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At least 397 records · Page 22

Probabilistic Analysis of a SiC/SiC Ceramic Matrix Composite Turbine Vane

To demonstrate the advanced composite materials technology under development within the Ultra-Efficient Engine Technology (UEET) Program, it was planned to fabricate, test, and analyze a turbine vane made entirely of silicon carbide-fiber-reinforced silicon carbide matrix composite (SiC/SiC CMC) material. The objective was to utilize a five-harness satin weave melt-infiltrated (MI) SiC/SiC composite material developed under this program to design and fabricate a stator vane that can endure 1000 hours of engine service conditions. The vane was designed such that the expected maximum stresses were kept within the proportional limit strength of the material. Any violation of this design requirement was considered as the failure. This report presents results of a probabilistic analysis and reliability assessment of the vane. Probability of failure to meet the design requirements was computed. In the analysis, material properties, strength, and pressure loading were considered as random variables. The pressure loads were considered normally distributed with a nominal variation. A temperature profile on the vane was obtained by performing a computational fluid dynamics (CFD) analysis and was assumed to be deterministic. The results suggest that for the current vane design, the chance of not meeting design requirements is about 1.6 percent.

Murthy, Pappu L. N.↗

Stochastic-Strength-Based Damage Simulation of Ceramic Matrix Composite Laminates

The Finite Element Analysis-Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to characterize and predict the progressive damage response of silicon-carbide-fiber-reinforced reaction-bonded silicon nitride matrix (SiC/RBSN) composite laminate tensile specimens. Studied were unidirectional laminates [0] (sub 8), [10] (sub 8), [45] (sub 8), and [90] (sub 8); cross-ply laminates [0 (sub 2) divided by 90 (sub 2),]s; angled-ply laminates [plus 45 (sub 2) divided by -45 (sub 2), ]s; doubled-edge-notched [0] (sub 8), laminates; and central-hole laminates. Results correlated well with the experimental data. This work was performed as a validation and benchmarking exercise of the FEAMAC/CARES program. FEAMAC/CARES simulates stochastic-based discrete-event progressive damage of ceramic matrix composite and polymer matrix composite material structures. It couples three software programs: (1) the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), (2) the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/Life), and (3) the Abaqus finite element analysis program. MAC/GMC contributes multiscale modeling capabilities and micromechanics relations to determine stresses and deformations at the microscale of the composite material repeating-unit-cell (RUC). CARES/Life contributes statistical multiaxial failure criteria that can be applied to the individual brittle-material constituents of the RUC, and Abaqus is used to model the overall composite structure. For each FEAMAC/CARES simulation trial, the stochastic nature of brittle material strength results in random, discrete damage events that incrementally progress until ultimate structural failure.

composite structures↗

Vibrations and structureborne noise in space station

Analytical models were developed to predict vibrations and structureborne noise generation of cylindrical and rectangular acoustic enclosures. These models are then used to determine structural vibration levels and interior noise to random point input forces. The guidelines developed could provide preliminary information on acoustical and vibrational environments in space station habitability modules under orbital operations. The structural models include single wall monocoque shell, double wall shell, stiffened orthotropic shell, descretely stiffened flat panels, and a coupled system composed of a cantilever beam structure and a stiffened sidewall. Aluminum and fiber reinforced composite materials are considered for single and double wall shells. The end caps of the cylindrical enclosures are modeled either as single or double wall circular plates. Sound generation in the interior space is calculated by coupling the structural vibrations to the acoustic field in the enclosure. Modal methods and transfer matrix techniques are used to obtain structural vibrations. Parametric studies are performed to determine the sensitivity of interior noise environment to changes in input, geometric and structural conditions.

Vaicaitis, R.↗

Stochastic Optimal Control via Bellman's Principle

This paper presents a method for finding optimal controls of nonlinear systems subject to random excitations. The method is capable to generate global control solutions when state and control constraints are present. The solution is global in the sense that controls for all initial conditions in a region of the state space are obtained. The approach is based on Bellman's Principle of optimality, the Gaussian closure and the Short-time Gaussian approximation. Examples include a system with a state-dependent diffusion term, a system in which the infinite hierarchy of moment equations cannot be analytically closed, and an impact system with a elastic boundary. The uncontrolled and controlled dynamics are studied by creating a Markov chain with a control dependent transition probability matrix via the Generalized Cell Mapping method. In this fashion, both the transient and stationary controlled responses are evaluated. The results show excellent control performances.

