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DOE OSTI2024

Random projection using random quantum circuits

The random sampling task performed by Google's Sycamore processor gave us a glimpse of the “quantum supremacy era.” This has definitely shed some light on the power of random quantum circuits in this abstract task of sampling outputs from the (pseudo)random circuits. In this paper, we explore a practical near-term use of local random quantum circuits in dimensional reduction of large low-rank data sets. We make use of the well-studied dimensionality reduction technique called the random projection method. This method has been extensively used in various applications such as image processing, logistic regression, entropy computation of low-rank matrices, etc. We prove that the matrix representations of local random quantum circuits with sufficiently shorter depths [ ∼ O ( n ) ] serve as good candidates for random projection. We demonstrate numerically that their projection abilities are not far off from the computationally expensive classical principal components analysis on MNIST and CIFAR-100 image datasets. We also benchmark the performance of quantum random projection against the commonly used classical random projection in the tasks of dimensionality reduction of image data sets and computing von Neumann entropies of large low-rank density matrices. And finally, using variational quantum singular value decomposition, we demonstrate a near-term implementation of extracting the singular vectors with dominant singular values after quantum random projecting a large low-rank matrix to lower dimensions. All such numerical experiments unequivocally demonstrate the ability of local random circuits to randomize a large Hilbert space at sufficiently shorter depths with robust retention of properties of large data sets in reduced dimensions. Published by the American Physical Society 2024

Kumaran, Keerthi (ORCID:0009000949125721)↗

DOE OSTI2020

Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. Additionally, the routinely used single-shot GW approximation (G 0 W 0 ) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth checking how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of noninteracting G such that only diagonal elements are retained, whereas the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle band gap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7%, which validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms such as the vertex correction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model

We analyze a two-body non-Hermitian two-site Sachdev–Ye–Kitaev (SYK) model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of second-order phase transitions, which is a consequence of the factorization of the partition function into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways: first in terms of the single-particle energies and second by solving the Schwinger–Dyson equations of the two-site model. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can also be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to the chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases, the free energy is determined by the spectral density. The chaotic four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. On the other hand, the low-temperature free energy of the two-body SYK model is not flat; in fact, it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive in the low-temperature phase, which most likely is a consequence of the non-hermiticity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

The microstructure and He + ion irradiation behavior of novel low-activation W-Ta-Cr-V refractory high entropy alloy for nuclear applications

Microstructure and nanohardness of a nearly equimolar W-Ta-Cr-V high entropy alloy (HEA), as well as its irradiation response under He + irradiation, were investigated. The single-phase body-centered cubic nanostructured alloy with a 1 µm thick layer was fabricated on a silicon substrate using a magnetron sputtering method. The HEA film has a complex microstructure consisting of micrometric domains that exhibit internal nanostructure controlled by their crystal orientation. The measured nanohardness of the W-Ta-Cr-V alloy is 13 ± 2 GPa, which significantly exceeds the hardness of nanocrystalline tungsten as a result of the high solid-solution strengthening effect. In order to evaluate the irradiation resistance of the HEA film, the material was irradiated with 200 keV He + ions at room temperature, with two different ion fluences: 1 × 10 16 and 5 × 10 16 ions/cm 2 . Using transmission electron microscopy, a high density of extremely fine He bubbles is observed that were uniformly distributed in the matrix. The increase of He + ion fluence increased the density of bubbles, whereas their size remained at a similar level, which indicates that the damage proceeds by the nucleation of additional He bubbles, not by their growth.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Growth of Cd 0.9 Zn 0.1 Te 1-y Se y Single Crystals for Room Temperature Gamma-Ray Detection

Quaternary Cd 0.9 Zn 0.1 Te 1-y Sey (CZTS) single crystals, a novel room-temperature nuclear radiation detector semiconductor material, have been grown using a modified vertical Bridgman method (VBM) and a travelling heater method (THM). The percentage concentration of selenium in the VBM-grown crystal was 3% and that in the THM-grown crystal was 2%. While the THM Frisch collar detector (4.4 × 4.4 × 10.7 mm 3 ) produced a highly resolved pulse height spectra (PHS) with a resolution of ~1.06% for 662-keV gamma rays without any correction, the VBM-grown detector (10 × 10 × 2 mm 3 ) offered a high energy resolution of ~2% after application of a digital biparametric correction. The high-resolution performance of these detectors has been attributed to the addition of Se in the Cd 0.9 Zn 0.1 Te (CZT) matrix. Ab-initio calculations based on density functional theory (DFT) also confirmed that the addition of Se in the CZT matrix helps to reduce the formation of TeCd and the TeZn anti-sites. The VBM-grown crystals were characterized using powder x-ray diffraction (XRD) and energy dispersive x-ray spectroscopy (EDS). While XRD results revealed sharp diffraction peaks confirming the crystalline nature of the grown crystal, the EDS results confirmed the targeted stoichiometry of the elemental composition. The bulk resistivity of the grown crystal was calculated to be ~3 × 10 10 Ω-cm from current-voltage characteristics recorded at room temperature in a planar configuration, ensuring that the grown CZTS crystals have low dark current as required for detector-grade crystals.

