Spatial Mode Structure Research Articles

Estimating direction of arrival in reverberant environments for wake-word detection using a single structural vibration sensora).

The vibrational response of an elastic panel to incident acoustic waves is determined by the direction-of-arrival (DOA) of the waves relative to the spatial structure of the panel's bending modes. By monitoring the relative modal excitations of a panel immersed in a sound field, the DOA of the source may be inferred. In reverberant environments, early acoustic reflections and the late diffuse acoustic field may obscure the DOA of incoming sound waves. Panel microphones may be especially susceptible to the effects of reverberation due to their large surface areas and long-decaying impulse responses. An investigation into the effect of reverberation on the accuracy of DOA estimation with panel microphones was made by recording wake-word utterances in eight spaces with reverberation times (RT60s) ranging from 0.27 to 3.00 s. The responses were used to train neural networks to estimate the DOA. Within ±5°, DOA estimation reliability was measured at 95.00% in the least reverberant space, decreasing to 78.33% in the most reverberant space, suggesting an inverse relationship between RT60 and DOA accuracy. Experimental results suggest that a system for estimating DOA with panel microphones can generalize to new acoustic environments by cross-training the system with data from multiple spaces with different RT60s.

Slow body magnetohydrodynamic waves in solar photospheric flux tubes with density inhomogeneity

ABSTRACT Pores and sunspots are ideal environments for the propagation of guided magnetohydrodynamic (MHD) waves. However, modelling such photospheric waveguides with varying background quantities such as plasma density and magnetic field has thus far been very limited. Such modelling is required to correctly interpret MHD waves observed in pores and sunspots with resolved inhomogeneities such as light bridges and umbral dots. This study will investigate the propagation characteristics and the spatial structure of slow body MHD modes in a magnetic flux tube with a circular cross-section with inhomogeneous equilibrium density distribution under solar photospheric conditions in the short wavelength limit. For simplicity, the equilibrium density profile is taken to have a circular density enhancement or depletion. The advantage of this is that the strength, size, and position of the density inhomogeneity can be easily changed. Calculating the eigenfrequencies and eigenfunctions of the slow body modes is addressed numerically with use of the Fourier–Chebyshev Spectral method. The radial and azimuthal variation of eigenfunctions is obtained by solving a Helmholtz-type partial differential equation with Dirichlet boundary conditions. The inhomogeneous equilibrium density profile results in modified eigenvalues and eigenvectors. It was found that a localized density inhomogeneity leads to a decrease in the eigenvalues and the spatial structure of modes ceases to be a global harmonic oscillation, as the modes migrate towards regions of lower density. Comparing the homogeneous case and the cases corresponding to depleted density enhancement, the dimensionless phase speed undergoes a significant drop in its value (at least 40 per cent).

Influence of the magnetic field and the mean flow configuration on spatial structure and growth rate of normal modes

The first part of the work presents the results of numerical experiments with the magnetohydrodynamic model of “shallow water” to assess the degree of influence of the magnetic field on the development of instabilities conditioned by a combination of inhomogeneities in the mean flow and the mean magnetic field. Normal mode calculations have confirmed the earlier obtained result on the different influence of weak and strong magnetic fields on the instability of differential rotation. Calculations have shown that a weak magnetic field stabilizes the development of instabilities, whereas a strong magnetic field, on the contrary, enhances the instability. Azimuthal inhomogeneities of differential rotation in all cases contribute to the development of instabilities. In the second part of the work, we examine the spatial structure of normal modes and make an attempt to interpret the torsional oscillations observed in the atmospheres of Earth and the Sun. Calculations have shown that regular axisymmetric disturbances can be caused by the formation of a cyclonic vortex above the pole, which is characteristic of Earth's atmosphere and, possibly, of the Sun's atmosphere. The least damped normal mode of a stable polar cyclone has a structure of torsional oscillations. Flow anomalies and the development of an anticyclonic eddy in winter at midlatitudes destroy torsional oscillations and lead to a rapid amplification of normal modes, which are more complex in structure.