Crespo, Luis G.↗

Effect of Ex Vivo Ionizing Radiation on Static and Fatigue Properties of Mouse Vertebral Bodies

For a variety of medical and scientific reasons, human bones can be exposed to a wide range of ionizing radiation levels. In vivo radiation therapy (0.05 kGy) is used in cancer treatment, and ex vivo irradiation (25-35 kGy) is used to sterilize bone allografts. Ionizing radiation in these applications has been shown to increase risk of fracture, decrease bone quality and degrade collagen integrity. Past studies have investigated the deleterious effects of radiation on cortical or trabecular bone specimens individually, but to date no studies have examined whole bones containing both cortical and trabecular tissue. Furthermore, a clear relationship between the dose and the mechanical and biochemical response of bone's extracellular matrix has yet to be established for doses ranging from cancer therapy to allograft sterilization (0.05-35 kGy). To gain insight into these issues, we conducted an ex vivo radiation study to investigate non-cellular (i.e. matrix) effects of ionizing radiation dose on vertebral whole bone mechanical properties, over a range of radiation doses (0.05-35 kGy), with a focus on any radiation-induced changes in collagen. With underlying mechanisms of action in mind, we hypothesized that any induced reductions in mechanical properties would be associated with changes in collagen integrity. METHODS: 20-week old female mice were euthanized and the lumbar spine was dissected using IACUC approved protocols. The lumbar vertebrae (L1- S1) were extracted from the spine via cuts through adjacent intervertebral discs, and the endplates, posterior processes, surrounding musculature, and soft tissues were removed (approx. 1.5mm diameter, approx. 2mm height). Specimens were randomly assigned to one of five groups for ex vivo radiation exposure: x-ray irradiation at 0.05, 1, 17, or 35 kGy, or a 0 kGy control. Following irradiation, the vertebrae were imaged using microcomputed tomography (micro-CT) and then subjected to either monotonic compressive loading to failure or uniform cyclic compressive loading. During cyclic testing, samples were loaded in force control to a force level that corresponded to a strain of 0.46%, as determined in advance by a linearly elastic micro-CT-based finite element analysis for each specimen. Tests were stopped at imminent fracture, defined as a rapid increase in strain. The main outcome for the monotonic test was the strength (maximum force); for cyclic testing it was the fatigue life (log of the number of cycles of loading at imminent failure). A fluorometric assay was used on the S1 vertebrae to measure the number of non-enzymatic collagen crosslinks[4]. A one-way ANOVA was performed on mechanical properties and collagen crosslinks; means were compared with controls using Dunnett's method, with a Tukey-Kramer post-hoc analysis when significance was found (p < or = 0.05). RESULTS: Compared to the unirradiated control group, the concentration of non-enzymatic collagen crosslinks was significantly increased for all irradiated groups (p < 0.0001), and being higher by at least 50% (Figure 1a). By contrast, the radiation effects on the collagen were only evident at the higher doses. For irradiation exposures of 17 kGy or more, strength decreased substantially as the radiation level was increased, but no effect was evident below 17 kGy (Figure 1b). There was no significant change in the stiffness or maximum displacement for any radiation dose (p>0.05). The finite element analysis prescribed force level for cyclic loading exceeded the measured (monotonic) strength of the 17 and 35 kGy irradiated groups (mean +/- SD, 20.6 +/- 5.6 N; 13.2 +/- 3.7 N, respectively) and therefore these groups were eliminated from the fatigue study. The fatigue life for the 0.05 and 1 kGy groups were similar to each other and were not statistically significantly different from the control group (Figure 1c).

radiation↗

High-Time-Resolution Study of Magnetic Holes in the Solar Wind

The objectives of this investigation are to determine the internal plasma structure of kinetic-scale and larger scale magnetic holes, and to determine their stability, their source mechanism(s), and their spatial extent. It is also of importance to determine the relationship between kinetic-scale holes and long-duration holes. As smaller and smaller magnetic depressions are investigated in order to make this a complete study, a robust criterion is necessary for distinguishing magnetic holes from random or unresolvable fluctuations in the interplanetary magnetic field. In order to resolve this ambiguity, we obtained from the MFI experiments magnetic field measurements from the WIND spacecraft at a time resolution of 46 to 184 ms over certain periods. We have also devised a measure of certainty for magnetic hole detections. The certainty factor, q, is defined as the difference between the mean magnetic field in the hole and the local magnetic field, in units of the local standard deviation of the field strength. For fullest generality, it is necessary to calculate this q over the range of available scales of interest, from 60 ms up to 300 s. This technique establishes a two dimensional matrix of relative probabilities that a hole of some duration (d) might exist in the data set at a given time (t). In identifying q-peaks in time and duration, we also come upon a natural method for distinguishing holes with internal structure from multiple holes in close proximity or holes nested inside of others. If two q-peaks are more than a half-width apart, they are simply said to be separate events.

