Optimization of First Passage Times by Multiple Cooperating Mobile Traps

@article{Lindsay2017OptimizationOF,
  title={Optimization of First Passage Times by Multiple Cooperating Mobile Traps},
  author={Alan E. Lindsay and J. C. Tzou and Theodore Kolokolnikov},
  journal={Multiscale Model. Simul.},
  year={2017},
  volume={15},
  pages={920-947}
}
We study the mean capture time of an unbiased random walker by multiple absorbing mobile traps in bounded domains of one and two spatial dimensions. In one dimension, we consider multiple traps undergoing prescribed oscillatory motion on an interval with reflecting or absorbing boundary conditions. We develop trap cooperation strategies which optimize the mean capture time. We find that as the frequency of oscillation passes through certain fixed values, the optimal trap strategy alternates… 
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References

SHOWING 1-10 OF 49 REFERENCES
First-passage times, mobile traps, and Hopf bifurcations.
TLDR
A surprising relation between the oscillating trap problem and a moving-sink problem that describes reduced dynamics of a single spike in a certain regime of the Gray-Scott model is found and is used to prove the uniqueness of the Hopf bifurcation.
Mean First Passage Time for a Small Rotating Trap inside a Reflective Disk
TLDR
This work determines the optimal radius of rotation that minimizes the average MFPT over the disk for a Brownian particle inside a two-dimensional disk with reflective boundaries and a small interior trap that is rotating at a constant angular velocity.
Narrow escape problem with a mixed trap and the effect of orientation.
TLDR
High-order asymptotic formulas for the MFPT and the fundamental eigenvalue of the Laplacian are derived and it is found that subdividing the absorbing portions of the trap reduces the mean first passage time of the diffusing particle.
Optimal strategy to capture a skittish lamb wandering near a precipice
We study the splitting probabilities for a one-dimensional Brownian motion in a cage whose two boundaries move at constant speeds $c_1$ and $c_2$. This configuration corresponds to the capture of a
An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part II: The Sphere
TLDR
The average MFPT is shown to be minimized for trap configurations that minimize a certain discrete variational problem, closely related to the well-known optimization problem of determining the minimum energy configuration for N repelling point charges on the unit sphere.
Exact asymptotics for one-dimensional diffusion with mobile traps.
TLDR
It is shown that the asymptotic behavior of the survival probability of the diffusing particle, P(t), satisfies lim([-ln(P(t)]/sqrt[rho2Dt]=4/ sqrt[pi], independent of D'.
Asymptotic Analysis of First Passage Time Problems Inspired by Ecology
TLDR
The hybrid approach has the advantage of eliminating the difficulty with resolving small spatial scales in a full numerical treatment of the partial differential equation (PDE).
FAST TRACK COMMUNICATION: The survival probability of a diffusing particle constrained by two moving, absorbing boundaries
We calculate the exact asymptotic survival probability, Q, of a one-dimensional Brownian particle, initially located at the point x (−L, L), in the presence of two moving, absorbing boundaries
Conditional Mean First Passage Times to Small Traps in a 3-D Domain with a Sticky Boundary: Applications to T Cell Searching Behavior in Lymph Nodes
TLDR
This work is motivated by the motion of a T cell of the immune system seeking a particular antigen-presenting cell within a large lymph node, which is modeled by a Robin boundary condition on the surface of the lymph node.
...
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