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At least 145 records · Page 8

Manipulating the Assembly and Architecture of Fibrillar Silk

Silk is a unique and exceptionally strong biological material. However, no synthetic method has yet come close to replicating the properties of natural silk. This shortfall is attributed to an insufficient understanding of both silk nanofibril structure and the mechanism of formation. Here in situ atomic force microscopy (AFM) and photo-induced force microscopy (PiFM) is utilized to investigate the formation process and define the basic structural paradigm of individual silk nanofibrils. By visualizing the multistage process of silk nanofibril formation, the importance of conformational transformations along the assembly pathway is revealed. Unfolded silk structures initially accumulate into amorphous clusters, which then evolve into crystal nuclei via conformational transformation into β-crystallites. Nanofibril elongation then occurs through the attachment of silk molecules at a single end of the nanofibril tip; this is facilitated through the formation of a new amorphous cluster that then repeats the aforementioned conformational transformation. However, enzymatic digestion of the amorphous regions leads to direct, rapid elongation of β-crystalline fibers. These findings imply that the energy landscape is characterized by shallow minima associated with intermediate states, which can be eliminated by introducing β-crystallites, and motivate research into the directed modification of the silk assembly pathway to select for features beneficial to specific applications.

36 MATERIALS SCIENCE↗

An Interactive Excel Program for Tracking a Single Droplet in Crossflow Computation

Spray jet in crossflow has been a subject of research because of its wide application in systems involving pollutant dispersion, jet mixing in the dilution zone of combustors, and fuel injection strategies. The focus of this work is to investigate dispersion of a 2-dimensional atomized spray jet into a 2-dimensional crossflow. A quick computational method is developed using available software. The spreadsheet can be used for any 2D droplet trajectory problem where the drop is injected into the free stream eventually coming to the free stream conditions. During the transverse injection of a spray into high velocity airflow, the droplets (carried along and deflected by a gaseous stream of co-flowing air) are subjected to forces that affect their motion in the flow field. Based on the Newton's Second Law of motion, four ordinary differential equations were used. These equations were then solved by a fourth-order Runge-Kutta method using Excel software. Visual basic programming and Excel macrocode to produce the data facilitate Excel software to plot graphs describing the droplet's motion in the flow field. This program computes and plots the data sequentially without forcing users to open other types of plotting programs. A user's manual on how to use the program is also included in this report.

Urip, E.↗

Challenges in Development of Online Visualization and Analysis Tools for Satellite Data

Over the years, various online visualization and analysis tools have been developed to facilitate satellite data access and help scientific users around the world to conduct research and develop applications (e.g., data product evaluation, what-if questions, etc.). For those who are new to satellite data products, using them can be a daunting task due to many obstacles in data processing such as data formats, complex data structures, special software packages, unfamiliar terminology, etc., especially when one is not sure whether a dataset is suitable for his/er research project. Even for experienced users, developing software for data processing and analysis can be a costly and time-consuming task. Online visualization tools can overcome many of these difficulties and allow users to focus on scientific questions. For example, Giovanni (the Geospatial Interactive Online Visualization and Analysis Infrastructure, https://giovanni.gsfc.nasa.gov), developed by the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC), allows access over 1900 satellite and model variables in 82 measurement groups of 8 disciplines without downloading data and software. Main features include basic functions for data analysis and visualization, data provenance, output data in different formats (ASCII, NetCDF, GeoTIFF), and more. Over the years, ~1700 peer-reviewed publications in different disciplines have been benefited from Giovanni in research activities (e.g. initial investigation, what-if questions, product evaluation). Despite the success of online visualization and analysis tools, challenges and new opportunities still exist and more can be done with new requirements and technology. Examples are: a) how to increase the efficiency of dataset search by enhancing intuitive aspects; b) how to facilitate interdisciplinary research; c) how to provide data quality information; d) how to engage users to participate in data quality assessment; and more. NASA Earth Observing System Data and Information System (EOSDIS) satellite-based data products are processed at various levels ranging from Level 0 to Level 4. While most users use data products at higher levels (Level-3 and 4), products at lower levels are still important for case studies, algorithm development, ground validation, etc. In this presentation, we will use Giovanni as an example to present and discuss challenges and near-future opportunities for satellite data online visualization and analysis tools.

