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NASA NTRS1995

Two-phase flow in helical and spiral coils

Coiled tube heat exchangers involving two-phase flows are used in a variety of application areas, extending from the aerospace industry to petrochemical, refrigeration land power generation industries. The optimal design in each situation requires a fundamental understanding of the heat, mass and momentum transfer characteristic of the flowing two-phase mixture. However, two-phase flows in lengths of horizontal or vertical straight channels with heat transfer are often quite difficult in themselves to understand sufficiently well to permit accurate system designs. The present study has the following general objectives: (1) Observe two-phase flow patterns of air-water and R-113 working fluids over a range of flow conditions, for helical and spiral coil geometries, of circular and rectangular cross-section; (2) Compare observed flow patterns with predictions of existing flow maps; (3) Study criteria for flow regime transitions for possible modifications of existing flow pattern maps; and (4) Measure associated pressure drops across the coiled test sections over the rage of flow conditions specified.

Keshock, Edward G.↗

NASA NTRS1997

Multitemporal and Multiscaled Fractal Analysis of Landsat Satellite Data Using the Image Characterization and Modeling System (ICAMS)

The Image Characterization And Modeling System (ICAMS) is a public domain software package that is designed to provide scientists with innovative spatial analytical tools to visualize, measure, and characterize landscape patterns so that environmental conditions or processes can be assessed and monitored more effectively. In this study ICAMS has been used to evaluate how changes in fractal dimension, as a landscape characterization index, and resolution, are related to differences in Landsat images collected at different dates for the same area. Landsat Thematic Mapper (TM) data obtained in May and August 1993 over a portion of the Great Basin Desert in eastern Nevada were used for analysis. These data represent contrasting periods of peak "green-up" and "dry-down" for the study area. The TM data sets were converted into Normalized Difference Vegetation Index (NDVI) images to expedite analysis of differences in fractal dimension between the two dates. These NDVI images were also resampled to resolutions of 60, 120, 240, 480, and 960 meters from the original 30 meter pixel size, to permit an assessment of how fractal dimension varies with spatial resolution. Tests of fractal dimension for two dates at various pixel resolutions show that the D values in the August image become increasingly more complex as pixel size increases to 480 meters. The D values in the May image show an even more complex relationship to pixel size than that expressed in the August image. Fractal dimension for a difference image computed for the May and August dates increase with pixel size up to a resolution of 120 meters, and then decline with increasing pixel size. This means that the greatest complexity in the difference images occur around a resolution of 120 meters, which is analogous to the operational domain of changes in vegetation and snow cover that constitute differences between the two dates.

Quattrochi, Dale A.↗

NASA NTRS2000

Suspended Patch Antenna Array With Electromagnetically Coupled Inverted Microstrip Feed

The paper demonstrates a four-element suspended patch antenna array, with a parasitic patch layer and an electromagnetically coupled inverted microstrip feed, for linear polarization at K-Band frequencies. This antenna has the following advantages over conventional microstrip antennas: First, the inverted microstrip has lower attenuation than conventional microstrip; hence, conductor loss associated with the antenna corporate feed is lower resulting in higher gain and efficiency. Second, conventional proximity coupled patch antennas require a substrate for the feed and a superstrate for the patch. However, the inverted microstrip fed patch antenna makes use of a single substrate, and hence, is lightweight and low cost. Third, electromagnetic coupling results in wider bandwidth. Details regarding the design and fabrication will be presented as well as measured results including return loss, radiation patterns and cross-polarization levels.

Simons, Rainee N.↗

NASA NTRS2003

Nonlinear Shell Modeling of Thin Membranes with Emphasis on Structural Wrinkling

Thin solar sail membranes of very large span are being envisioned for near-term space missions. One major design issue that is inherent to these very flexible structures is the formation of wrinkling patterns. Structural wrinkles may deteriorate a solar sail's performance and, in certain cases, structural integrity. In this paper, a geometrically nonlinear, updated Lagrangian shell formulation is employed using the ABAQUS finite element code to simulate the formation of wrinkled deformations in thin-film membranes. The restrictive assumptions of true membranes, i.e. Tension Field theory (TF), are not invoked. Two effective modeling strategies are introduced to facilitate convergent solutions of wrinkled equilibrium states. Several numerical studies are carried out, and the results are compared with recent experimental data. Good agreement is observed between the numerical simulations and experimental data.

