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DOE OSTI2017

Beyond 100 Gb/s: Capacity, Flexibility, and Network Optimization

Here, we discuss building blocks that enable the exploitation of optical capacities beyond 100 Gb/s. Optical networks will benefit from more flexibility and agility in their network elements, especially from coherent transceivers. To achieve capacities of 400 Gb/s and more, coherent transceivers will operate at higher symbol rates. This will be made possible with higher bandwidth components using new electro-optic technologies implemented with indium phosphide and silicon photonics. Digital signal processing will benefit from new algorithms. Multi-dimensional modulation, of which some formats are already in existence in current flexible coherent transceivers, will provide improved tolerance to noise and fiber nonlinearities. Constellation shaping will further improve these tolerances while allowing a finer granularity in the selection of capacity. Frequency-division multiplexing will also provide improved tolerance to the nonlinear characteristics of fibers. Algorithms with reduced computation complexity will allow the implementation, at speeds, of direct pre-compensation of nonlinear propagation effects. Advancement in forward error correction will shrink the performance gap with Shannon's limit. At the network control and management level, new tools are being developed to achieve a more efficient utilization of networks. This will also allow for network virtualization, orchestration, and management. Lastly, FlexEthernet and FlexOTN will be put in place to allow network operators to optimize capacity in their optical transport networks without manual changes to the client hardware.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Data augmentation for disruption prediction via robust surrogate models

The goal of this work is to generate large statistically representative datasets to train machine learning models for disruption prediction provided by data from few existing discharges. Such a comprehensive training database is important to achieve satisfying and reliable prediction results in artificial neural network classifiers. Here, we aim for a robust augmentation of the training database for multivariate time series data using Student-t process regression. We apply Student-t process regression in a state space formulation via Bayesian filtering to tackle challenges imposed by outliers and noise in the training data set and to reduce the computational complexity. Thus, the method can also be used if the time resolution is high. We use an uncorrelated model for each dimension and impose correlations afterwards via coloring transformations. We demonstrate the efficacy of our approach on plasma diagnostics data of three different disruption classes from the DIII-D tokamak. To evaluate if the distribution of the generated data is similar to the training data, we additionally perform statistical analyses using methods from time series analysis, descriptive statistics, and classic machine learning clustering algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Gas-Liquid Flow Modeling for Renewable Fuels Production

Aerobic/anaerobic and gas fermentation pathways have emerged as promising new technologies for the generation of renewable fuels/chemicals from biomass derived sugars, and mixtures of greenhouse/energy rich gas streams (CO2/CH4/H2/CO) via microbial action. Example pathways include sugars-to-ethanol conversion, biomethanation (CO2/H2 to CH4), biogas upgrading, CO fermentation and wet-waste conversion. Gas and liquid phase transport, mass-transfer, and mixing physics at large length scales can significantly affect microbial conversion rates, particularly when the microbial reaction requires a narrow set of conditions. These phenomena are difficult to study in small-scale bench-top reactors that are typically well-mixed. Predictive computational fluid dynamics (CFD) based simulations can therefore aid in the scale-up, design and optimization of these reactors. This work presents multiphase Euler-Euler CFD simulations of at-scale (~500 m3) bioreactors. Our mathematical model treats the gas and liquid as interpenetrating phases. This approach reduces the computational complexity of tracking individual gas bubbles that are several orders of magnitude smaller than reactor dimensions. We solve the Reynolds averaged Navier-Stokes (RANS) multiphase equations that account for phase and chemical species transport, interphase mass and momentum transfer and uses a phenomenological model for gas uptake by microbes. We use a customized solver derived from open-source CFD toolbox, OpenFOAM [1], to perform these simulations, which has been validated against small-scale reactors in our previous work [2]. There is currently a knowledge-gap regarding bubble-size distributions when using gas mixtures with vastly different properties, which can have a significant impact overall mass-transfer. For example, hydrogen bubbles are more buoyant compared to other relatively heavier gases (CO2/CH4/CO), resulting in a large distribution of residence times and bubble sizes. This work therefore develops a deeper understanding of bubble dynamics and interphase mass transfer in such heterogenous gas mixtures through well-resolved computational models. We use a population balance model (PBM) for bubble-size-distribution modeling that is validated against small-scale experiments in our solver with an uncertainty quantification study for bubble coalescence and break-up model parameters. Results pertaining to multiple simulations of gas-fermentation reactors are presented where gas mixtures with varying compositions of CO2/CH4/CO/H2 are imposed at the sparger boundaries. The spatio-temporal variations in bubble-size distribution and mass transfer coefficient are analyzed for varying superficial velocities and gas-compositions for varying sizes of bubble-column and airlift reactors. This work will also examine the performance of different reactor designs, viz. bubble column reactor, airlift reactor with an internal draft tube, and a stirred-tank reactor with Rushton impellers. Reactor mass-transfer coefficient, gas hold-up, and dissolved gas distribution are critically analyzed among reactors, and sensitivity studies pertaining to gas flow rates and reactor geometry will be presented. [1] Weller, H., Tabor, G., Jasak, H. and Fureby, C., A tensorial approach to computational continuum mechanics using object-oriented techniques, Computers in physics, 12, 6, 620--631, 1998. [2] Rahimi, M., Sitaraman, H., Humbird, D. and Stickel, J., Computational fluid dynamics study of full-scale aerobic bioreactors: Evaluation of gas-liquid mass transfer, oxygen uptake, and dynamic oxygen distribution, Chemical Engineering Research and Design, 139: 283-295.

