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DOE OSTI2024

Structure Factors for Hot Neutron Matter from Ab Initio Lattice Simulations with High-Fidelity Chiral Interactions

We present the first ab initio lattice calculations of spin and density correlations in hot neutron matter using high-fidelity interactions at next-to-next-to-next-to-leading order in chiral effective field theory. These correlations have a large impact on neutrino heating and shock revival in core-collapse supernovae and are encapsulated in functions called structure factors. Unfortunately, calculations of structure factors using high-fidelity chiral interactions were well out of reach using existing computational methods. In this Letter, we solve the problem using a computational approach called the rank-one operator (RO) method. The RO method is a general technique with broad applications to simulations of fermionic many-body systems. It solves the problem of exponential scaling of computational effort when using perturbation theory for higher-body operators and higher-order corrections. Using the RO method, we compute the vector and axial static structure factors for hot neutron matter as a function of temperature and density. Here, the ab initio lattice results are in good agreement with virial expansion calculations at low densities but are more reliable at higher densities. Random phase approximation codes used to estimate neutrino opacity in core-collapse supernovae simulations can now be calibrated with ab initio lattice calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Improving Medication Regimen Recommendation for Parkinson’s Disease Using Sensor Technology

Parkinson’s disease medication treatment planning is generally based on subjective data obtained through clinical, physician-patient interactions. The Personal KinetiGraph™ (PKG) and similar wearable sensors have shown promise in enabling objective, continuous remote health monitoring for Parkinson’s patients. In this proof-of-concept study, we propose to use objective sensor data from the PKG and apply machine learning to cluster patients based on levodopa regimens and response. The resulting clusters are then used to enhance treatment planning by providing improved initial treatment estimates to supplement a physician’s initial assessment. We apply k-means clustering to a dataset of within-subject Parkinson’s medication changes—clinically assessed by the MDS-Unified Parkinson’s Disease Rating Scale-III (MDS-UPDRS-III) and the PKG sensor for movement staging. A random forest classification model was then used to predict patients’ cluster allocation based on their respective demographic information, MDS-UPDRS-III scores, and PKG time-series data. Clinically relevant clusters were partitioned by levodopa dose, medication administration frequency, and total levodopa equivalent daily dose—with the PKG providing similar symptomatic assessments to physician MDS-UPDRS-III scores. A random forest classifier trained on demographic information, MDS-UPDRS-III scores, and PKG time-series data was able to accurately classify subjects of the two most demographically similar clusters with an accuracy of 86.9%, an F1 score of 90.7%, and an AUC of 0.871. A model that relied solely on demographic information and PKG time-series data provided the next best performance with an accuracy of 83.8%, an F1 score of 88.5%, and an AUC of 0.831, hence further enabling fully remote assessments. These computational methods demonstrate the feasibility of using sensor-based data to cluster patients based on their medication responses with further potential to assist with medication recommendations.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Predicted Ferromagnetism in Discovered Co–Bi Binary Phases

Binary solid-state materials offer unique insight into how the interplay of factors such as stoichiometry and bonding interactions affects magnetism and electronic properties. In this work, we considered systems where a transition metal provides the spin moment and a heavy main group element bolsters strong spin–orbit coupling. Within this context, cobalt, a known component of permanent magnets, and bismuth, functionally the heaviest element stable to radioactive decay, form a compelling combination. The Co–Bi system has been previously shown to exhibit superconductivity in a phase recovered from high pressure. We expected the Co−Bi system could also be ferromagnetic, resulting in two sets of compounds within one chemical system, one superconducting and one ferromagnetic. Subsequently, we investigated the Co–Bi system through both experimental and theoretical approaches to discover new candidates for permanent magnets. Ab initio random structure searching calculations identified five new compounds with diverse structural motifs that may form at higher pressures than previously reported. Experimental high-pressure synthesis yielded four compounds: α-CoBi, α-CoBi 2 , β-CoBi, and β-CoBi 2 . Three of these phases, α-CoBi 2 , β-CoBi, and β-CoBi 2 , were consistent with the calculated structures, corresponding to a 60% success rate for our structure search and underscoring the strength of combining computation with experiment. Theory predicts β-CoBi and β-CoBi2 are ferromagnetic, with β-CoBi possessing larger magnetocrystalline anisotropy energy than familiar permanent magnets such as CoPt and Nd–Fe–B. These results suggest the Co–Bi system could be a platform for understanding the factors that underpin magnetism and, to an extent, superconductivity in a chemically simple binary system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Classical field approximation of ultralight dark matter: Quantum break times, corrections, and decoherence