Tessler, Alexander↗

NASA NTRS2004

Development of an Intelligent Videogrammetric Wind Tunnel Measurement System

A videogrammetric technique developed at NASA Langley Research Center has been used at five NASA facilities at the Langley and Ames Research Centers for deformation measurements on a number of sting mounted and semispan models. These include high-speed research and transport models tested over a wide range of aerodynamic conditions including subsonic, transonic, and supersonic regimes. The technique, based on digital photogrammetry, has been used to measure model attitude, deformation, and sting bending. In addition, the technique has been used to study model injection rate effects and to calibrate and validate methods for predicting static aeroelastic deformations of wind tunnel models. An effort is currently underway to develop an intelligent videogrammetric measurement system that will be both useful and usable in large production wind tunnels while providing accurate data in a robust and timely manner. Designed to encode a higher degree of knowledge through computer vision, the system features advanced pattern recognition techniques to improve automated location and identification of targets placed on the wind tunnel model to be used for aerodynamic measurements such as attitude and deformation. This paper will describe the development and strategy of the new intelligent system that was used in a recent test at a large transonic wind tunnel.

Graves, Sharon S.↗

NASA NTRS2002

Galacturonomannan and Golgi-derived membrane linked to growth and shaping of biogenic calcite

The coccolithophores are valuable models for the design and synthesis of composite materials, because the cellular machinery controlling the nucleation, growth, and patterning of their calcitic scales (coccoliths) can be examined genetically. The coccoliths are formed within the Golgi complex and are the major CaCO(3) component in limestone sediments-particularly those of the Cretaceous period. In this study, we describe mutants lacking a sulfated galacturonomannan and show that this polysaccharide in conjunction with the Golgi-derived membrane is directly linked to the growth and shaping of coccolith calcite but not to the initial orientated nucleation of the mineral phase.

NASA Discipline Cell Biology↗

NASA NTRS1988

An extreme-halophile archaebacterium possesses the interlock type of prephenate dehydratase characteristic of the Gram-positive eubacteria

The focal point of phenylalanine biosynthesis is a dehydratase reaction which in different organisms may be prephenate dehydratase, arogenate dehydratase, or cyclohexadienyl dehydratase. Gram-positive, Gram-negative, and cyanobacterial divisions of the eubacterial kingdom exhibit different dehydratase patterns. A new extreme-halophile isolate, which grows on defined medium and is tentatively designated as Halobacterium vallismortis CH-1, possesses the interlock type of prephenate dehydratase present in Gram-positive bacteria. In addition to the conventional sensitivity to feedback inhibition by L-phenylalanine, the phenomenon of metabolic interlock was exemplified by the sensitivity of prephenate dehydratase to allosteric effects produced by extra-pathway (remote) effectors. Thus, L-tryptophan inhibited activity while L-tyrosine, L-methionine, L-leucine and L-isoleucine activated the enzyme. L-Isoleucine and L-phenylalanine were effective at micromolar levels; other effectors operated at mM levels. A regulatory mutant selected for resistance to growth inhibition caused by beta-2-thienylalanine possessed an altered prephenate dehydratase in which a phenomenon of disproportionately low activity at low enzyme concentration was abolished. Inhibition by L-tryptophan was also lost, and activation by allosteric activators was diminished. Not only was sensitivity to feedback inhibition by L-phenylalanine lost, but the mutant enzyme was now activated by this amino acid (a mutation type previously observed in Bacillus subtilis). It remains to be seen whether this type of prephenate dehydratase will prove to be characteristic of all archaebacteria or of some archaebacterial subgroup cluster.