Влияние магнитного поля и конфигурации среднего течения на пространственную структуру и скорость роста нормальных мод

The first part of the work presents the results of numerical experiments with the magnetohydrodynamic model of “shallow water” to assess the degree of influence of the magnetic field on the development of instabilities conditioned by a combination of inhomogeneities in the mean flow and the mean magnetic field. Numerical simulation of normal modes has confirmed the earlier obtained result on the different influence of weak and strong magnetic fields on the instability of differential rotation. Calculations have shown that a weak magnetic field stabilizes the development of instabilities, whereas a strong magnetic field, on the contrary, enhances the instability. Azimuthal inhomogeneities of differential rotation in all cases contribute to the development of instabilities. In the second part of the work, we examine the spatial structure of normal modes and make an attempt to interpret the torsional oscillations observed in the atmospheres of Earth and the Sun. Calculations have shown that regular axisymmetric disturbances (torsional oscillations) can be caused by the formation of a cyclonic vortex above the pole, which is characteristic of Earth’s atmosphere and, possibly, of the Sun’s atmosphere. The least damped normal mode of a stable polar cyclone has a structure of torsional oscillations. Flow anomalies and the development of an anticyclonic eddy in winter at midlatitudes destroy torsional oscillations and lead to a rapid amplification of normal modes, which are more complex in structure.

SLOW ELECTROMAGNETIC WAVES IN PLANAR THREE-COMPONENT WAVEGUIDE STRUCTURE WITH MU-NEGATIVE METAMATERIAL

This work is devoted to study of the dispersive properties of the slow electromagnetic waves that propagate along the planar waveguide structure that consists of semi-bounded plasma region, metamaterial slab and semibounded region of ordinary dielectric. It is studied the case when all media are homogeneous and isotropic. The dispersion properties, the phase and group velocities, as well as the electromagnetic field spatial structure of the eigen TE modes are studied in the frequency range where the metamaterial possess negative permeability.

Trapped atoms in spatially-structured vector light fields

Spatially-structured laser beams, eventually carrying orbital angular momentum, affect electronic transitions of atoms and their motional states in a complex way. We present a general framework, based on the spherical tensor decomposition of the interaction Hamiltonian, for computing atomic transition matrix elements for light fields of arbitrary spatial mode and polarization structures. We study both the bare electronic matrix elements, corresponding to transitions with no coupling to the atomic center-of-mass motion, as well as the matrix elements describing the coupling to the quantized atomic motion in the resolved side-band regime. We calculate the spatial dependence of electronic and motional matrix elements for tightly focused Hermite–Gaussian, Laguerre–Gaussian and for radially and azimuthally polarized beams. We show that near the diffraction limit, all these beams exhibit longitudinal fields and field gradients, which strongly affect the selection rules and could be used to tailor the light-matter interaction. The presented framework is useful for describing trapped atoms or ions in spatially-structured light fields and therefore for designing new protocols and setups in quantum optics, -sensing and -information processing. We provide open code to reproduce our results or to evaluate interaction matrix elements for different transition types, beam structures and interaction geometries.

Potential impacts of 1.5 °C and 2 °C global warming levels on drought modes over Eastern Africa

This study examines the impacts of 1.5 °C and 2.0 °C global warming levels (GWLs) on the characteristics of four major drought modes over Eastern Africa in the future under two climate forcing scenarios (RCP4.5 and RCP8.5). The droughts were quantified using two drought indices: the standardized precipitation evapotranspiration index (SPEI) and the standardized precipitation index (SPI) at 12-month scale. Four major drought modes were identified with the principal component analysis (PCA). Multi-model simulation datasets from the Coordinated Regional Climate Downscaling Experiment (CORDEX) were analysed for the study. The skill of the models to reproduce the spatial distribution and frequency of past drought modes over Eastern Africa was examined by comparing the simulated results with the Climate Research Unit (CRU) observation. The models give realistic simulations of the historical drought modes over the region. The correlation between the simulated and observed spatial pattern of the drought modes is high (r ≥ 0.7). Over the hotspot of the drought modes, the observed drought frequency is within the simulated values, and the simulations agree with the observation that the frequency of SPI-12 droughts is less than that of SPEI-12 droughts. For both RCP4.5 and RCP8.5 scenarios, the simulation ensemble projects no changes in the spatial structure of the drought modes but suggests an increase in SPEI-12 drought intensity and frequency over the hotspots of the drought modes. The magnitude of the increase, which varies over the drought mode hotspots, is generally higher at 2 °C than at 1.5 °C global warming levels. More than 75% of the simulations agree on these projections. The projections also show that the increase in drought intensity and frequency is more from increased potential evapotranspiration than from reduced precipitation. Hence, the study suggests that to reduce impacts of global warming on future drought, the adaptation activities should focus on reducing evaporative loss surface water.

