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28 records · Page 2

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. Here, we address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

97 MATHEMATICS AND COMPUTING

Osmotic control of the spacing of parallel shear cracks in shale growing subcritically in geologic past

The geological genesis of natural cracks in sedimentary rocks such as shale is a problem that needs to be understood to improve the technology of hydraulic fracturing as well as deep sequestration of harmful fluids. Why are the vertical natural cracks roughly parallel and equidistant, and why is the spacing roughly 10 cm rather than 1 cm or 100 cm? Fracture mechanics of critical cracks cannot answer this question. Neither can the material heterogeneity. The growth of critical parallel cracks is impossible because the relative crack face displacements would immediately localize into one crack, leading to an earthquake. The cracks must have formed, on the tectonic time scale, by a slow growth of subcritical shear cracks governed by the Charles-Evans law. The idea advanced here is that what controls the crack spacing is the balance between the reduction, due to shear dilatancy, of the concentration of ions such as Na + and Cl - in each fracture process zone (PFZ), which decelerates the cracks, and the restoration of ion concentration by diffusion of ions from the space between the cracks into the FPZ. This diffusion of water is driven mainly by the osmotic pressure gradient, which offsets the deceleration and depends strongly on the crack spacing. A simple analytical solution of the steady state is rendered possible by approximating the ion concentration profiles between adjacent cracks by parabolic arcs. Applying this theory to Woodford shale yields the approximate crack spacing of 10 cm, which is realistic. Furthermore, the stability of unlimited parallel mode II frictional crack growth is proven by examining the second variation of the free energy. Water concentration drop in the FPZ due to shear dilatancy and its restoration by water diffusion from the inter-crack space have similar effect, although probably much weaker.

42 ENGINEERING

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization

Here we develop an explicit staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen into natural gas pipelines to reduce end use carbon emissions while using existing pipeline systems throughout their planned lifetimes. Our computational method accommodates an arbitrary number of constituent gases with very different physical properties that may be injected into a network with significant spatiotemporal variation. In this setting, the gas flow physics are highly location- and time- dependent, so that local composition and nodal mixing must be accounted for. The resulting conservation laws are formulated in terms of pressure, partial densities and flows, and volumetric and mass fractions of the constituents. We include non-ideal equations of state that employ linear approximations of gas compressibility factors, so that the pressure dynamics propagate locally according to a variable wave speed that depends on mixture composition and density. We derive compatibility relationships for network edge boundary values that are more complex than for a homogeneous gas. The simulation method is evaluated on initial boundary value problems for a single pipe and a small network, is cross-validated with a lumped element simulation, and used to demonstrate a local monitoring and control policy for maintaining allowable concentration levels.

97 MATHEMATICS AND COMPUTING

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING

Elastic strain engineering of lattice thermal conductivity of silicon: An ab-initio study

Silicon (Si) is the most essential material in the semiconductor industry. It is important to manage the thermal properties of crystalline Si. Elastic strain engineering (ESE) has proven to be an effective tool in controlling the electrical conductivity of Si in strained-silicon technology; its effects on the thermal conductivity of silicon, therefore, warrants careful investigation. The ESE effect is much more pronounced for nanostructured materials due to the ultralarge elastic strains (on the order of 10%) achievable at the nanoscale. In this work, the lattice thermal conductivity (κ L ) of Si under hydrostatic, biaxial, and uniaxial strain states is studied with ab-initio simulations, and the values of strain-dependent κ L compare well with experimental results and existing molecular dynamics simulations. To understand the mechanisms of strain-modulated κ L , the phonon bands, scattering rate, and Grüneisen parameters of phonon modes are computed. It is shown that strain can significantly change the anharmonicity of the crystal system, thus changing phonon scattering rates and κ L . Our results demonstrate that ESE can reduce silicon κ L by up to approximately 90%. Furthermore, uniaxial and biaxial strains can induce highly anisotropic thermal conductivity in Si, with relative variations up to 58.5% and 14.5%, respectively.

Anisotropy in Thermal Conductivity

Constraining Black Carbon Aging in Global Models to Reflect Timescales for Internal Mixing

The radiative effects of black carbon depend critically on its atmospheric lifetime, which is controlled by the rate at which freshly emitted combustion particles become internally mixed with other aerosol components. Global aerosol models strive to represent this process, but the timescale for aerosol mixing is not easily constrained using observations. In this study, we apply a timescale parameterization derived from particle‐resolved simulations to quantify, in a global aerosol model, the timescale for internal mixing. We show that, while highly variable, the average timescale for internal mixing is approximately 3 hr, which is much shorter than the 24‐hr aging timescale traditionally applied in bulk aerosol models. We then use the mixing timescale to constrain the aging criterion in the Modal Aerosol Module. Our analysis reveals that, to best reflect timescales for internal mixing, modal models should assume that particles transition from the hydrophobic (fresh) to the hydrophilic (aged) class once they accumulate a coating thickness equal to four monolayers of sulfuric acid, as opposed to the model's current aging criterion of eight monolayers. We show that, in remote regions like the Arctic and Antarctic, predictions of black carbon loading and its seasonal variation are particularly sensitive to the model representation of aging. By constraining aging in global models to reflect mixing timescales simulated by the particle‐resolved model, we eliminate one of the free parameters governing black carbon's long‐range transport and spatiotemporal distribution.

