlenbeck process with stochastic resetting

Dubey,

Pal

2023

J. Phys. A: Math. Theor.

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We study the statistical properties of first-passage Brownian functionals (FPBFs) of an Ornstein-Uhlenbeck (OU) process in the presence of stochastic resetting. We consider a one dimensional set-up where the diffusing particle sets off from $x_0$ and resets to $x_R$ at a certain rate $r$. The particle diffuses in a harmonic potential (with strength $k$) which is centered around the origin. The center also serves as an absorbing boundary for the particle and we denote the first passage time of the particle to the center as $t_f$. In this set-up, we investigate the following functionals: (i) local time $T_{loc} = \int _0^{t_f}d \tau ~ \delta (x-x_R)$ i.e., the time a particle spends around $x_R$ until the first passage, (ii) occupation or residence time $T_{res} = \int _0^{t_f} d \tau ~\theta (x-x_R)$ i.e., the time a particle typically spends above $x_R$ until the first passage and (iii) the first passage time $t_f$ to the origin. We employ the Feynman-Kac formalism for renewal process to derive the analytical expression for the first moment of all the three FPBFs mentioned above. In particular, we find that resetting can either prolong or shorten the mean residence and first passage time depending on the system parameters. The transition between these two behaviors or phases can be characterized precisely in terms of optimal resetting rates, which interestingly undergo a continuous transition as we vary the trap stiffness $k$. We characterize this transition and identify the critical -parameter \& -coefficient for both the cases. We also showcase other interesting interplay between the resetting rate and potential strength on the statistics of these observables. Our analytical results are in excellent agreement with the numerical simulations.

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“…Molini et al [31] make a study on first passage statistics of BM with purely time dependent drift and diffusion terms using method of images. Recently, Dubey et al studied several interesting PDFs for the snow melt dynamics and DNA unzipping process under rapid forcing [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Polymer translocation across an oscillating nanopore: study of several distribution functions of relevant Brownian functionals

Dubey

Bandyopadhyay

2019

Eur. Phys. J. B

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In this paper, we study polymer translocation dynamics across an oscillating nanopore by proposing and inspecting several probability distribution functions (PDFs) of relevant Brownian functionals which specify the translocation across the nanopore. We model such translocation process by an overdamped Langevin equation of collective variable x. We introduce several probability distribution functions (PDFs) to identify the translocation process. We consider elegant backward Fokker-Planck method to derive analytically closed form expressions of several PDFs associated with such stochastic process. For instance, an important quantity for translocation processes is the first passage time, i.e. the time the molecule takes to cross the nanopore with initial collective value of the molecule x0. We derive analytical expressions for: (i) the PDF P (t f |x0) of the first passage time t f which specify the lifetime of protein translocation process, (ii) the PDF P (A|x0) of the area A till the first passage time and it provides us numerous valuable information about the average size and reactivity of the process, and (iii) the PDF P (M ) associated with the maximum value of collective mode, M , of the translocation process before the first passage time. Our analysis is limited to a regime where both drift and diffusion have the same periodic time dependence with a constant ratio between them. We further confirm our analytical predictions by computing the same PDFs with direct numerical simulations of the corresponding Langevin equation. We obtain a very good agreement of our theoretical predictions with the numerically simulated results. Finally, several nontrivial scaling behaviour in the asymptotic limits for the above mentioned PDFs are predicted, which can be verified further from experimental observation.

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Study of Brownian functionals for a Brownian process model of snow melt dynamics with purely time dependent drift and diffusion

Cited by 4 publications

References 55 publications

Statistics of the first passage area functional for an Ornstein–Uhlenbeck process

Statistics of the first passage area functional for an Ornstein–Uhlenbeck process

First-passage functionals for Ornstein–Uhlenbeck process with stochastic resetting

Polymer translocation across an oscillating nanopore: study of several distribution functions of relevant Brownian functionals

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