41 citations · 72 across the 7 of their papers we have counts for
7 papers
Eigenvalue Variations of the Neumann Laplace Operator Due to Perturbed Boundary Conditions
Medet Nursultanov, William Trad, Justin Tzou +1
This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold under the singular perturbation. This perturbation involve…
A Counterexample to the Lévy Flight Foraging Hypothesis in the Narrow Capture Framework
J. C. Tzou, Leo Tzou
The Lévy flight foraging hypothesis asserts that biological organisms have evolved to employ (truncated) Lévy flight searches due to such strategies being more efficient than those…
The narrow capture problem on general Riemannian surfaces
Medet Nursultanov, William Trad, Justin C. Tzou +1
In this article, we study the narrow capture problem on a Riemannian 2-manifold. This involves the derivation of the mean first passage (sojourn) time of a surface-bound ion modell…
On the Mean First Arrival Time of Brownian Particles on Riemannian Manifolds
Medet Nursultanov, Justin C. Tzou, Leo Tzou
We use geometric microlocal methods to compute an asymptotic expansion of mean first arrival time for Brownian particles on Riemannian manifolds. This approach provides a robust wa…
Hybrid asymptotic-numerical approach for estimating first passage time densities of the two-dimensional narrow capture problem
Alan E. Lindsay, Ryan T. Spoonmore, Justin C. Tzou
A hybrid asymptotic-numerical method is presented for obtaining the full probability distribution of capture times of a random walker by multiple small traps located inside a bound…
Mean first passage time for a small rotating trap inside a reflective disk
Justin C. Tzou, Theodore Kolokolnikov
We compute the mean first passage time (MFPT) for a Brownian particle inside a two-dimensional disk with reflective boundaries and a small interior trap that is rotating at a const…
Slowly varying control parameters, delayed bifurcations and the stability of spikes in reaction-diffusion systems
Justin C. Tzou, Michael J. Ward, Theodore Kolokolnikov
We present three examples of delayed bifurcations for spike solutions of reaction-diffusion systems. The delay effect results as the system passes slowly from a stable to an unstab…