NASA Discipline Number 52-30↗

NASA NTRS2005

An XML Representation for Crew Procedures

NASA ensures safe operation of complex systems through the use of formally-documented procedures, which encode the operational knowledge of the system as derived from system experts. Crew members use procedure documentation on the ground for training purposes and on-board space shuttle and space station to guide their activities. Investigators at JSC are developing a new representation for procedures that is content-based (as opposed to display-based). Instead of specifying how a procedure should look on the printed page, the content-based representation will identify the components of a procedure and (more importantly) how the components are related (e.g., how the activities within a procedure are sequenced; what resources need to be available for each activity). This approach will allow different sets of rules to be created for displaying procedures on a computer screen, on a hand-held personal digital assistant (PDA), verbally, or on a printed page, and will also allow intelligent reasoning processes to automatically interpret and use procedure definitions. During his NASA fellowship, Dr. Simpson examined how various industries represent procedures (also called business processes or workflows), in areas such as manufacturing, accounting, shipping, or customer service. A useful method for designing and evaluating workflow representation languages is by determining their ability to encode various workflow patterns, which depict abstract relationships between the components of a procedure removed from the context of a specific procedure or industry. Investigators have used this type of analysis to evaluate how well-suited existing workflow representation languages are for various industries based on the workflow patterns that commonly arise across industry-specific procedures. Based on this type of analysis, it is already clear that existing workflow representations capture discrete flow of control (i.e., when one activity should start and stop based on when other activities start and stop), but do not capture the flow of data, materials, resources or priorities. Existing workflow representation languages are also limited to representing sequences of discrete activities, and cannot encode procedures involving continuous flow of information or materials between activities.

Simpson, Richard C.↗

NASA NTRS2019

Low-Loss Microstrip Transmission Line Fabricated with Improved Liftoff Process

The µ-Spec integrated spectrometer operating at ~500 GHz, employs thin film superconducting Nb microstrip transmission lines deposited directly on a thin (450 nm) single-crystal silicon dielectric. This single-crystal silicon layer is chosen as the dielectric layer due to its low intrinsic loss, with the goal of achieving both high- efficiency and precise phase control in a compact spectrometer architecture. To avoid roughening or etching through the thin single-crystal silicon dielectric a liftoff technique was developed for patterning these microstrip transmission lines and ground plane structures. This two- layer liftoff process was designed for use with sputter deposition and resulted in a US patent. Although this original technique provided precise control of linewidth, results of initial prototype spectrometer devices and separate diagnostic co-planer waveguide resonator devices showed that unexpected loss was being introduced due to the lift-off process. This extra loss was believed to be due to the “tails” (thin tapered regions) at the edge of the metal traces resulting from the sputtering process, as well as an amorphous oxide layer at the Nb-Si interface. We have since demonstrated an improved lift-off technique, which provides a clean metal-Si interface and removes the loss-inducing tails by a two-step selective etching method. This results in a decrease in microwave loss by more than an order of magnitude when measured in co-planar waveguide microwave resonator structures. We present these microwave test results and also SEM and TEM images of the microstrip interfaces and edge profiles before and after application of the improved process.

Hess, Larry A.↗

DOE OSTI2023

Development of Large-Volume-Diamond Anvil Cell for Neutron Diffraction: The Neutron Diamond Anvil Cell Project at ORNL

10 years ago, Dave Mao, director of EFree (energy frontier research in extreme environments), a DOE energy frontier recognized the importance of neutron science for energy research. The subsequent establishment of a neutron group within EFree lead to the establishment of an “Instrument Development Team” for SNAP, the High-Pressure beamline at the Spallation Neutron Source at Oak Ridge National Laboratory in Tennessee. The idea was to develop novel high pressure techniques to expand the pressure range for neutron diffraction. A goal was set to reach half megabar levels (50 GPa), which at the time was considered as extremely challenging. Here we will give a brief overview of the developments during the last decade in this novel area of research. Fortunately, during this period multi carat diamond anvils have become available mainly by the chemical vapor deposition process (CVD), making research in this pressure range and beyond rather routine. This paper shows the latest developments in large anvil designs, compact multiple ton diamond cells and some examples of high-quality neutron diffraction patterns of sample sizes far below conventional levels.

Boehler, Reinhard↗

NASA NTRS1980

Analytical design of multispectral sensors

An optimal design based on the criterion of minimum mean square representation error using the Karhunen-Loeve expansion was developed to represent the spectral response functions from a stratum based upon a stochastic process scene model. From the overall pattern recognition system perspective, the effect of the representation accuracy on a typical performance criterion (the probability of correct classification) is investigated. The optimum sensor design provides a standard against which practical (suboptimum) operational sensors can be compared. An example design is provided and its performance is illustrated. Although developed primarily for the purpose of sensor design, the procedure has potential for making important contributions to scene understanding. Spectral channels which have narrow bandwidths relative to current sensor systems may be necessary to provide adequate spectral representation and improved classification performance.

