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What is the gradient of a scalar function defined on a subspace of square matrices?

We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), https://doi.org/10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. Here, we examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 x 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.

97 MATHEMATICS AND COMPUTING↗

A fusion of the Bacteroides fragilis ferrous iron import proteins reveals a role for FeoA in stabilizing GTP-bound FeoB

Iron is an essential element for nearly all organisms, and under anoxic and/or reducing conditions, Fe 2+ is the dominant form of iron available to bacteria. The ferrous iron transport (Feo) system is the primary prokaryotic Fe 2+ import machinery, and two constituent proteins (FeoA and FeoB) are conserved across most bacterial species. However, how FeoA and FeoB function relative to one another remains enigmatic. In this work, we explored the distribution of feoAB operons encoding a fusion of FeoA tethered to the N-terminal, G-protein domain of FeoB via a connecting linker region. We hypothesized that this fusion poises FeoA to interact with FeoB to affect function. To test this hypothesis, we characterized the soluble NFeoAB fusion protein from Bacteroides fragilis, a commensal organism implicated in drug-resistant infections. Using X-ray crystallography, we determined the 1.50-Å resolution structure of BfFeoA, which adopts an SH3-like fold implicated in protein–protein interactions. Using a combination of structural modeling, small-angle X-ray scattering, and hydrogen–deuterium exchange mass spectrometry, we show that FeoA and NFeoB interact in a nucleotide-dependent manner, and we mapped the protein–protein interaction interface. Finally, using guanosine triphosphate (GTP) hydrolysis assays, we demonstrate that BfNFeoAB exhibits one of the slowest known rates of Feo-mediated GTP hydrolysis that is not potassium-stimulated. Importantly, truncation of FeoA from this fusion demonstrates that FeoA–NFeoB interactions function to stabilize the GTP-bound form of FeoB. Taken together, our work reveals a role for FeoA function in the fused FeoAB system and suggests a function for FeoA among prokaryotes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fabricating Reactive Surfaces with Brush-like and Crosslinked Films of Azlactone-Functionalized Block Co-Polymers

Here in this work, fabrication methods that generate novel surfaces using the azlactone-based block co-polymer, poly (glycidyl methacrylate)-block-poly (vinyl dimethyl azlactone) (PGMA-b-PVDMA), are presented. Due to the high reactivity of azlactone groups towards amine, thiol, and hydroxyl groups, PGMA-b-PVDMA surfaces can be modified with secondary molecules to create chemically or biologically functionalized interfaces for a variety of applications. Previous reports of patterned PGMA-b-PVDMA interfaces have used traditional top-down patterning techniques that generate non-uniform films and poorly controlled background chemistries. Here, we describe customized patterning techniques that enable precise deposition of highly uniform PGMA-b-PVDMA films in backgrounds that are chemically inert or that have biomolecule-repellent properties. Importantly, these methods are designed to deposit PGMA-b-PVDMA films in a manner that completely preserves azlactone functionality through each processing step. Patterned films show well-controlled thicknesses that correspond to polymer brushes (~90 nm) or to highly crosslinked structures (~1-10 μm). Brush patterns are generated using either the parylene lift-off or interface directed assembly methods described and are useful for precise modulation of overall chemical surface reactivity by adjusting either the PGMA-b-PVDMA pattern density or the length of the VDMA block. In contrast, the thick, crosslinked PGMA-b-PVDMA patterns are obtained using a customized micro-contact printing technique and offer the benefit of higher loading or capture of secondary material due to higher surface area to volume ratios. Lastly, detailed experimental steps, critical film characterizations, and trouble-shooting guides for each fabrication method are discussed.

36 MATERIALS SCIENCE↗

Sequestration of U(VI) from Acidic, Alkaline, and High Ionic-Strength Aqueous Media by Functionalized Magnetic Mesoporous Silica Nanoparticles: Capacity and Binding Mechanisms

Uranium(VI) exhibits little adsorption onto sediment minerals in acidic, alkaline or high ionic-strength aqueous media that often occur in U mining or contaminated sites, which makes U(VI) very mobile and difficult to sequester. In this work, magnetic mesoporous silica nanoparticles (MMSNs) were functionalized with several organic ligands. The functionalized MMSNs were highly effective and had large binding capacity for U sequestration from high salt water (HSW) simulant (54 mg U/g sorbent). The functionalized MMSNs, after U exposure in HSW simulant, pH 3.5 and 9.6 artificial groundwater (AGW), were characterized by a host of spectroscopic methods. Among the key novel findings in this work was that in the HSW simulant or high pH AGW, the dominant U species bound to the functionalized MMSNs were uranyl or uranyl hydroxide, rather than uranyl carbonates as expected. The surface functional groups appear to be out-competing the carbonate ligands associated with the aqueous U species. The uranyl-like species were bound with N ligand as η 2 bound motifs or phosphonate ligand as a monodentate, as well as on tetrahedral Si sites as an edge-sharing bidentate. Conclusively, the N and phosphonate ligand-functionalized MMSNs hold promise as effective sorbents for sequestering U from acidic, alkaline or high ionic-strength contaminated aqueous media.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Three-Dimensional Thermodynamically Based Function for the Progressive Failure of Unidirectional Composites

