Lévy flights in the presence of a point sink of finite strength

Janakiraman, Deepika

doi:10.1103/physreve.95.012154

Cited by 11 publications

(25 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If this is large compared to the mutation rate, then homozygosity will be high, ψ(0) ≈ 1, while if coalescence is slow compared to mutation, homozygosity will be low, ψ(0) ∼ 1/(µρx). A more detailed analysis (see Methods) yields numerical factors, and the leading distance dependence was found by Janakiraman [2017]:…”

Section: Nearby Pairs: Moderately Long-range Dispersalmentioning

confidence: 99%

“…For α > 1, the lineages will sometimes be in exactly the same place, and we can model coalescence with a δ distribution, i.e., as taking place at rate 1 ρ δ(X t ). The problem then becomes mathematically identical to that considered by Janakiraman [2017], and we will follow her approach, along with deriving new asymptotic approximations. For α ≤ 1, however, they will never coincide [Palyulin et al, 2014], and we must allow coalescence to take place at a finite distance.…”

Section: Analytical Model In One Dimensionmentioning

confidence: 99%

See 1 more Smart Citation

Isolation by Distance in Populations with Power-law Dispersal

2020

Preprint

View full text Add to dashboard Cite

Limited dispersal results in isolation by distance in spatially structured populations, in which individuals found further apart tend to be less related to each other. Models of populations undergoing short-range dispersal predict a close relation between the distance individuals disperse and the length scale over which two sampled individuals are likely to be closely related. In this work, we study the effect of long jumps on patterns of isolation by distance by replacing the typical short-range dispersal kernel with a long-range, power-law kernel. We find that incorporating long jumps leads to a slower decay of relatedness with distance, and that the quantitative form of this slow decay contains visible signatures of the underlying dispersal process. K 1 (y|t) = 1 2π ∞ −∞ dk exp (−iky − D α t|k| α ) .(1)

show abstract

Section: Nearby Pairs: Moderately Long-range Dispersalmentioning

confidence: 99%

Section: Analytical Model In One Dimensionmentioning

confidence: 99%

Isolation by Distance in Populations with Power-law Dispersal

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…In Ref. [114] the fractional Fokker-Planck equation for search processes was considered for different point sink strengths for free diffusion, diffusion with a constant bias, and for an harmonic external potential. A finite strength of the sink describes a finite probability of absorption.…”

Section: Lévy Search In the Presence Of A Biasmentioning

confidence: 99%

Comparison of pure and combined search strategies for single and multiple targets

et al. 2017

View full text Add to dashboard Cite

Abstract. We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with Lévy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a Lévy searcher.

show abstract

“…Consequently, the method by which to distinguish between the two cases in Lévy motion, where the discontinuous sample paths create an important distinction between first passage and arrival, has not always been clear, and has led to some confusion until very recently. For example, while the finite-strength point sink absorbs the particle when it arrives exactly at the point, in order to construct a perfectly absorptive wall in the sense of [31] a finite-strength Heaviside function sink (or any function with support equal to the complement of the allowed region Ω) is required. First passage, on the other hand, has classically referred to the passage out of finite or semi-infinite regions, which in both cases has an infinite region as its complement.…”

Section: Discussionmentioning

confidence: 99%

First passage leapovers of Lévy flights and the proper formulation of absorbing boundary conditions

Wardak

2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

An important open problem in the theory of Lévy flights concerns the analytically tractable formulation of absorbing boundary conditions. Although numerical studies using the correctly defined nonlocal approach have yielded substantial insights regarding the statistics of first passage, the resultant modifications to the dynamical equations hinder the detailed analysis possible in the absence of these conditions. In this study it is demonstrated that using the first-hit distribution, related to the first passage leapover, as the absorbing sink preserves the tractability of the dynamical equations for a particle undergoing Lévy flight. In particular, knowledge of the first-hit distribution is sufficient to fully determine the first passage time and position density of the particle, without requiring integral truncation or numerical simulations. In addition, we report on the first-hit and leapover properties of first passages and arrivals for Lévy flights of arbitrary skew parameter, and extend these results to Lévy flights in a certain ubiquitous class of potentials satisfying an integral condition.

show abstract

Lévy flights in the presence of a point sink of finite strength

Abstract: In this paper, the absorption of a particle undergoing Lévy flight in the presence of a point sink of arbitrary strength and position is studied. The motion of such a particle is given by a

Cited by 11 publications

References 35 publications

Isolation by Distance in Populations with Power-law Dispersal

Isolation by Distance in Populations with Power-law Dispersal

Comparison of pure and combined search strategies for single and multiple targets

First passage leapovers of Lévy flights and the proper formulation of absorbing boundary conditions

Contact Info

Product

Resources

About