Wiersma, D. J.↗

NASA NTRS1975

Flow characteristics of various swirl-can module designs

Flow measurements were performed on each of six swirl-can combustor module designs under simulated combustor operating conditions to find the design which exhibited a small recirculation zone, intense air mixing, and good fuel distribution in its wake. Conditions that are favorable for producing low oxides of nitrogen emissions and high combustion efficiency were investigated. The recirculation zone, the turbulence intensity and the fuel distribution pattern are obtained in the wake region of the center module of a three module array. The most promising swirl-can module design incorporates two air swirlers which discharge air in opposite directions (contraswirl), mixes the fuel and air upstream of the inner swirler, and has a flow area blockage of 64.3% for the three module array.

Mularz, E. J.↗

NASA NTRS1992

PERCIVAL mission to Mars

With the downturn of the world economy, the priority of unmanned exploration of the solar system has been lowered. Instead of foregoing all missions to our neighbors in the solar system, a new philosophy of exploration mission design has evolved to insure the continued exploration of the solar system. The 'Discovery-class' design philosophy uses a low cost, limited mission, available technology spacecraft instead of the previous 'Voyager-class' design philosophy that uses a 'do-everything at any cost' spacecraft. The Percival Mission to Mars was proposed by Ares Industries as one of the new 'Discovery-class' of exploration missions. The spacecraft will be christened Percival in honor of American astronomer Percival Lowell who proposed the existence of life on Mars in the early twentieth century. The main purpose of the Percival mission to Mars is to collect and relay scientific data to Earth suitable for designing future manned and unmanned missions to Mars. The measurements and observations made by Percival will help future mission designers to choose among landing sites based on the feasibility and scientific interest of the sites. The primary measurements conducted by the Percival mission include gravity field determination, surface and atmospheric composition, sub-surface soil composition, sub-surface seismic activity, surface weather patterns, and surface imaging. These measurements will be taken from the orbiting Percival spacecraft and from surface penetrators deployed from Mars orbit. The design work for the Percival Mission to Mars was divided among four technical areas: Orbits and Propulsion System, Surface Penetrators, Gravity and Science Instruments, and Spacecraft Structure and Systems. The results for each of the technical areas is summarized and followed by a design cost analysis and recommendations for future analyses.

Reed, David W.↗

NASA NTRS2022

PAAV Concept Document

The Pathfinding for Airspace with Autonomous Vehicles (PAAV) Concept Document, version 1.0, lays out the key challenges and potential solutions for the use of uncrewed aircraft (UA) technology for future regional air cargo operations. The challenges and solutions described in this document were informed by communications with the UA industry community (e.g., RTCA, the Federal Aviation Administration, and regional air cargo business operators), as well as the PAAV team’s research activities during the last two years including four tabletop exercises, a human-in-the-loop simulation study, a numerical simulation study, a functional allocation study, and flight data analysis (Appendix A). This document first describes the expected operational context of PAAV (Section 2), such as the flight mission, baseline UAS components, nominal operations, m:N operations (i.e., "m" remote pilots per "N" aircraft), and off-nominal operations. This context sets the scope for the PAAV concept development work. PAAV concept development assumes that UA operations will be increasingly autonomous. Thus, near- and far-term assumptions are defined (Section 3). PAAV identified seven key challenges for UA operations (Section 4): - Flight route planning - Separation and flow management - Traffic pattern integration - Contingency management - Taxi, takeoff, and landing - m:N operations - Communications operations The following 13 potential solutions to these challenges are then described (Section 5): - Scalable communications architecture - Data link - Designated UAS corridors - Crew planning for m:N operations - Flight route optimization - Traffic load-level control - Trajectory solutions with data link - Automated hazard avoidance for m:N operations - Traffic pattern integration (TPI) tool - Standard lost command and control (C2) link (LC2L) procedures - Automated hazard avoidance under LC2L - Auto-taxi, auto-takeoff, and auto-land - Ground control station (GCS) user interface for m:N operations The document attempts to link each of these solutions to one or more of the challenge areas. Novel solutions involving numerous automation technologies are needed to mitigate traffic and airspace management challenges, especially for realizing m:N operations and ensuring safety under LC2L conditions. The purpose of this document is to help understand alternatives and tradeoffs among potential solutions and provide a foundation for a cohesive PAAV concept that will be described and refined in subsequent concept versions.