54 ENVIRONMENTAL SCIENCES

Surface and Buried Thermal, and RGB Unexploded Ordnance Data Collection

This document provides a description of a data collection campaign of unexploded ordnance (UXOI) set. The dataset captures a controlled UAV imaging campaign designed to support detection of UXO across varied environmental conditions. Data were collected during three campaigns in Norris and Northeast Knoxville, Tennessee, using RGB, and thermal sensors mounted on Parrot UKR. In total, the dataset contains 9925 images, 26 full-motion video, and approximately 81.99 GB of data, collected across late spring/summer conditions, every hour during sunlight, and multiple surface contexts, including tall grass, short grass, gravel, as well as buried in sand, and other gravel mixtures. The collection was designed to capture thermal and visual variability relevant to UXO detection in agricultural land, bare earth, and subsurface. Review of the imagery showed that ordnance was most detectable during periods of changing solar input, especially approximately 10-60 minutes after sunrise, approximately 20-60 minutes after sunset, and 2-3 min after cloud cover interrupted prolonged solar heating. These conditions increased thermal contrast because many ordnance items retained or released heat differently than the surrounding vegetation and ground surface. This dataset provides a useful resource for developing and evaluating airborne UXO detection methods under realistic field conditions. All ordnance used in the study was inert, and thermal behavior may differ from that of live ordnance. In addition, variation in ordnance type, composition, and placement introduced differences in thermal response that should be considered when interpreting results.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF

THE DESIGN OF RADIAL HONEYCOMB LATTICES FOR IMPACT ENERGY ABSORPTION IN RADIOACTIVE MATERIALS PACKAGES

In this research we present a variation on the corrugation technique of honeycomb lattices, for cylindrical honeycombs, making them much easier to design for impact energy absorption in radioactive materials packages. This variation, termed radial honeycomb lattices, eliminates the residual strain and saddle effect. The use of honeycomb lattices provides advantages over the typically used foams. While foams are effective at absorbing impact energy, they can burn, their material properties are difficult to control, they can degrade over time, and procurement of raw materials can be dependent on timing of manufacturer batch runs. While the weaknesses of foam are strengths for honeycomb lattices, lattices have a different set of problems. Typically, when cylindrical honeycomb lattices are manufactured, they are manufactured flat, wrapped around a mandrel of the desired radius, and then brazed. This approach introduces residual strains, resulting in the saddle effect, which limits both the radial thickness and cylinder length. The radial honeycomb lattice approach presented here makes the design of thicker and longer cylinder honeycombs possible. To address these issues, we propose a honeycomb lattice which changes in cross-section from the inner to the outer radius of the cylinder. This causes the lattice to automatically wrap into a cylinder as it exits the corrugating gears. The theoretically bounding case, of a square cross-section at the inner radius, transitioning through a hexagon, to a diamond cross-section at the outer radius, results in a maximum thickness of approximately 41% of the inner radius. Full mathematical derivations, implemented in computer code, allow for the design of an entire radial honeycomb lattice, including the corrugating gears. To accomplish this only the radial thickness, inner cross-section shape, cell size, and nominal gear radius need to be specified, making the design of these lattices very efficient. Radial honeycomb lattice prototypes have demonstrated that the honeycomb does indeed wrap into a cylinder as intended, without the saddle effect, and can therefore be used to create thick-walled cylinders of any length. These design improvements make cylindrical honeycomb lattices much more accessible as a design element for radioactive materials packages

Johnson, William R. [Savannah River National Labor

Counterdiabatic Driving with Performance Guarantees

Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations that do not have performance guarantees. We propose and analyze a nonvariational, system-agnostic CD expansion method and analytically show that it converges exponentially quickly in the expansion order. In finite systems, the required resources scale inversely with the spectral gap, which we argue is asymptotically optimal. To extend our method to the thermodynamic limit and suppress errors stemming from high-frequency transitions, we leverage finite-time adiabatic protocols. In particular, we show that a time determined by the quantum speed limit is sufficient to prepare the desired ground state, without the need to optimize the adiabatic trajectory. Numerical tests of our method on the quantum Ising chain show that our method can outperform state-of-the-art variational CD approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Comparison of removal and spatial mark‐resight models for estimating wild pig density

Density estimation is critical to effectively manage invasive species and elucidate areas of highest concern. For wild pigs (Sus scrofa), the ability to estimate density is complicated because of their variable home range sizes and social structure. Common methods for estimating density (e.g., mark-recapture) may be unsuitable in management applications because additional data needs to be collected before and after management. Removal models offer a suitable alternative to estimate density changes following management and can be applied broadly across areas where management of wild pigs is ongoing. We collected wild pig removal and camera trap data from 25 private properties ranging in size from approximately 0.5 km 2 to 95 km 2 across 3 ecoregions in South Carolina, USA, from 2020–2023. We compared factors affecting consistency and precision of property-level density estimates between removal and spatial mark-resight (SMR) models. In general, excluding 1 large outlier, density estimates from removal models were between 0.60 and 15.85 wild pigs/km 2 (median = 5.34) with a median coefficient of variation (CV) of 0.76 and 95% confidence intervals for the CV between 0.70 and 0.94. Similarly, excluding 1 large outlier, density estimates from SMR were between 0.22 and 30.97 wild pigs/km 2 (median = 5.48) with a median CV of 0.39 and 95% confidence intervals for the CV between 0.38 and 1.20. We found the precision of removal models was affected primarily by the number of wild pigs dispatched in the removal period (3 months) and the ecoregion in which they were removed. None of the covariates, including the number of recaptures (a corresponding measure of sample size), influenced precision of the SMR models, although recaptures did influence the density estimates. At the individual property level, density estimates from our 2 estimators were dissimilar from each other in approximately 80% of instances, although none of the covariates we examined influenced dissimilarity. Our results provide unique insight into how sample size affects density estimates using 2 common methods and into novel SMR models that incorporate both marked and unmarked detections. In addition, the density estimates in this study can be used as a reference for wild pig densities in common land cover types throughout the southeastern United States.

60 APPLIED LIFE SCIENCES