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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Composite binder, processing, and particle size effects on mechanical properties of non-hazardous high explosive surrogates

Plastic-bonded explosives (PBX) are polymer matrix composites that are highly loaded with micron-scale explosive crystals. The thermal and mechanical properties of these materials must be well-understood so that appropriate engineering models can be developed, but testing such properties under many scenarios can be hazardous and expensive. A non-hazardous PBX surrogate (“mock”) may be used in place of a PBX in many experiments if the thermomechanical properties are well-matched. Our previous research has shown that 5-iodo-2'-deoxyuridine (IDOX) is a promising crystalline filler material for the explosive cyclotetramethylene-tetranitramine (HMX). In this study, we investigate how the binder composition, variations in the IDOX particle size distribution, and pressing temperature affect the compressive strength and elastic modulus. We observe that while the binder system used in the composite dominates the mechanical response, the particle size distribution and pressing conditions do have a measurable effect on the material compliance and strength.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2024

Self-healing carbon fiber/epoxy laminates with particulate interlayers of a low-melting-point alloy

In order to prolong the service life of fiber-reinforced polymer composites, the implementation of self-healing ability with the micro-encapsulated healing agent has been extensively studied. However, such microcapsule-based self-healing composites typically suffer from degraded mechanical properties due to the liquid-phase inclusions, thereby limiting their proliferation. Here, in this study, a low-melting-point alloy is utilized as the particulate inclusions of carbon fiber/epoxy laminated composites. Field's Metal particles (melting point: 62 °C) are distributed between woven carbon fiber preforms followed by the resin impregnation to realize laminated composites with a Field's Metal-enhanced interlayer(s). The resulting laminated composites demonstrate the autonomic repair of interlaminar failure with a 40 % of healing efficiency. Most of all, the mechanical properties of these self-healing laminated composites are comparable to the conventional laminated composites attributed to the rigid inclusions that can be compressed to increase the fiber volume. Since the Field's Metal particle inclusions can bestow polymer composites with self-healing ability and the potential increase in mechanical properties, Field's Metal-enhanced fiber-reinforced polymer composites are expected to unlock the practical utility of self-healing composites.

A. polymer-matrix composites (PMCs)↗
DOE OSTI2025

Sizing comingled CF/PA 6 fibers with cellulose nanofibrils for enhanced performance properties

Compatibility between the reinforcing phase and the polymer matrix is critical to achieving the desired mechanical and thermal performance of composite materials. Several mechanisms can enhance this interfacial interaction, including surface treatments (e.g., oxidation, plasma, or irradiation), in-situ nanoparticle deposition, and fiber sizing. Here, in this study, cellulose nanofibrils (CNF) were employed as a sustainable sizing agent to modify the interface in commingled carbon fiber (CF)/polyamide 6 (PA 6) yarns, in which CF and PA6 filaments are intimately blended to enable simultaneous consolidation. A 0.25 wt% CNF aqueous suspension was applied under bath sonication to ensure uniform dispersion and minimize agglomeration. CNF-sized and unsized yarns were used to fabricate unidirectional composite plates via filament winding on a flat mandrel, followed by compression molding. Scanning electron microscopy confirmed CNF presence on both CF and PA6 filaments. CNF-sized composites exhibited increments in interlaminar shear strength (ILSS) by 50%, flexural strength by 11%, and tensile strength by 2.5% compared to unsized composites. Thermal analysis showed minimal changes in degradation temperature and crystallinity. These findings demonstrate that CNF sizing enhances interfacial bonding and mechanical performance, offering a scalable and environmentally friendly strategy for thermoplastic composite manufacturing along with yarn/tow handleability.

Cellulose nanofibrils (CNF)↗
NASA NTRS1996

Cyclic Load Effects on Long Term Behavior of Polymer Matrix Composites

A methodology to compute the fatigue life for different ratios, r, of applied stress to the laminate strength based on first ply failure criteria combined with thermal cyclic loads has been developed and demonstrated. Degradation effects resulting from long term environmental exposure and thermo-mechanical cyclic loads are considered in the simulation process. A unified time-stress dependent multi-factor interaction equation model developed at NASA Lewis Research Center has been used to account for the degradation of material properties caused by cyclic and aging loads. Effect of variation in the thermal cyclic load amplitude on a quasi-symmetric graphite/epoxy laminate has been studied with respect to the impending failure modes. The results show that, for the laminate under consideration, the fatigue life under combined mechanical and low thermal amplitude cyclic loads is higher than that due to mechanical loads only. However, as the thermal amplitude increases, the life also decreases. The failure mode changes from tensile under mechanical loads only to the compressive and shear at high mechanical and thermal loads. Also, implementation of the developed methodology in the design process has been discussed.