Unmanned aircraft, uncrewed aircraft, regional air↗

DOE OSTI2021

Mask Free OLED Fabrication Process for Non-Tunable and Tunable White OLED Panels

In this program we demonstrated a method for mask free fabrication of OLEDs. Conventional OLEDs use at least 2 shadowmasks during the fabrication process to define the deposition pattern for the organic layers and for the cathode layer. Although effective, the use of masks requires mask handling and mask change equipment which increases the cost of the OLED deposition system. New sets of masks are required for every new product design, and the mask sets require frequent cleaning as organic material builds up on the masks over time and can be a source of particle defects resulting in yield loss. The method investigated in this program uses laser removal of organic material to pattern the organic layers and define a moisture impermeable seal region. This method is digital and can be applied to any new panel design, avoiding the costs of new masks sets and associated yield loss. In addition, we developed a platform technology for producing white color tunable or dim-to-warm white OLEDs and demonstrated patterning of tunable white OLEDs using the low-cost mask free fabrication process.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS2012

Theory of a Traveling Wave Feed for a Planar Slot Array Antenna

Planar arrays of waveguide-fed slots have been employed in many radar and remote sensing applications. Such arrays are designed in the standing wave configuration because of high efficiency. Traveling wave arrays can produce greater bandwidth at the expense of efficiency due to power loss in the load or loads. Traveling wave planar slot arrays may be designed with a long feed waveguide consisting of centered-inclined coupling slots. The feed waveguide is terminated in a matched load, and the element spacing in the feed waveguide is chosen to produce a beam squinted from the broadside. The traveling wave planar slot array consists of a long feed waveguide containing resonant-centered inclined coupling slots in the broad wall, coupling power into an array of stacked radiating waveguides orthogonal to it. The radiating waveguides consist of longitudinal offset radiating slots in a standing wave configuration. For the traveling wave feed of a planar slot array, one has to design the tilt angle and length of each coupling slot such that the amplitude and phase of excitation of each radiating waveguide are close to the desired values. The coupling slot spacing is chosen for an appropriate beam squint. Scattering matrix parameters of resonant coupling slots are used in the design process to produce appropriate excitations of radiating waveguides with constraints placed only on amplitudes. Since the radiating slots in each radiating waveguide are designed to produce a certain total admittance, the scattering (S) matrix of each coupling slot is reduced to a 2x2 matrix. Elements of each 2x2 S-matrix and the amount of coupling into the corresponding radiating waveguide are expressed in terms of the element S11. S matrices are converted into transmission (T) matrices, and the T matrices are multiplied to cascade the coupling slots and waveguide sections, starting from the load end and proceeding towards the source. While the use of non-resonant coupling slots may provide an additional degree of freedom in the design, resonant coupling slots simplify the design process. The amplitude of the wave going to the load is set at unity. The S11 parameter, r of the coupling slot closest to the load, is assigned an arbitrary value. A larger value of r will reduce the power dissipated in the load while increasing the reflection coefficient at the input port. It is now possible to obtain the excitation of the radiating waveguide closest to the load and the coefficients of the wave incident and reflected at the input port of this coupling slot. The next coupling slot parameter, r , is chosen to realize the excitation of that radiating waveguide. One continues this process moving towards the source, until all the coupling slot parameters r and hence the S11 parameter of the 4-port coupler, r, are known for each coupling slot. The goal is to produce the desired array aperture distribution in the feed direction. From an interpolation of the computed moment method data for the slot parameters, all the coupling slot tilt angles and lengths are obtained. From the excitations of the radiating waveguides computed from the coupling values, radiating slot parameters may be obtained so as to attain the desired total normalized slot admittances. This process yields the radiating slot parameters, offsets, and lengths. The design is repeated by choosing different values of r for the last coupling slot until the percentage of power dissipated in the load and the input reflection coefficient values are satisfactory. Numerical results computed for the radiation pattern, the tilt angles and lengths of coupling slots, and excitation phases of the radiating waveguides, are presented for an array with uniform amplitude excitation. The design process has been validated using computer simulations. This design procedure is valid for non-uniform amplitude excitations as well.

