Related papers: Travelling times in scattering by obstacles
We consider travelling times of billiard trajectories in the exterior of an obstacle K on a two-dimensional Riemannian manifold M. We prove that given two obstacles with almost the same travelling times, the generalised geodesic flows on…
A construction is given for the recovery of a disjoint union of strictly convex smooth planar obstacles from travelling-time information. The obstacles are required to be such that no Euclidean line meets more than two of them.
Noakes and Stoyanov (2021) introduced a method of recovering strictly convex planar obstacles from their set of travelling times. We provide an extension of this construction for obstacles on Riemannian surfaces under some general curvature…
The scattering data of a Riemannian manifold with boundary record the incoming and outgoing directions of each geodesic passing through. We show that the scattering data of a generic Riemannian surface with no trapped geodesics and no…
Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a general introduction to systematic…
We discuss the properties of the residence time in presence of moving defects or obstacles for a particle performing a one dimensional random walk. More precisely, for a particle conditioned to exit through the right endpoint, we measure…
We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a…
In this paper we consider the unique determination of inhomogeneities together with possible buried obstacles by scattering measurements. Under the assumption that the buried obstacles have only planar contacts with the inhomogeneities, we…
After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for…
Consider the scattering of an acoustic plane wave by a bounded elastic obstacle which is immersed in an open space filled with a homogeneous medium. This paper concerns the mathematical analysis of the coupled two- and three-dimensional…
We consider higher-dimensional generalizations of the $\alpha$-Grushin plane, focusing on the problem of classification of geodesics that minimize length, also known as optimal synthesis. Solving Hamilton's equations on these spaces using…
The general and explicit relation between the phase time and the dwell time for quantum tunneling or scattering is investigated. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, here we…
We prove that if two non-trapping obstacles in $\mathbb{R}^n$ satisfy some rather weak non-degeneracy conditions and the scattering rays in their exteriors have (almost) the same travelling times or (almost) the same scattering length…
Travel-time tomography seeks to recover a hidden environment from external measurements generated by propagation through an anomalous region. Standard formulations treat propagation as passive, so the environment influences observations…
We investigate local and global properties of timelike geodesics in three static spherically symmetric spacetimes. These properties are of its own mathematical relevance and provide a solution of the physical `twin paradox' problem. The…
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…
This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…
The formulation of gravity theory is considered where space-time is a 4-dimensional surface in flat ten-dimensional space. The possibility of using the "external" time (the time of ambient space) in this approach is investigated. The…
An integral stability estimate is proved for refraction coefficients of two conformal metrics in a plane domain in terms of its travel times. No assumption on absence of conjugate points of geodesics is made.
It is known that for a variety of choices of metrics, including the standard bottleneck distance, the space of persistence diagrams admits geodesics. Typically these existence results produce geodesics that have the form of a convex…