Liu, Zhong↗

Ambient Single-Cell Analysis and Native Tissue Imaging Using Laser-Ablation Electrospray Ionization Mass Spectrometry with Increased Spatial Resolution

Laser ablation electrospray ionization mass spectrometry (LAESI-MS) is an emerging method that has the potential to transform the field of metabolomics. This is in part due to LAESI-MS being an ambient ionization method that requires minimal sample preparation and uses (endogenous) water for in situ analysis. This application note details the employment of the ‘LAESI microscope’ source to perform spatially resolved MS analysis of cells and MS imaging (MSI) of tissues at high spatial resolution. This source configuration utilizes a long-working distance reflective objective that permits both visualization of the sample and a smaller LAESI laser beam profile than conventional LAESI setups. In this work, we analyzed 200 single cells of Allium cepa (red onion) and imaged Fittonia argyroneura (nerve plant) in high spatial resolution using this source coupled to a Fourier transform mass spectrometer for high mass resolution and high mass accuracy metabolomics.

59 BASIC BIOLOGICAL SCIENCES↗

Bacterial diversity dynamics in microbial consortia selected for lignin utilization

Lignin is nature’s largest source of phenolic compounds. Its recalcitrance to enzymatic conversion is still a limiting step to increase the value of lignin. Although bacteria are able to degrade lignin in nature, most studies have focused on lignin degradation by fungi. To understand which bacteria are able to use lignin as the sole carbon source, natural selection over time was used to obtain enriched microbial consortia over a 12-week period. The source of microorganisms to establish these microbial consortia were commercial and backyard compost soils. Cultivation occurred at two different temperatures, 30°C and 37°C, in defined culture media containing either Kraft lignin or alkaline-extracted lignin as carbon source. iTag DNA sequencing of bacterial 16S rDNA gene was performed for each of the consortia at six timepoints (passages). The initial bacterial richness and diversity of backyard compost soil consortia was greater than that of commercial soil consortia, and both parameters decreased after the enrichment protocol, corroborating that selection was occurring. Bacterial consortia composition tended to stabilize from the fourth passage on. After the enrichment protocol, Firmicutes phylum bacteria were predominant when lignin extracted by alkaline method was used as a carbon source, whereas Proteobacteria were predominant when Kraft lignin was used. Bray-Curtis dissimilarity calculations at genus level, visualized using NMDS plots, showed that the type of lignin used as a carbon source contributed more to differentiate the bacterial consortia than the variable temperature. The main known bacterial genera selected to use lignin as a carbon source were Altererythrobacter , Aminobacter , Bacillus , Burkholderia , Lysinibacillus , Microvirga , Mycobacterium , Ochrobactrum , Paenibacillus , Pseudomonas , Pseudoxanthomonas , Rhizobiales and Sphingobium . These selected bacterial genera can be of particular interest for studying lignin degradation and utilization, as well as for lignin-related biotechnology applications.

59 BASIC BIOLOGICAL SCIENCES↗

Bent DNA Bows as Sensing Amplifiers for Detecting DNA-Interacting Salts and Molecules

Due to the central role of DNA, its interactions with inorganic salts and small organic molecules are important. For example, such interactions play important roles in various fundamental cellular processes in living systems and are involved in many DNA-damage related diseases. Strategies to improve the sensitivity of existing techniques for studying DNA interactions with other molecules would be appreciated in situations where the interactions are too weak. Here we report our development and demonstration of bent DNA bows for amplifying, sensing, and detecting the interactions of 14 inorganic salts and small organic molecules with DNA. With the bent DNA bows, these interactions were easily visualized and quantified in gel electrophoresis, which were difficult to measure without bending. In addition, the strength of the interactions of DNA with the various salts/molecules were quantified using the modified Hill equation. This work highlights the amplification effects of the bending elastic energy stored in the DNA bows and the potential use of the DNA bows for quantitatively measuring DNA interactions with small molecules as simple economic methods; it may also pave the way for exploiting the bent DNA bows for other applications such as screening DNA-interacting molecules and drugs.