Rengarajan, Sembiam↗

NASA NTRSDate not supplied

A Flat-Panel 8x8 Sequentially Rotated Wideband Microstrip Patch Phased Array Antenna for K/Ka-band 6U CubeSat Communications Applications

Flat-panel electronically-scanned phased arrays have recently become a mainstream technology in the areas of radar and satellite applications, particularly due to their low profile and not having to steer the beams mechanically, both of which helps in realizing a lightweight phased array solution that also occupies a smaller volume. Typically for satellite applications, circularly polarized element radiators are often employed in order to deal with the signal fading problem. In this project, the main objective was to design a flat-panel phased array solution for 6U CubeSat communication applications. As for the required specifications, the array should have two operating bands: 22.55–23.55 GHz and 25.5–27.5 GHz, which span part of the K and Ka bands. For both these bands, the panel should be able to radiate dual circular polarization, in both transmit and receive modes, and with a stable gain performance. Since the individual bands are very closely spaced, it was realized that a single wideband design would be a better solution than a closely spaced dual-band design. Thus, a stacked microstrip patch configuration was selected for the element radiator design, which is known to be wideband. Now, it is rather difficult to realize both wide impedance and axial ratio bandwidths simultaneously, and at high frequencies, without complicating the element stacked patch design.. As a result, a sequential rotation technique wasemployed to significantly improves the axial ratio bandwidth and circular polarization purity of an array, all the while improving the pattern symmetry (P. S. Hall, “Application of Sequential Feeding to Wide Bandwidth, Circularly Polarised Microstrip Patch Arrays,” IEE Proc. H (Microw., Antennas Propag.), vol. 136, no. 5, pp. 390–398, Oct. 1989). The designed element radiator is a circularly-polarized probe-fed stacked patch antenna, which has a 10-dB matching bandwidth of 22.3– 30 GHz, with only a 5.14% axial ratio bandwidth around the center frequency of the required band, i.e., ~25 GHz. However, the resulting array demonstrates a very low axial ratio (≪ 3 dB) over the entire bandwidth, due to the application of the sequential rotation technique. The 8×8 array was able to scan up to ±51° and ±40° at frequencies 23.05 GHz and 26.5 GHz (center frequencies of the lower and upper bands), respectively, while maintaining a ≤ 3 dB axial ratio and a ≤ 3 dB gain drop from the corresponding peak broadside value at both the principle and the diagonal radiation planes. The designed layout for the 8×8 phased array prototype is shown in Fig. 1, which is currently undergoing fabrication and RF assembly. The antenna will be tested in the far-field anechoic chambers of the Antenna and Microwave Laboratory (AML) at San Diego State University and at NASA Glenn Research Center (GRC).

5G↗

DOE OSTI2021

A Deep Learning Modeling Framework to Capture Mixing Patterns in Reactive-Transport Systems

Prediction and control of chemical mixing are vital for many scientific areas such as subsurface reactive transport, climate modeling, combustion, epidemiology, and pharmacology. Due to the complex nature of mixing in heterogeneous and anisotropic media, the mathematical models related to this phenomenon are not analytically tractable. Numerical simulations often provide a viable route to predict chemical mixing accurately. However, contemporary modeling approaches for mixing cannot utilize available spatial-temporal data to improve the accuracy of the future prediction and can be compute-intensive, especially when the spatial domain is large and for long-term temporal predictions. To address this knowledge gap, in this work we will present in this paper a deep learning (DL) modeling framework applied to predict the progress of chemical mixing under fast bimolecular reactions. This framework uses convolutional neural networks (CNN) for capturing spatial patterns and long short-term memory (LSTM) networks for forecasting temporal variations in mixing. By careful design of the framework—placement of non-negative constraint on the weights of the CNN and the selection of activation function, the framework ensures non-negativity of the chemical species at all spatial points and for all times. Our DL-based framework is fast, accurate, and requires minimal data for training. The time needed to obtain a forecast using the model is a fraction (≈ O(-6)) of the time needed to obtain the result using a high-fidelity simulation. To achieve an error of 10% (measured using the infinity norm) for capturing local-scale mixing features such as interfacial mixing, only 24% to 32% of the sequence data for model training is required. To achieve the same level of accuracy for capturing global-scale mixing features, the sequence data required for model training is 64% to 70% of the total spatial-temporal data. Hence, the proposed approach—a fast and accurate way to forecast long-time spatial-temporal mixing patterns in heterogeneous and anisotropic media—will be a valuable tool for modeling reactive-transport in a wide range of applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