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DOE OSTI2026

Confinement and String Breaking in the Compact Abelian Higgs Model

While real-time simulation of Quantum Chromodynamics remains technologically out of reach, simplified models for studying elements of QCD phenomenology abound. This work presents a simple model, a spin-1 truncation of the Compact Abelian Higgs Model simulated on qutrit sites, in which confinement and string breaking is accessible to current simulation methods. In the low-energy regime of 1+1D scalar electrodynamics, the heavy modes are integrated out, producing a spin chain effective Hamiltonian in which Gauss' law is implicitly satisfied. We study the spectrum of string-like excitations using DMRG methods on the order of 100 sites. We demonstrate that an added, local chemical potential, playing a role analogous to external charges, permits parameter-dependent measurements of physical features of interest like the string tension and effective meson mass. Varying the chemical potential also permits a characterization of string stability not assessed in prior studies of confining lattice models.

Senseman, Blake [Iowa U.]↗

DOE OSTI2023

Application of Machine Learning to Assist a Moisture Durability Tool

The design of moisture-durable building enclosures is complicated by the number of materials, exposure conditions, and performance requirements. Hygrothermal simulations are used to assess moisture durability, but these require in-depth knowledge to be properly implemented. Machine learning (ML) offers the opportunity to simplify the design process by eliminating the need to carry out hygrothermal simulations. ML was used to assess the moisture durability of a building enclosure design and simplify the design process. This work used ML to predict the mold index and maximum moisture content of layers in typical residential wall constructions. Results show that ML, within the constraints of the construction, including exposure conditions, does an excellent job in predicting performance compared to hygrothermal simulations with a coefficient of determination, R2, over 0.90. Furthermore, the results indicate that the material properties of the vapor barrier and continuous insulation layer are strongly correlated to performance.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Generalized spin σ -SCF method

We introduce a generalization of the σ-SCF method to approximate noncollinear spin ground and excited single-reference electronic states by minimizing the Hamiltonian variance. The new method is based on the σ-SCF method, originally proposed by Ye et al. [J. Chem. Phys. 147, 214104 (2017)], and provides a prescription to determine ground and excited noncollinear spin states on an equal footing. Our implementation was carried out utilizing an initial simulated annealing stage followed by a mean-field iterative self-consistent approach to simplify the cumbersome search introduced by generalizing the spin degrees of freedom. The simulated annealing stage ensures a broad exploration of the Hilbert space spanned by the generalized spin single-reference states with random complex element-wise rotations of the generalized density matrix elements in the simulated annealing stage. The mean-field iterative self-consistent stage employs an effective Fockian derived from the variance, which is utilized to converge tightly to the solutions. This process helps us to easily find complex spin structures, avoiding manipulating the initial guess. As proof-of-concept tests, we present results for Hn (n = 3–7) planar rings and polyhedral clusters with geometrical spin frustration. We show that most of these systems have noncollinear spin excited states that can be interpreted in terms of geometric spin frustration. These states are not directly targeted by energy minimization methods, which are meant to converge to the ground state. This stresses the capability of the σ-SCF methodology to find approximate noncollinear spin structures as mean-field excited states.

