Convex Obstacles from Travelling Times

@article{Noakes2020ConvexOF,
  title={Convex Obstacles from Travelling Times},
  author={Lyle Noakes and Luchezar Stoyanov},
  journal={Mathematics},
  year={2020}
}
We consider situations where rays are reflected according to geometrical optics by a set of unknown obstacles. The aim is to recover information about the obstacles from the travelling-time data of the reflected rays using geometrical methods and observations of singularities. Suppose that, for a disjoint union of finitely many strictly convex smooth obstacles in the Euclidean plane, no Euclidean line meets more than two of them. We then give a construction for complete recovery of the… 
1 Citations

Figures from this paper

Recovering obstacles from their traveling times.

Noakes and Stoyanov [Mathematics 9, 2434 (2021)] introduced a method of recovering strictly convex planar obstacles from their set of traveling times. We provide an extension of this construction for

References

SHOWING 1-10 OF 29 REFERENCES

Travelling times in scattering by obstacles

Lens rigidity in scattering by non-trapping obstacles

We prove that if two non-trapping obstacles in $$\mathbb {R}^n$$Rn satisfy some rather weak non-degeneracy conditions and the scattering rays in their exteriors have (almost) the same travelling

Rigidity of Scattering Lengths and Traveling Times for Disjoint Unions of Convex Bodies

Obstacles $K$ and $L$ in $R^d$ ($d\geq 2$) are considered that are finite disjoint unions of strictly convex domains with $C^3$ boundaries. We show that if $K$ and $L$ have (almost) the same

Rigidity of the scattering length spectrum

Abstract. In this paper we consider properties of obstacles satisfying some non-degeneracy conditions that can be recovered from the scattering length spectrum (SLS). Clearly the latter tells us

The scattering of sound waves by an obstacle

In this paper we study the scattering of acoustic waves by an obstacle . We establish the following relation between the scattering kernel S(s, θ, ω) and the support function h of the obstacle:

Boundary rigidity with partial data

We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of

Marked boundary rigidity for surfaces

We show that, on an oriented compact surface, two sufficiently $C^{2}$ -close Riemannian metrics with strictly convex boundary, no conjugate points, hyperbolic trapped set for their geodesic flows

Santalo's formula and stability of trapping sets of positive measure

Obstacles with non-trivial trapping sets in higher dimensions

Using a well-known example of Livshits, for every $${n > 2}$$n>2 we construct obstacles K in $${\mathbb{R}^n}$$Rn such that the set of trapped points for the billiard flow in the exterior of K has a

Lens rigidity for manifolds with hyperbolic trapped set

For a Riemannian manifold $(M,g)$ with strictly convex boundary $\partial M$, the lens data consists in the set of lengths of geodesics $\gamma$ with endpoints on $\partial M$, together with their