Experimental realization of linearly polarized X-ray detected ferromagnetic resonance

We present the first theoretical and experimental evidence of time-resolved dynamic X-ray magnetic linear dichroism (XMLD) measurements of GHz magnetic precessions driven by ferromagnetic resonance in both metallic and insulating thin films. Our findings show a dynamic XMLD in both ferromagnetic Ni80Fe20 and ferrimagnetic Ni0.65Zn0.35Al0.8Fe1.2O4 for different measurement geometries and linear polarizations. A detailed analysis of the observed signals reveals the importance of separating different harmonic components in the dynamic signal in order to identify the XMLD response without the influence of competing contributions. In particular, RF magnetic resonance elicits a large dynamic XMLD response at the fundamental frequency under experimental geometries with oblique x-ray polarization. The geometric range and experimental sensitivity can be improved by isolating the 2ω Fourier component of the dynamic response.These results illustrate the potential of dynamic XMLD and represent a milestone accomplishment towards the study of GHz spin dynamics in systems beyond ferromagnetic order.

Fourier-component engineering to control light diffraction beyond subwavelength limit

Resonant physical phenomena in planar photonic lattices, such as bound states in the continuum (BICs) and Fano resonances with 100% diffraction efficiency, have garnered significant scientific interest in recent years owing to their great ability to manipulate electromagnetic waves. In conventional diffraction theory, a subwavelength period is considered a prerequisite to achieving the highly efficient resonant physical phenomena. Indeed, most of the previous studies, that treat anomalous resonance effects, utilize quasiguided Bloch modes at the second stop bands open in the subwavelength region. Higher (beyond the second) stop bands open beyond the subwavelength limit have attracted little attention thus far. In principle, resonant diffraction phenomena are governed by the superposition of scattering processes, owing to higher Fourier harmonic components of periodic modulations in lattice parameters. But only some of Fourier components are dominant at band edges with Bragg conditions. Here, we present new principles of light diffraction, that enable identification of the dominant Fourier components causing multiple diffraction orders at the higher stopbands, and show that unwanted diffraction orders can be suppressed by engineering the dominant Fourier components. Based on the new diffraction principles, novel Fourier-component-engineered (FCE) metasurfaces are introduced and analyzed. It is demonstrated that these FCE metasurfaces with appropriately engineered spatial dielectric functions can exhibit BICs and highly efficient Fano resonances even beyond the subwavelength limit.

A new method to generate superoscillating functions and supershifts

Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics and in many fields of science and technology such as optics, signal processing and antenna theory. In this paper, we introduce a new method to generate superoscillatory functions that allows us to construct explicitly a very large class of superoscillatory functions.

Protection and Identification of Thermoacoustic Azimuthal Modes

This paper first characterizes the acoustic field of two annular combustors by means of data from acoustic pressure sensors. In particular, the amplitude, orientation, and nature of the acoustic field of azimuthal order n are characterized. The dependence of the pulsation amplitude on the azimuthal location in the chamber is discussed, and a protection scheme making use of just one sensor is proposed. The governing equations are then introduced, and a low-order model of the instabilities is discussed. The model accounts for the nonlinear response of M distinct flames, for system acoustic losses by means of an acoustic damping coefficient α and for the turbulent combustion noise, modeled by means of the background noise coefficient σ. Keeping the response of the flames arbitrary and in principle different from flame to flame, we show that, together with α and σ, only the sum of their responses and their 2n Fourier component in the azimuthal direction affect the dynamics of the azimuthal instability. The existing result that only this 2n Fourier component affects the stability of standing limit-cycle solutions is recovered. It is found that this result applies also to the case of a nonhomogeneous flame response in the annulus, and to flame responses that respond to the azimuthal acoustic velocity. Finally, a parametric flame model is proposed, depending on a linear driving gain β and a nonlinear saturation constant κ. The model is first mapped from continuous time to discrete time, and then recast as a probabilistic Markovian model. The identification of the parameters {α,β,κ,σ} is then carried out on engine time-series data. The optimal four parameters {α,σ,β,κ} are estimated as the values that maximize the data likelihood. Once the parameters have been estimated, the phase space of the identified low-order problem is discussed on selected invariant manifolds of the dynamical system.

