Search NASA⌕ Search

SEARCH · Search NASA

Results for “Linear approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14

Predicting the Slowing of Stellar Differential Rotation by Instability-driven Turbulence

Abstract Differentially rotating stars and planets transport angular momentum (AM) internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich–Schubert–Fricke instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing AM gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or “parasitic saturation” models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline-instability-driven turbulence in certain regimes.

Astronomy & Astrophysics↗

Orientation-dependent structural properties during growth and growth mechanism of CoO films

The orientation-dependent local structural properties of CoO films on sapphire substrates during growth were investigated through linearly-polarized extended X-ray absorption fine structure (EXAFS) measurements. Specifically, CoO(1 1 1) and (100) crystals with a rock-salt structure (Fm3m) were epitaxially grown on alpha-Al2O3(0001) and (1012) substrates, respectively, at 700 degrees C using a radio-frequency sputtering system. The local structural properties of CoO films in the in-plane and out-of-plane orientations were quantitatively determined using linearly-polarized EXAFS at the Co K-edge during growth. The EXAFS analysis revealed that during the initial stages of growth, the local structural properties exhibit significant differences compared to thick films, with short atomic distances and large (small) Debye-Waller factors observed in the out-of-plane (in-plane) orientations. The local structural strain mostly diminished when approximately 20 CoO layers accumulated on the substrate. Density functional theory (DFT) calculations further supported these findings by confirming that cobalt atoms initially form stable bonds with the sapphire surface, leading to the simultaneous growth of oxygen and cobalt layers in a coordinated manner through layer-by-layer growth.

36 MATERIALS SCIENCE↗

An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model

A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density $f$ = $f$ ($x, v, t$) converges to an isotropic function $M (v)$$ρ$$(x, t)$, called the drift-diffusion limit, where $M$ is a Maxwellian and the physical density $ρ$ satisfies a second-order parabolic PDE known as the drift-diffusion equation. Numerical approximations that mirror this property are said to be asymptotic preserving. In this paper we build a discontinuous Galerkin method to the semiconductor model, and we show this scheme is both uniformly stable in $ε$, where 1/$ε$ is the scale of the collision frequency, and asymptotic preserving. Here in particular, we discuss what properties the discrete Maxwellian must satisfy in order for the schemes to converge in $ε$ to an accurate $h$-approximation of the drift-diffusion limit. Discrete versions of the drift-diffusion equation and error estimates in several norms with respect to $ε$ and the spacial resolution are also included.

97 MATHEMATICS AND COMPUTING↗

Baryon fraction from the BAO amplitude: a consistent approach to parameterizing perturbation growth

Galaxy clustering constrains the baryon fraction Omega_b/Omega_m through the amplitude of baryon acoustic oscillations and the suppression of perturbations entering the horizon before recombination. This produces a different pre-recombination distribution of baryons and dark matter. After recombination, the gravitational potential responds to both components in proportion to their mass, allowing robust measurement of the baryon fraction. This is independent of new-physics scenarios altering the recombination background (e.g. Early Dark Energy). The accuracy of such measurements does, however, depend on how baryons and CDM are modeled in the power spectrum. Previous template-based splitting relied on approximate transfer functions that neglected part of information. We present a new method that embeds an extra parameter controlling the balance between baryons and dark matter in the growth terms of the perturbation equations in the CAMB Boltzmann solver. This approach captures the baryonic suppression of CDM prior to recombination, avoids inconsistencies, and yields a clean parametrization of the baryon fraction in the linear power spectrum, separating out the simple physics of growth due to the combined matter potential. We implement this framework in an analysis pipeline using Effective Field Theory of Large-Scale Structure with HOD-informed priors and validate it against noiseless LCDM and EDE cosmologies with DESI-like errors. The new scheme achieves comparable precision to previous splitting while reducing systematic biases, providing a more robust way to baryon-fraction measurements. In combination with BBN constraints on the baryon density and Alcock-Paczynski estimates of the matter density, these results strengthen the use of baryon fraction measurements to derive a Hubble constant from energy densities, with future DESI and Euclid data expected to deliver competitive constraints.