BIOMASS FUELS↗

DOE OSTI2021

Risk-averse optimization for resilience enhancement of complex engineering systems under uncertainties

With the growth of complexity and extent, large scale interconnected network systems, e.g., transportation networks or infrastructure networks, become more vulnerable to external disturbances. Hence, managing potential disruptive events during the design, operating, and recovery phase of an engineered system and therefore improving the system’s resilience is an important yet challenging task. Here, to ensure system resilience after the occurrence of failure events, this study proposes a mixed-integer linear programming (MILP) based restoration framework using heterogeneous dispatchable agents. The scenario-based stochastic optimization (SO) technique is adopted to deal with the inherent uncertainties imposed on the recovery process from nature. Moreover, different from conventional SO using deterministic equivalent formulations, the CVaR risk measure is implemented for this study because of the temporal sparsity of the decision making in applications such as the recovery from extreme events. The resulting restoration framework involves a large-scale MILP problem and thus an adequate decomposition technique i.e. modified Lagrangian dual decomposition, is also employed to achieve tractable computational complexity. Case study results based on the IEEE 37-bus test feeder demonstrate the benefits of using the proposed framework for resilience improvement as well as the advantages of adopting SO formulations.

42 ENGINEERING↗

DOE OSTI2026

ToPolyAgent: AI agents for coarse-grained bead-spring topological polymer simulations

We introduce ToPolyAgent, a multi-agent AI framework for performing coarse-grained molecular dynamics (MD) simulations of topological polymers through natural language instructions. By integrating large language models (LLMs) with domain-specific computational tools, ToPolyAgent supports both interactive and autonomous simulation workflows across diverse polymer architectures, including linear, ring, brush, and star polymers, as well as dendrimers. The system consists of four LLM-powered agents: a Config Agent for generating initial polymer–solvent configurations, a Simulation Agent for executing LAMMPS-based MD simulations and conformational analyses, a Report Agent for compiling markdown reports, and a Workflow Agent for streamlined autonomous operations. Interactive mode incorporates user feedback loops for iterative refinements, while autonomous mode enables end-to-end task execution from detailed prompts. We demonstrate ToPolyAgent's versatility through case studies involving diverse polymer architectures under varying solvent conditions, thermostats, and simulation lengths. Furthermore, we highlight its potential as a research assistant by directing it to investigate the effect of interaction parameters on the linear polymer conformation, and the influence of grafting density on the persistence length of the brush polymer. By coupling natural language interfaces with rigorous simulation tools, ToPolyAgent lowers barriers to complex computational workflows and advances AI-driven materials discovery in polymer science. It lays the foundation for autonomous and extensible multi-agent scientific research ecosystems.