59 BASIC BIOLOGICAL SCIENCES↗

GLobal Integrated Design Environment

The GLobal Integrated Design Environment (GLIDE) is a collaborative engineering application built to resolve the design session issues of real-time passing of data between multiple discipline experts in a collaborative environment. Utilizing Web protocols and multiple programming languages, GLIDE allows engineers to use the applications to which they are accustomed in this case, Excel to send and receive datasets via the Internet to a database-driven Web server. Traditionally, a collaborative design session consists of one or more engineers representing each discipline meeting together in a single location. The discipline leads exchange parameters and iterate through their respective processes to converge on an acceptable dataset. In cases in which the engineers are unable to meet, their parameters are passed via e-mail, telephone, facsimile, or even postal mail. The result of this slow process of data exchange would elongate a design session to weeks or even months. While the iterative process remains in place, software can now exchange parameters securely and efficiently, while at the same time allowing for much more information about a design session to be made available. GLIDE is written in a compilation of several programming languages, including REALbasic, PHP, and Microsoft Visual Basic. GLIDE client installers are available to download for both Microsoft Windows and Macintosh systems. The GLIDE client software is compatible with Microsoft Excel 2000 or later on Windows systems, and with Microsoft Excel X or later on Macintosh systems. GLIDE follows the Client-Server paradigm, transferring encrypted and compressed data via standard Web protocols. Currently, the engineers use Excel as a front end to the GLIDE Client, as many of their custom tools run in Excel.

Kunkel, Matthew↗

The Effect of Surface Topography on the Nonlinear Dynamics of Rossby Waves

Boussinesq convection in rotating systems attracts a sustained attention of the fluid dynamics community, because it has intricate non-linear dynamics (Cross & Hohenberg 1993) and plays an important role in geophysical and astrophysical applications, such as the motion of the liquid outer core of Earth, the Red Spot in Jupiter, the giant cells in the Sun etc. (Alridge et al. 1990). A fundamental distinction between the real geo- and astrophysical problems and the idealized laboratory studies is that natural systems are inhomogeneous (Alridge et al. 1990). Heterogeneities modulate the flow and influence significantly the dynamics of convective patterns (Alridge et al. 1990; Hide 1971). The effect of modulations on pattern formation and transition to turbulence in Boussinesq convection is far from being completely understood (Cross & Hohenberg 1993; Aranson & Kramer 2002). It is generally accepted that in the liquid outer core of the Earth the transport of the angular momentum and internal heat occurs via thermal Rossby waves (Zhang et al. 2001; Kuang & Bloxham 1999). These waves been visualized in laboratory experiments in rotating liquid-filled spheres and concentric spherical shells (Zhang et al. 2001; Kuang & Bloxham 1999). The basic dynamical features of Rossby waves have been reproduced in a cylindrical annulus, a system much simpler than the spherical ones (Busse & Or 1986; Or & Busse 1987). For convection in a cylindrical annulus, the fluid motion is two-dimensional, and gravity is replaced by a centrifugal force, (Busse & Or 1986; Or & Busse 1987). Hide (1971) has suggested that the momentum and heat transport in the core might be influenced significantly by so-called bumps, which are heterogeneities on the mantle-core boundary. To model the effect of surface topography on the transport of momentum and energy in the liquid outer core of the Earth, Bell & Soward (1996), Herrmann & Busse (1998) and Westerburg & Busse (2001) have studied the nonlinear dynamics of thermal Rossby waves in a cylindrical annulus with azimuthally modulated height.

Abarzhi, S. I.↗

Potential applications of multipolarization SAR for pine plantation biomass estimation

This study was conducted as a part of the research tasks under the Radar Land Cover Analysis Program. The Radar Land Cover Analysis objective is, through utilization of multisensor data, to gain a basic understanding of the measurements and data characteristics in the visible-IR-microwave regions of the electromagnetic spectrum associated with specific surface features and cover types. Since the results of analysis of data acquired by Shuttle Imaging Radar (SIR-A) and LANDSAT Thematic Mapper (TM) over the study area were reported (NSTL/ERL Report No. 228, December 1984), this study focused on the analysis and evaluation of the L-band multipolarization airborne SAR data acquired over a southeastern pine forest scene. The data acquisition mission was flown on September 8 and 9, 1983. The HH, HV polarizations and the VV, VH polarizations were used on the first and the second day, respectively. Due to instrumentation difficulties, the digital recorder recorded only the second day's data. Because of this, only the VV and VH polarization data were used in this analysis. However, the HH and HV polarization images were available for visual comparison. It appears that SAR digital numbers correlate with the index of green biomass.