Crespi, Andrea [U. Waterloo (main); Waterloo U., I↗

Nonequilibrium steady-state thermoelectrics of Kondo-correlated quantum dots

The transport across a Kondo-correlated quantum dot coupled to two leads with independent temperatures and chemical potentials is studied using a controlled nonperturbative, and in this sense numerically exact, treatment based on a hybrid numerical renormalization group combined with time-dependent density matrix renormalization group (NRG-tDMRG). In the Kondo regime, for sufficiently large fixed voltage bias V ≳ T K , with T K the Kondo temperature, we find a peak in the conductance vs the temperature gradient Δ⁢T = T R - T L across left and right lead. Focusing then on zero voltage bias but finite ΔT far beyond linear response, we reveal the dependence of the characteristic zero-bias conductance on the individual lead temperatures. Here, we find that the finite-Δ⁢T data behaves quantitatively similar to linear response with an effective equilibrium temperature derived from the different lead temperatures. The regime of sign changes in the Seebeck coefficient, signaling the presence of Kondo correlations, and its dependence on the individual lead temperatures provide a complete picture of the Kondo regime in the presence of finite-temperature gradients. The results from the zero-bias conductance and Seebeck coefficient studies unveil an approximate “Kondo circle” in the T L /T R plane as the regime within which the Kondo correlations dominate. We also study the heat current and the corresponding heat conductance vs finite Δ⁢T. We provide a polynomial fit for our numerical results for the thermocurrent as a function of the individual lead temperatures, which may be used to fit experimental data in the Kondo regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Adsorptive denitrogenation of model aviation fuel using mesoporous silica in a packed bed adsorption system

This study aims to understand the effects of system process parameters such as flow rate, adsorbent particle size, and use of recycled adsorbent on denitrogenation performance of a model fuel using mesoporous silica gel. The goal is to reduce the nitrogen content of the model fuel from 1500 parts per million to single-digit ppm to meet ASTM specifications for drop-in fuels. This work was done with the intent of applying adsorptive denitrogenation to sustainable aviation fuel (SAF) product fractions produced via hydrothermal liquefaction (HTL). The adsorption performance of the silica is evaluated via packed column breakthrough data, with data generated from collecting from the column outlet and quantifying nitrogen content via gas chromatography. Select experiments use a significantly larger (2.5x column diameter and length) column to demonstrate linear scalability of the process. Thermogravimetric analysis data is collected to evaluate the effects of thermal calcination as a sorbent regeneration method. Effects of a more complex feed are also investigated using a known reference fuel with additional added nitrogen containing compounds. The results presented in this work successfully demonstrate up to 99.8 % removal of NCCs from a model fuel fraction at an original NCC concentration of approximately 1500 ppm to single-digit parts per million after treatment. We also examine calcination of sorbent materials to remove the adsorbed species to enable sorbent reuse and minimize waste generation and show that the calcined material can be reused up to 5 cycles with reduced adsorption capacity. Overall, this work indicates that adsorptive denitrogenation using silica gel is a viable solution to enable the integration of HTL-derived aviation fuels into existing fuel infrastructure.

Adsorption techniques↗

A fast and robust computational modeling approach for density and shape predictions in powder metallurgy hot isostatic pressing

