arXiv subjects

Ashwin Tarikere

Publications and source records attributed to Ashwin Tarikere.

4 recordsLinked to original sources

arXiv2026

Determination of Wave Speed from interior sources

We consider the wave equation with variable wave speed in Euclidean space, with point sources modeled by Dirac delta initial displacement data. There are three special subsets of the whole space: (1) the source set where the delta initial conditions are supported, (2) the unknown set where the wave speed is not known a priori, and (3) the receiver set where the waves are measured. The inverse problem is to reconstruct the wave speed uniquely in the unknown set from an unlabeled collection of waves generated by point sources and measured in the receiver set. We use propagation of singularities and sharp finite speed of propagation to reduce this data to geometric travel-time data, whose form depends on how the three sets lie in relation to each other. We give three scenarios where this procedure leads to unique determination of the wave speed.

math.AP↗

arXiv2026

Reconstruction of Rough Conductivities from Boundary Measurements

We show the validity of Nachman's procedure (Ann. Math. 128(3):531-576, 1988) for reconstructing a conductivity function $γ$ in a smooth bounded domain $Ω\subset \mathbb{R}^n$ ($n\geq 3$) from its Dirichlet-to-Neumann map $Λ_γ$ for less regular conductivities, specifically $γ\in H^{3/2,2n}(Ω)$ such that $γ\equiv 1$ near $\partial Ω$. We also obtain a log-type stability estimate for the inverse problem when $γ$ has slightly higher regularity, i.e., $γ\in H^{2-s,n/s}(Ω)$ for $0 < s <1/2$.

math.AP↗

arXiv2024

Stability and Statistical Inversion of Travel time Tomography

In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under some a priori conditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measurements.

math.DG↗

arXiv2017

Approximate Isotropic Cloak for the Maxwell equations

We construct a regular isotropic approximate cloak for the Maxwell system of equations. The method of transformation optics has enabled the design of electromagnetic parameters that cloak a region from external observation. However, these constructions are singular and anisotropic, making practical implementation difficult. Thus, regular approximations to these cloaks have been constructed that cloak a given region to any desired degree of accuracy. In this paper, we show how to construct isotropic approximations to these regularized cloaks using homogenization techniques, so that one obtains cloaking of arbitrary accuracy with regular and isotropic parameters.

math.AP↗