Ding, Lijie [Oak Ridge National Laboratory (ORNL),↗

DOE OSTI2019

Static subspace approximation for the evaluation of G 0 W 0 quasiparticle energies within a sum-over-bands approach

Many-body perturbation theory within the GW approach has been established as a quantitatively accurate approach for predicting the quasiparticle and excited-state properties of a wide variety of materials. However, the successful application of the method is often complicated by the computational complexity associated with the evaluation and inversion of the frequency-dependent dielectric matrix ε(ω). Here, we describe an approach to speed up the evaluation of the frequency-dependent part of ε(ω) in the traditional sum-over-states GW framework based on the low-rank approximation of the static dielectric matrix, a technique often used in GW implementations that are based on a starting mean field within density-functional perturbation theory. We show that the overall accuracy of the approach, independently from other calculation parameters, is solely determined by the threshold on the eigenvalues of the static dielectric matrix, ε(ω = 0) , and that it can yield orders-of-magnitude speed-ups in full-frequency G W calculations. In this work, we validate our implementation with several benchmark calculations ranging from bulk materials to systems with reduced dimensionality, and show that this technique allows one not only to study larger systems, but also to carefully consider the convergence of computationally demanding systems, such as ZnO, without relying on plasmon-pole models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Reconstruction of jointly sparse vectors via manifold optimization

In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This result reveals a reduction in the computational complexity of the original problem and enables a simple implementation of joint sparse recovery algorithms for full-rank setting. Secondly, we propose a new method for joint sparse recovery in the form of a non-convex optimization problem on a non-compact Stiefel manifold. In our numerical experiments our method outperforms the commonly used l 2,1 minimization in the sense that much fewer measurements are required for accurate sparse reconstructions. Here, we postulate this approach possesses the desirable rank aware property, that is, being able to take advantage of the rank of the unknown matrix to improve the recovery.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Optimization of the generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double- β decay: Ridge regression for nuclei with axial deformation

The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. In this work, we propose a subspace-reduction algorithm that employs optimal statistical ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra and the NME of ground state to ground state 0νββ decay based on the orthogonality condition (OC) and the energy-transition-orthogonality procedure (ENTROP), respectively. For simplicity, the polynomial ridge regression (RR) algorithm is used to learn the norm and Hamiltonian kernels of axially deformed configurations. The efficiency and accuracy of this algorithm are illustrated for 76 Ge and 76 Se by comparing results obtained using the optimal RR models to direct GCM calculations. The low-lying energy spectra of 76 Ge and 76 Se, as well as the 0νββ-decay NME between their ground states, are computed. Furthermore, the results show that the performance of the GCM+OC/ENTROP+RR is more robust than that of the GCM+RR alone, and the former can reproduce the results of the original GCM calculation accurately with a significantly reduced computational cost.