Powder metallurgy hot isostatic pressing (PM-HIP) is an advanced manufacturing process that produces near-net-shape parts with high material utilization and uniform microstructures. PM-HIP is frequently used for producing small-scale parts with complicated geometries and is potentially economical for producing large-scale parts. However, excessive post-HIP shape distortions can reduce its effectiveness and economic advantage, especially for larger parts. A PM-HIP computational model can predict and help mitigate these distortions. However, due to complex deformation mechanisms and thermo-mechanical coupling present in PM-HIP processes, these non-linear computational models sometimes become numerically unstable. The numerical instabilities in these models can lead to very slow convergence or no convergence at all, which often translates to slow and unreliable models. These limitations are more pronounced in large models with complicated geometries. Hence, in this work, an alternative modeling approach is presented that improves numerical stability and computational performance. The presented approach achieves these improvements through approximating the fully coupled thermo-mechanical PM-HIP model as a decoupled model and adding inertial damping to the model’s mechanical part. In conclusion, a comparison with the fully coupled model indicated a slight dip in prediction accuracy (<5% error) but significant improvements in numerical stability (>20 times larger time step size) and computational performance (5-10 times speed-up with less computational resource usage) when using the presented approach.

Hot isostatic pressing↗

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Using Separation-Enhanced Isotope Ratio Mass Spectrometry to Enable Increased Renewable Carbon Content in Transportation Fuels (CRADA 525)

Stable isotope ratio measurements of carbon atoms using isotope ratio mass spectrometry (IRMS) can be an effective tool for quantifying biogenic carbon in co-processed fuels, with results approaching the precision and accuracy of accelerator mass spectrometry (AMS). The lower cost of an IRMS may enable deployment to refineries, improving access and analysis turnaround times (≤2 hours), and, by extension, provide data that can allow process optimization to maximize renewable carbon in desired refinery products. This project explored the integration of chemical separation with IRMS analyses to enable highly detailed tracking of biogenic carbon into fuel product streams separated by boiling point range, chemical class, or specific compound. Forty-nine fuels and fuel components of fossil and biogenic origin, spanning gasoline and diesel boiling point ranges, were received from three refiners and were analyzed for their δ 13 C values via IRMS. Results spanned a 13 C range from ca. 10‰ to 44‰ and reflect materials derived from sustainable sources (e.g., C4 or C3 plants, animal-based pathways, syngas) or from fossil-derived fuels. Common ranges are approximately 18‰ to 9‰ and approximately 30‰ to 20‰ for C4 and C3 plants, respectively, and approximately 34‰ to 24‰ and approximately 70‰ to 33‰ for petroleum-derived fuels and methane, respectively. Fuel-like standards were developed and tested using direct-injection elemental analyzer (EA) IRMS for liquid fuels. This method was compared with the published methods, yielding statistically similar results. Four blend curve sets were produced ranging from 0% to 100% of a fuel containing biogenic carbon, focusing on 0% to 10% biogenic carbon. Linear fits were the most applicable for two of the four blend curve sets; however, two sets were found to exhibit slightly quadratic behavior, which was more pronounced in low biogenic blend samples, necessitating second-order fits. The origin of the slight quadratic behavior remains unclear; however, the discussion points to possible interpretations. CanmetENERGY thoroughly characterized a majority of the samples using one- and two-dimensional gas chromatography (GC and GC×GC, respectively) and other analyses. Selected samples were subjected to solid phase extraction (SPE) for saturate, olefin, aromatic, and polar (SOAP) analysis, and the resulting solvent-diluted fractions containing saturates and aromatics were returned to Pacific Northwest National Laboratory (PNNL), where the solvent was removed via evaporation or physical separation using GC techniques. Characterization and separations provided an understanding of saturate and aromatic content, as well as boiling point ranges for each sample and sample fraction. Samples resulting from SPE were examined using EA-IRMS and gas chromatography combustion IRMS (GC-C-IRMS) analyses. Both approaches suggest that the range in values between end-members can be increased by selecting the paraffinic or aromatic fraction of the end-member or by selecting among individual compounds resulting from GC separation of the paraffinic fractions. Considerable work remains to put these approaches into practice and statistically validate the benefit for using a fraction or individual compound over bulk analysis of a sample. However, initial results suggest that separations provide advantages for samples having blend ratios of less than 10% biogenic blendstocks. 13 C results showed statistically similar biofuel blend results to those obtained at PNNL, although additional work is needed to obtain better reproducibility. Select samples were sent to Los Alamos National Laboratory (LANL) for IRMS measurements and Beta Analytics for AMS measurements. This work suggests that IRMS and AMS yield closely comparable results and in some circumstances, IRMS could serve as a surrogate for AMS. While additional work is needed to better resolve statistical advantages for separations and better show the comparable nature of IRMS and AMS in both the biogenic carbon analysis of bulk chemical classes, initial results from this study suggest that these should be pursued in order to proliferate this approach for quantifying biogenic carbon in transportation fuels to the refinery level, thereby potentially enabling process optimization in co-processing scenarios.