Chemistry↗

DOE OSTI2023

Structure-Based Design of Dual Bactericidal and Bacteria-Releasing Nanosurfaces

Here, we report synergistic nanostructured surfaces combining bactericidal and bacteria-releasing properties. A polystyrene-block-poly(methyl methacrylate) (PS-block-PMMA) diblock copolymer is used to fabricate vertically oriented cylindrical PS structures (“PS nanopillars”) on silicon substrates. The results demonstrate that the PS nanopillars (with a height of about 10 nm, size of about 50 nm, and spacing of about 70 nm) exhibit highly effective bactericidal and bacteria-releasing properties (“dual properties”) against Escherichia coli for at least 36 h of immersion in an E. coli solution. Interestingly, the PS nanopillars coated with a thin layer (≈3 nm thick) of titanium oxide (TiO 2 ) (“TiO 2 nanopillars”) show much improved dual properties against E. coli (a Gram-negative bacterium) compared to the PS nanopillars. Moreover, the dual properties emerge against Listeria monocytogenes (a Gram-positive bacterium). To understand the mechanisms underlying the multifaceted property of the nanopillars, coarse-grained molecular dynamics (MD) simulations of a lipid bilayer (as a simplified model for E. coli) in contact with a substrate containing hexagonally packed hydrophilic nanopillars were performed. The MD results demonstrate that when the bacterium–substrate interaction is strong, the lipid heads adsorb onto the nanopillar surfaces, conforming the shape of a lipid bilayer to the structure/curvature of nanopillars and generating high stress concentrations within the membrane (i.e., the driving force for rupture) at the edge of the nanopillars. Membrane rupture begins with the formation of pores between nanopillars (i.e., bactericidal activity) and ultimately leads to the membrane withdrawal from the nanopillar surface (i.e., bacteria-releasing activity). In the case of Gram-positive bacteria, the adhesion area to the pillar surface is limited due to the inherent stiffness of the bacteria, creating higher stress concentrations within a bacterial cell wall. In conclusion, the present study provides insight into the mechanism underlying the “adhesion-mediated” multifaceted property of nanosurfaces, which is crucial for the development of next-generation antibacterial surface coatings for relevant medical applications.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Generalized Quantum Signal Processing

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that | P | ≤ 1 , a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where P and Q are known. In cases where only P is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding Q for polynomials of degree on the order of 10 7 . We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the ϵ -approximate fractional query problem that requires O ( ( 1 / δ ) + log ( 1 / ϵ ) ) queries to perform where O ( 1 / δ ) is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a novel framework for the implementation of normal matrices, demonstrating its applicability through synthesis of diagonal matrices, as well as the development of a new algorithm for convolution through synthesis of circulant matrices using only O ( d log N + log 2 N ) 1 and 2-qubit gates for a filter of lengths d . Published by the American Physical Society 2024

Motlagh, Danial↗

DOE OSTI2024

Integrated Spatial, Spectral, & Temporal Optical Reflectance System for Precision Occupancy & Location Sensing to Improve Building Energy Efficiency

Buildings consume approximately 35% of the electricity used in the U.S. and building owners can significantly reduce this energy use by providing services like heating, electrical power and lighting only when people are present. The ARPAe funded program titled “INTEGRATED SPATIAL, SPECTRAL, & TEMPORAL OPTICAL REFLECTANCE SYSTEM FOR PRECISION OCCUPANCY & LOCATION SENSING TO IMPROVE BUILDING ENERGY EFFICIENCY” demonstrates how a low cost sensor technology developed for measuring distances can be used to count and locate occupants with a high degree of precision with a very low error rates. This platform tells a building control system where occupants are located (but not who they are) so that energy consuming services can be provided only when the services are needed by building occupants. The original proof of concept involved using low cost, commercially available time-of-flight (TOF) sensors that measure distance, but the performance of these existing sensors was lacking, as they could not operate properly in the presence of sunlight, which blinded the simple TOF sensors and limited their utility in buildings. This project proposed a powerful new class of TOF sensors that used state-of-the-art integrated circuit (IC) fabrication processes that combined advanced photonics with conventional silicon chip circuitry for improved sensor performance. An equally important part of this project was to find ways to maximize occupant count and location accuracy while using the fewest number of sensors possible, in order to keep costs low. By using building blueprints to create digital twins of commercial building spaces, the team developed new algorithms to maximize occupant count and tracking accuracy by properly locating the minimum number of sensors at just the right spots in the building. This capability not only minimizes system costs but also simplified sensor installation and system commissioning. Our simulations of our sensor networks for a range of commercial floorplan designs demonstrated that our installed cost target of $0.08/sqft was attainable, though not fully demonstrated during the project. Finally, we noted that the TOF sensor concept could provide a valuable role in health and eldercare by tracking patients without the need for worn sensors and would be useful for fall detection and other patient safety metrics, including tracking healthcare/patient interactions. We feel that, when fully developed, this new class of sophisticated TOF sensors and support software will be a powerful new approach to improving building energy efficiency based on occupant centric control platforms and will also open new levels of patient safety in healthcare operations. To realize this potential, the team formed the Troy Sensor Company LLC to oversee licensing of the programs patents and continue to seek commercialization of this program’s activity sensing technologies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2020

