Related papers: Four Aspects of Superoscillations
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small…
In this survey, we explore how superorthogonality amongst functions in a sequence $f_1,f_2,f_3,\ldots$ results in direct or converse inequalities for an associated square function. We distinguish between three main types of…
Sunspots are known to be strong absorbers of solar oscillation modal power. The most convincing way to demonstrate this is done via Fourier-Hankel decomposition (FHD), where the local oscillation field is separated into in- and outgoing…
Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring…
The low frequency part of the gravitational wave spectrum generated by local physics, such as a phase transition or parametric resonance, is largely fixed by causality, offering a clean window into the early Universe. In this work, this low…
The goal of this work is to introduce and study fuzzy limits of functions. Two approaches to fuzzy limits of a function are considered. One is based on the concept of a fuzzy limit of a sequence, while another generalizes the conventional…
Accurate and powerful analytic and computational methods developped by the author allow to obtain the highly non trivial total absorption spectrum of the Black Hole, as well as phase shifts and cross sections (elastic and inelastic), the…
The maximum amplitude of mechanical oscillators coupled to optical cavities are studied both analytically and numerically. The optical backaction on the resonator enables self-sustained oscillations whose limit cycle is set by the dynamic…
Ultracold bosons in rotating ring lattices have previously been shown to form macroscopic superpositions of different quasi-momentum states. We demonstrate that the generation of such kind of states using slightly non-uniform ring lattices…
A novel supersonic jet oscillating method is investigated both experimentally and numerically. A rectangular primary supersonic jet is issued into a confined chamber with sudden enlargement. Secondary control jets are issued from the top,…
We investigate estimating scalar oscillatory integrals by integrating by parts in directions based on $(x_1 \partial_{x_1} f(x) ,..., x_n \partial_{x_n}f(x))$, where $f(x)$ is the phase function. We prove a theorem which provides estimates…
In conventional diffraction theory, a subwavelength period is considered a prerequisite to achieve interesting resonance-assisted physical phenomena, such as bound states in the continuum and diverse zero-order spectral responses with…
We study the possibility of occurrence of vibrational resonance in a softening Duffing oscillator in the underdamped and overdamped cases both theoretically as well as numerically. The oscillator is driven by two periodic forces.…
We demonstrate that the rapidity and robustness of slow contraction in homogenizing and flattening the universe found in simulations in which the initial conditions were restricted to non-perturbative variations described by a single…
Extremely fast rotating molecules carrying significantly more energy in their rotation than in any other degree of freedom are known as "super rotors". It has been speculated that super rotors may exhibit a number of unique properties.…
The analysis of signals created by a variety of instruments involves calculating the phase of a sinusoidal type signal. One widely used method to extract this information is through the use of Fourier transforms, but it is known that…
We use dispersive Fourier transformation to measure shot-to-shot spectral instabilities in femtosecond supercontinuum generation. We study both the onset phase of supercontinuum generation with distinct dispersive wave generation, as well…
We use rich clusters of galaxies in the Northern and Southern Galactic hemispheres up to a redshift z=0.12 to determine the cluster correlation function. We show that superclusters of galaxies and voids between them form a moderately…
In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for finer simulation of the objects of the nature or outcomes of scientific experiments that reveal one or more structures embedded in to another.…
It is common knowledge that the Fourier transform enjoys the convolution property, i.e., it turns convolution in the time domain into multiplication in the frequency domain. It is probably less known that this property characterizes the…