Related papers: Broken ray transform for twisted geodesics on surf…
We define an ending lamination for a Weil-Petersson geodesic ray. Despite the lack of a natural visual boundary for the Weil-Petersson metric, these ending laminations provide an effective boundary theory that encodes much of its asymptotic…
Many natural real-valued functions of closed curves are known to extend continuously to the larger space of geodesic currents. For instance, the extension of length with respect to a fixed hyperbolic metric was a motivating example for the…
Geometrically decorated two-dimensional (2D) discrete surfaces can be more effective than conventional smooth reflectors in managing wave radiation. Constructive non-specular wave scattering permits the scattering angle to be other than…
Recently, the complexity behind manipulations of reflected fields by metasurfaces has been addressed showing that, even in the simplest scenarios, non-local response and excitation of auxiliary evanescent fields are required for perfect…
Let $S$ be a surface of nonpositive curvature of genus bigger than 1 (i.e. not the torus). We prove that any flat strip in the surface is in fact a flat cylinder. Moreover we prove that the number of homotopy classes of such flat cylinders…
The famous Uniformization Theorem states that on closed Riemannian surfaces there always exists a metric of constant curvature for the Levi-Cevita connection. In this article we prove that an analogue of the uniformization theorem also…
Recent advances in high-energy and high-peak-power laser systems have opened up new possibilities for fundamental physics research. In this work, the potential of twisted light for the generation of gravitational waves in the high frequency…
We prove that, generically, magnetic geodesics on surfaces will turn away from points with lightlike tangent planes, and we motivate our result with numerical solutions for closed magnetic geodesics.
Curving beams are a promising new method for bypassing obstacles in future millimeter-wave to sub-terahertz (sub-THz) networks but lack a general predictive model for their reflections from arbitrary surfaces. We show that, unfortunately,…
Optical Faraday rotation is one of the most direct and practically important manifestations of magnetically broken time-reversal symmetry. The rotation angle is proportional to the distance traveled by the light, and up to now sizeable…
We study mean curvature flows in a warped product manifold defined by a closed Riemannian manifold and $\mathbb{R}$. In such a warped product manifold, we can define the notion of a graph, called a geodesic graph. We prove that the curve…
The present study focuses on the interaction of gravity waves in the atmosphere with the tropopause. As the vertical extent of the latter is small compared to the density scale height, wave propagation is described by the Taylor-Goldstein…
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part…
The detection of gravitational waves based on the geodesic deviation equation is discussed. In particular, it is shown that the only non-vanishing components of the wave field in the conventional traceless-transverse gauge in linearized…
We propose a new condition $\aleph$ which enables to get new results on integrable geodesic flows on closed surfaces. This paper has two parts. In the first, we strengthen Kozlov's theorem on non-integrability on surfaces of higher genus.…
We describe all pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta. As an application, we solve the Beltrami problem on closed surfaces and prove the nonexistence of…
We derive the paraxial meridional ray tracing equations from the unified reflection-refraction law using geometric algebra. This unified law states that the normal vector to the interface is a rotation of the incident ray or of the…
In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray…
The ability to identify and characterize spontaneous symmetry breaking is central to our understanding of 2D materials with strong correlation, such as the moir\'e flat bands in magic-angle twisted graphene bilayer and trilayer. In this…
The evolution of RHEED reflexes intensity during reconstructed transitions characterizes (often implicitly) reconstructed surface state peculiarities. The approaches of a correct RHEED data interpretation, aimed at obtaining information…