42 ENGINEERING↗

DOE OSTI2023

Low-velocity repeated impact behaviors of Polymer Fiber Reinforced Plastics (PFRPs)

Modern fiber-reinforced composites have become ubiquitous across multiple industries due to their excellent weight-to-strength ratio. Typically glass or carbon fibers are widely used. While Glass or Carbon Fiber-Reinforced Plastics (GFPRs or CFPRs) have good stiffness, strength, and fatigue life, they are expensive and difficult to recycle. Researchers are exploring Polymer Fiber-Reinforced Plastics (PFRPs) as an alternative solution. PFRPs utilize polymer fibers and a polymer matrix. A wide range of materials options is available, including low-cost thermoplastics such as polyethylene or polypropylene. These thermoplastics are easy to handle and recyclable without special methods. Manufacturing parts using thermoplastics are well-established as well. However, their mechanical performances have not been extensively studied compared to GFRPs or CFRPs. This study examines the low-velocity impact resistance of PFRPs made of different thermoplastics. The low-velocity impacts are applied through a drop-weight tower. The experiment is divided into two cases: a single perforation impact and low-energy repeated impacts. Energy absorption and the number of impacts to failure are measured. The results are compared to traditional CFRPs which have a thermoset matrix. The PFRPs demonstrate energy absorption capabilities comparable to or greater than those of CFRPs with respect to specimen thickness and density. Additionally, the PFRPs show significantly higher impacts-to-failure than the CFRPs in low-energy repeated impact tests. This is particularly noteworthy considering that the PFRPs are much simpler and more economical to manufacture than CFRPs. To further

Ko, Seunghyun↗

DOE OSTI2024

In Situ Prediction of Microstructure and Mechanical Properties in Laser-Remelted Al-Si Alloys: Towards Enhanced Additive Manufacturing

Laser surface remelting of aluminum alloys has emerged as a promising technique to enhance mechanical properties through refined microstructures. This process involves rapid cooling rates ranging from 10 3 to 10 8 °C/s, which increase solid solubility within aluminum alloys, shifting their eutectic composition to a larger value of silicon content. Consequently, the resulting microstructure combines a strengthened aluminum matrix with silicon fibers. This study focuses on the laser scanning of Al-Si aluminum alloy to reduce the size of aluminum matrix spacings and transform fibrous silicon particles from micrometer to nanometer dimensions. Analysis revealed that the eutectic structure contained 17.55% silicon by weight, surpassing the equilibrium eutectic composition of 12.6% silicon. Microstructure dimensions within the molten zones, termed ‘melt pools’, were extensively examined using Scanning Electron Microscopy (SEM) at intervals of approximately 20 μm from the surface. A notable increase in hardness, exceeding 50% compared to the base plate, was observed in the melt pool regions. Thus, it is exemplified that laser surface remelting introduces a novel strengthening mechanism in the alloy. Moreover, this study develops an in situ method for predicting melt pool properties and dimensions. A predictive model is proposed, correlating energy density and spectral signals emitted during laser remelting with mechanical properties and melt pool dimensions. This method significantly reduces characterization time from days to seconds, offering a streamlined approach for future studies in additive manufacturing.

36 MATERIALS SCIENCE↗

DOE OSTI2022

The many-body expansion for metals. I. The alkaline earth metals Be, Mg, and Ca

We examine the many-body expansion (MBE) for alkaline earth metal clusters, Be n , Mg n , Ca n ( n = 4, 5, 6), at the Møller–Plesset second order perturbation theory, coupled-cluster singles and doubles with perturbative triples, multi-reference perturbation theory, and multi-reference configuration interaction levels of theory. The magnitude of each term in the MBE is evaluated for several geometrical configurations. We find that the behavior of the MBE for these clusters depends strongly on the geometrical arrangement and, to a lesser extent, on the level of theory used. Another factor that affects the MBE is the in situ (ground or excited) electronic state of the individual atoms in the cluster. For most geometries, the three-body term is the largest, followed by a steady decrease in absolute energy for subsequent terms. Though these systems exhibit non-negligible multi-reference effects, there was little qualitative difference in the MBE when employing single vs multi-reference methods. Useful insights into the connectivity and stability of these clusters have been drawn from the respective potential energy surfaces and quasi-atomic orbitals for the various dimers, trimers, and tetramers. Through these analyses, we investigate the similarities and differences in the binding energies of different-sized clusters for these metals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Constraining Hamiltonians from chiral effective field theory with neutron-star data