09 BIOMASS FUELS↗

Precise Modeling of a Complex Solenoidal Magnetic Field Using a Combination of Analytic Functions and a PINN

We demonstrate an iterative approach to modeling a sparsely measured magnetic field in a large-bore solenoid. This approach uses a hybrid of traditional and machine learning techniques. The traditional technique is a linear least-squares fit using a series solution to Laplace's equation, while the machine learning technique involves the training of a physics-informed neural network (PINN) on the least-squares fit residuals. We use a newly defined activation function "DELTAsnake," a modification to the snake activation function proposed by Ziyin et al. that allows for stronger curvature and non-monotonicity. The combined model approximately obeys Maxwell's equations to a level sufficient for producing high quality physics simulations and analysis. Our approach is applied to a highly realistic calculation of the expected magnetic field in the Mu2e experiment's Detector Solenoid which includes a simple model for the expected statistical measurement uncertainties. Using ten toy measurement simulations, we demonstrate the capabilities of our model in comparison to the least-squares method alone; the least-squares method alone results in a reduced chi-squared statistic of ${2.15 \pm 0.01}$, while our approach improves the reduced chi-square to ${1.034 \pm 0.005}$. Furthermore, for an average toy simulation, we show that the range of the RMS of the three field component residuals reduces from ${0.07-0.37}$ Gauss to ${0.05-0.07}$ Gauss. We find that this novel method is robust against a realistic systematic uncertainty deriving from Hall probe calibration bias and can be used to significantly reduce the number of measurements required to achieve an accurate model.

Kampa, Cole [Caltech] (ORCID:0000000192972920)↗

Cr plasma-material-interaction in PISCES-RF: D thermal release, retention, and erosion

Pure chromium (Cr) targets were exposed to high-flux deuterium (D) plasmas in the Pisces-RF linear plasma device, and measurements of D retention, release, and erosion were subsequently performed. Post-exposure D retention was quantified using temperature-programmed desorption on Cr targets irradiated by 50 eV ions over a broad range of exposure temperatures (423–873 K) and ion fluences (3 × 10 24 – 3 × 10 26 m −2 ). The retained D inventory was observed to decrease rapidly with increased exposure temperature, from approximately ∼7 × 10 20 m −2 at ∼ 420 K, to then saturate near ∼ 10 20 m −2 for exposure temperatures above ∼550 K. Separately, at fixed exposure temperature (∼450 K), D retention was found to have only a weak dependence on increasing ion fluence. Lastly, the erosion of Cr in D plasma was investigated for ion impact energies in the range 40 ≤ E i ≤ 250 eV. Erosion was inferred using optical emission spectroscopy (OES) from the ratio of emission lines (Cr I (425.4 nm)/D I (656.1 nm)) measured close to the target. Conversion of the OES yield data to net erosion yield was made with singular ion energy target mass-loss measurements. These net erosion yield data were then further corrected to obtain gross erosion yield by accounting for a re-deposition factor, computed using a simple model. The gross erosion yield is found to be 2–4 times lower than predicted by SDTrimSP, consistent with that typically observed for light-ion sputtering under high-flux plasma conditions.

