Solution to the telegrapher’s equation in the presence of reflecting and partly reflecting boundaries

Masoliver, Jaume; Porrà, Josep M.; Weiss, George H.

doi:10.1103/physreve.48.939

Cited by 71 publications

(66 citation statements)

References 14 publications

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“…Recently this basic model has been extended in several directions, such as two and three dimensions, with reflecting and absorbing boundaries. Only a few of these works consider partly reflecting boundaries [6], [10], and references therein. However, in none of these previous works a stationary distribution for the particle position is presented, as we did in this paper.…”

Section: Discussionmentioning

confidence: 99%

“…We assume that the random variables τ (1) i and τ (2) i are independent. Similar partly reflecting (or trapping) boundaries have been considered in [6] for the case of one-dimensional motion, and they may be found in optical photon propagation in a turbid medium or chemical processes with sticky layers or boundaries. We believe that our model is more realistic for these applications.…”

Section: Introductionmentioning

confidence: 99%

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Limiting distribution of random motion in a n-dimensional parallelepiped

Pogorui

Rodríguez‐Dagnino

2006

rand oper stoch equ

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Abstract-In this paper we study a continuous time random walk in a n-dimensional parallelepiped with pairs of boundaries [a i , b i ]. In a pair of boundaries the particle can move in any of two directions with different velocities v i . We consider a special type of boundary which can trap the particle for a random time, and we found the limiting distribution of this random motion for the position of the particle. Our formulation allows us to find the limiting distribution for a broad class of alternating semi-Markov processes.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Limiting distribution of random motion in a n-dimensional parallelepiped

Pogorui

Rodríguez‐Dagnino

2006

rand oper stoch equ

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“…Equation (B 10) when the left boundary is at the origin has been derived in the past in Masoliver et al [41] and can also be found in Polyanin [31]. The simplified expression when s 0 ¼ 0 and L s ¼ 0 has been reported in equation (2.1) of the main text.…”

Section: A2 Circular Territoriesmentioning

confidence: 99%

Predicting oscillatory dynamics in the movement of territorial animals

Giuggioli

Potts

2012

J. R. Soc. Interface.

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Understanding ecological processes relies upon the knowledge of the dynamics of each individual component. In the context of animal population ecology, the way animals move and interact is of fundamental importance in explaining a variety of observed patterns. Here, we present a theoretical investigation on the movement dynamics of interacting scent-marking animals. We study how the movement statistics of territorial animals is responsible for the appearance of damped oscillations in the mean square displacement (MSD) of the animals. This non-monotonicity is shown to depend on one dimensionless parameter, given by the ratio of the correlation distance between successive steps to the size of the territory. As that parameter increases, the time dependence of the animal's MSD displays a transition from monotonic, characteristic of Brownian walks, to non-monotonic, characteristic of highly correlated walks. The results presented here represent a novel way of determining the degree of persistence in animal movement processes within confined regions.

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“…When the particle reaches boundary a or b it will stay at that boundary a random time given by the time the particle remains in the same direction up to the time such a particle changes direction. Similar partly reflecting (or trapping) boundaries have been considered in [5], and they may be found in optical photon propagation in turbid medium or chemical processes with sticky layers or boundaries.…”

Section: Introductionmentioning

confidence: 99%

Stationary Distribution of Random Motion with Delay in Reflecting Boundaries

Pogorui¹,

Rodríguez‐Dagnino

2010

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In this paper we study a continuous time random walk in the line with two boundaries [a,b], a < b. The particle can move in any of two directions with different velocities v 1 and v 2 . We consider a special type of boundary which can trap the particle for a random time. We found closed-form expressions for the stationary distribution of the position of the particle not only for the alternating Markov process but also for a broad class of semi-Markov processes.

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Solution to the telegrapher’s equation in the presence of reflecting and partly reflecting boundaries

Cited by 71 publications

References 14 publications

Limiting distribution of random motion in a n-dimensional parallelepiped

Limiting distribution of random motion in a n-dimensional parallelepiped

Predicting oscillatory dynamics in the movement of territorial animals

Stationary Distribution of Random Motion with Delay in Reflecting Boundaries

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