Shah, A. R.↗
NASA NTRS2014

Evaluation of RTM370 Polyimide Composites by Resin Film Infusion (RFI)

RTM370 imide oligomer based on 2,3,3',4'-biphenyl dianhydride (a-BPDA), 3,4'-oxydianiline (3,4'-ODA) and terminated with the 4-phenylethynylphthalic (PEPA) endcap has been shown to exhibit a low melt viscosity (10-30 poise) at 280 C with a pot-life of 1-2 h and a high cured glass-transition temperature (Tg) of 370 C. RTM370 resin has been successfully infused into fiberglass-stitched T650-35 carbon-fabric preforms (ranged from 3- to 6-mm thick) by resin film infusion (RFI). The resulting composite panels were inspected by ultrasonic C-scan and by photomicrographs before and after post-curing as a quality control. Mechanical tests such as unnotched compression (UNC), open-hole compression (OHC), and short-beam shear strength (SBS) at ambient and elevated temperatures were performed before and after isothermal aging at 288 C for 1000 h to assess high-temperature performance. Thermal cycling of RTM370 stitched composites was also conducted from -54 C to 288 C for up to 1600 cycles to evaluate the microcrack resistance of RTM370 polyimide composites fabricated by RFI.

Polyimide↗
NASA NTRS2017

Development of an Input Suite for an Orthotropic Composite Material Model

An orthotropic three-dimensional material model suitable for use in modeling impact tests has been developed that has three major components elastic and inelastic deformations, damage and failure. The material model has been implemented as MAT213 into a special version of LS-DYNA and uses tabulated data obtained from experiments. The prominent features of the constitutive model are illustrated using a widely-used aerospace composite the T800S3900-2B[P2352W-19] BMS8-276 Rev-H-Unitape fiber resin unidirectional composite. The input for the deformation model consists of experimental data from 12 distinct experiments at a known temperature and strain rate: tension and compression along all three principal directions, shear in all three principal planes, and off axis tension or compression tests in all three principal planes, along with other material constants. There are additional input associated with the damage and failure models. The steps in using this model are illustrated composite characterization tests, verification tests and a validation test. The results show that the developed and implemented model is stable and yields acceptably accurate results.

finite element method↗
DOE OSTI2021

First-principles study of electron transport in ScN

We investigate the conduction-band structure and electron mobility in rocksalt ScN based on density functional theory. The first-principles band structure allows us to obtain band velocities and effective masses as a function of energy. Electron-phonon scattering is assessed by explicitly computing the q-dependent electron-phonon matrix elements, with the inclusion of the long-range electrostatic interaction. The influence of free-carrier screening on the electron transport is assessed using the random phase approximation. We find a notable enhancement of electron mobility when the carrier concentration exceeds 10 20 cm -3 . We calculate the room-temperature electron mobility in ScN to be 587 cm2 /Vs at low carrier concentrations. When the carrier concentration is increased, the electron mobility starts to decrease significantly around n = 10 19 cm -3 , and drops to 240 cm 2 /Vs at n = 10 21 cm -3 . We also explore the influence of strain in (111)- and (100)-oriented ScN films. For (111) films, we find that a 1.0% compressive epitaxial strain increases the in-plane mobility by 72 cm 2 /Vs and the out-of-plane mobility by 50 cm 2 /Vs. For (100) films, a 1.0% compressive epitaxial strain increases the out-of-plane mobility by as much as 172 cm2 /Vs, but has a weak impact on the in-plane mobility. Our study sheds light on electron transport in ScN at different electron concentrations and shows how strain engineering could increase the electron mobility.

36 MATERIALS SCIENCE↗
DOE OSTI2020

An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations

Here, we propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection, sparsification, and low-rank compression. After eliminating all interiors at a given level of the elimination tree, the algorithm sparsifies all separators corresponding to the interiors. This operation reduces the size of the separators by eliminating some degrees of freedom but without introducing any fill-in. This is done at the expense of a small and controllable approximation error. The result is an approximate factorization that can be used as an efficient preconditioner. We then perform several numerical experiments to evaluate this algorithm. We demonstrate that a version using orthogonal factorization and block-diagonal scaling takes fewer CG iterations to converge than previous similar algorithms on various kinds of problems. Furthermore, this algorithm is provably guaranteed to never break down and the matrix stays symmetric positive-definite throughout the process. We evaluate the algorithm on some large problems show it exhibits near-linear scaling. The factorization time is roughly $\mathcal{O}$(N), and the number of iterations grows slowly with N.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Preconditioned conjugate-gradient methods for low-speed flow calculations