Lazarus, Alan↗

Perceptually Lossless Wavelet Compression

The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp -1), where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We propose a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a 'perceptually lossless' quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

Watson, Andrew B.↗

Visibility of Wavelet Quantization Noise

The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp)-L , where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We describe a mathematical model to predict DWT noise detection thresholds as a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

Watson, Andrew B.↗

Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Polarization↗

FIRM image analysis: A machine learning workflow for quantifying extracellular matrix components from electron microscopy images

The extracellular matrix (ECM) is a complex network of biomolecules that plays an integral role in the structure, processes, and signaling mechanisms of cells and tissues. Identifying and quantifying changes in these matrix components provides insight into the mechanisms behind specific tissue remodeling processes; however, quantifying these changes is challenging due to difficult imaging conditions, complexity of the ECM, and the subtlety of these changes. Current imaging techniques allow us to visualize these critical remodeling events and developments in image analysis have employed a combination of analysis software and machine learning techniques to improve the efficiency and accuracy with which features are measured. Although image analysis has seen much improvement in recent years, there has been no technique developed to address ambiguity in feature edges in electron microscopy images. Presented here is a new machine learning-based workflow for the analysis of microscopy images named FIRM (Feature Identification from Raw Microscopy) that uses a random forest classifier to identify ECM features of interest and generate binary segmentation masks for quantification with ImageJ-FIJI. FIRM performed with an F1 score of 0.794 and greater than 80% accuracy for number and size of features detected. FIRM had similar deviation from the ground truth in the number of identified fibrils, fibril size, and size distributions when compared to human analyses. The results suggest that FIRM performs as well as manual analysis and requires a fraction of the time. This analysis technique is more efficient, eliminates user bias, and can be easily optimized to identify a variety of features, making it useful for any discipline requiring image analysis.

Science & Technology - Other Topics↗

NASA Tech Briefs, February 2007

Topics covered include: Calibration Test Set for a Phase-Comparison Digital Tracker; Wireless Acoustic Measurement System; Spiral Orbit Tribometer; Arrays of Miniature Microphones for Aeroacoustic Testing; Predicting Rocket or Jet Noise in Real Time; Computational Workbench for Multibody Dynamics; High-Power, High-Efficiency Ka-Band Space Traveling-Wave Tube; Gratings and Random Reflectors for Near-Infrared PIN Diodes; Optically Transparent Split-Ring Antennas for 1 to 10 GHz; Ice-Penetrating Robot for Scientific Exploration; Power-Amplifier Module for 145 to 165 GHz; Aerial Videography From Locally Launched Rockets; SiC Multi-Chip Power Modules as Power-System Building Blocks; Automated Design of Restraint Layer of an Inflatable Vessel; TMS for Instantiating a Knowledge Base With Incomplete Data; Simulating Flights of Future Launch Vehicles and Spacecraft; Control Code for Bearingless Switched- Reluctance Motor; Machine Aided Indexing and the NASA Thesaurus; Arbitrating Control of Control and Display Units; Web-Based Software for Managing Research; Driver Code for Adaptive Optics; Ceramic Paste for Patching High-Temperature Insulation; Fabrication of Polyimide-Matrix/Carbon and Boron-Fiber Tape; Protective Skins for Aerogel Monoliths; Code Assesses Risks Posed by Meteoroids and Orbital Debris; Asymmetric Bulkheads for Cylindrical Pressure Vessels; Self-Regulating Water-Separator System for Fuel Cells; Self-Advancing Step-Tap Drills; Array of Bolometers for Submillimeter- Wavelength Operation; Delta-Doped CCDs as Detector Arrays in Mass Spectrometers; Arrays of Bundles of Carbon Nanotubes as Field Emitters; Staggering Inflation To Stabilize Attitude of a Solar Sail; and Bare Conductive Tether for Decelerating a Spacecraft.

