Related papers: The head wave transform
This paper focus on the theoretical analysis and simulation of electromagnetic wave transforms, which is widely encountered in teaching physics. When the electromagnetic wave is not consistent with the shape of the object, it is often…
The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a manifold can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear…
This PhD thesis studies the broken ray transform, a generalization of the geodesic X-ray transform where geodesics are replaced with broken rays that reflect on a part of the boundary. The fundamental question is whether this transform is…
We propose wave and ray approaches for modelling mid- and high- frequency structural vibrations through smoothed joints on thin shell cylindrical ridges. The models both emerge from a simplified classical shell theory setting. The ray model…
We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity…
This PhD dissertation is concerned with integral geometric inverse problems. The geodesic ray transform is an operator that encodes the line integrals of a function along geodesics. The dissertation establishes many conditions when such…
Accurate and efficient prediction of three-dimensional (3D) fields in wave interactions with large, complex-shaped objects is essential for applications in electromagnetic computation, computer graphics, optical metrology, and freeform…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…
Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper we explore such a scenario with one dimensional models. We adopt wave packets with…
Excitation of waves in a three-layer acoustic wavegide is studied. The wave field is presented as a sum of integrals. The summation is held over all waveguide modes. The integration is performed over the temporal frequency axis. The…
The paper demonstrates the geometric optic properties of the transition radiation (TR) of an ultrarelativistic point-like charged particle crossing the transverse wall of a circular semi-infinite waveguide with ideally conducting walls. It…
The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from…
Starting from well-known absolute instruments for perfect imaging, we introduce a type of rotational-symmetrical compact closed manifolds, namely geodesic lenses. We demonstrate that light rays confined on geodesic lenses are closed…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
The paper presents a model of a dynamic crack with a wavy surface. So far, theoretical analysis of crack front waves has been performed only for in-plane perturbations of the crack front. In the present paper, generalisation is given to a…
In this paper, we study wave transmission in a rotating fluid with multiple alternating convectively stable and unstable layers. We have discussed wave transmissions in two different circumstances: cases where the wave is propagative in…
We survey the close relationship between sound and light rays and geometry. In the case where the medium is at rest, the geometry is the classical geometry of Riemann. In the case where the medium is moving, the more general geometry known…
We show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary…
In its broadest sense the term bent wave rays hints at light or electromagnetic waves bending in a strong gravitational field or in their progress through a transparent medium of nonuniform index of refraction. However, there are instances…