There have been many approaches to this end. An electrical wave travelling through heterogeneous heart tissue is usually simulated using a sophisticated system of coupled ODEs and PDEs. These equations are solved on a realistic geometric mesh with numerical schemes (an example using finite element techniques is shown in §1.1). In cases where a fast approximation to the wave dynamics is needed, ...

The transformation of the eikonal equation from depth coordinates (z, x) into verticaltraveltime coordinates (τ ,ξ ) enables the computation of reflections traveltimes independent of depth-mapping. This separation allows the focusing and mapping steps to be performed sequentially even in the presence of complex velocity functions, that otherwise would “require” depth migration. The traveltimes ...

We investigate how a catastrophic event (modeled as a temporary fall of the reproduction rate) increases the extinction probability of an isolated self-regulated stochastic population. Using a variant of the Verhulst logistic model as an example, we combine the probability generating function technique with an eikonal approximation to evaluate the exponentially large increase in the extinction ...

We propose an efficient computational solver for the eikonal equations on parametric three-dimensional manifolds. Our approach is based on the fast marching method for solving the eikonal equation in O(n log n) steps by numerically simulating wavefront propagation. The obtuse angle splitting problem is reformulated as a set of small integer linear programs, that can be solved in O(n). Numerical...

A simple algorithm to calculate the maximum torsional load for a cylindrical shaft is presented. The algorithm is based on the notion of viscosity solutions to the eikonal equation, and is not restricted to simply-connected cross-sections. Applications to other, related problems, such as ferromagnetic thin lms, and elastic buckling of thin lm blisters are also discussed. 1. Introduction A class...