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1. Modal analysis in curvilinear coordinates

   Parthasarathy, A.; Saxton-Fox, T. (August 2021, International Conference on Theoretical and Applied Mechanics Proceedings)

   Modal analysis techniques have proven useful in understanding and modeling turbulent phenomena. However, these techniques are more efficient in parallel flows where Fourier transforms can be taken along homogeneous directions. We suggest that quasi-1D methods can be applied to mildly non-canonical flows by using a curvilinear coordinate system. For a given base flow, we identify a curvilinear coordinate system that allows the Fourier-transformed equations of motion to be simplified into a quasi-1D system that can be efficiently analyzed. 

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2. Improved Precipitation Typing Using POSS Spectral Modal Analysis

   https://doi.org/10.1175/JTECH-D-20-0075.1  

   Sheppard, Brian E.; Thurai, Merhala; Rodriguez, Peter; Kennedy, Patrick C.; Hudak, David R. (March 2021, Journal of Atmospheric and Oceanic Technology)

   null (Ed.)

   Abstract The Precipitation Occurrence Sensor System (POSS) is a small X-band Doppler radar that measures the Doppler velocity spectra from precipitation falling in a small volume near the sensor. The sensor records a 2D frequency of occurrence matrix of the velocity and power at the mode of each spectrum measured over 1 min. The centroid of the distribution of these modes, along with other spectral parameters, defines a data vector input to a multiple discriminant analysis (MDA) for classification of the precipitation type. This requires the a priori determination of a training set for different types, particle size distributions (PSDs), and wind speed conditions. A software model combines POSS system parameters, a particle scattering cross section, and terminal velocity models, to simulate the real-time Doppler signal measured by the system for different PSDs and wind speeds. This is processed in the same manner as the system hardware to produce bootstrap samples of the modal centroid distributions for the MDA training set. MDA results are compared to images from the Multi-Angle Snowflake Camera (MASC) at the MASCRAD site near Easton, Colorado, and to the CSU–CHILL X-band radar observations from Greeley, Colorado. In the four case studies presented, POSS successfully identified precipitation transitions through a range of types (rain, graupel, rimed dendrites, aggregates, unrimed dendrites). Also two separate events of hail were reported and confirmed by the images. 

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3. Modal analysis of blood flows in saccular aneurysms

   https://doi.org/10.1063/5.0243383  

   Nguyen, Thien-Tam; Kasperski, Davina; Huynh, Phat Kim; Le, Trung Quoc; Le, Trung Bao (January 2025, Physics of Fluids)

   Currently, it is challenging to investigate aneurismal hemodynamics based on current in vivo data such as Magnetic Resonance Imaging or Computed Tomography due to the limitations in both spatial and temporal resolutions. In this work, we investigate the use of modal analysis at various resolutions to examine its usefulness for analyzing blood flows in brain aneurysms. Two variants of Dynamic Mode Decomposition (DMD): (i) Hankel-DMD; and (ii) Optimized-DMD, are used to extract the time-dependent dynamics of blood flows during one cardiac cycle. First, high-resolution hemodynamic data in patient-specific aneurysms are obtained using Computational Fluid Dynamics. Second, the dynamics modes, along with their spatial amplitudes and temporal magnitudes are calculated using the DMD analysis. Third, an examination of DMD analyses using a range of spatial and temporal resolutions of hemodynamic data to validate the applicability of DMD for low-resolution data, similar to ones in clinical practices. Our results show that DMD is able to characterize the inflow jet dynamics by separating large-scale structures and flow instabilities even at low spatial and temporal resolutions. Its robustness in quantifying the flow dynamics using the energy spectrum is demonstrated across different resolutions in all aneurysms in our study population. Our work indicates that DMD can be used for analyzing blood flow patterns of brain aneurysms and is a promising tool to be explored in in vivo. 

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4. Modal analysis of computational human brain dynamics during helmeted impacts

   https://doi.org/10.1016/j.brain.2023.100082  

   Rezayaraghi, Fargol; Abderezaei, Javid; Ozkaya, Efe; Stein, Devlin; Pionteck, Aymeric; Kurt, Mehmet (December 2023, Brain Multiphysics)
5. Modal sensitivity analysis of acoustic metamaterials for structural damage detection

   https://doi.org/10.1016/j.ijmecsci.2023.108571  

   Xu, Y.F.; Huang, G.L. (December 2023, International Journal of Mechanical Sciences)