Multi-messenger observations of neutron stars (NSs) and their mergers have placed strong constraints on the dense-matter equation of state (EOS). The EOS, in turn, depends on microscopic nuclear interactions that are described by nuclear Hamiltonians. These Hamiltonians are commonly derived within chiral effective field theory (EFT). Ideally, multi-messenger observations of NSs could be used to directly inform our understanding of EFT interactions, but such a direct inference necessitates millions of model evaluations. This is computationally prohibitive because each evaluation requires us to calculate the EOS from a Hamiltonian by solving the quantum many-body problem with methods such as auxiliary-field diffusion Monte Carlo (AFDMC), which provides very accurate and precise solutions but at a significant computational cost. Additionally, we need to solve the stellar structure equations for each EOS which further slows down each model evaluation by a few seconds. In this work, we combine emulators for AFDMC calculations of neutron matter, built using parametric matrix models, and for the stellar structure equations, built using multilayer perceptron neural networks, with the PyCBC data-analysis framework to enable a direct inference of coupling constants in an EFT Hamiltonian using multi-messenger observations of NSs. We find that astrophysical data can provide informative constraints on two-nucleon couplings despite the high densities probed in NS interiors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Hadron spectroscopy of pseudoscalar and vector meson photoproduction using linearly polarised photons at CLAS

The field of hadron spectroscopy is informed by experiments which study excited states of the nucleon by detecting the decay products following excitation with a hadronic, leptonic or electromagnetic probe. Experiments using a polarised beam of photons provide an important contribution to the world data. This thesis describes the analysis of data from one such experiment, the CEBAF Large Acceptance Spectrometer at Jefferson Laboratory, Virginia, USA. In the experiment, an incident beam of electrons passes through a diamond radiator producing a linearly polarised photon beam of energy from 1.1 to 2.1 GeV on a liquid hydrogen target. The analysis method and results for two reaction channels are presented. In the first analysis, the polarisation observables {?, P, T, Ox, Oz} for the reaction ??? p ? K0 S ?+ are extracted simultaneously using likelihood sampling with Markov-Chain Monte-Carlo. The results are presented as angular distributions (cos ?K0S) for bins in photon energy E? for a total of 21 bins. The values extracted for T , Ox and Oz are a first measurement of these quantities for this reaction and the beam asymmetry (?) measurement supplements the one previous measurement for this quantity and extends the energy range over which it has been extracted. The measurement of the recoil polarisation, P, is consistent with previous measurements. In a second analysis, the spin density matrix elements (SDMEs) for ? p ? p ? are extracted using similar analysis techniques. The results are presented as angular distributions (cos ?? ) for bins in photon energy E? for a total of 24 bins. This work is the first to extract all nine SDMEs for the full angular range of the ? meson production. A comparison is made to the predictions of the Vector Meson Dominance (VMD) model and the results provide evidence for contributing processes other than VMD, particularly at more backward angles of the ? meson production. The data also indicate non-helicity conserving process in both the s-channel and the t-channel. The results from the first analysis have been passed to the Juelich-Bonn theory group and the effect of including the new data within their dynamical coupled channel model is described. Several nucleon resonances are affected and the impact on the pole positions, widths and photon decay amplitudes of the affected resonances is described.