Dynamic mode decomposition for data-driven analysis and reduced-order modeling of E × B plasmas: I. Extraction of spatiotemporally coherent patterns

The advent of data-driven/machine-learning based methods and the increase in data available from high-fidelity simulations and experiments has opened new pathways toward realizing reduced-order models for plasma systems that can aid in explaining the complex, multi-dimensional phenomena and enable forecasting and prediction of the systems’ behavior. In this two-part article, we evaluate the utility and the generalizability of the dynamic mode decomposition (DMD) algorithm for data-driven analysis and reduced-order modeling of plasma dynamics in cross-field E × B configurations. The DMD algorithm is an interpretable data-driven method that finds a best-fit linear model describing the time evolution of spatiotemporally coherent structures (patterns) in data. We have applied the DMD to extensive high-fidelity datasets generated using a particle-in-cell (PIC) code based on the cost-efficient reduced-order PIC scheme. In this part, we first provide an overview of the concept of DMD and its underpinning proper orthogonal and singular value decomposition methods. Two of the main DMD variants are next introduced. We then present and discuss the results of the DMD application in terms of the identification and extraction of the dominant spatiotemporal modes from high-fidelity data over a range of simulation conditions. We demonstrate that the DMD variant based on variable projection optimization (OPT-DMD) outperforms the basic DMD method in identification of the modes underlying the data, leading to notably more reliable reconstruction of the ground-truth. Furthermore, we show in multiple test cases that the discrete frequency spectrum of OPT-DMD-extracted modes is consistent with the temporal spectrum from the fast Fourier transform of the data. This observation implies that the OPT-DMD augments the conventional spectral analyses by being able to uniquely reveal the spatial structure of the dominant modes in the frequency spectra, thus, yielding more accessible, comprehensive information on the spatiotemporal characteristics of the plasma phenomena.

Quantum Entanglement: Examining its Nature and Implications

When two or more systems exhibit correlations that are stronger than those that can be explained traditionally, notwithstanding their spatial separation, this phenomenon is known as quantum entanglement. It is regarded as a key component of upcoming quantum technologies and one of the distinctive qualities of quantum physics. The transverse spatial degree of freedom in photonic experiments gives enormous opportunity to investigate different fascinating properties of light. This thesis has therefore focused on the photonic entanglement of transverse spatial formations in order to better explore the nature of quantum entanglement. The orbital angular momentum of photons is an intriguing characteristic caused by their spatial mode structure. Surprisingly, the maximum number of orbital angular momentum quanta that a single photon may carry is unbounded theoretically. As a result, it seems like a good candidate for evaluating photonic entanglement of macroscopic values. It may also add to discussions on macroscopicity and a potential breakdown of quantum mechanics beyond a certain point. Quantum entanglement is a fascinating phenomenon that lies at the heart of quantum mechanics, challenging our traditional understanding of the physical world. This paper aims to provide an overview of quantum entanglement, its experimental verification, and the implications it has on our comprehension of reality. By delving into its theoretical underpinnings and discussing the ongoing debates, we seek to answer the question: Does quantum entanglement make sense?

The Temporal and Spatial Evolution of Magnetohydrodynamic Wave Modes in Sunspots

Through their lifetime, sunspots undergo a change in their area and shape and, as they decay, they fragment into smaller structures. Here, for the first time we analyze the spatial structure of the magnetohydrodynamic (MHD) slow-body and fast-surface modes in the observed umbrae as their cross-sectional shape changes. The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques were used to analyze 3 and 6 hr Solar Dynamics Observatory/Helioseismic and Magnetic Imager time series of Doppler velocities at the photospheric level of approximately circular and elliptically shaped sunspots. Each time series was divided into equal time intervals to evidence the change in the shape of the sunspots. To identify the physical wave modes, the POD/DMD modes were cross-correlated with a slow-body mode model using the exact shape of the umbra, whereas the shape obtained by applying a threshold level of the mean intensity for every time interval. Our results show that the spatial structure of MHD modes are affected, even by apparently small changes in the umbral shape, especially in the case of the higher-order modes. For the data sets used in our study, the optimal time intervals to consider the influence of the change in the shape on the observed MHD modes is 37–60 minutes. The choice of these intervals is crucial to properly quantify the energy contribution of each wave mode to the power spectrum.

Analysis of Turbulence Driven Particle Transport in PANTA by Using Multi-Field Singular Value Decomposition

Multi-field singular value decompositions (SVDs) is applied to turbulence obtained in a cylindrical magnetized plasma, PANTA. This method enables us to obtain the spatial mode structures with common temporal evolution of different physical quantities, such as the fluctuations of density and flows. Turbulence driven particle transport is evaluated by the method. It is shown that only the coupling of the same mode drives the transport, which stems from the orthogonality of the SVD. Thanks to this characteristics, the number of degrees of freedom which plays roles for the transport dynamics could be significantly reduced.