Wu, S. T.↗

Modeling Boundary-Layer Transition in Subsonic Flow over a Swept Wing

Predicting the onset of boundary-layer transition is often more accurate using physics-based models that directly compute disturbance growth rather than phenomenological models often implemented into industrial CFD codes. The aim of this ongoing study is to calibrate linear, physics-based computations of transition in subsonic flows over swept wings against a large set of experimental data. Advancing the calibration of linear models of transition contributes to the CFD-Vision-2030 goal of automated boundary-layer transition prediction. This progress report uses the dual N-factor method to model transition over the swept NACA 64-2-015A wing. The flow conditions match selected test conditions from an extensive experimental dataset acquired from the NASA Ames 12-ft Pressure Tunnel. The OVERFLOW 2.4b flow solver is used to obtain laminar basic states based on an infinite-span assumption. Stability analyses are performed on 365 distinct configurations with linear stability theory (LST) and parabolized stability equations (PSE) from the Langley Stability and Transition Analysis Codes (LASTRAC), modeling the growth of Tollmien-Schlichting (TS) and stationary crossflow (SCF) disturbances. From a total of 67 data points for unswept, i.e., TS-dominant configurations, the critical N-factor based on PSE is found to be N_TS = 9. The SCF critical N-factor is found to be near 8 for the highly swept, SCF-dominant configurations. Dual N-factor curves for both LST and PSE computations demonstrate a high level of interaction between TS and SCF. It may be worthwhile to investigate an alternate metric to visualize maximal SCF amplification upstream of the transition location to account for the growth of SCF modes near the leading edge, which is not considered in the conventional applications of the dual N-factor criterion.

boundary-layer transition↗

Modeling Boundary-Layer Transition in Subsonic Flow over a Swept Wing

Predicting the onset of boundary-layer transition is often more accurate using physics-based models that directly compute disturbance growth rather than phenomenological models often implemented into industrial CFD codes. The aim of this ongoing study is to calibrate linear, physics-based computations of transition in subsonic flows over swept wings against a large set of experimental data. Advancing the calibration of linear models of transition contributes to the CFD-Vision-2030 goal of automated boundary-layer transition prediction. This progress report uses the dual N-factor method to model transition over the swept NACA 64-2-015A wing. The flow conditions match selected test conditions from an extensive experimental dataset acquired from the NASA Ames 12-ft Pressure Tunnel. The OVERFLOW 2.4b flow solver is used to obtain laminar basic states based on an infinite-span assumption. Stability analyses are performed on 365 distinct configurations with linear stability theory (LST) and parabolized stability equations (PSE) from the Langley Stability and Transition Analysis Codes (LASTRAC), modeling the growth of Tollmien-Schlichting (TS) and stationary crossflow (SCF) disturbances. From a total of 67 data points for unswept, i.e., TS-dominant configurations, the critical N-factor based on PSE is found to be N_TS = 9. The SCF critical N-factor is found to be near 8 for the highly swept, SCF-dominant configurations. Dual N-factor curves for both LST and PSE computations demonstrate a high level of interaction between TS and SCF. It may be worthwhile to investigate an alternate metric to visualize maximal SCF amplification upstream of the transition location to account for the growth of SCF modes near the leading edge, which is not considered in the conventional applications of the dual N-factor criterion.

computational modeling↗

Biological Visualization, Imaging and Simulation(Bio-VIS) at NASA Ames Research Center: Developing New Software and Technology for Astronaut Training and Biology Research in Space