Perfect representation of a convex 2D contour with only one Fourier component

Shape analysis of a closed 2D contour is an important topic within biological shape analysis, where Fourier methods to reproduce the shape with a limited number of parameters have been and still are of vital importance. An example is within marine management research on fish, where shape analysis of otolith (earstone) contours is performed for species identification as well as for stock discrimination purposes. In both cases, it is expected that the fewer parameters that are needed in a method to reproduce the contour sufficiently good, the better. This contribution outlines how a convex contour of any shape can be represented to any wanted accuracy by only one Fourier component. The key idea is to allow a flexible choice of a predetermined number of x-values along an x-axis that goes through the two most distant points of the contour. The y-variable along the perpendicular y-axis is then monotonically transformed to a z-variable so that the minium and maximum z-values on the contour have the same distance from the x-axis. The x-values of the contour points are now chosen so that the corresponding z-values on the contour follows a perfect sinusoid if the x-values were equidistant. The method is illustrated by application to lasso contours of Norwegian Coastal Cod (NCC) and North East Arctic Cod (NEAC) otolith images, where the average new x-positions for the individual otolith contours were applied to all otoliths. The results show that a considerably better fit to the original individual otolith contours were obtained by applying the invers FFT to the new y-values than by the frequently applied 2D EFDs (Elliptical Fourier Descriptors) approach, for the same number, m < 11, of frequency components. A promising classification result was also obtained by the linear Fisher discrimination method and cross validation applied to the individual x-values for the NCC and NEAC otoliths, with 82% score for NCC and 80% score for NEAC with sample sizes 367 and 240, respectively.

Protection and Identification of Thermoacoustic Azimuthal Modes

This paper first characterizes the acoustic field of two annular combustors by means of data from acoustic pressure sensors. In particular the amplitude, orientation, and nature of the acoustic field of azimuthal order n is characterized. The dependence of the pulsation amplitude on the azimuthal location in the chamber is discussed, and a protection scheme making use of just one sensor is proposed. The governing equations are then introduced, and a low-order model of the instabilities is discussed. The model accounts for the nonlinear response of M distinct flames, for system acoustic losses by means of an acoustic damping coefficient α and for the turbulent combustion noise, modelled by means of the background noise coefficient σ. Keeping the response of the flames arbitrary and in principle different from flame to flame, we show that, together with α and σ, only the sum of their responses and their 2n Fourier component in the azimuthal direction affect the dynamics of the azimuthal instability. The existing result that only this 2n Fourier component affects the stability of standing limit-cycle solutions is recovered. It is found that this result applies also to the case of a non-homogeneous flame response in the annulus, and to flame responses that respond to the azimuthal acoustic velocity. Finally, a parametric flame model is proposed, depending on a linear driving gain β and a nonlinear saturation constant κ. The model is first mapped from continuous time to discrete time, and then recast as a probabilistic Markovian model. The identification of the parameters {α, β, κ, σ} is then carried out on engine timeseries data. The optimal four parameters {α, σ, β, κ} are estimated as the values that maximize the data likelihood. Once the parameters have been estimated, the phase space of the identified low-order problem is discussed on selected invariant manifolds of the dynamical system.

A parametric stationarity test with smooth breaks

We propose a test to investigate the stationarity null against the unit-root alternative where a Fourier component is employed to approximate nonlinear deterministic trend of unknown form. A parametric adjustment is also adopted to accommodate possible stationary error. The asymptotic distribution of the test under the null is derived, and the asymptotic critical values are tabulated. We also show that it is a consistent test. Even with small sample sizes often encountered in empirical applications, our parametric stationarity test employing Fourier term has good size and power properties when trend breaks are gradual. The validity of the Fisher hypothesis for 15 OECD countries is investigated to illustrate the usefulness of our test.

Does Fourier analysis yield reliable amplitudes of quantum oscillations?

Quantum oscillation amplitudes of multiband metals, such as high-Tc superconductors in the normal state, heavy fermions or organic conductors, are generally determined through Fourier analysis of the data even though the oscillatory part of the signal is field dependent. It is demonstrated that the amplitude of a given Fourier component can strongly depend on both the nature of the windowing (either flat, Hahn or Blackman window) and, since oscillations are obtained within a finite field range, the window width. Consequences on the determination of the Fourier amplitudes, hence of the effective masses, are examined in order to determine the conditions for reliable data analysis.

Szegö kernel asymptotic expansion on strongly pseudoconvex CR manifolds with S1 action

Let [Formula: see text] be a compact connected strongly pseudoconvex Cauchy–Riemann (CR) manifold of real dimension [Formula: see text] with a transversal CR [Formula: see text] action on [Formula: see text]. We establish an asymptotic expansion for the [Formula: see text]th Fourier component of the Szegö kernel function as [Formula: see text], where the expansion involves a contribution in terms of a distance function from lower dimensional strata of the [Formula: see text] action. We also obtain explicit formulas for the first three coefficients of the expansion.