Chromium↗

Increasing Branching and Functionalization Decreases Crystallinity and Crystallization Rate in Linear EVOH

Here, we report the crystallization behavior of a linear poly(ethylene-co-vinyl alcohol) (LEVOH) under isothermal crystallization as a function of both OH incorporation and undercooling, and compare the results to conventional branched EVOH. This LEVOH is synthesized by post-polymerization functionalization of polycyclooctene, and it exhibits a half-crystallization time and primary crystallization rate nearly an order of magnitude faster than branched EVOH at ~ 6 mol% OH incorporation. While the LEVOH obtains approximately twice the extent of crystallization compared to the branched equivalent, as OH incorporation increases, the crystallization kinetics and crystallinity of LEVOH decrease. The crystal structure of LEVOH is orthorhombic at low functionalization (≤ 11 mol% OH), a mixture of orthorhombic and hexagonal at moderate functionalization (17 - 21 mol%), and hexagonal at high functionalization (23 %). The LEVOH crystallizes into plates, with crystallite widths ~ 20 - 60 times the crystallite thickness. Ultimately, we show LEVOH crystallizes faster and to a greater extent than commercial branched EVOH, a potential advantage of post-polymerization functionalization as part of polymer-to-polymer upcycling.

36 MATERIALS SCIENCE↗

Tetraquarks in the Born-Oppenheimer approximation

The conventional loosely bound molecule interpretation of the X(3872) is not compatible with the recent LHCb experimental measurement of the ratio of branching fractions $\mathcal{R}$ = Br(X → ψ′γ)/Br(X → ψγ). We systematically determine the entire tetraquark spectrum for J = 0, 1, 2 and refine the calculation of $\mathcal{R}$ in an improved Born-Oppenheimer description of the X(3872) compact tetraquark. This refinement yields a significantly better agreement with experimental data on $\mathcal{R}$ and on the spectroscopy of the states themselves. Extending the diquark-antidiquark paradigm to encompass tetraquarks that are linear super-positions of open charm singlets and color octets, we discover that these exotic resonances manifest as compact shallow bound states of quarks in color force potentials.

Effective Field Theories of QCD↗

Transmission Interface Limits for High-Spatial Resolution Capacity Expansion Modeling

Large-scale capacity expansion models typically rely on estimates of the power transfer limits between modeled zones. Accurate estimation of these interface transfer limits (ITLs) requires modeling the underlying transmission network. Here we expand on a maximum flow optimization method that uses linearized power flow to estimate transfer limits. We apply this method to a data set of the U.S. transmission network to estimate ITLs between U.S. counties. By calculating ITLs using different subsets of the network, we evaluate how the size of the network used in the estimation affects the results. The results show diminishing returns to ITL accuracy after six hops, suggesting that a network subset can reasonably be used to approximate ITLs. The county-level estimates produced in this study will support more spatially resolved capacity expansion modeling and will help inform policy making at local and national levels.

capacity planning↗

Evolution of the Antarctic Ice Sheet from 2000–2300 and beyond: model sensitivity and uncertainty analysis using MPAS-Albany Land Ice

We present a description of the Antarctic Ice Sheet model configuration submitted to the ISMIP6-Antarctica-2300 experiment using the MPAS-Albany Land Ice model, along with three new sets of simulations: (1) a set of extended simulations to 2500 for three forced experiments and to 2775 for the control experiment; (2) a sensitivity analysis of our model configuration to parameters controlling basal sliding and sub-shelf melt, and to model structural choices including the choice of the energy and stress balances; and (3) a 72-member ensemble run on graphics processing units (GPUs) and analysis of variance to determine the primary sources of uncertainty in our ice-sheet model projections. Our extended simulations predict rapid retreat beginning after 2300 for SSP1-2.6 forcing and after 2500 for present-day (control) forcing, primarily in the Amundsen Sea Embayment. We find that varying the sub-shelf melt parameter between the 5th to 95th percentile values for a mean-Antarctic calibration target results in an up to ∼ ± 40 % change in sea-level contribution relative to our baseline simulations that used the median value. Using a linear basal sliding law reduces sea-level contribution by 51 %–73 % relative to our baseline nonlinear sliding law with an exponent of 1/5. When using basal sliding law exponents of 1/3 and 1/10, the overall difference from our baseline simulations at 2300 is on the order of 10 %. The Amundsen Sea Embayment region displays a strongly non-linear dependence of mass loss on the sliding law exponent, with no discernible relationship between the sliding law exponent and the mass loss by 2300, while the sectors feeding the Ross and Filchner-Ronne ice shelves exhibit more mass loss with a more-plastic sliding law. Our model fidelity sensitivity experiments reveal a 9 %–31 % increase in sea-level contribution when using a depth-integrated stress balance approximation relative to our three-dimensional solver, while using a fixed-in-time temperature field increases sea-level contribution by 14 %–88 % relative to two thermomechanically coupled configurations. Our 72-member ensemble and analysis of variance show that the uncertainty in long-term projections is dominated by the choice of Earth system model forcing and the presence or absence of hydrofracture forcing, rather than uncertainty in sliding and sub-shelf melt parameters.

