Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInvisibility on demand based on a generalized Hilbert transform
65
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Designing invisible objects without the usage of extreme materials is a long-sought goal for photonic applications. Invisibility techniques demonstrated so far typically require high anisotropy, gain and losses, while also not being flexible. Here we propose an invisibility approach to suppress the scattering of waves from/to given directions and for particular frequency ranges, i.e. invisibility on demand. We derive a Born approximation-based generalized Hilbert transform for a specific invisibility arrangement relating the two quadratures of the complex permittivity of an object. The theoretical proposal is confirmed by numerical calculations, indicating that near-perfect invisibility can be attained for arbitrary objects with low-index contrast. We further demonstrate the cases where the idea can be extended to high-index objects or restricted to within practical limits by avoiding gain areas. The proposed concept opens a new route for the practical implementation of complex-shaped objects with arbitrarily suppressed scatterings determined on demand.
rate research
Read More
The Ninja data analysis challenge allowed the study of the sensitivity of data analysis pipelines to binary black hole numerical relativity waveforms in simulated Gaussian noise at the design level of the LIGO observatory and the VIRGO observatory. We analyzed NINJA data with a pipeline based on the Hilbert Huang Transform, utilizing a detection stage and a characterization stage: detection is performed by triggering on excess instantaneous power, characterization is performed by displaying the kernel density enhanced (KD) time-frequency trace of the signal. Using the simulated data based on the two LIGO detectors, we were able to detect 77 signals out of 126 above SNR 5 in coincidence, with 43 missed events characterized by signal to noise ratio SNR less than 10. Characterization of the detected signals revealed the merger part of the waveform in high time and frequency resolution, free from time-frequency uncertainty. We estimated the timelag of the signals between the detectors based on the optimal overlap of the individual KD time-frequency maps, yielding estimates accurate within a fraction of a millisecond for half of the events. A coherent addition of the data sets according to the estimated timelag eventually was used in a characterization of the event.
Let $ v$ be a smooth vector field on the plane, that is a map from the plane to the unit circle. We study sufficient conditions for the boundedness of the Hilbert transform operatorname H_{v, epsilon}f(x) := text{p.v.}int_{-epsilon}^ epsilon f(x-yv(x)) frac{dy}y where $ epsilon $ is a suitably chosen parameter, determined by the smoothness properties of the vector field. It is a conjecture, due to E.thinspace M.thinspace Stein, that if $ v$ is Lipschitz, there is a positive $ epsilon $ for which the transform above is bounded on $ L ^{2}$. Our principal result gives a sufficient condition in terms of the boundedness of a maximal function associated to $ v$. This sufficient condition is that this new maximal function be bounded on some $ L ^{p}$, for some $ 1<p<2$. We show that the maximal function is bounded from $ L ^{2}$ to weak $ L ^{2}$ for all Lipschitz maximal function. The relationship between our results and other known sufficient conditions is explored.
This paper presents a robust method to monitor heart rate (HR) from BCG (Ballistocardiography) signal, which is acquired from the sensor embedded in a chair or a mattress. The proposed algorithm addresses the shortfalls in traditional Fast Fourier Transform (FFT) based approaches by introducing Hilbert Transform to extract the pulse envelope that models the repetition of J-peaks in BCG signal. The frequency resolution is further enhanced by applying FFT and phase vocoder to the pulse envelope. The performance of the proposed algorithm is verified by experiment from 7 subjects. For HR estimation, mean absolute error (MAE) of 0.90 beats per minute (BPM) and standard deviation of absolute error (STD) of 1.14 BPM are obtained. Pearson correlation coefficient between estimated HR and ground truth HR of 0.98 is also achieved.
133 -
Zhaxylyk A. Kudyshev
, Alexander V. Kildishev
, Alexandra Boltasseva andn Vladimir M. Shalaev
2019
On-demand, switchable phase transitions between topologically non-trivial and trivial photonic states are demonstrated. Specifically, it is shown that integration of a 2D array of coupled ring resonators within a thermal heater array enables unparalleled control over topological protection of photonic modes. Importantly, auxiliary control over spatial phase modulation opens up a way to guide topologically protected edge modes along generated virtual boundaries. The proposed approach can lead to practical realizations of topological phase transitions in many photonic applications, including topologically protected photonic memory/logic devices, robust optical modulators, and switches.
We establish the sharp growth rate, in terms of cardinality, of the $L^p$ norms of the maximal Hilbert transform $H_Omega$ along finite subsets of a finite order lacunary set of directions $Omega subset mathbb R^3$, answering a question of Parcet and Rogers in dimension $n=3$. Our result is the first sharp estimate for maximal directional singular integrals in dimensions greater than 2. The proof relies on a representation of the maximal directional Hilbert transform in terms of a model maximal operator associated to compositions of two-dimensional angular multipliers, as well as on the usage of weighted norm inequalities, and their extrapolation, in the directional setting.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