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations is integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the Lower-Upper Successive Symmetric Over-Relaxation iterative scheme is more efficient than a preconditioner based on Incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional Line Gauss-Seidel Relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Ajmani, Kumud↗
DOE OSTI2024

Geometry-aware training of factorized layers in tensor Tucker format

Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during train and inference of large networks. Given its easy implementation and flexibility, one promising approach is layer factorization, which reshapes weight tensors into a matrix format and parameterizes it as the product of two rank-r matrices. However, this family of approaches often requires an initial full-model warm-up phase, prior knowledge of a feasible rank, and it is sensitive to parameter initialization.In this work, we introduce a novel approach to train the factors of a Tucker decomposition of the weight tensors. Our training proposal proves to be optimal in locally approximating the original unfactorized dynamics and stable for the initialization. Furthermore, the rank of each mode is dynamically updated during training.We provide a theoretical analysis of the algorithm, showing convergence, approximation and local descent guarantees. The method's performance is further illustrated through a variety of experiments, showing remarkable training compression rates and comparable or even better performance than the full baseline and alternative layer factorization strategies.

Zangrando, Emanuele [Gran Sasso Science Institute ↗
NASA NTRS2002

Unsteady Pressures in a Transonic Fan Cascade Due to a Single Oscillating Airfoil

An extensive set of unsteady pressure data was acquired along the midspan of a modern transonic fan blade for simulated flutter conditions. The data set was acquired in a nine-blade linear cascade with an oscillating middle blade to provide a database for the influence coefficient method to calculate instantaneous blade loadings. The cascade was set for an incidence of 10 dg. The data were acquired on three stationary blades on each side of the middle blade that was oscillated at an amplitude of 0.6 dg. The matrix of test conditions covered inlet Mach numbers of 0.5, 0.8, and 1.1 and the oscillation frequencies of 200, 300, 400, and 500 Hz. A simple quasiunsteady two-dimensional computer simulation was developed to aid in the running of the experimental program. For high Mach number subsonic inlet flows the blade pressures exhibit very strong, low-frequency, self-induced oscillations even without forced blade oscillations, while for low subsonic and supersonic inlet Mach numbers the blade pressure unsteadiness is quite low. The amplitude of forced pressure fluctuations on neighboring stationary blades strongly depends on the inlet Mach number and forcing frequency. The flowfield behavior is believed to be governed by strong nonlinear effects due to a combination of viscosity, compressibility, and unsteadiness. Therefore, the validity of the quasi-unsteady simplified computer simulation is limited to conditions when the flowfield is behaving in a linear, steady manner. Finally, an extensive set of unsteady pressure data was acquired to help development and verification of computer codes for blade flutter effects.

Lepicovsky, J.↗
NASA NTRS2011

Approaches for Tensile Testing of Braided Composites

For angleply composites, lamina tension and compression strengths are commonly determined by applying classical lamination theory to test data obtained from testing of angleply composite specimens. For textile composites such as 2D triaxial braids, analysis is more complex and standard test methods do not always yield reliable strength measurements. This paper describes recent research focused on development of more reliable tensile test methods for braided composites and presents preliminary data for various approaches. The materials investigated in this work have 0deg+/-60 2D triaxial braid architecture with nearly equal fiber volume fraction in each of the three fiber directions. Flat composite panels are fabricated by resin transfer molding (RTM) using six layers of the braided preform aligned along the 0deg fiber direction. Various epoxy resins are used as matrix materials. Single layer panels are also fabricated in order to examine local variations in deformation related to the braid architecture. Specimens are cut from these panels in the shape of standard straight-sided coupons, an alternative bowtie geometry, and an alternative notched geometry. Axial tensile properties are measured using specimens loaded along the 0deg fiber direction. Transverse tensile properties are measured using specimens loaded perpendicular to the 0deg fibers. Composite tubes are also fabricated by RTM. These tubes are tested by internal pressurization using a soft rubbery material sealed between the inside diameter of the tube and the load fixtures. The ends of the tube are unconstrained, so the primary load is in the hoop direction. Tubes are fabricated with the 0deg fibers aligned along the tube axis by overbraiding the preform on a mandrel. Since the loading is in the hoop direction, testing of the overbraided tube provides a measure of transverse tensile strength. Previous work has indicated that straight-sided coupons yield a transverse tensile strength that is much lower than the expected material strength because of premature edge-initiated failure. Full-field strain measured during transverse tensile tests clearly showed accumulation of edge damage prior to failure. In the current work, high speed video and testing of single layer specimens are used to investigate potential failure mechanisms in more detail. High speed video clearly shows the edge initiation in six layer transverse tensile test coupons. Specimens with the bowtie geometry and the notched geometry minimize this edge effect and yield significantly higher transverse tensile strength values compared to the straight-sided coupons. However, bowtie and notched specimens geometries are not ideal because of the non-uniform stress and strain fields in the region of failure. Testing of tubes using internal pressurization eliminates edge-initiated failure and provides a more uniform state of stress and strain. Preliminary results indicate that bowtie, notched, and tube specimens yield comparable values for transverse tensile strength and that these values are much higher than the strength measured using a straight-sided coupon.