Clark, Louise↗

DOE OSTI2024

Direct Feed High-Level Waste APPS Model Glass Testing (DFHLW APPS) Matrix

This report summarizes the data collected during the batching and melting of the Direct Feed High-Level Waste APPS Model Glass Matrix (DFHLW APPS) to serve as a quality-assured validation of the Aspen Process Performance Simulation (APPS) formulation method. Of 15 glasses tested, 12 satisfied all target property constraints. Two glasses, APPS-05 and -06, formed nepheline on canister centerline cooling heat-treatment and failed the Product Consistency Test response limits. Glass APPS-07-2 formed unacceptably high concentrations of crystals (primarily Na3Nd(PO4)2) when heat treated at 950 °C. All other glasses were found to be satisfactory. The measured property values were compared to predicted values from a set of current models. In many cases the current models were found to be inadequate for design of DFHLW glasses. These models are being adjusted to correct for mispredictions. Other models, e.g., density, toxicity characteristic leaching procedure, and sulfur solubility, are adequate for formulation of DFHLW glasses.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Efficient Langevin dynamics for “noisy” forces

Efficient Boltzmann-sampling using first-principles methods is challenging for extended systems due to the steep scaling of electronic structure methods with the system size. Additionally, stochastic approaches provide a gentler system-size dependency at the cost of introducing “noisy” forces, which could limit the efficiency of the sampling. When the forces are deterministic, the first-order Langevin dynamics (FOLD) offers efficient sampling by combining a well-chosen preconditioning matrix S with a time-step-bias-mitigating propagator [G. Mazzola and S. Sorella, Phys. Rev. Lett. 118, 015703 (2017)]. However, when forces are noisy, S is set equal to the force-covariance matrix, a procedure that severely limits the efficiency and the stability of the sampling. Here, we develop a new, general, optimal, and stable sampling approach for FOLD under noisy forces. We apply it for silicon nanocrystals treated with stochastic density functional theory and show efficiency improvements by an order-of-magnitude.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Too big, too small, or just right? A benchmark assessment of density functional theory for predicting the spatial extent of the electron density of small chemical systems

Multipole moments are the first-order responses of the energy to spatial derivatives of the electric field strength. The quality of density functional theory prediction of molecular multipole moments thus characterizes errors in modeling the electron density itself, as well as the performance in describing molecules interacting with external electric fields. However, only the lowest non-zero moment is translationally invariant, making the higher-order moments origin-dependent. Therefore, instead of using the 3 × 3 quadrupole moment matrix, we utilize the translationally invariant 3 × 3 matrix of second cumulants (or spatial variances) of the electron density as the quantity of interest (denoted by K). The principal components of K are the square of the spatial extent of the electron density along each axis. A benchmark dataset of the principal components of K for 100 small molecules at the coupled cluster singles and doubles with perturbative triples at the complete basis set limit is developed, resulting in 213 independent K components. The performance of 47 popular and recent density functionals is assessed against this Var213 dataset. Several functionals, especially double hybrids, and also SCAN and SCAN0 predict reliable second cumulants, although some modern, empirically parameterized functionals yield more disappointing performance. The H, Li, and Be atoms, in particular, are challenging for nearly all methods, indicating that future functional development could benefit from the inclusion of their density information in training or testing protocols.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

DMRG on Top of Plane-Wave Kohn–Sham Orbitals: A Case Study of Defected Boron Nitride

In this paper, we analyze the numerical aspects of the inherent multi reference density matrix renormalization group (DMRG) calculations on top of the periodic Kohn-Sham density functional theory using the complete active space approach. The potential of the framework is illustrated by studying hexagonal boron nitride nanoflakes embedding a charged single boron vacancy point defect by revealing a vertical energy spectrum with a prominent multireference character. We investigate the consistency of the DMRG energy spectrum from the perspective of sample size, basis size, and active space selection protocol. Results obtained from standard quantum chemical atom-centered basis calculations and plane-wave based counterparts show excellent agreement. Furthermore, we also discuss the spectrum of the periodic sheet which is in good agreement with extrapolated data of finite clusters. These results pave the way toward applying the DMRG method in extended correlated solid-state systems, such as point defect qubit in wide band gap semiconductors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Methodology for Generating Covariance Data of Thermal Neutron Scattering Cross Sections

This paper details and implements a framework for evaluating thermal neutron scattering cross sections that provide S(α,β) data and covariance data for hydrogen in light water. This methodology involves perturbing model parameters of molecular dynamics potentials and fitting the simulation results to experimental data. The framework is general and can be applied to any material or simulation method. The fit is made using the Unified Monte Carlo method to experimentally measure double-differential scattering cross sections of light water at the Spallation Neutron Source at Oak Ridge National Laboratory. Mean values and covariance data were generated for model parameters, phonon density of states, double-differential cross sections, and total scattering cross sections. These posterior parameter values were very similar to their prior values with a maximum relative error of 0.54%. This falls within in the Unified Monte Carlo–calculated uncertainties on the order of 2.7%. Additionally, posterior double-differential cross sections agree favorably with ENDF/B-VIII.0 cross sections. The new thermal scattering law was tested by comparing it against benchmarks from the International Criticality Safety Benchmark Evaluation Project Handbook, which showed a slight improvement over the ENDF/B-VIII.0 library. Additionally, the covariance matrix of the phonon density of states was validated to confirm that the spread of k eff from the density of states used to generate the covariance matrix was similar to the spread of k eff from the density of states of the sampled covariance matrix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Chlorophylls as primary electron acceptors in reaction centers