The classical field approximation is widely used to better understand the predictions of ultralight dark matter. Here, in this work, we use the truncated Wigner approximation method to test the classical field approximation of ultralight dark matter. This method approximates a quantum state as an ensemble of independently evolving realizations drawn from its Wigner function. The method is highly parallelizable and allows the direct simulation of quantum corrections and decoherence times in systems many times larger than have been previously studied in reference to ultralight dark matter. Our study involves simulation of systems in 1, 2, and 3 spatial dimensions. We simulate three systems, the condensation of a Gaussian random field in three spatial dimensions, a stable collapsed object in three spatial dimensions, and the merging of two stable objects in two spatial dimensions. We study the quantum corrections to the classical field theory in each case. We find that quantum corrections grow exponentially during nonlinear growth with the timescale being approximately equal to the system dynamical time. In stable systems the corrections grow quadratically. We also find that the primary effect of quantum corrections is to reduce the amplitude of fluctuations on the de Broglie scale in the spatial density. Finally, we find that the timescale associated with decoherence due to gravitational coupling to baryonic matter is at least as fast as the quantum corrections due to gravitational interactions. These results are consistent with the predictions of the classical field theory being accurate.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Large-eddy Simulations of Spray Variability Effects on Flow Variability in a Direct-injection Spark-ignition Engine Under Non-combusting Operating Conditions

Large-eddy Simulations (LES) have been carried out to investigate spray variability and its effect on cycle-to-cycle flow variability in a direct-injection spark-ignition (DISI) engine under non-reacting conditions. Initial simulations were performed of an injector in a constant volume spray chamber to validate the simulation spray set-up. Comparisons showed good agreement in global spray measures such as the penetration. Local mixing data and shot-to-shot variability were also compared using Rayleigh-scattering images and probability contours. The simulations were found to reasonably match the local mixing data and shot-to-shot variability using a random-seed perturbation methodology. After validation, the same spray set-up with only minor changes was used to simulate the same injector in an optically accessible DISI engine. Particle Image Velocimetry (PIV) measurements were used to quantify the flow velocity in a horizontal plane intersecting the spark plug gap. The engine was operated in a skip-fired operating mode and comparisons focused on cycles that included fuel injection, but no spark event and therefore no combustion. 105 total LES engine cycles were simulated using a parallel cycle simulation approach and 3 different perturbation methods in an attempt to isolate the effects of shot-to-shot spray variability and the initial turbulent flow field as well as their interaction effects on overall engine CCVs. The experimental mean and standard deviations were reasonably well matched by the simulations, though quantitative comparisons near the injection event during the intake stroke were difficult due to the high uncertainty in the PIV measurements at these crank angles. The 3 simulation perturbation methods resulted in very similar results, though further analysis found the current parallel cycle approach may be limiting the ability of the simulations to isolate the spray and flow effects.

Cycle-to-cycle Variability↗

DOE OSTI2022

A generalized 3D elastic model for nanoscale, self-assembled oxide-metal thin films with pillar-in-matrix configurations

In recent years, functional oxide-metal based vertically aligned nanocomposite (VAN) thin films have gained interest due to their intriguing physical properties and multifunctionalities stemming from the complex interactions between the two phases in the film and the substrate. In this work, we develop a model for studying the energetics of these thin film systems, including the effects of both lattice mismatch and capillary forces due to interface curvature. Each phase is incorporated into the model using a phase indicator function, and we introduce the capillary forces as body forces using a vector density representation of the interface. The model is implemented using the finite element method to study the deformation of the thin film which is composed of Au nanopillars embedded in a La 0.7 Sr 0.3 MnO 3 (LSMO) matrix on an SrTiO 3 (STO) substrate. Further, the results suggest that the total energy is lowest for random configurations of pillars compared to ordered square and hexagonal lattice configurations, consistent with the random distribution of pillars found in experiments. Furthermore, we find that the interfacial energy dominates the total energy of each configuration, suggesting that interfacial energy in the system is an important design parameter for nanocomposite growth, along with the lattice mismatch.

36 MATERIALS SCIENCE↗

NASA NTRS1994

Software reliability studies

There are many software reliability models which try to predict future performance of software based on data generated by the debugging process. Our research has shown that by improving the quality of the data one can greatly improve the predictions. We are working on methodologies which control some of the randomness inherent in the standard data generation processes in order to improve the accuracy of predictions. Our contribution is twofold in that we describe an experimental methodology using a data structure called the debugging graph and apply this methodology to assess the robustness of existing models. The debugging graph is used to analyze the effects of various fault recovery orders on the predictive accuracy of several well-known software reliability algorithms. We found that, along a particular debugging path in the graph, the predictive performance of different models can vary greatly. Similarly, just because a model 'fits' a given path's data well does not guarantee that the model would perform well on a different path. Further we observed bug interactions and noted their potential effects on the predictive process. We saw that not only do different faults fail at different rates, but that those rates can be affected by the particular debugging stage at which the rates are evaluated. Based on our experiment, we conjecture that the accuracy of a reliability prediction is affected by the fault recovery order as well as by fault interaction.

