Signatures of midlatitude heat waves in Rossby wave variability spectra

<p>This work aims at identifying extreme circulation conditions such as heat waves in modal space which is defined by eigensolutions of the linearized primitive equations. Here, the Rossby waves are represented in terms of Hough harmonics that are an orthogonal and complete expansion set allowing Rossby wave diagnostics in terms of their total (kinetic and available potential) energies. We expect that this diagnostic provides a more clear picture of the Rossby wave variability spectra compared to the common Fourier decomposition along a latitude belt. </p> <p>The probability distributions of Rossby wave energies are analysed separately for the zonal mean flow, for the planetary and synoptic zonal wavenumbers. The robustness is ensured by considering the four reanalyses ERA5, ERA-Interim, JRA-55 and MERRA. A single wave is characterized by Gaussianity in the complex Hough amplitudes and by a chi-square distribution for the energies. We find that the distributions of the energy anomalies in the wavenumber space are non-Gaussian with almost the same positive skewness in the four reanalyses.  The skewness increases during persistent heat waves for all energy anomaly distributions, in agreement with the recent trend of increased subseasonal variance in large-scale Rossby waves and decreased variance at synoptic scales. The new approach offers a selective filtering to physical space. The reconstructed circulation during heat waves is dominated by large-scale anticyclonic systems in northeastern Europe with zonal wavenumbers 2 and 3, in agreement with previous studies, thereby demonstrating physical meaningfulness of the skewness. </p> <p> </p>

Synchronization of low Reynolds number plane Couette turbulence

We demonstrate that in plane Couette turbulence a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition allows us to identify an active subspace comprising a small number of the gravest streamwise components of the flow that can synchronize all the remaining streamwise flow components. The critical streamwise wavelength, $\ell _{x c}$ , that separates the active from the synchronized passive subspace is identified as the streamwise wavelength at which perturbations to the time-dependent turbulent flow with streamwise wavelengths $\ell _x<\ell _{xc}$ have negative characteristic Lyapunov exponents. The critical wavelength is found to be approximately 130 wall units and obeys viscous scaling at these Reynolds numbers.

General 3D Analytical Method for Eddy-Current Coupling with Halbach Magnet Arrays Based on Magnetic Scalar Potential and H-Functions

Rapid and accurate eddy-current calculation is necessary to analyze eddy-current couplings (ECCs). This paper presents a general 3D analytical method for calculating the magnetic field distributions, eddy currents, and torques of ECCs with different Halbach magnet arrays. By using Fourier decomposition, the magnetization components of Halbach magnet arrays are determined. Then, with a group of H-formulations in the conductor region and Laplacian equations with magnetic scalar potential in the others, analytical magnetic field distributions are predicted and verified by 3D finite element models. Based on Ohm’s law for moving conductors, eddy-current distributions and torques are obtained at different speeds. Finally, the Halbach magnet arrays with different segments are optimized to enhance the fundamental amplitude and reduce the harmonic contents of air-gap flux densities. The proposed method shows its correctness and validation in analyzing and optimizing ECCs with Halbach magnet arrays.

Doppler Slicing for Ultrasound Super-Resolution Without Contrast Agents

Much of the information needed for diagnosis and treatment monitoring of diseases like cancer and cardiovascular disease is found at scales below the resolution limit of classic ultrasound imaging. Recently introduced vascular super-localization methods provide more than a ten-fold improvement in spatial resolution by precisely estimating the positions of microbubble contrast agents. However, most vascular ultrasound scans are currently performed without contrast agents due to the associated cost, training, and post-scan monitoring. Here we show that super-resolution ultrasound imaging of dense vascular structures can be achieved using the natural contrast of flowing blood cells. Instead of relying on separable targets, we used Fourier-based decomposition to separate signals arising from the different scales of vascular structures while removing speckle noise using multi-ensemble processing. This approach enabled the use of compressed sensing for super-resolution imaging of the underlying vascular structures, improving resolution by a factor of four. Reconstruction of ultrafast mouse brain scans revealed details that could not be resolved in regular Doppler images, agreeing closely with bubble-based super-localization microscopy of the same fields of view. By combining multi-ensemble Doppler acquisitions with narrowband Fourier decomposition and computational super-resolution imaging, this approach opens new opportunities for affordable and scalable super-resolution ultrasound imaging.

Sparse Representations of Random Signals

Sparse (fast) representations of deterministic signals have been well studied. Among other types there exists one called adaptive Fourier decomposition (AFD) for functions in analytic Hardy spaces. Through the Hardy space decomposition of the $L^2$ space the AFD algorithm also gives rise to sparse representations of signals of finite energy. To deal with multivariate signals the general Hilbert space context comes into play. The multivariate counterpart of AFD in general Hilbert spaces with a dictionary has been named pre-orthogonal AFD (POAFD). In the present study we generalize AFD and POAFD to random analytic signals through formulating stochastic analytic Hardy spaces and stochastic Hilbert spaces. To analyze random analytic signals we work on two models, both being called stochastic AFD, or SAFD in brief. The two models are respectively made for (i) those expressible as the sum of a deterministic signal and an error term (SAFDI); and for (ii) those from different sources obeying certain distributive law (SAFDII). In the later part of the paper we drop off the analyticity assumption and generalize the SAFDI and SAFDII to what we call stochastic Hilbert spaces with a dictionary. The generalized methods are named as stochastic pre-orthogonal adaptive Fourier decompositions, SPOAFDI and SPOAFDII. Like AFDs and POAFDs for deterministic signals, the developed stochastic POAFD algorithms offer powerful tools to approximate and thus to analyze random signals.

The Chow ring of hyperkähler varieties of $$K3^{[2]}$$-type via Lefschetz actions

We propose an explicit conjectural lift of the Neron–Severi Lie algebra of a hyperkähler variety X of $$K3^{[2]}$$ K 3 [ 2 ] -type to the Chow ring of correspondences $$\mathrm{CH}^*(X \times X)$$ CH ∗ ( X × X ) in terms of a canonical lift of the Beauville–Bogomolov class obtained by Markman. We give evidence for this conjecture in the case of the Hilbert scheme of two points of a K3 surface and in the case of the Fano variety of lines of a very general cubic fourfold. Moreover, we show that the Fourier decomposition of the Chow ring of X of Shen and Vial agrees with the eigenspace decomposition of a canonical lift of the cohomological grading operator.