59 ≤ A ≤ 89↗

NASA NTRS2024

EdgeCortix SAKURA-I Machine-Learning, PCIe Accelerator SEE Heavy Ion Test Report

To enable autonomy in space, machine-learning and computer vision applications become invaluable for sensor processing. However, these algorithms are computationally complex and unfeasible for many embedded central processing units (CPUs) and usually require external coprocessors, such as graphics processing units (GPUs) or accelerators specific to the application, including application specific integrated circuits (ASICs). In power-constrained systems, GPUs tend to consume more power than is acceptable (>40W), so lower-power accelerators have shown promise to provide the performance needed under spacecraft constraints. For radiation engineers, developing methodologies that can properly test CPUs, GPUs, and accelerators, and enable comparisons between them remains a necessary complication to solve as the devices become more complex. The methodology in this test aims to be a start in developing a baseline single-event effect (SEE) test for client-device machine learning accelerators. This category of devices do not host their own operating system. This testing campaign is a continuation of a previous 200 MeV proton test performed in January 2024. This report covers two heavy ion tests of the SAKURA-I card: one in April 2024, and one in June 2024. Additional data was needed after the April test due to ion-range issues experienced at higher linear-energy transfers (LETs). These range issues are described in more detail in Section 8. This experiment characterizes SEEs and data error susceptibility of the EdgeCortix SAKURA-I machine-learning accelerator under heavy ions. The device was monitored for single event upsets (SEUs) and single event functional interrupts (SEFIs) at the Lawrence Berkeley National Laboratory’s 88-inch cyclotron. The SAKURA-I board accelerates machine-learning inference applications on a host computer through a PCIex16 connection. For the purposes of devising an end to end automated analysis workflow for this experiment, the YOLO-V5 and SSD300 objection-detection models, and the ResNet-50, EfficientNet, and MobileNetV2 image classification models were used as a representative suite of analytical machine-learning models.

Seth S Roffe↗

DOE OSTI2020

sMF-BO-2CoGP: A sequential multi-fidelity constrained Bayesian optimization framework for design applications

Bayesian optimization (BO) is an effective surrogate-based method that has been widely used to optimize simulation-based applications. While the traditional Bayesian optimization approach only applies to single-fidelity models, many realistic applications provide multiple levels of fidelity with various levels of computational complexity and predictive capability. In this work, we propose a multi-fidelity Bayesian optimization method for design applications with both known and unknown constraints. The proposed framework, called sMF-BO-2CoGP, is built on a multi-level CoKriging method to predict the objective function. An external binary classifier, which we approximate using a separate CoKriging model, is used to distinguish between feasible and infeasible regions. Finally, the sMF-BO-2CoGP method is demonstrated using a series of analytical examples and a flip-chip application for design optimization to minimize the deformation due to warping under thermal loading conditions.

42 ENGINEERING↗

DOE OSTI2016

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Connected three-body terms in single-reference unitary many-body theories: Iterative and perturbative approximations

This work introduces various approaches to include connected three-body terms in unitary many-body theories, focusing on the driven similarity renormalization group (DSRG). Starting from the least approximate method—the linearized DSRG truncated to one-, two-, and three-body operators [LDSRG(3)]—we develop several approximate LDSRG(3) models with reduced computational cost. Through a perturbative analysis, we motivate a family of iterative LDSRG(3)-n and -n' (n = 1, 2, 3, 4) methods that contain a subset of the LDSRG(3) diagrams. Among these variants, the LDSRG(3)-2 scheme has the same computational complexity of coupled cluster theory with singles, doubles, and triples (CCSDT), but it outperforms CCSDT in the accuracy of the predicted correlation energies. We also propose and implement two perturbative triples corrections based on the linearized DSRG truncated to one- and two-body operators augmented with recursive semi-quadratic commutators [qDSRG(2)]. Overall, the resulting qDSRG(2)+(T) approach matches the accuracy of the “gold-standard” coupled cluster theory with singles, doubles, and perturbative triples model on the energetics of twenty-eight closed-shell atoms and small molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Testing convolutional neural network based deep learning systems: a statistical metamorphic approach

Machine learning technology spans many areas and today plays a significant role in addressing a wide range of problems in critical domains,i.e., healthcare, autonomous driving, finance, manufacturing, cybersecurity,etc. Metamorphic testing (MT) is considered a simple but very powerful approach in testing such computationally complex systems for which either an oracle is not available or is available but difficult to apply. Conventional metamorphic testing techniques have certain limitations in verifying deep learning-based models (i.e., convolutional neural networks (CNNs)) that have a stochastic nature (because of randomly initializing the network weights) in their training. In this article, we attempt to address this problem by using a statistical metamorphic testing (SMT) technique that does not require software testers to worry about fixing the random seeds (to get deterministic results) to verify the metamorphic relations (MRs). We propose seven MRs combined with different statistical methods to statistically verify whether the program under test adheres to the relation(s) specified in the MR(s). We further use mutation testing techniques to show the usefulness of the proposed approach in the healthcare space and test two CNN-based deep learning models (used for pneumonia detection among patients). The empirical results show that our proposed approach uncovers 85.71% of the implementation faults in the classifiers under test (CUT). Furthermore, we also propose an MRs minimization algorithm for the CUT, thus saving computational costs and organizational testing resources.