The Bio- Visualization, Imaging and Simulation (BioVIS) Technology Center at NASA's Ames Research Center is dedicated to developing and applying advanced visualization, computation and simulation technologies to support NASA Space Life Sciences research and the objectives of the Fundamental Biology Program. Research ranges from high resolution 3D cell imaging and structure analysis, virtual environment simulation of fine sensory-motor tasks, computational neuroscience and biophysics to biomedical/clinical applications. Computer simulation research focuses on the development of advanced computational tools for astronaut training and education. Virtual Reality (VR) and Virtual Environment (VE) simulation systems have become important training tools in many fields from flight simulation to, more recently, surgical simulation. The type and quality of training provided by these computer-based tools ranges widely, but the value of real-time VE computer simulation as a method of preparing individuals for real-world tasks is well established. Astronauts routinely use VE systems for various training tasks, including Space Shuttle landings, robot arm manipulations and extravehicular activities (space walks). Currently, there are no VE systems to train astronauts for basic and applied research experiments which are an important part of many missions. The Virtual Glovebox (VGX) is a prototype VE system for real-time physically-based simulation of the Life Sciences Glovebox where astronauts will perform many complex tasks supporting research experiments aboard the International Space Station. The VGX consists of a physical display system utilizing duel LCD projectors and circular polarization to produce a desktop-sized 3D virtual workspace. Physically-based modeling tools (Arachi Inc.) provide real-time collision detection, rigid body dynamics, physical properties and force-based controls for objects. The human-computer interface consists of two magnetic tracking devices (Ascention Inc.) attached to instrumented gloves (Immersion Inc.) which co-locate the user's hands with hand/forearm representations in the virtual workspace. Force-feedback is possible in a work volume defined by a Phantom Desktop device (SensAble inc.). Graphics are written in OpenGL. The system runs on a 2.2 GHz Pentium 4 PC. The prototype VGX provides astronauts and support personnel with a real-time physically-based VE system to simulate basic research tasks both on Earth and in the microgravity of Space. The immersive virtual environment of the VGX also makes it a useful tool for virtual engineering applications including CAD development, procedure design and simulation of human-system systems in a desktop-sized work volume.

Smith, Jeffrey↗

Carbohydrate-Containing Conjugated Polymers: Solvent-Resistant Materials for Greener Organic Electronics

Organic semiconducting polymers are exciting materials for electronic applications because of their good mechanical and optoelectronic properties. A major advantage of organic semiconductors is their solution processability. This allows access to a variety of simple and cost-effective device fabrication methods compared to the expensive, high-temperature processing methods required for silicon-based electronics. However, these materials often have low solubility, which limits their processing to toxic halogenated solvents. Also, their limited solubility often leads to interfacial mixing during device fabrication. Herein, this work explores the incorporation of environmentally friendly carbohydrate side chains in conjugated polymers to enhance processability in eco-friendly solvents. Moreover, a mild postprocessing treatment was designed to enable solvent resistance. Isoindigo-based polymers with varied ratios of acetyl-protected galactose side chains were synthesized to improve solubility in o-anisole in the protected state, while inducing solvent resistance through intramolecular hydrogen bonding in the deprotected state. Solvent resistance was confirmed both visually upon submersion in various solvents and using UV–visible spectroscopy. Importantly, the mild basic treatment to achieve solvent resistance has no negative impact on the electronic performance of these materials in organic field-effect transistors, even after subsequent submersion in various solvents, making them a valuable platform for the production of green processable multilayer electronics.

36 MATERIALS SCIENCE↗

GeneLab: Current and Future Omics Data Integration Between Space Biology and HRP

For the past five years, the Biological and Physical Sciences Division has pioneered Open Science in Space Biology by funding the NASA GeneLab project. Along with the Ames Life Sciences Data Archive, GeneLab has quickly become the world leader in archiving and scientifically curating spaceflight and spaceflight relevant multi-omics data. Specifically, the GeneLab Data System has become a full enterprise solution providing advanced mining capabilities, several application programming interfaces for data federation and machine learning approaches, and delivering to the world an analytical and visualization platform which has enabled collaboration within the scientific community. Over the past three years, large meta-analysis and modeling studies have been published by the GeneLab Analysis Working Groups (AWGs), which are comprised of ~200 volunteer scientists. One natural extension of GeneLab data reuse has recently turned towards linking animal data with human data, which is the next necessary step to further validate animal models for inferring biological risks to humans conducting LEO, lunar or Martian missions. As such, data from the Human Research Program are an essential component of GeneLab and ALSDA. At the moment, simulated space radiation experiments conducted at Brookhaven National Laboratory make the most of HRP GeneLab data, and the scientific community has been eager to also link their animal spaceflight results to actual Astronaut data and human analog data. We will discuss further the current status of knowledge and future approaches to accelerate our basics understanding of the impact of space stressors on humans using latest omics technology.

