Cauchy problem for ultrasound-modulated EIT

Cauchy problem for Ultrasound Modulated EIT

Ultrasound modulation of electrical or optical properties of materials offers the possibility to devise hybrid imaging techniques that combine the high electrical or optical contrast observed in many settings of interest with the high resolution of ultrasound. Mathematically, these modalities require that we reconstruct a diffusion coefficient σ(x) for x ∈ X, a bounded domain in Rn, from knowle...

Scaling the EIT Problem

There are a number of interesting problems that could be tackled if the computing capacity of current EIT systems can be improved. We examined the performance of two such systems and found that a noticeable portion of the compute time is spent in finding the solution of sparse matrices. We developed and used a new sparse matrix testbench, Meagre-Crowd, to evaluate a selection of these sparse ma...

The Cauchy Problem for Membranes

We show existence and uniqueness for timelike minimal submanifolds (world volume of p-branes) in ambient Lorentz manifolds admitting a time function in a neighborhood of the initial submanifold. The initial value formulation introduced and the conditions imposed on the initial data are given in purely geometric terms. Only an initial direction must be prescribed in order to provide uniqueness f...

Inhomogeneous Two-Parameter Abstract Cauchy Problem

Lectures on Cauchy Problem

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