TY - JOUR
T1 - Mean first passage time for diffuse and rest search in a confined spherical domain
AU - Mutothya, Nicholas Mwilu
AU - Xu, Yong
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/4/1
Y1 - 2021/4/1
N2 - Many search processes in nature exhibit saltatory behavior, alternating phases of diffusive movement with resting. The first passage time is an important measure to describe the efficiency of such processes in different domains. Here, we presented a theoretical formula for the mean first passage time to a small target located in the bulk of confined spherical domain, where the search combines phases of the standard diffusion and resting with the target detectable only during the diffusion phase. We used a two-state system to model the switching mechanism, which yields a system with two coupled differential equations. We solved the obtained system to obtain an analytical formula for computing the mean first passage time and analyzed its dependence on the transition rates between the two phases. Our results indicate that, the mean first passage time for this scenario was greater than for the pure diffusion. Further, it grew linearly with increasing the rate from diffusion to resting while decayed with increasing the rate from resting to diffusion. For comparison, we provided numerical simulation. There is good a agreement between the theoretical and the simulation results. Our model could be used to design and accelerate the target search like ecological, biochemical and biological processes.
AB - Many search processes in nature exhibit saltatory behavior, alternating phases of diffusive movement with resting. The first passage time is an important measure to describe the efficiency of such processes in different domains. Here, we presented a theoretical formula for the mean first passage time to a small target located in the bulk of confined spherical domain, where the search combines phases of the standard diffusion and resting with the target detectable only during the diffusion phase. We used a two-state system to model the switching mechanism, which yields a system with two coupled differential equations. We solved the obtained system to obtain an analytical formula for computing the mean first passage time and analyzed its dependence on the transition rates between the two phases. Our results indicate that, the mean first passage time for this scenario was greater than for the pure diffusion. Further, it grew linearly with increasing the rate from diffusion to resting while decayed with increasing the rate from resting to diffusion. For comparison, we provided numerical simulation. There is good a agreement between the theoretical and the simulation results. Our model could be used to design and accelerate the target search like ecological, biochemical and biological processes.
KW - Confined domain
KW - Diffuse and rest
KW - First passage time
KW - Intermittent search
UR - http://www.scopus.com/inward/record.url?scp=85098721090&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2020.125667
DO - 10.1016/j.physa.2020.125667
M3 - 文章
AN - SCOPUS:85098721090
SN - 0378-4371
VL - 567
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
M1 - 125667
ER -