Computer Science↗

DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Sub-grid drag model for immersed vertical cylinders in fluidized beds

Immersed vertical cylinders are often used as heat exchanger in gas-solid fluidized beds. Computational Fluid Dynamics (CFD) simulations are computationally expensive for large scale systems with bundles of cylinders. Therefore sub-grid models are required to facilitate simulations on a coarse grid, where internal cylinders are treated as a porous medium. The influence of cylinders on the gas-solid flow tends to enhance segregation and affect the gas-solid drag. A correction to gas-solid drag must be modeled using a suitable sub-grid constitutive relationship. In the past, Sarkar et al. have developed a sub-grid drag model for horizontal cylinder arrays based on 2D simulations. However, the effect of a vertical cylinder arrangement was not considered due to computational complexities. In this study, highly resolved 3D simulations with vertical cylinders were performed in small periodic domains. These simulations were filtered to construct a sub-grid drag model which can then be implemented in coarse-grid simulations. Gas-solid drag was filtered for different solids fractions and a significant reduction in drag was identified when compared with simulation without cylinders and simulation with horizontal cylinders. Slip velocities significantly increase when vertical cylinders are present. Lastly, vertical suspension drag due to vertical cylinders is insignificant however substantial horizontal suspension drag is observed which is consistent to the finding for horizontal cylinders.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Order parameter re-mapping algorithm for 3D phase field model of grain growth using FEM

Phase field modeling (PFM) is a well-known technique for simulating microstructural evolution. To model grain growth using PFM, typically each grain is assigned a unique non-conserved order parameter and each order parameter field is evolved in time. Traditional approaches using a one-to-one mapping of grains to order parameters present a challenge when modeling large numbers of grains due to the computational expense of using many order parameters. This problem is exacerbated when using an implicit finite element method (FEM), as the global matrix size is proportional to the number of order parameters. While previous work has developed methods to reduce the number of required variables and thus computational complexity and run time, none of the existing approaches can be applied for an implicit FEM implementation of PFM. Here, we present a modular, dynamic, scalable reassignment algorithm suitable for use in such a system. Polycrystal modeling with grain growth and stress require careful tracking of each grain’s position and orientation which is lost when using a reduced order parameter set. In conclusion, the method presented in this paper maintains a unique ID for each grain even after reassignment, to allow the PFM to be tightly coupled to calculations of the stress throughout the polycrystal. Implementation details and comparative results of our approach are presented.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Rapid sampling of stochastic displacements in Brownian dynamics simulations

Here, we present a new method for sampling stochastic displacements in Brownian Dynamics (BD) simulations of colloidal scale particles. The method relies on a new formulation for Ewald summation of the Rotne-Prager-Yamakawa (RPY) tensor, which guarantees that the real-space and wave-space contributions to the tensor are independently symmetric and positive-definite for all possible particle configurations. Brownian displacements are drawn from a superposition of two independent samples: a wave-space (far-field or long-ranged) contribution, computed using techniques from fluctuating hydrodynamics and non-uniform fast Fourier transforms; and a real-space (near-field or short-ranged) correction, computed using a Krylov subspace method. The combined computational complexity of drawing these two independent samples scales linearly with the number of particles. The proposed method circumvents the super-linear scaling exhibited by all known iterative sampling methods applied directly to the RPY tensor that results from the power law growth of the condition number of tensor with the number of particles. For geometrically dense microstructures (fractal dimension equal three), the performance is independent of volume fraction, while for tenuous microstructures (fractal dimension less than three), such as gels and polymer solutions, the performance improves with decreasing volume fraction. This is in stark contrast with other related linear-scaling methods such as the force coupling method and the fluctuating immersed boundary method, for which performance degrades with decreasing volume fraction. Calculations for hard sphere dispersions and colloidal gels are illustrated and used to explore the role of microstructure on performance of the algorithm. In practice, the logarithmic part of the predicted scaling is not observed and the algorithm scales linearly for up to 4×10 6 particles, obtaining speed ups of over an order of magnitude over existing iterative methods, and making the cost of computing Brownian displacements comparable to the cost of computing deterministic displacements in BD simulations. Finally, a high-performance implementation employing non-uniform fast Fourier transforms implemented on graphics processing units and integrated with the software package HOOMD-blue is used for benchmarking.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1999