58 GEOSCIENCES↗

Transmission Interface Limits for High-Spatial Resolution Capacity Expansion Modeling

Large-scale capacity expansion models typically rely on estimates of the power transfer limits between modeled zones. Accurate estimation of these interface transfer limits (ITLs) requires modeling the underlying transmission network. Here we expand on a maximum flow optimization method that uses linearized power flow to estimate transfer limits. We apply this method to a data set of the U.S. transmission network to estimate ITLs between U.S. counties. By calculating ITLs using different subsets of the network, we evaluate how the size of the network used in the estimation affects the results. The results show diminishing returns to ITL accuracy after six hops, suggesting that a network subset can reasonably be used to approximate ITLs. The county-level estimates produced in this study will support more spatially resolved capacity expansion modeling and will help inform policy making at local and national levels.

capacity planning↗

Slow-Light Mid-IR Silicon Photonic Chips for NO 2 and CH 4 Gas Detection

A compact, chip-scale mid-infrared gas sensor is demonstrated, leveraging a two-dimensional photonic crystal waveguide (PCW) fabricated on a silicon-on-insulator (SOI) platform. The PCW comprises a hexagonal lattice with lattice constant a = 860 nm and hole radius r = 0.22a, incorporating a central line defect of reduced-radius holes (r s = 0.7r) to induce slow-light propagation near the photonic band edge with a group index of approximately 73, thereby enhancing light-matter interaction. The sensor operates at fundamental absorption wavelengths of 3.42 μm for nitrogen dioxide (NO 2 ) and 3.40 μm for methane (CH 4 ), utilizing the strongest molecular vibrational transitions for maximum sensitivity. Experimental validation was conducted using dynamically diluted gas mixtures generated by mass flow controllers, with signal acquisition performed by a liquid nitrogen-cooled InSb detector. For NO 2 , the sensor exhibited excellent linear response over 5–25 ppm (part per million) with coefficient of determination R 2 = 0.9934, achieving a detection limit of 210 ppb (part per billion)─representing the first reported silicon photonic-based NO 2 detection. For CH 4 , exposure to 25 ppm resulted in a 6.4% decrease in transmitted intensity, demonstrating multigas sensing capability. The CMOS-compatible fabrication process and compact 3 mm device footprint establish this SOI-PCW platform as a scalable, low-power solution for integrated mid-infrared gas sensing, with significant potential for environmental monitoring and industrial safety applications.

Crystals↗

Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality reduction, such as the singular value decomposition (SVD) or interpolative (ID) and CUR decompositions. Recent advances in randomized dimensionality reduction are discussed, including new methods of fast matrix sketching and sampling techniques, which are incorporated into classical matrix algorithms for fast low-rank matrix approximations. The extension of randomized matrix algorithms to tensors is then explored for several low-rank tensor decompositions in the CP and Tucker formats, including the higher-order SVD, ID, and CUR decomposition.

Pearce, Katherine J. [The University of Texas at A↗