A geospatial model for the analysis of time-dependent land subsidence induced by reservoir depletion

Land subsidence due to fluid depletion is an outcome of physical processes operating across a wide range of time and length scales. Although geomechanical models are crucial to simulate reservoir compaction and predict its long-term fate, their use across large regions often bears prohibitive computational costs. To overcome this obstacle, this paper proposes a simplified modelling framework consisting of (i) a near-field numerical solver simulating the coupling between fluid flow and rock deformation with reference to a simplified one-dimensional geometry and (ii) a far-field geospatial algorithm mapping ground settlements across a region through the superposition of poroelastic computations at multiple wells. The model computes the delay between depletion history and reservoir compaction in proximity of a producing well by assuming basal depletion of a fluid-saturated deformable disk, while the Geertsma solution of nucleus of strain is used to extrapolate the impact of such time-varying reservoir compaction around the well. This approach has been used to back-analyze the spatio-temporal progression of subsidence at the Groningen gas field. The results are compared against measurements collected over 50 year of production at 25 benchmark locations scattered over an area of 900 km 2 . It is shown that coupled simulations based on average values of rock compressibility and permeability lead to nonlinear trends of subsidence evolution in good agreement with field measurements, while uncoupled analyses overpredict settlements by more than 70%. Lastly, synthetic forecasts based on different rates of depletion were provided. The results suggest that slower depletion rates lead to lower subsidence at a given time, and that residual subsidence may continue to develop for several decades after interruption of production activities.

58 GEOSCIENCES↗

DOE OSTI2021

Ion-temperature-gradient stability near the magnetic axis of quasisymmetric stellarators

Abstract The stability of the ion-temperature gradient mode in quasisymmetric stellarators is assessed. This is performed using a set of analytical estimates together with linear gyrokinetic simulations. The peak growth rates, their corresponding real frequencies and wave-vectors are identified. A comparison is made between a first-order near-axis expansion model and eleven realistic designs obtained using numerical optimization methods. It is found that while the near-axis expansion is able to replicate the growth rates, real frequencies and perpendicular wave-vector at the inner core (both using simplified dispersion relations and first-principle gyrokinetic simulations), it leads to an overestimation of the growth rate at larger radii. An approximate analytic solution of the ITG dispersion relation for the non-resonant limit suggests growth rates could be systematically higher in quasi-axisymmetric (QA) configurations compared to quasi-helically (QH) symmetric ones. However except for very close to the axis, linear gyrokinetic simulations do not show systematic differences between QA and QH configurations.

Physics↗

DOE OSTI2021

Fast All-sky Radiation Model for Solar applications (FARMS) [SWR-16-18]

The Fast All-sky Radiation Model for Solar applications (FARMS) is used to compute cloudy irradiance. Radiative transfer (RT) models simulating broadband solar radiation have been widely used by atmospheric scientists to model solar resources for various energy applications such as operational forecasting. Due to the complexity of solving the RT equation, the computation under cloudy conditions can be extremely time consuming though many approximations (e.g. two-stream approach and delta-M truncation scheme) have been utilized. Thus, a more efficient RT model is crucial for model developers as a new option for approximating solar radiation at the land surface with minimal loss of accuracy. We have developed a fast all-sky radiation model for solar applications (FARMS) using the simplified clear-sky RT model, REST2, and simulated cloud transmittances and reflectances from the Rapid Radiation Transfer Model (RRTM) with a sixteen-stream Discrete Ordinates Radiative Transfer (DISORT). Simulated lookup tables (LUTs) of cloud transmittances and reflectances were created by varying cloud optical thicknesses, cloud particle sizes, and solar zenith angles. Equations with optimized parameters were fitted to the cloud transmittances and reflectances to develop the model. Using this model the all-sky solar irradiance at the land surface can be computed rapidly by combining REST2 with the cloud transmittances and reflectances. This new RT model is more than 1000 times faster than those currently utilized in solar resource assessment and forecasting since it does not explicitly solve the RT equation for each individual cloud condition. Our results indicate the accuracy of the fast radiative transfer model is comparable to or better than two-stream approximation in term of computing cloud transmittance and solar radiation.