Source record↗

Validation of the DESI 2024 Lyα forest BAO analysis using synthetic datasets

The first year of data from the Dark Energy Spectroscopic Instrument (DESI) contains the largest set of Lyman-α (Lyα) forest spectra ever observed. This data, collected in the DESI Data Release 1 (DR1) sample, has been used to measure the Baryon Acoustic Oscillation (BAO) feature at redshift z = 2.33. In this work, we use a set of 150 synthetic realizations of DESI DR1 to validate the DESI 2024 Lyα forest BAO measurement presented in [1]. The synthetic data sets are based on Gaussian random fields using the log-normal approximation. We produce realistic synthetic DESI spectra that include all major contaminants affecting the Lyα forest. The synthetic data sets span a redshift range 1.8 < z < 3.8, and are analyzed using the same framework and pipeline used for the DESI 2024 Lyα forest BAO measurement. To measure BAO, we use both the Lyα auto-correlation and its cross-correlation with quasar positions. We use the mean of correlation functions from the set of DESI DR1 realizations to show that our model is able to recover unbiased measurements of the BAO position. We also fit each mock individually and study the population of BAO fits in order to validate BAO uncertainties and test our method for estimating the covariance matrix of the Lyα forest correlation functions. Finally, we discuss the implications of our results and identify the needs for the next generation of Lyα forest synthetic data sets, with the top priority being to simulate the effect of BAO broadening due to non-linear evolution.

79 ASTRONOMY AND ASTROPHYSICS↗

Computer-aided analysis for the Mechanics of Granular Materials (MGM) experiment

The Mechanics of Granular Materials (MGM) program is planned to provide experimental determinations of the mechanics of granular materials under very low gravity conditions. The initial experiments will use small glass beads as the granular material, and a precise tracking of individual beads during the test is desired. Real-time video images of the experimental specimen were taken with a television camera, and subsequently digitized by a frame grabber installed in a microcomputer. Easily identified red tracer beads were randomly scattered throughout the test specimen. A set of Pascal programs was written for processing and analyzing the digitized images. Filtering the image with Laplacian, dilation, and blurring filters when using a threshold function produced a binary (black on white) image which clearly identified the red beads. The centroids and areas for each bead were then determined. Analyzing a series of the images determined individual red bead displacements throughout the experiment. The system can provide displacement accuracies on the order of 0.5 to 1 pixel is the image is taken directly from the video camera. Digitizing an image from a video cassette recorder introduces an additional repeatability error of 0.5 to 1 pixel. Other programs were written to provide hardcopy prints of the digitized images on a dot-matrix printer.

Parker, Joey K.↗

A Convex Optimization Approach to Improving Suboptimal Hyperparameters of Sliced Normal Distributions

Sliced Normal (SN) distributions are a generalization of Gaussian distributions where the quadratic argument of the exponential is replaced with a sum of squares polynomial. SNs may be used to represent the distribution of a diverse set of random variables including multi-modal, non-symmetric, and skewed distributions. Unfortunately, the likelihood function of a SN includes a normalization constant and the inclusion of this normalization constant makes the likelihood a non-convex function of the hyperparameters which define the SN. In previous work, suboptimal fitting of the hyperparameters was performed by transforming the given data into a higher dimensional monomial basis and selecting the optimal hyperparameters of a Gaussian fit in this space. However, this approach did not account for the effect of lifting on the normalization constant. Indeed, it was observed that as the number of monomials is increased the likelihood of the Sliced Normal can decrease. In this paper, we increase the likelihood of Sliced Normals found using the previous method by developing a convex formulation which scales the covariance matrix of the Gaussian fit such that the likelihood of the Sliced Normal is maximized. The result is significant improvements of the log likelihood of fitted SN distributions, including a significant increase, especially for problems with 500+ monomials.

Convex optimization approach to improving suboptim↗

Calculation of the Frequency Distribution of the Energy Deposition in DNA Volumes by Heavy Ions

Radiation quality effects are largely determined by energy deposition in small volumes of characteristic sizes less than 10 nm representative of short-segments of DNA, the DNA nucleosome, or molecules initiating oxidative stress in the nucleus, mitochondria, or extra-cellular matrix. On this scale, qualitatively distinct types of molecular damage are possible for high linear energy transfer (LET) radiation such as heavy ions compared to low LET radiation. Unique types of DNA lesions or oxidative damages are the likely outcome of the energy deposition. The frequency distribution for energy imparted to 1-20 nm targets per unit dose or particle fluence is a useful descriptor and can be evaluated as a function of impact parameter from an ions track. In this work, the simulation of 1-Gy irradiation of a cubic volume of 5 micron by: 1) 450 (1)H(+) ions, 300 MeV; 2) 10 (12)C(6+) ions, 290 MeV/amu and 3) (56)Fe(26+) ions, 1000 MeV/amu was done with the Monte-Carlo simulation code RITRACKS. Cylindrical targets are generated in the irradiated volume, with random orientation. The frequency distribution curves of the energy deposited in the targets is obtained. For small targets (i.e. <25 nm size), the probability of an ion to hit a target is very small; therefore a large number of tracks and targets as well as a large number of histories are necessary to obtain statistically significant results. This simulation is very time-consuming and is difficult to perform by using the original version of RITRACKS. Consequently, the code RITRACKS was adapted to use multiple CPU on a workstation or on a computer cluster. To validate the simulation results, similar calculations were performed using targets with fixed position and orientation, for which experimental data are available [5]. Since the probability of single- and double-strand breaks in DNA as function of energy deposited is well know, the results that were obtained can be used to estimate the yield of DSB, and can be extended to include other targeted or non-target effects.