Hoppa, Mary Ann↗

DOE OSTI2018

On thermalization in the SYK and supersymmetric SYK models

The eigenstate thermalization hypothesis is a compelling conjecture which strives to explain the apparent thermal behavior of generic observables in closed quantum systems. Although we are far from a complete analytic understanding, quantum chaos is often seen as a strong indication that the ansatz holds true. In this paper, we address the thermalization of energy eigenstates in the Sachdev-Ye-Kitaev model, a maximally chaotic model of strongly-interacting Majorana fermions. We numerically investigate eigenstate thermalization for specific few-body operators in the original SYK model as well as its N = 1 supersymmetric extension and find evidence that these models satisfy ETH. In conclusion, we discuss the implications of ETH for a gravitational dual and the quantum information-theoretic properties of SYK it suggests.

2D Gravity↗

NASA NTRS1973

Plasma electrolytes, pH, and ECG during and after exhaustive exercise.

Ten men worked on a bicycle ergometer at increasing work loads to exhaustion in 15 min. Each performed one test breathing air and another with added CO2 in random sequence. ECG was recorded during exercise and for 30 min of recovery. Arterial samples for blood gases, pH, and electrolytes were drawn at rest, in the last minute of exercise and at 1, 4, 10, 20, and 30 min thereafter. A striking increase in the amplitude of T and P waves was observed reaching a maximum in the first 2 min after exercise. All electrolytes measured were increased at the end of exercise, most markedly potassium (60%) and phosphorus (53%). Potassium dropped faster than all others to below resting values in 4 min coinciding with the lowest levels in plasma bicarbonate. ECG alterations were not closely related in time with any single factor such as potassium, but appeared to reflect an interaction of the transient mineral and acid-base imbalance during and immediately following exhaustive exercise.

Coester, N.↗

DOE OSTI2018

Locality-aware and load-balanced static task scheduling for MapReduce

Task scheduling for MapReduce jobs has been an active area of research with the objective of decreasing the amount of data transferred during the shuffle phase via exploiting data locality. In the literature, generally only the scheduling of reduce tasks is considered with the assumption that scheduling of map tasks is already determined by the input data placement. However, in cloud or HPC deployments of MapReduce, the input data is located in a remote storage and scheduling map tasks gains importance. Here, we propose models for simultaneous scheduling of map and reduce tasks in order to improve data locality and balance the processors’ loads in both map and reduce phases. Our approach is based on graph and hypergraph models which correctly encode the interactions between map and reduce tasks. Partitions produced by these models are decoded to schedule map and reduce tasks. A two-constraint formulation utilized in these models enables balancing processors’ loads in both map and reduce phases. The partitioning objective in the hypergraph models correctly encapsulates the minimization of data transfer when a local combine step is performed prior to shuffle, whereas the partitioning objective in the graph models achieve the same feat when a local combine is not performed. Here, we show the validity of our scheduling on the MapReduce parallelizations of two important kernel operations – sparse matrix–vector multiplication (SpMV) and generalized sparse matrix–matrix multiplication (SpGEMM) – that are widely encountered in big data analytics and scientific computations. Compared to random scheduling, our models lead to tremendous savings in data transfer by reducing data traffic from several hundreds of megabytes to just a few megabytes in the shuffle phase and consequently leading up to 2.6x and 4.2x speedup for SpMV and SpGEMM, respectively.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians

Motivated by the ground state structure of quantum models with all-to-all interactions such as mean-field quantum spin glass models and the Sachdev-Ye-Kitaev (SYK) model, we propose a tensor network architecture which can accomodate volume law entanglement and a large ground state degeneracy. We call this architecture the non-local renormalization ansatz (NoRA) because it can be viewed as a generalization of MERA, DMERA, and branching MERA networks with the constraints of spatial locality removed. We argue that the architecture is potentially expressive enough to capture the entanglement and complexity of the ground space of the SYK model, thus making it a suitable variational ansatz, but we leave a detailed study of SYK to future work. We further explore the architecture in the special case in which the tensors are random Clifford gates. Here the architecture can be viewed as the encoding map of a random stabilizer code. We introduce a family of codes inspired by the SYK model which can be chosen to have constant rate and linear distance at the cost of some high weight stabilizers. We also comment on potential similarities between this code family and the approximate code formed from the SYK ground space.