Xie, Yu↗

DOE OSTI2023

Fast All-sky Radiation Model for Solar applications (FARMS) 2023 [SWR-16-18]

Xie, Yu↗

DOE OSTI2020

Model bias in simulating major chemical components of PM 2.5 in China

High concentrations of PM 2.5 (particulate matter with an aerodynamic diameter less than 2.5 µm) in China have caused severe visibility degradation. Accurate simulations of PM 2.5 and its chemical components are essential for evaluating the effectiveness of pollution control strategies and the health and climate impacts of air pollution. In this study, we compared the GEOS-Chem model simulations with comprehensive datasets for organic aerosol (OA), sulfate, nitrate, and ammonium in China. Model results are evaluated spatially and temporally against observations. The new OA scheme with a simplified secondary organic aerosol (SOA) parameterization significantly improves the OA simulations in polluted urban areas, highlighting the important contributions of anthropogenic SOA from semivolatile and intermediate-volatility organic compounds. The model underestimates sulfate and overestimates nitrate for most of the sites throughout the year. More significant underestimation of sulfate occurs in winter, while the overestimation of nitrate is extremely large in summer. The model is unable to capture some of the main features in the diurnal pattern of the PM 2.5 chemical components, suggesting inaccuracies in the presented processes. Potential model adjustments that may lead to a better representation of the boundary layer height, the precursor emissions, hydroxyl radical concentrations, the heterogeneous formation of sulfate and nitrate, and the wet deposition of nitric acid and nitrate have been tested in the sensitivity analysis. The results show that uncertainties in chemistry perhaps dominate the model biases. The proper implementation of heterogeneous sulfate formation and the good estimates of the concentrations of sulfur dioxide, hydroxyl radical, and aerosol liquid water are essential for the improvement of the sulfate simulation. The update of the heterogeneous uptake coefficient of nitrogen dioxide significantly reduces the modeled concentrations of nitrate. However, the large overestimation of nitrate concentrations remains in summer for all tested cases. The possible bias in the chemical production and the wet deposition of nitrate cannot fully explain the model overestimation of nitrate, suggesting issues related to the atmospheric removal of nitric acid and nitrate. A better understanding of the atmospheric nitrogen budget, in particular, the role of the photolysis of particulate nitrate, is needed for future model developments. Moreover, the results suggest that the remaining underestimation of OA in the model is associated with the underrepresented production of SOA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Simplified Approximations of Direct Cumulus Entrainment and Detrainment

Abstract In recent years, direct calculations of simulated cumulus entrainment and detrainment have facilitated new physical insights into these highly elusive but critically important processes. However, these calculations require substantial computational resources that may limit their widespread usage. To facilitate such calculations, two simplified approximations of direct cumulus entrainment and detrainment are examined herein. The first approximation, termed the “semidirect” method, follows a standard bulk approach but makes more realistic assumptions about the sources of entrained and detrained air near the cloud edges. In contrast, the second approximation (the “projection” method) uses the governing equations of motion to project whether grid points near the cloud edge will entrain or detrain as the mean cloud ascends by one grid point. Verification exercises using large-eddy simulations reveal that both methods generally agree better with corresponding direct entrainment/detrainment estimates than the traditional bulk formulation, with the projection method outperforming the semidirect method. The two methods can be used in a synergistic fashion, with the semidirect method helping to optimize the projection method, to suit a wide range of applications. Because the latter incorporates the essential dynamics of entrainment and detrainment at the local scale, it can be used to gain physical insight into the causal mechanisms regulating these complex processes.