Plante, Ianik↗

High-Performance SiC/SiC Ceramic Composite Systems Developed for 1315 C (2400 F) Engine Components

As structural materials for hot-section components in advanced aerospace and land-based gas turbine engines, silicon carbide (SiC) ceramic matrix composites reinforced by high performance SiC fibers offer a variety of performance advantages over current bill-of-materials, such as nickel-based superalloys. These advantages are based on the SiC/SiC composites displaying higher temperature capability for a given structural load, lower density (approximately 30- to 50-percent metal density), and lower thermal expansion. These properties should, in turn, result in many important engine benefits, such as reduced component cooling air requirements, simpler component design, reduced support structure weight, improved fuel efficiency, reduced emissions, higher blade frequencies, reduced blade clearances, and higher thrust. Under the NASA Ultra-Efficient Engine Technology (UEET) Project, much progress has been made at the NASA Glenn Research Center in identifying and optimizing two highperformance SiC/SiC composite systems. The table compares typical properties of oxide/oxide panels and SiC/SiC panels formed by the random stacking of balanced 0 degrees/90 degrees fabric pieces reinforced by the indicated fiber types. The Glenn SiC/SiC systems A and B (shaded area of the table) were reinforced by the Sylramic-iBN SiC fiber, which was produced at Glenn by thermal treatment of the commercial Sylramic SiC fiber (Dow Corning, Midland, MI; ref. 2). The treatment process (1) removes boron from the Sylramic fiber, thereby improving fiber creep, rupture, and oxidation resistance and (2) allows the boron to react with nitrogen to form a thin in situ grown BN coating on the fiber surface, thereby providing an oxidation-resistant buffer layer between contacting fibers in the fabric and the final composite. The fabric stacks for all SiC/SiC panels were provided to GE Power Systems Composites for chemical vapor infiltration of Glenn designed BN fiber coatings and conventional SiC matrices. Composite panels with system B were heat treated at Glenn, and the pores that remained open were filled by silicon melt infiltration (MI). Panels with system A and the other SiC/SiC systems were not heat treated, and remaining open pores in these systems were filled with SiC slurry and silicon MI.

DiCarlo, James A.↗

Vibratory tactile display for textures

We have developed a tactile display that produces vibratory stimulus to a fingertip in contact with a vibrating tactor matrix. The display depicts tactile surface textures while the user is exploring a virtual object surface. A piezoelectric actuator drives the individual tactor in accordance with both the finger movement and the surface texture being traced. Spatiotemporal display control schemes were examined for presenting the fundamental surface texture elements. The temporal duration of vibratory stimulus was experimentally optimized to simulate the adaptation process of cutaneous sensation. The selected duration time for presenting a single line edge agreed with the time threshold of tactile sensation. Then spatial stimulus disposition schemes were discussed for representation of other edge shapes. As an alternative means not relying on amplitude control, a method of augmented duration at the edge was investigated. Spatial resolution of the display was measured for the lines presented both in perpendicular and parallel to a finger axis. Discrimination of texture density was also measured on random dot textures.

Ikei, Yasushi↗

A supersymmetric SYK model with a curious low energy behavior

We consider N = 2,4 supersymmetric SYK models that have a peculiar low energy behavior, with the entropy going like S = S 0 + (constant)T a , where a ≠ 1. The large N equations for these models are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing the BFSS matrix quantum mechanics or other related matrix models. Here we reanalyze these equations in order to better understand the low energy physics of these models. We find that the scalar fields develop large expectation values which explore the low energy valleys in the potential. The low energy physics is dominated by quadratic fluctuations around these values. These models were previously conjectured to have a spin glass phase. We did not find any evidence for this phase by using the usual diagnostics, such as searching for replica symmetry breaking solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