Physics↗

DOE OSTI2020

Anisotropic Characterizations of Electrospun PAN Nanofiber Mats Using Design of Experiments

This paper deals with the dielectric and mechanical characterizations of polyacrylonitrile (PAN)-aligned electrospun nanofiber mats. A two factor three level full factorial experiment is conducted to understand the effect of various parameters on dielectric and mechanical responses. These responses are recorded against randomly oriented and aligned nanofiber mats. Improved properties of electrospun mats have applications in the field of energy storage and nanocomposite reinforcement. Dielectric and mechanical characterizations of PAN mats are vital, as the aligned electrospun mats were found to be useful in advanced energy and mechanical reinforcement applications. Therefore, it is paramount to understand the effects of system parameters to these properties. The design of experiment (DoE) includes two factors and three level full factorial experiments with concentrations of PAN solutions at 8 wt.%, 9 wt.%, and 10 wt.%, and speed of the rotating mandrel (collector) at 3 volt (V), 4 V, and 5 V inputs. The electric field intensity used in the experiment is 1 kV/cm. DoE is conducted to understand the nonlinear interactions of parameters to these responses. The dielectric and mechanical characterizations of 8 wt.%, 9 wt.%, and 10 wt.% with different speeds for the original and improved systems are discussed. It was observed that at 9 wt.% and at all mandrel speeds, the dielectric and tensile properties are optimum.

42 ENGINEERING↗

NASA NTRS1999

A Critical Examination of Wind-Wave Spectral Functional Form

Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. The spectral forms of the ocean waves are very different. This new method offers the first physical meaningful view of the wave spectrum. Data from laboratory and field will be presented to illustrate the differences.

Huang, Norden E.↗

DOE OSTI2018

Influence of hydrophilic groups and metal-ion adsorption on polymer-chain conformation of amidoxime-based uranium adsorbents

In this study, we focus on the influence of hydrophilic groups and metal-ion loading on adsorbent polymer conformation, which controls access to adsorption sites and may limit adsorption capacity. Gaining a better understanding of the factors that influence conformation may yield higher-capacity adsorbents. Polyamidoxime (PAO), deuterated-PAO polyacrylic acid diblock copolymers (d-PAO-b-PAA), and randomly configured copolymers (PAO-co-PAA) were synthesized and characterized by neutron reflectometry in air and D 2 O. For d-PAO-b-PAA, characterization was also performed after alkali conditioning and in simulated seawater. PAO and PAO-co-PAA, with similar molecular weight and grafting density, extended from 95-Å thickness in air to 180 and 280-Å in D 2 O, respectively. This result suggests that polymer swelling may cause the additional adsorption capacity observed when polymer hydrophilicity increases. Two d-PAO-b-PAA samples, A and B, with a d-PAO thickness of 55-Å swelled to 110-Å and 140-Å, respectively, with an overall thickness increase of ~160% in D 2 O. After alkali conditioning, molecular interactions increased the density of PAA near the PAO-PAA interface, while the d-PAO thickness only decreased by ~10 Å. The d-PAO thickness of both samples declined to ~90-Å after adsorption in simulated seawater due to polymer-chain crosslinking. In conclusion, these results are expected to aid in improving adsorbent synthesis to increase uranium capacity.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2017

Phase stability, ordering tendencies, and magnetism in single-phase fcc Au-Fe nanoalloys

Bulk Au-Fe alloys separate into Au-based fcc and Fe-based bcc phases, but L1 0 and L1 2 orderings were reported in single-phase Au-Fe nanoparticles. Motivated by these observations, we study the structural and ordering energetics in this alloy by combining density functional theory (DFT) calculations with effective Hamiltonian techniques: a cluster expansion with structural filters, and the configuration-dependent lattice deformation model. The phase separation tendency in Au-Fe persists even if the fcc-bcc decomposition is suppressed. The relative stability of disordered bcc and fcc phases observed in nanoparticles is reproduced, but the fully ordered L1 0 AuFe, L1 2 Au 3 Fe, and L1 2 AuFe 3 structures are unstable in DFT. But, a tendency to form concentration waves at the corresponding [001] ordering vector is revealed in nearly-random alloys in a certain range of concentrations. Furthermore, this incipient ordering requires enrichment by Fe relative to the equiatomic composition, which may occur in the core of a nanoparticle due to the segregation of Au to the surface. Effects of magnetism on the chemical ordering are also discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2022

