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[Formulation of broadband array problems using polynomial matrix notation; polynomial matrix factorisations; broadband AoA estimation via polynomial matrix techniques; broadband MVDR adaptive beamforming.]

We report on the presence of the boundary zonal flow in rotating Rayleigh–Bénard convection evidenced by two-dimensional particle image velocimetry. Experiments were conducted in a cylindrical cell of aspect ratio $\varGamma =D/H=1$ between its diameter ( $D$ ) and height ( $H$ ). As the working fluid, we used various mixtures of water and glycerol, leading to Prandtl numbers in the range $6.6 \lesssim \textit {Pr} \lesssim 76$ . The horizontal velocity components were measured at a horizontal cross-section at half height. The Rayleigh numbers were in the range $10^8 \leq \textit {Ra} \leq 3\times 10^9$ . The effect of rotation is quantified by the Ekman number, which was in the range $1.5\times 10^{-5}\leq \textit {Ek} \leq 1.2\times 10^{-3}$ in our experiment. With our results we show the first direct measurements of the boundary zonal flow (BZF) that develops near the sidewall and was discovered recently in numerical simulations as well as in sparse and localized temperature measurements. We analyse the thickness $\delta _0$ of the BZF as well as its maximal velocity as a function of Pr, Ra and Ek, and compare these results with previous results from direct numerical simulations.

UC and UMeC2 (Me = Fe, Zr, Mo) carbides were studied by the high-energy-resolution fluorescence-detected X-ray absorption (HERFD-XAS) technique at the U M 4 and L 3 edges. Both U M 4 and L 3 HERFD-XAS reveal some differences between UMeC2 and UC; there are differences also between the M 4 and L 3 edge results for both types of carbide in terms of the spectral width and energy position. The observed differences are attributed to the consequences of the U 5f, 6d–4d(3d) hybridization in UMeC2. Calculations of the U M 4 HERFD-XAS spectra were also performed using the Anderson impurity model (AIM). Based on the analysis of the data, the 5f occupancy in the ground state of UC was estimated to be 3.05 electrons. This finding is also supported by the analysis of U N 4,5 XAS of UC and by the results of the AIM calculations of the U 4f X-ray photoelectron spectrum of UC.

Direction of arrival (DoA) estimation for sound source localization is increasingly prevalent in modern devices. In this paper, we explore a polynomial extension to the multiple signal classification (MUSIC) algorithm, spatio-spectral polynomial (SSP)-MUSIC, and evaluate its performance when using speech sound sources. In addition, we also propose three essential enhancements for SSP-MUSIC to work with noisy reverberant audio data. This paper includes an analysis of SSP-MUSIC using speech signals in a simulated room for different noise and reverberation conditions and the first task of the LOCATA challenge. We show that SSP-MUSIC is more robust to noise and reverberation compared to independent frequency bin (IFB) approaches and improvements can be seen for single sound source localization at signal-to-noise ratios (SNRs) below 5 dB and reverberation times (T60s) larger than 0.7 s.

The second order sequential best rotation (SBR2) algorithm is a popular algorithm to decompose a parahermitian matrix into approximated polynomial eigenvalues and eigen-vectors. The work horse behind SBR2 is a Givens rotation interspersed by delay operations. In this paper, we investigate and analyse the application of a fast Givens rotation in order to reduce the computation complexity of SBR2. The proposed algorithm inherits the SBR2's proven convergence to a diagonalised and spectrally majorised solution for the polynomial eigenvalues. We provide some analysis and examples for the execution speed of this fast Givens-based SBR2 compared to a standard SBR2 implementation.

We have proposed a broadband subspace approach to detect the presence of weak transient signals; this is based on second order statistics of sensor array data — the space-time covariance matrix — and a polynomial matrix EVD; this covariance matrix and its decomposition can be computed off-line; a subspace decomposition for the noise-only subspace determines a syndrome vector; in the absence of a transient signal, this syndrome only contains noise; a transient signal is likely to protrude into the noise-only subspace, and a change in energy can be detected even if the signal is weak; discrimination can be traded off against decision time; further work: (i) impact of time-varying channels, and (ii) forensic investigation of the transient source once detected.

As part of the last day of the UDRC 2021 summer school, this presentation provides an overview over polynomial matrix methods. The use of polynomial matrices is motivated through a number of broadband multichannel problems, involving space-time covariance matrices, filter banks, or wideband MIMO systems. We extend the utility of EVD from narrowband to broadband solutions via a number of factorisation algorithms belonging to the second order sequential rotation or sequential matrix diagonalisation families of algorithms. In a second part of this presentation, a number of application areas are explored, ranging from precoder and equaliser design for broadband MIMO communications systems, to broadband angle of arrival estimation, broadband beamforming, and the problem of identifying source-sensor transfer paths from the second order statistics of the sensor signals.