Meteorology & Atmospheric Sciences↗

DOE OSTI2025

stor4build

The EnergyPlus simulation engine supports modeling and simulation of thermal energy storage (TES) systems in several ways, including using the Python-EMS feature, which extends the operation of the engine with custom code written in Python. Creation of models using this feature can be tedious and error prone, with the connection of the model components to the Python code a particularly troublesome area. The stor4build Python package simplifies this process by modifying an input model to add a selected TES technology (implemented with the Python-EMS feature) and runs the simulation. The package leverages the OpenStudio middleware software development kit to automate this process as much as possible, eliminating potential errors and simplifying usage of EnergyPlus. The package provides objects, functions, and OpenStudio measures that implement the necessary operations to automate the creation of EnergyPlus models that integrate TES technologies with building systems. In addition, two user interfaces are provided: a command line interface and a web application programming interface. The automated process implemented by the package greatly simplifies the modeling and simulation process, allowing for parametric studies to be executed much more efficiently and effectively. The OpenStudio-based workflow is also very flexible and will allow for future additions of new technologies.

DeGraw, JasonWilliam [Oak Ridge National Laborator↗

DOE OSTI2024

Simulation-based inference for parameter estimation of complex watershed simulators

High-resolution, spatially distributed process-based (PB) simulators are widely employed in the study of complex catchment processes and their responses to a changing climate. However, calibrating these PB simulators using observed data remains a significant challenge due to several persistent issues, including the following: (1) intractability stemming from the computational demands and complex responses of simulators, which renders infeasible calculation of the conditional probability of parameters and data, and (2) uncertainty stemming from the choice of simplified representations of complex natural hydrologic processes. Here, we demonstrate how simulation-based inference (SBI) can help address both of these challenges with respect to parameter estimation. SBI uses a learned mapping between the parameter space and observed data to estimate parameters for the generation of calibrated simulations. To demonstrate the potential of SBI in hydrologic modeling, we conduct a set of synthetic experiments to infer two common physical parameters – Manning's coefficient and hydraulic conductivity – using a representation of a snowmelt-dominated catchment in Colorado, USA. We introduce novel deep-learning (DL) components to the SBI approach, including an “emulator” as a surrogate for the PB simulator to rapidly explore parameter responses. We also employ a density-based neural network to represent the joint probability of parameters and data without strong assumptions about its functional form. While addressing intractability, we also show that, if the simulator does not represent the system under study well enough, SBI can yield unreliable parameter estimates. Approaches to adopting the SBI framework for cases in which multiple simulator(s) may be adequate are introduced using a performance-weighting approach. The synthetic experiments presented here test the performance of SBI, using the relationship between the surrogate and PB simulators as a proxy for the real case.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Modeling a Thermionic Electron Source Using a Physics-Informed Neural Network

We explore the application of Physics-Informed Neural Networks (PINNs) for simulation of thermionic electron sources. This is motivated by the need for quick surrogate models used to simulate such sources within a digital twin of a complete particle accelerator. Here, a PINN was developed on a simplified model of the thermionic source: the planar diode. This model very accurately simulated the system, and performed significantly better than a traditional neural network while also using less training data. We hope to apply this proof-of-concept in motivating the development of a PINN model for a full thermionic electron source at the University of Chicago.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

The Effect of Spectral Resolution of Light Sources on Photopic and a-opic Quantities

There is a growing interest in including light source spectrum in advanced lighting software tools and simulations. Given that traditional lighting software tools have been used primarily for calculating photometric quantities, their simplifying assumptions may not be suitable for calculating other a-opic quantities. Commonly used simulation tools use three values to represent the three primary colors (red, green, and blue), but others have expanded the number of bands (i.e., the spectral resolution) to 9, 27, or 81 in an attempt to more accurately represent variations in light source spectrum and downstream spectrally-derived quantities. It remains unclear, however, to what extent spectral resolution affects calculated quantities. To address this gap, a numerical analysis was completed using a large spectral power distribution database (n = 1,302 light sources). Calculated illuminance, a-opic irradiance, luminous efficacy of radiation (LER), melanopic efficacy of radiation (MER), and melanopic to photopic (M/P) ratio were compared for spectral resolutions of 3 and 9 bands compared to a baseline of 81 bands. Across all examined lighting quantities, considerable errors—a mean absolute percent error of 18.4%—were found when using 3 band calculations. These were reduced to 4% for 9 band calculations. The errors varied by metric and light source type. The results suggest that the use of 9 bands can more accurately characterize performance of different light source types across a range of metrics compared to using 3 bands.