A Machine‐Learning‐Assisted Stochastic Cloud Population Model as a Parameterization of Cumulus Convection

Abstract A machine‐learning‐assisted stochastic cloud population model is coupled with the Advanced Research Weather Research and Forecasting (WRF) model to represent fluctuations in the cloud‐base mass flux associated with the life cycles and interactions among cumulus convection cells. In this cloud population model, the size distribution and the associated cloud‐base mass flux of the convective cells are related to their previous state and to the change in the total convective area via a transition function. The convective area tendency in turn is assumed to depend on the cloud‐base mass flux that is resolved by the host WRF model. The transition function is represented by a single hidden‐layer neural network trained by the evolution of convective cell size distributions in a 1‐km grid‐spacing WRF simulation run over the Australian Monsoon region. At every grid point of the host model, the cloud population model predicts the cell size and cloud‐base mass flux distributions from which a random sample of cells is fed to an entraining parcel model that calculates precipitation as well as the associated liquid water potential temperature and total moisture tendencies. These tendencies are averaged over the cells and provided to the host model. Several regional simulations are performed over tropical and midlatitude domains to test this as a potential approach to scale‐aware parameterization. It is shown that such an approach could be a new promising path to simulating realistic precipitation statistics and propagation of precipitation associated with the Madden‐Julian Oscillation while maintaining realistic depictions of the diurnal cycle over both land and ocean.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2009

Spatial and Alignment Analyses for a Field of Small Volcanic Vents South of Pavonis Mons and Implications for the Tharsis Province, Mars

A field of small volcanic vents south of Pavonis Mons was mapped with each vent assigned a two-dimensional data point. Nearest neighbor and two-point azimuth analyses were applied to the resulting location data. Nearest neighbor results show that vents within this field are spatially random in a Poisson sense, suggesting that the vents formed independently of each other without sharing a centralized magma source at shallow depth. Two-point azimuth results show that the vents display north-trending alignment relationships between one another. This trend corresponds to the trends of faults and fractures of the Noachian-aged Claritas Fossae, which might extend into our study area buried beneath more recently emplaced lava flows. However, individual elongate vent summit structures do not consistently display the same trend. The development of the volcanic field appears to display tectonic control from buried Noachian-aged structural patterns on small, ascending magma bodies while the surface orientations of the linear vents might reflect different, younger tectonic patterns. These results suggest a complex interaction between magma ascension through the crust, and multiple, older, buried Tharsis-related tectonic structures.

Bleacher, Jacob E.↗

NASA NTRS2001

Probabilistic Structural Analysis and Reliability Using NESSUS With Implemented Material Strength Degradation Model

This project included both research and education objectives. The goal of this project was to advance innovative research and education objectives in theoretical and computational probabilistic structural analysis, reliability, and life prediction for improved reliability and safety of structural components of aerospace and aircraft propulsion systems. Research and education partners included Glenn Research Center (GRC) and Southwest Research Institute (SwRI) along with the University of Texas at San Antonio (UTSA). SwRI enhanced the NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) code and provided consulting support for NESSUS-related activities at UTSA. NASA funding supported three undergraduate students, two graduate students, a summer course instructor and the Principal Investigator. Matching funds from UTSA provided for the purchase of additional equipment for the enhancement of the Advanced Interactive Computational SGI Lab established during the first year of this Partnership Award to conduct the probabilistic finite element summer courses. The research portion of this report presents the cumulation of work performed through the use of the probabilistic finite element program, NESSUS, Numerical Evaluation and Structures Under Stress, and an embedded Material Strength Degradation (MSD) model. Probabilistic structural analysis provided for quantification of uncertainties associated with the design, thus enabling increased system performance and reliability. The structure examined was a Space Shuttle Main Engine (SSME) fuel turbopump blade. The blade material analyzed was Inconel 718, since the MSD model was previously calibrated for this material. Reliability analysis encompassing the effects of high temperature and high cycle fatigue, yielded a reliability value of 0.99978 using a fully correlated random field for the blade thickness. The reliability did not change significantly for a change in distribution type except for a change in distribution from Gaussian to Weibull for the centrifugal load. The sensitivity factors determined to be most dominant were the centrifugal loading and the initial strength of the material. These two sensitivity factors were influenced most by a change in distribution type from Gaussian to Weibull. The education portion of this report describes short-term and long-term educational objectives. Such objectives serve to integrate research and education components of this project resulting in opportunities for ethnic minority students, principally Hispanic. The primary vehicle to facilitate such integration was the teaching of two probabilistic finite element method courses to undergraduate engineering students in the summers of 1998 and 1999.

Bast, Callie C.↗