Computer Modeling of Sand Transport on Mars Using a Compart-Mentalized Fluids Algorithm (CFA)

It has been postulated that aeolian transport on Mars may be significantly different from that on Earth. From laboratory experiments simulating martian grain transport [2], it has been observed that (saltating) grains striking the bed can cause hundreds of secondary reptation trajectories when impact occurs at speeds postulated for Mars. Some of the ballistically induced trajectories "die ouf' and effectively join the ranks on the creep population that is merely nudged along by impact. Many of the induced reptation trajectories, however, are sufficiently high for the grains to become part of the saltation load (it is irrelevant to the boundary layer how a grain attained its initial lift force). When these grains, in turn, strike the surface, they too are capable of inducing more reptating grains. This cascading effect has been discussed in connection with terrestrial aeolian transport in an attempt to dispel the notion that sand motion is divisible only into creep and saltation loads. On Earth, only a few grains are splashed by impact. On Mars, it may be hundreds. We developed a computer model to address this phenomenon because there are some important ramifications: First, this ratio may mean that martian aeolian transport is dominated by reptation flux rather than saltation. On Earth, the flux would be a roughly balanced mixture between reptation/creep and saltation. On Venus, there would be no transport other than by saltation. In other words, an understanding of planetary aeolian processes may not be necessarily understood by extrapolating from the "Earth case", with only gravity and atmospheric density/viscosity being considered as variables. Second, the reptation flux on Mars may be self sustaining, so that little input is required by the wind once transport has been initiated. The number of grains saturating the boundary layer near the bed may mean that average grain speed on Mars might conceivably be less than that on Earth. This would say much for models of sand comminution on Mars. A multiple-grain transport model using just the equations of grain motion describing lift and drag is impossible to develop owing to stochastic effects --the very effects we wish to model. Also, unless we were to employ supercomputing techniques and extremely complex computer codes that could deal with millions of grains simultaneously, it would also be difficult to model grain transport if we attempted to consider every grain in motion. No existing computer models were found that satisfactorily used the equations of motion to arrive at transport flux numbers for the different populations of saltation and reptation. Modeling all the grains in a transport system was an intractable problem within our resources, and thus we developed what we believe to be a new modeling approach to simulating grain transport. The CFA deals with grain populations, but considers them to belong to various compartmentalized fluid units in the boundary layer. In this way, the model circumvents the multigrain problem by dealing primarily with the consequences of grain transport --momentum transfer between air and grains, which is the physical essence of a dynamic grain-fluid mixture. We thus chose to model the aeolian transport process as a superposition of fluids. These fluids include the air as well as particle populations of various properties. The prime property distinguishing these fluids is upward and downward grain motion. In a normal saltation trajectory, a grain's downwind velocity increases with time, so a rising grain will have a smaller downwind velocity than a failing grain. Because of this disparity in rising and falling grain proper-ties, it seemed appropriate to track these as two separate grain populations within the same physical space. The air itself can be considered a separate fluid superimposed within and interacting with the various grain-cloud "fluids". Additional informaiton is contained in the original.

Marshall, J.↗