Related papers: Orange Peels and Fresnel Integrals

We investigate the generation of entanglement (spin squeezing) in an optical-transition atomic clock through the coupling to a vacuum electromagnetic field that is enhanced by an optical cavity. We show that if each atom is prepared in a…

Fresnel diffraction calculation on an arbitrary shape surface is proposed. This method is capable of calculating Fresnel diffraction from a source surface with an arbitrary shape to a planar destination surface. Although such calculation…

We present some approaches to the computation of ultra-fast laser pulses capable of selectively breaking molecular bonds. The calculations are based on a mixed quantum-classical description: The electrons are treated quantum mechanically…

Several, recently proposed methods of surface manufacturing based on ion beam sputtering, which involve dual beam setups, sequential application of ion beams from different directions, or sample rotation, are studied with the method of…

We present a theoretical model to sufficiently investigate the optical rotational Doppler effect based on modal expansion method. We find that the frequency shift content is only determined by the surface of spinning object and the reduced…

We consider piecewise linear interpolation from the perspective of kernel interpolation and quadrature. If the Sobolev space $W_2^1(0, 1)$ is equipped with a suitable inner product, its reproducing kernel is piecewise linear and gives rise…

We show that a compact manifold admitting a Killing foliation with positive transverse curvature fibers over finite quotients of spheres or weighted complex projective spaces, provided that the singular foliation defined by the closures of…

We show that narrow filaments or sheets of over- or under-dense plasma, or "noodles," with fluctuations of scattering phase of less than a radian, can form the scintillation arcs seen for many pulsars. The required local fluctuations of…

We show that we can know more than the orthodox view does, as one example, we make a new analysis about double-slit experiment, and demonstrate that we can measure the objective state of the particles passing through the two slits while not…

A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and…

This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the signal can be modeled by generalized Gaussian random variables, we compute a critical thresholding…

Analogous to the famous Euler angle parametrization in three-dimensional Euclidean space, a reflection-free Lorentz transformation in (2+1)-dimensional Minkowski space can be decomposed into three simple parts. Applying this decomposition…

We present an analytical and numerical investigation of double-slit diffraction under coherent illumination by three plane waves: one normally incident and two symmetrically angled at plus/minus theta. By imposing an edge-zero condition on…

The unfolding of a gamma ray spectrum experience many difficulties due to noise in the recorded data, that is based mainly on the change of photon energy due to scattering mechanisms (either in the detector or the medium), the accumulation…

Optical spectroscopy is an important and widely used technique, for instance, to characterize new materials and to identify unknown compounds. Spectra are typically reported as a function of the wavelength of light, yet the information…

This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…

This experiment was conceived of as a method of transmitting information from inside a black hole to the outside. As it turns out, it doesn't work in the form described (and possibly not in any form), but the way in which Nature prevents…

The influence of the topology and curvature of objects on photonic properties represents an intriguing fundamental problem from cosmology to nanostructure physics. The classical topological transition from a ring to a M\"obius strip is…

Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting…

We establish a quantitative necessary and sufficient condition for a spiral arc to be a H\"older arc. The class of spiral arcs contains the polynomial spirals studied by Fraser, and the elliptical spirals studied by Burrell-Falconer-Fraser.…