Analyzing slightly inclined cylindrical binary fluid convection via higher order dynamic mode decomposition

An extended dynamical system is considered that shows some striking, very complex spatio-temporal patterns. Specifically, we consider superhighway patterns that appear in binary fluid convection in slightly inclined, shallow cylindrical containers. These patterns show a number of parallel thermal lanes, each containing aligned coherent structures that counterpropagate in adjacent lanes. Several types of superhighway convection states have been obtained by direct numerical simulation. The numerical outcomes are analyzed using a recent data processing tool, known as higher order dynamic mode decomposition, which efficiently identifies relevant spatio-temporal patterns in numerically computed data.Postprint (author's final draft

Higher Order Dynamic Mode Decomposition of an experimental trailing vortex

The decay of trailing vortices is a fundamental problem in fluid mechanics and constitutes the basis of control applications that intend to alleviate the wake hazard. In order to progress, we use the recently developed modal-decomposition technique to identify the governing dynamics in an experimental trailing vortex. A particular emphasis is on the difficulty and usefulness of applying such tools to noisy experimental data. We conducted a water-tunnel experiment at a chord-based Reynolds number Re = 4 x 10^4 using stereoscopic particle image velocimetry measurements over a downstream range of 36 chords. The downstream evolution of the maximum of vorticity suggests that the whole wake can be partitioned into three consecutive regimes. A higher-order dynamic mode decomposition of the streamwise vorticity in each such part of the wake shows that the decay is well approximated by at most three modes. Additionally, our study provides evidence for the existence of several instabilities after the vortex roll up beyond about 6.5 chords

Energy Modelling and Forecasting for an Underground Agricultural Farm using a Higher Order Dynamic Mode Decomposition Approach

This paper presents an approach based on higher order dynamic mode decomposition (HODMD) to model, analyse, and forecast energy behaviour in an urban agriculture farm situated in a retrofitted London underground tunnel, where observed measurements are influenced by noisy and occasionally transient conditions. HODMD is a data-driven reduced order modelling method typically used to analyse and predict highly noisy and complex flows in fluid dynamics or any type of complex data from dynamical systems. HODMD is a recent extension of the classical dynamic mode decomposition method (DMD), customised to handle scenarios where the spectral complexity underlying the measurement data is higher than its spatial complexity, such as is the environmental behaviour of the farm. HODMD decomposes temporal data as a linear expansion of physically-meaningful DMD-modes in a semi-automatic approach, using a time-delay embedded approach. We apply HODMD to three seasonal scenarios using real data measured by sensors located at at the cross-sectional centre of the the underground farm. Through the study we revealed three physically-interpretable mode pairs that govern the environmental behaviour at the centre of the farm, consistently across environmental scenarios. Subsequently, we demonstrate how we can reconstruct the fundamental structure of the observed time-series using only these modes, and forecast for three days ahead, as one, compact and interpretable reduced-order model. We find HODMD to serve as a robust, semi-automatic modelling alternative for predictive modelling in Digital Twins

Magnetohydrodynamic wave mode identification in circular and elliptical sunspot umbrae: evidence for high order modes

In this paper we provide clear direct evidence of multiple concurrent higher order magnetohydrodynamic (MHD) modes in circular and elliptical sunspots by applying both Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) techniques on solar observational data. These techniques are well documented and validated in the areas of fluid mechanics, hydraulics, and granular flows, yet are relatively new to the field of solar physics. While POD identifies modes based on orthogonality in space and it provides a clear ranking of modes in terms of their contribution to the variance of the signal, DMD resolves modes that are orthogonal in time. The clear presence of the fundamental slow sausage and kink body modes, as well as higher order slow sausage and kink body modes have been identified using POD and DMD analysis of the chromospheric H$\alpha$ line at 6562.808~{\AA} for both the circular and elliptical sunspots. Additionally, to the various slow body modes, evidence for the presence of the fast surface kink mode was found in the circular sunspot. All the MHD modes patterns were cross-correlated with their theoretically predicted counterparts and we demonstrated that ellipticity cannot be neglected when interpreting MHD wave modes. The higher-order MHD wave modes are even more sensitive to irregularities in umbral cross-sectional shapes, hence this must be taken into account for more accurate modelling of the modes in sunspots and pores.Comment: Figures 21 and 22 should be presented in the appendix section and then followed by reference

On Optimizing Distributed Tucker Decomposition for Dense Tensors

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component analysis (PCA)and finds applications in diverse domains such as signal processing, computer vision and text analytics. Our objective is to develop an efficient distributed implementation for the case of dense tensors. The implementation is based on the HOOI (Higher Order Orthogonal Iterator) procedure, wherein the tensor-times-matrix product forms the core routine. Prior work have proposed heuristics for reducing the computational load and communication volume incurred by the routine. We study the two metrics in a formal and systematic manner, and design strategies that are optimal under the two fundamental metrics. Our experimental evaluation on a large benchmark of tensors shows that the optimal strategies provide significant reduction in load and volume compared to prior heuristics, and provide up to 7x speed-up in the overall running time.Comment: Preliminary version of the paper appears in the proceedings of IPDPS'1

Impact and mitigation of wavefront distortions in precision interferometry

Wavefront distortions, arising from mismatches, degrade quantum noise mitigation strategies in precision metrological devices, such as LIGO. Direct mode decomposition quantifies wavefront distortions in terms of solutions to the paraxial wave equation. The first part of this thesis develops high dynamic range mode decomposition, by using photodiode readout and developing novel alignment strategies. Limiting noise sources are suppressed and the noise performance is characterized in the 1\,mHz to 10\,kHz frequency range. Higher order, Hermite-Gauss, spatial modes may be used in precision metrology to sidestep thermal noise. This thesis demonstrates the production of higher order, Hermite-Gauss spatial modes, but, also finds that these modes are more susceptible to mode mismatch losses than the fundamental mode. Another form of precision metrology is atomic interferometry. Optical cavities reject wavefront distortions in the laser beams used to manipulate the atoms; however, they introduce an elongation of the beam-splitter pulses. A numerical study finds that this elongation suppresses the atomic excitation probability, when the transition is not exactly on resonance, reducing atomic flux. Long baseline, high finesse resonators are particularly affected. The closing section of this thesis describes a tool used to validate numerical models used throughout this work

Tensor-based dynamic mode decomposition

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially high-dimensional data sets to compute the corresponding DMD modes and eigenvalues. The goal is to reduce the computational complexity and also the amount of memory required to store the data in order to mitigate the curse of dimensionality. The efficiency of these tensor-based methods will be illustrated with the aid of several different fluid dynamics problems such as the von K\'arm\'an vortex street and the simulation of two merging vortices