A. K. Nandakumaran

Study of turbid media with light: Recovery of mechanical and optical properties from boundary measurement of intensity autocorrelation of light

We discuss the inverse problem associated with the propagation of the field autocorrelation of light through a highly scattering object like tissue. In the first part of the work, we reconstruct the optical absorption coefficient mu(a) and particle diffusion coefficient D(B) from simulated measurements which are integrals of a quantity computed from the measured intensity and intensity autocorrelation g(2)(tau) at the boundary. In the second part we recover the mean square displacement (MSD) distribution of particles in an inhomogeneous object from the sampled g(2)(tau) measured on the boundary. From the MSD, we compute the storage and loss moduli distributions in the object. We have devised computationally easy methods to construct the sensitivity matrices which are used in the iterative reconstruction algorithms for recovering these parameters from the measurements. The results of the reconstruction of mu(a), D(B), MSD and the viscoelastic parameters, which are presented, show reasonably good position and quantitative accuracy.

Periodic Controls in an Oscillating Domain: Controls via Unfolding and Homogenization

An optimal control problem in a two-dimensional domain with a rapidly oscillating boundary is considered. The main features of this article are on two points, namely, we consider periodic controls in the thin periodic slabs of period

Ultrasound-modulated optical tomography: recovery of amplitude of vibration in the insonified region from boundary measurement of light correlation

\epsilon >0

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

, a small parameter, and height

Stokes’ System in a Domain with Oscillating Boundary: Homogenization and Error Analysis of an Interior Optimal Control Problem

O(1)

Exact Controllability of a Semilinear Thermoelastic System

in the oscillatory part, and the controls are characterized using unfolding operators. We then do a homogenization analysis of the optimal control problems as

A FrameWork for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to C 0 IP Methods

\epsilon \rightarrow 0

Ultrasound-modulated optical tomography: direct recovery of elasticity distribution from experimentally measured intensity autocorrelation

with

Ordinary differential equations : principles and applications

L^2

Exact controllability of the nonlinear third-order dispersion equation

as well as Dirichlet (gradient-type) cost functionals.