Investigating the Linear Dynamics of the Near-Field of a Turbulent High-Speed Jet Using Dual-Particle Image Velocimetry (PIV) and Dynamic Mode Decomposition (DMD)

The quest for the physical mechanisms underlying turbulent high-speed jet flows is underpinned by the extraction of spatio-temporal coherent structures from their flow fields. Experimental measurements to enable data decomposition need to comprise time-resolved velocity fields with a high-spatial resolution—qualities which current particle image velocimetry hardware are incapable of providing. This paper demonstrates a novel approach that addresses this challenge through the implementation of an experimental high-spatial resolution dual-particle image velocimetry methodology coupled with dynamic mode decomposition. This new approach is exemplified by its application in studying the dynamics of the near-field region of a turbulent high-speed jet, enabling the spatio-temporal structure to be investigated by the identification of the spatial structure of the dominant dynamic modes and their temporal dynamics. The spatial amplification of these modes is compared with that predicted by classical linear stability theory, showing close agreement, which demonstrates the powerful capability of this technique to identify the dominant frequencies and their associated spatial structures in high-speed turbulent flows.

Tuning the topological state of a helical atom chain via a Josephson phase

By solving the Bogoliubov-de Gennes equations, we study the quasiparticle spectrum of a magnetic atom chain placed inside a short constriction-type Josephson junction. A helical magnetic order of the atomic spins is assumed, so that a topologically nontrivial state with Majorana edge modes at the ends of the chain can appear. It is found that in the presence of a nonzero Josephson phase the subgap spectrum of an infinite chain consists of four branches (Shiba bands). This spectrum is almost certainly gapped if the atomic spins form a coplanar spiral. The Majorana number of the given system is calculated analytically. It is demonstrated that a Josephson phase shift can be used to drive the system into a topologically nontrivial state and to tune the size of the topological gap. The spatial structure of Majorana edge modes is studied as well. We generalize the effective model based on discrete Bogoliubov-de Gennes equations developed by Pientka et al. for a bulk superconductor to the case of a Josephson junction. Using these discrete equations, the wave functions of Majorana zero modes are calculated analytically for a coplanar atomic spin spiral with arbitrary pitch. The wave functions exhibit an intermediate asymptotic behavior with a nonexponential fall-off with distance from the edge of the atomic chain.

Stress tunable dynamic susceptibility of a magnetic vortex in a flexible Fe81Ga19 nanoring

Introducing a flexible substrate in functional devices often brings about stress-tunable properties. Ferromagnetic nanorings fabricated on flexible substrates hold promise for microwave applications based on a stretchable functional system. Here, through micromagnetic simulations, we report high-frequency dynamic properties of such FeGa nanorings each with a magnetic vortex, concentrating on the dynamic susceptibility and the spatial structure of relevant resonance modes in response to an induced tensile or compressive stress. It is seen that the fundamental resonance frequency varies significantly with the mechanical stress and ring width. Furthermore, spatial profiles of the resonance modes are found to evolve with the stress and ring width, resulting in a repeated fluctuation in dynamic susceptibility. Our findings provide guidance for the design of stress tunable microwave devices.

High order modes of intense second harmonic light produced from a plasma aperture

Because of their ability to sustain extremely high-amplitude electromagnetic fields and transient density and field profiles, plasma optical components are being developed to amplify, compress, and condition high-power laser pulses. We recently demonstrated the potential to use a relativistic plasma aperture—produced during the interaction of a high-power laser pulse with an ultrathin foil target—to tailor the spatiotemporal properties of the intense fundamental and second-harmonic light generated [Duff et al., Sci. Rep. 10, 105 (2020)]. Herein, we explore numerically the interaction of an intense laser pulse with a preformed aperture target to generate second-harmonic laser light with higher-order spatial modes. The maximum generation efficiency is found for an aperture diameter close to the full width at half maximum of the laser focus and for a micrometer-scale target thickness. The spatial mode generated is shown to depend strongly on the polarization of the drive laser pulse, which enables changing between a linearly polarized TEM01 mode and a circularly polarized Laguerre–Gaussian LG01 mode. This demonstrates the use of a plasma aperture to generate intense higher-frequency light with selectable spatial mode structure.