Photosynthetic Reaction Centers (RCs) can be considered blueprints for highly efficient energy transfer. Embedded with an array of cofactors, including (bacterio)chlorophyll ((B)Chl) and (B)pheophytin ((B)Pheo) molecules, RCs function with a high quantum yield that spans a wide spectral range. Understanding the principles that underlie their function can influence the design of the next generation of artificial photosynthetic devices. We are particularly interested in the factors that influence the early stages of light-driven charge separation in RCs. With the recent publication of several highly anticipated RC structures and advanced computational methods available, it is possible to probe both the geometric and electronic structures of an array of RCs. In this chapter, we review the electronic and geometric structures of the (B)Chl and (B)Pheo primary electron acceptors from fiveRCs, comprising both Type I and Type II RCs and representing both heterodimeric and homodimeric systems. We showcase the dimeric A0•- state of Type I RCs, whereby the unpaired electron is delocalized, to various extents, over two (B)Chl molecules (B)Chl2 and (B)Chl3. This delocalization is controlled by several factors, including the structure of the (B)Chls, interactions with the surrounding protein matrix, and the orientation and distances of the cofactors themselves. In contrast, the primary acceptors of Type II RCs are entirely monomeric, with electron density residing solely on the (B)Pheo. We compare the natural design of the primary acceptors of the Type I and Type II RCs from both an evolutionary and application based perspective.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Bio-inspired redox mediated electrolyte for high performance flexible supercapacitor applications over broad temperature domain

For practical supercapacitors, recent advances in electrolytes have diminished long-standing problems such chemical stability, low ionic conductivity and limited electrochemical performance. Herewith, we communicate a facile method to produce anhydrous redox-active Bio-inspired electrolytes for flexible supercapacitors with application over a broad temperature range. The glycerol (Gly) gel electrolyte consists of various fractions of potassium hydroxide (KOH) and redox active unit, i.e., ammonium molybdate, (NH 4 ) 2 MoO 4 (abbreviated as Mo), in the anhydrous state. The doped glycerol matrix acts as a framework that provides a stable gel electrolyte, forming hierarchical pathway for ion diffusion. The developed gel network with Gly-KOH-MoX (X = 3, 5, 10, and 15%, w/w) provides an effective route to carry the ions onto the pores of the electrodes. The supercapacitor with Gly-KOH5-Mo10 gel provides a specific capacitance of 328 F g –1 , and the same device achieved an energy density of 45.6 Wh kg –1 at a power density of 497 W kg –1 . In addition, the supercapacitor maintained extraordinary cyclic robustness and wide temperature tolerance. Thus, the low cost and environmentally benign, cyclic durability of Gly-KOH-Mo makes these gel electrolytes a potential candidate for use in various energy storage devices.

25 ENERGY STORAGE↗

DOE OSTI2020

Evaluation of a Geotechnical Compaction Model to Estimate Sediment Deformation

When surface ruts from vehicle activity occur above archeological deposits, there is a potential for an impact to the archeological record to occur. While impacts to the soil surface are relatively straightforward to describe, sub-surface disturbances are more difficult to quantify. In particular, disturbances to buried archeological materials can be difficult to characterize. Materials can be damaged by surface disturbances, but they can also be impacted even if they stay intact. Interpretation of intact materials relocated within the sediment column can be problematic. Traditional characterization methods (e.g. excavation) can also disturb archaeological materials. Here, we present a geotechnical compaction model that can be used to assist with sub-surface characterization under vehicle ruts formed during off-road travel. The model is based on a Boussinesq analysis of stress increase below a surface load. The change in bulk density resulting from compaction is assumed to be proportional to the stress increase. The model results were compared against pilot scale tests conducted with homogeneous sediment and field scale in-situ tests. The results indicate that the model generally agreed with measurements to within 20%, although only a single soil type was evaluated in these studies, with a narrow range of initial bulk densities and rut depths. While application of the model across a broader matrix of soil types, bulk densities and rut depths would increase confidence in the model, it appears that the model may be suitable for use in archeological field investigations. Potential uses include both compliance and research based field applications.

Fritz, Brad G.↗