Abboushi, Belal K.↗

DOE OSTI2024

Rancor-HUNTER: A Virtual Plant and Operator Environment for Predicting Human Performance

Advances in simulation capabilities to model physical systems have outpaced the development of simulations for humans using those physical systems. There is an argument that the infinite span of potential human behaviors inherently render human modeling more challenging than physical systems. Despite this challenge, the need for modeling humans interacting with these complex systems is paramount. As technologies have improved, many of the failure modes originating from the physical systems have been solved. This means the overall proportion of human errors has increased, such that it is not uncommon to be the primary driver of system failure in modern complex systems. Moreover, technologies such as automated systems may introduce emerging contexts that can cause new, unanticipated modes of human error. Therefore, it is now more important than ever to develop models of human behavior to realize overall system error reductions and achieve established safety margins. To support new and novel concepts of operations for the anticipated wave of advanced nuclear reactor deployments, human factors and human reliability analysis researchers need to develop advanced simulation-based approaches. This talk presents a simulation environment suitable to both collect data and then perform Monte Carlo simulations to evaluate human performance and develop better models of human behavior. Specifically, the Rancor Microworld Simulator models a complex energy production system in a simplified manner. Rancor includes computer-based procedures, which serve as a framework to automatically classify human behaviors without manual, subjective experimenter coding during scenarios. This method supports a detailed level of analysis at the task level. It is feasible for collecting large sample sizes required to develop quantitative modelling elements that have historically challenged traditional full-scope simulator study approaches. Additionally, the other portion of this experimental platform, the Human Unimodel for Nuclear Technology to Enhance Reliability (HUNTER), is presented to show how the collected data can be used to evaluate novel scenarios based on the contextual factors, or performance shaping factors, derived from Rancor simulations. Rancor-HUNTER is being used to predict operator performance with new procedures, such as results from control room modernization or new-build situations. Rancor-HUNTER is also proving a useful surrogate platform to model human performance for other complex systems.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2024

Detonation structure in the presence of mixture stratification using reaction-resolved simulations

Many investigations of detonation-based combustors have identified reactant mixture inhomogeneity as having a leading-order impact on wave dynamics and combustion efficiency. To examine this phenomenon in a simplified context, an array of two- and three-dimensional channel detonation simulations are conducted in the present work. The reactant mixture consists of stratified fuel and air, wherein the randomly distributed equivalence ratio field features a characteristic stratification length scale. Detailed chemical kinetics are implemented in an adaptive mesh refinement solution framework where the region near the shock front is resolved with Ο (100) cells per representative ZND induction length. The results show that in comparison to baseline cases with uniform reactant mixtures, reactant stratification has a marked impact on the detonation structure. Increasing the stratification length scale increases the size and irregularity of the detonation cells, yielding larger variations in wave speed. Triple point collisions in fuel-rich regions lead to local wave speeds above the notional mean CJ speed, but wave passage through inert regions causes the local wave speed and strength to diminish. Further, conditional statistics show that increasing the stratification length scale increases the variance in pressure and temperature in the primary reaction zone, as well as the variance in heat release over a range of mixture conditions. In addition to the reactant mixture, the impact of the boundary condition behind the detonation is also investigated. The results show that an inflow boundary condition acts to over-drive the wave, leading to higher peak pressures, smaller detonation cells, and increased reactant consumption. On the other hand, cases with a wall behind the wave exhibit weaker waves with lower peak pressures and heat release rates, as well as greater variance in conditional quantities. Comparisons between complementary two- and three-dimensional simulations show reasonable qualitative agreement in wave structure, speed, and conditional statistics.

42 ENGINEERING↗