Phenomenology and capabilities of mutually guided laser and neutral particle beams for deep space propulsion

Here we present a detailed analysis of a new concept for beam propulsion that extends the propagation range through space by circumventing fundamental limitations on the beam divergence. Using a combination of spatially overlapped continuous laser and neutral particle beams, opto-mechanical forces and light refraction are simultaneously exploited to produce self-guided modes. The aim of the present work is to elucidate the relevant physical phenomena, their relation to the conditions for self-guiding, and practical considerations for the design parameters of such a propulsion system. Methods for computing the lowest order axisymmetric self-guided modes are presented along with the resulting spatial mode structure. Key non-dimensional parameters are derived, including the use of linear stability analysis to determine features of the dynamic interaction. Based on these findings, a beam parameter optimization framework is proposed and applied to a 100-year interstellar flyby mission to Proxima b. With 200 GW of combined laser and particle beam power, we find that a 0.3 kg spacecraft could be accelerated to 0.044c over a distance of 4.37×106 km (0.029 AU) using a small 1 m2 beam cross-section. Compared to an equivalent particle beam with no self-guiding, this represents an over 50× increase in payload. Similar payload mass would be possible by laser propulsion with an approximately 104 m2 area laser array. These results suggest that self-guided beam propulsion possesses unique attributes that could enable the acceleration of larger spacecraft to relativistic velocities and enhance scientific capabilities for future interstellar and interstellar-precursor missions.

Polarized coherent microwave supercontinua with a terawatt laser driver

Ultrafast laser-plasma interactions driven by ultrashort terawatt laser pulses are shown to give rise to a bright multioctave microwave radiation, whose polarization and spatial mode structure provides a sensitive probe for laser-driven plasma electrodynamics, helping detect the symmetries of plasma currents and signatures of multiple ionization. Polarization mode structure of this radiation is dominated, as polarization-resolved measurements show, by a radially polarized mode, indicating the significance of ponderomotively driven plasma currents as sources of microwave emission. Angle-resolved analysis of microwave supercontinua reveals regimes in which the microwave emission is drastically enhanced, via coherence buildup, manifested in a well-resolved Cherenkov-emission cone.

Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

We perform a linear stability analysis of viscoelastic plane Couette and plane Poiseuille flows with free-slip boundary conditions. The fluid is described by the Oldroyd-B constitutive model, and the flows are driven by a suitable body force. We find that both types of flow become linearly unstable, and we characterise the spatial structure of the unstable modes. By performing a boundary condition homotopy from the free-slip to no-slip boundaries, we demonstrate that the unstable modes are directly related to the least stable modes of the no-slip problem, destabilised under the free-slip situation. We discuss how our observations can be used to study recently discovered purely elastic turbulence in parallel shear flows.

A linear benchmark between HYMAGYC, MEGA and ORB5 codes using the NLED-AUG test case to study Alfvénic modes driven by energetic particles

One of the major challenges in magnetic confinement thermonuclear fusion research concerns the confinement of the energetic particles (EPs) produced by fusion reactions and/or by additional heating systems. In such experiments, EPs can resonantly interact with the shear Alfvén waves. In the frame of the EUROfusion 2019–2020 Enabling Research project ‘multi-scale energetic particle transport in fusion devices’ (MET), a detailed benchmark activity has been undertaken among few of the state-of-the-art codes available to study the self-consistent interaction of an EP population with the shear Alfvén waves. In this paper linear studies of EP driven modes with toroidal mode number n = 1 will be presented, in real magnetic equilibria and in regimes of interest for the forthcoming generation devices (e.g. ITER, JT-60SA, DTT). The codes considered are HYMAGYC, MEGA, and ORB5, the first two being hybrid MHD-gyrokinetic codes (bulk plasma is represented by MHD equations, while the EP species is treated using the gyrokinetic formalism), the third being a global electromagnetic gyrokinetic code. The so-called NLED-AUG reference case has been considered, both for the peaked on-axis and peaked off-axis EP density profile cases, using its shaped cross section version. Comparison of the spatial mode structure, growth rate and real frequency of the modes observed will be considered in detail. The dependence of mode characteristics when several parameters are varied, as, e.g. the ratio between EP and bulk ion density and EP temperature, will be presented. A remarkable agreement is observed among the three codes for the peaked off-axis case, obtaining all of them a TAE localized close to the magnetic axis. On the other hand, some differences are observed when considering the peaked on-axis case, where two modes are observed (a TAE localized in the radial external region, and an RSAE around mid-radius). A careful analysis of the stability of this equilibrium, in particular by varying self-consistently the EP drive, will allow to reconcile the results of the three codes.

Polarization and Spatial Mode Structure of Mid-Infrared-Driven Terahertz-to-Microwave Radiation

Polarization and Spatial Mode Structure of Mid-Infrared-Driven Terahertz-to-Microwave Radiation