omics↗

Bundle Data Approach at GES DISC Targeting Natural Hazards

Severe natural phenomena such as hurricane, volcano, blizzard, flood and drought have the potential to cause immeasurable property damages, great socioeconomic impact, and tragic loss of human life. From searching to assessing the Big, i.e., massive and heterogeneous scientific data (particularly, satellite and model products) in order to investigate those natural hazards, it has, however, become a daunting task for Earth scientists and applications researchers, especially during recent decades. The NASA Goddard Earth Sciences Data and Information Service Center (GES DISC) has served Big Earth science data, and the pertinent valuable information and services to the aforementioned users of diverse communities for years. In order to help and guide our users to online readily (i.e., with a minimum effort) acquire their requested data from our enormous resource at GES DISC for studying their targeted hazard event, we have thus initiated a Bundle Data approach in 2014, first targeting the hurricane event topic. We have recently worked on new topics such as volcano and blizzard. The bundle data of a specific hazard event is basically a sophisticated integrated data package consisting of a series of proper datasets containing a group of relevant (knowledge--based) data variables readily accessible to users via a system-prearranged table linking those data variables to the proper datasets (URLs). This online approach has been developed by utilizing a few existing data services such as Mirador as search engine; Giovanni for visualization; and OPeNDAP for data access, etc. The online Data Cookbook site at GES DISC is the current host for the bundle data. We are now also planning on developing an Automated Virtual Collection Framework that shall eventually accommodate the bundle data, as well as further improve our management in Big Data.

GES DISC↗

rcsb-api : Python Toolkit for Streamlining Access to RCSB Protein Data Bank APIs

The Protein Data Bank (PDB) was founded in 1971 as the first open-access digital data resource in biology to serve as the single global archive for three-dimensional (3D) macromolecular structure data. Current PDB holdings exceed 230,000 experimentally determined structures of proteins, nucleic acids, viruses, and macromolecular machines. The RCSB Protein Data Bank RCSB.org research-focused web portal facilitates search, analyses, and visualization of every PDB structure along with more than one million Computed Structure Models from AlphaFold DB and the ModelArchive. It is powered by a set of publicly available Application Programming Interfaces (APIs) that both support RCSB.org users and provide programmatic access to PDB data. Given the breadth and levels of granularity encompassed in this rich data collection, efficiently accessing the information programmatically may be challenging for new users. RCSB PDB has developed a Python software package, rcsb-api , that facilitates easy and efficient use of RCSB PDB APIs within a Python environment. This software tool is designed to streamline access to the extensive corpus of data housed within the PDB, enabling researchers to search, retrieve, and analyze 3D biostructure data seamlessly. Its use will accelerate research in structural biology, molecular biology and biochemistry, drug discovery, and bioinformatics by providing more efficient tools for data integration and analysis. The new toolkit is available on GitHub (github.com/rcsb/py-rcsb-api) and published to the public Python package repository (PyPI) to foster wider usage and support basic and applied research in fundamental biology, biomedicine, and the energy sciences.

FAIR principles↗

Investigating the Impacts of Outdoor Lighting (Final Report)

This report documents the research associated with the Depart of Energy supported project “Investigating the Health Impact of Outdoor Lighting.” This project was developed to consider how alternative solid state lighting options, particularly the spectral power distribution, effected the hormone melatonin which ultimately could lead to potential health issues. The project also provides an opportunity to gather other secondary data with respect to visual performance in a controlled environment. These tasks were developed to consider how alternative solid state lighting applications impacted performance. This report is a complete documentation of the tasks undertaken as part of this project. The report includes a literature review and consideration of the background data which are part of this field of study as well as a documentation of the methods developed as part of the project. The melatonin results, the primary dependent variable are included in the attached peer-review paper that has been recent published (Gibbons et al., 2022). Our discussion of these results are included in that publication. Other results from this project will be documented in one or more future publications.

59 BASIC BIOLOGICAL SCIENCES↗

The Topology of Symmetric Tensor Fields

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Levin, Yingmei↗