Roberts, Gary D.↗
NASA NTRS1995

Bend stress relaxation and tensile primary creep of a polycrystalline alpha-SiC fiber

Understanding the thermomechanical behavior (creep and stress relaxation) of ceramic fibers is of both practical and basic interest. On the practical level, ceramic fibers are the reinforcement for ceramic matrix composites which are being developed for use in high temperature applications. It is important to understand and model the total creep of fibers at low strain levels where creep is predominantly in the primary stage. In addition, there are many applications where the component will only be subjected to thermal strains. Therefore, the stress relaxation of composite consituents in such circumstances will be an important factor in composite design and performance. The objective of this paper is to compare and analyze bend stress relaxation and tensile creep data for alpha-SiC fibers produced by the Carborundum Co. (Niagara Falls, NY). This fiber is of current technical interest and is similar in composition to bulk alpha-SiC which has been studied under compressive creep conditions. The temperature, time, and stress dependences will be discussed for the stress relaxation and creep results. In addition, some creep and relaxation recovery experiments were performed in order to understand the complete viscoelastic behavior, i.e. both recoverable and nonrecoverable creep components of these materials. The data will be presented in order to model the deformation behavior and compare relaxation and/or creep behavior for relatively low deformation strain conditions of practical concern. Where applicable, the tensile creep results will be compared to bend stress relaxation data.

Hee Man, Yun↗
NASA NTRS2004

Structural Benchmark Testing of Superalloy Lattice Block Subelements Completed

Superalloy lattice block panels, which are produced directly by investment casting, are composed of thin ligaments arranged in three-dimensional triangulated trusslike structures (see the preceding figure). Optionally, solid panel face sheets can be formed integrally during casting. In either form, lattice block panels can easily be produced with weights less than 25 percent of the mass of a solid panel. Inconel 718 (IN 718) and MarM-247 superalloy lattice block panels have been developed under NASA's Ultra-Efficient Engine Technology Project and Higher Operating Temperature Propulsion Components Project to take advantage of the superalloys' high strength and elevated temperature capability with the inherent light weight and high stiffness of the lattice architecture (ref. 1). These characteristics are important in the future development of turbine engine components. Casting quality and structural efficiency were evaluated experimentally using small beam specimens machined from the cast and heat treated 140- by 300- by 11-mm panels. The matrix of specimens included samples of each superalloy in both open-celled and single-face-sheet configurations, machined from longitudinal, transverse, and diagonal panel orientations. Thirty-five beam subelements were tested in Glenn's Life Prediction Branch's material test machine at room temperature and 650 C under both static (see the following photograph) and cyclic load conditions. Surprisingly, test results exceeded initial linear elastic analytical predictions. This was likely a result of the formation of plastic hinges and redundancies inherent in lattice block geometry, which was not considered in the finite element models. The value of a single face sheet was demonstrated by increased bending moment capacity, where the face sheet simultaneously increased the gross section modulus and braced the compression ligaments against early buckling as seen in open-cell specimens. Preexisting flaws in specimens were not a discriminator in flexural, shear, or stiffness measurements, again because of redundant load paths available in the lattice block structure. Early test results are available in references 2 and 3; more complete analyses are scheduled for publication in 2004.

Source record↗
NASA NTRS2012

OVERSMART Reporting Tool for Flow Computations Over Large Grid Systems

Structured grid solvers such as NASA's OVERFLOW compressible Navier-Stokes flow solver can generate large data files that contain convergence histories for flow equation residuals, turbulence model equation residuals, component forces and moments, and component relative motion dynamics variables. Most of today's large-scale problems can extend to hundreds of grids, and over 100 million grid points. However, due to the lack of efficient tools, only a small fraction of information contained in these files is analyzed. OVERSMART (OVERFLOW Solution Monitoring And Reporting Tool) provides a comprehensive report of solution convergence of flow computations over large, complex grid systems. It produces a one-page executive summary of the behavior of flow equation residuals, turbulence model equation residuals, and component forces and moments. Under the automatic option, a matrix of commonly viewed plots such as residual histograms, composite residuals, sub-iteration bar graphs, and component forces and moments is automatically generated. Specific plots required by the user can also be prescribed via a command file or a graphical user interface. Output is directed to the user s computer screen and/or to an html file for archival purposes. The current implementation has been targeted for the OVERFLOW flow solver, which is used to obtain a flow solution on structured overset grids. The OVERSMART framework allows easy extension to other flow solvers.

