scholarly journals Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: experiments, theory and numerical tests

2021 ◽  
Vol 2021 (11) ◽  
pp. 113203
Author(s):  
F Faisant ◽  
B Besga ◽  
A Petrosyan ◽  
S Ciliberto ◽  
Satya N Majumdar
Keyword(s):  
Brownian Particle ◽  
First Passage Time ◽  
Passage Time ◽  
Critical Value ◽  
Initial Position ◽  
Two Dimensions ◽  
Mean First Passage Time ◽  
First Passage ◽  
Numerical Tests ◽  
Mean Time

Abstract We experimentally, numerically and theoretically study the optimal mean time needed by a Brownian particle, freely diffusing either in one or two dimensions, to reach, within a tolerance radius R tol, a target at a distance L from an initial position in the presence of resetting. The reset position is Gaussian distributed with width σ. We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full first-passage probability distribution that displays spectacular spikes immediately after each resetting time for close targets. We study the optimal mean first-passage time as a function of the resetting period/rate for different target distances (values of the ratios b = L/σ) and target size (a = R tol/L). We find an interesting phase transition at a critical value of b, both in one and two dimensions. The details of the calculations as well as the experimental setup and limitations are discussed.

ASYMPTOTIC ANALYSIS FOR THE MEAN FIRST PASSAGE TIME IN FINITE OR SPATIALLY PERIODIC 2D DOMAINS WITH A CLUSTER OF SMALL TRAPS

2021 ◽  
pp. 1-22
Author(s):  
S. IYANIWURA ◽  
M. J. WARD
Keyword(s):  
Brownian Particle ◽  
First Passage Time ◽  
Hexagonal Lattice ◽  
Passage Time ◽  
Lattice Points ◽  
Bravais Lattice ◽  
Mean First Passage Time ◽  
First Passage ◽  
Spatially Periodic ◽  
The Mean

Abstract A hybrid asymptotic-numerical method is developed to approximate the mean first passage time (MFPT) and the splitting probability for a Brownian particle in a bounded two-dimensional (2D) domain that contains absorbing disks, referred to as “traps”, of asymptotically small radii. In contrast to previous studies that required traps to be spatially well separated, we show how to readily incorporate the effect of a cluster of closely spaced traps by adapting a recently formulated least-squares approach in order to numerically solve certain local problems for the Laplacian near the cluster. We also provide new asymptotic formulae for the MFPT in 2D spatially periodic domains where a trap cluster is centred at the lattice points of an oblique Bravais lattice. Over all such lattices with fixed area for the primitive cell, and for each specific trap set, the average MFPT is smallest for a hexagonal lattice of traps.

Asymptotic analysis for the mean first passage time in finite or spatially periodic 2D domains with a cluster of small traps

2021 ◽  
Vol 63 ◽  
pp. 1-22
Author(s):  
Sarafa Iyaniwura ◽  
Michael Ward
Keyword(s):  
Brownian Particle ◽  
First Passage Time ◽  
Hexagonal Lattice ◽  
Passage Time ◽  
Lattice Points ◽  
Bravais Lattice ◽  
Mean First Passage Time ◽  
First Passage ◽  
Spatially Periodic ◽  
The Mean

A hybrid asymptotic-numerical method is developed to approximate the mean first passage time (MFPT) and the splitting probability for a Brownian particle in a bounded two-dimensional (2D) domain that contains absorbing disks, referred to as "traps”, of asymptotically small radii. In contrast to previous studies that required traps to be spatially well separated, we show how to readily incorporate the effect of a cluster of closely spaced traps by adapting a recently formulated least-squares approach in order to numerically solve certain local problems for the Laplacian near the cluster. We also provide new asymptotic formulae for the MFPT in 2D spatially periodic domains where a trap cluster is centred at the lattice points of an oblique Bravais lattice. Over all such lattices with fixed area for the primitive cell, and for each specific trap set, the average MFPT is smallest for a hexagonal lattice of traps. doi:10.1017/S1446181121000018

scholarly journals Mean first-passage time of a tumor cell growth system with time delay and colored cross-correlated noises excitation

2017 ◽  
Vol 37 (2) ◽  
pp. 191-198 ◽  
Author(s):  
Shenghong Li ◽  
Yong Huang
Keyword(s):  
Time Delay ◽  
Noise Intensity ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
Tumor Cell Growth ◽  
First Passage ◽  
Growth System ◽  
The Mean ◽  
Correlated Noises

In this paper, the mean first-passage time of a delayed tumor cell growth system driven by colored cross-correlated noises is investigated. Based on the Novikov theorem and the method of probability density approximation, the stationary probability density function is obtained. Then applying the fastest descent method, the analytical expression of the mean first-passage time is derived. Finally, effects of different kinds of delays and noise parameters on the mean first-passage time are discussed thoroughly. The results show that the time delay included in the random force, additive noise intensity and multiplicative noise intensity play a positive role in the disappearance of tumor cells. However, the time delay included in the determined force and the correlation time lead to the increase of tumor cells.

Sign in / Sign up

Export Citation Format

Share Document