Kao, David L.↗
NASA NTRS1993

Preconditioned Conjugate Gradient methods for low speed flow calculations

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Ajmani, Kumud↗
DOE OSTI2020

Mechanical Properties of Permanent Foaming Fixatives for Deactivation and Decommissioning Activities

DOE-EM have identified an operational requirement for a fixative that can immobilize and/or encapsulate residual contamination in 3D void volumes (pipes, gloveboxes, waste containers, etc.) during D and D activities. Failure to safely and effectively immobilize residual contamination can: Put workers at risk, Contaminate the public and environment, Drive up operational costs. Commercial-off-the-shelf (COTS) polyurethane (PU) foams is one possible solution and is currently being investigated in collaboration with Savannah River National Lab (SRNL). Mechanical property testing will dictate how well PU foams can withstand physical stressors outlined in safety documents while immobilizing residual contamination. Results can provide a performance criteria for Section 5 of ASTM E3191: Standard Specification for Permanent Foaming Fixatives Used to Mitigate Spread of Radioactive Contamination. Polyurethanes consists of repeating units of urethanes which are produced from an exothermic reaction between a polyol (an alcohol with two or more hydroxyl groups in a molecule) and an isocyanate [2]. PUs consists of 3D cells that are formed by a blowing agent which is normally water. Water interacting with the isocyanate creates carbon dioxide and urea which contributes to cells' growth and expansion. The cross-linking between the polyol and isocyanate solidify the cell faces and walls. Micro scale properties that can influence mechanical properties include: Relative density (ratio between density of cellular material and density of the solid of which the cell walls are made of). Cells connectivity between edges and faces, and number of cells contact neighbors [3]. Whether a foam is open-celled or closed-celled. Closed-celled foams have a thin membrane that encloses each cell which can contribute to the stiffness of the foam. Incorporating fillers in the PU matrix like carbon-based nanoparticles in the form of expandable graphite (EG) can increase the thermal and mechanical performance [4]. When exposed to heat, EG produces a char layer that prevents heat and oxygen transfer which is known as intumescing. Mechanical performance is dependent on amount of EG loading since the cell sizes are linearly dependent on it. Overall, the rigid foams (I-R2) proved superior. SEM Analysis: I-R2 had the most consistent spherical sizes (average cell diameter: 489 μm), which enhance the relative density the most [5]. Tensile Testing Results: I-R2 experienced the largest breaking load (103.65 lbf) and stress (289.42 psi). I-R2 also had a higher Young's Modulus compared to R1 (2.99 ksi to 2.09 ksi). Compression Testing Results: I-R2 had the highest stress at 80% deflection (360.67 psi), load (1387.48 lbf) and modulus (3.92 ksi)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1994

A visual detection model for DCT coefficient quantization

The discrete cosine transform (DCT) is widely used in image compression and is part of the JPEG and MPEG compression standards. The degree of compression and the amount of distortion in the decompressed image are controlled by the quantization of the transform coefficients. The standards do not specify how the DCT coefficients should be quantized. One approach is to set the quantization level for each coefficient so that the quantization error is near the threshold of visibility. Results from previous work are combined to form the current best detection model for DCT coefficient quantization noise. This model predicts sensitivity as a function of display parameters, enabling quantization matrices to be designed for display situations varying in luminance, veiling light, and spatial frequency related conditions (pixel size, viewing distance, and aspect ratio). It also allows arbitrary color space directions for the representation of color. A model-based method of optimizing the quantization matrix for an individual image was developed. The model described above provides visual thresholds for each DCT frequency. These thresholds are adjusted within each block for visual light adaptation and contrast masking. For given quantization matrix, the DCT quantization errors are scaled by the adjusted thresholds to yield perceptual errors. These errors are pooled nonlinearly over the image to yield total perceptual error. With this model one may estimate the quantization matrix for a particular image that yields minimum bit rate for a given total perceptual error, or minimum perceptual error for a given bit rate. Custom matrices for a number of images show clear improvement over image-independent matrices. Custom matrices are compatible with the JPEG standard, which requires transmission of the quantization matrix.

Ahumada, Albert J., Jr.↗