A thermodynamically-based work potential theory for modeling progressive damage for laminated, unidirectional composites assuming plane stress (2D Schaperystheory) is extended to three dimensioanl (3D). An internal state variable, S, is defined to account for the dissipated energy due to damage evolution in the form of microstructure changes in the matrix. With the stationary of the total work potential with respect to the internal state variable, a thermodynamically-consistent set of evolution equationsis derived. The internal state variable is related to the transverse and shear modulithrough microdamage functions. In the first part of this work, coupon specimensare prepared to conduct experiments to characterize the relations between the internalstate variable and the transverse modulus as well as shear modulus. The informationis subsequent used for the prediction of three point bending test. In the second partof this work, objectivity is studied. Three separate methods utilizing different definitions of a reduced internal state variable or of the order of the polynomials are used to represent the matrix micro-damage functions are employed. The three methods are implemented in a user defined subroutine within a commercial finite element method software package. Results from numerical simulations of a center-notched composites panel are compared. The agreement in the maximum stress predictions among the three methods indicates that objectivity, with respect to the functional form of themicrodamage functions, is satisfied.

carbon fiber reinforced polymer composites↗

A Novel Method for Characterizing Spacesuit Mobility Through Metabolic Cost

Historically, spacesuit mobility has been characterized by directly measuring both range of motion and joint torque of individual anatomic joints. The work detailed herein aims to improve on this method, which is often prone to uncertainly, lack of repeatability, and a general lack of applicability to real-world functional tasks. Specifically, the goal of this work is to characterize suited mobility performance by directly measuring the metabolic performance of the occupant. Pilot testing was conducted in 2013, employing three subjects performing a range of functional tasks in two different suits prototypes, the Mark III and Z-1. Cursory analysis of the results shows the approach has merit, with consistent performance trends toward one suit over the other. Forward work includes the need to look at more subjects, a refined task set, and another suit in a different mass/mobility regime to validate the approach.

McFarland, Shane M.↗

Microbial Ecology Toy Library

These are miscellaneous utility functions that I've developed and found useful in working with sequencing counts. Purpose: To collect often reused procedures in one open source location that can be shared and worked on publicly, and perhaps contributed back to other open source projects. Function: Adds, divides, filters, summarizes tables of counts. Capabilities: Currently, the main capability is to reformat count tables for use with the ALDEx2 package.

Herrera, AramAvila↗

Soil Water Retention and Hydraulic Conductivity Data and Model at Pump House in East River Watershed, Colorado 2019-2024

This data package includes soil water retention and hydraulic conductivity data and model fitting results from measurements of ex-situ soil samples and in-situ soil sensors near Pump House at Mount Crested Butte in the East River Watershed. Soil water retention curves (SWRC) characterize soil water content as a function of soil water potential. SWRC depends on soil texture and pore structure and can be used to describe the constraints on biogeochemical processes in terms of soil water availability. In this data package, the sample identification follows the format ER-X-Y, where ER refers to East River, X is the location identifier, and Y is the depth identifier at the same X (shallow Y=1). Specifically, ER-PHS, ER-LMC, ER-LMF, and ER-SMN are associated with ecohydrology sites under the East-Taylor Watershed Community Observatory Sites directory, and ER-RBTn (upslope n=1) are sampling transects during the 2019 Rootball Campaign. The sample and location information can be found in metadata.csv. Sampling and Measurements Each sample falls into one of the three sampling methods – (1) intact cores, (2) repacked samples, or (3) soil sensors – and one of the two measurement methods – (a) laboratory or (b) in-situ. Both intact cores and repacked samples were measured using the laboratory methods, which include measurements of soil water potential (HYPROP & WP4C, METER), saturated (KSAT, METER) and unsaturated hydraulic conductivity (HYPROP). The in-situ method uses a pair of co-located soil sensors to measure volumetric water content (TEROS12, METER) and soil water potential (TEROS21, METER), and the hydraulic conductivity was not measured. In comparison, the laboratory methods progress from full saturation to dry conditions, and the in-situ method includes both dry-to-wet and wet-to-dry cycles. The sampling and measurement methods for each sample can be found in metadata.csv, and more information about the measurements is detailed in the Methods section below. Models Retention and hydraulic conductivity data were fitted with four van-Genuchten-type models (specified by “model_name” column in the files): (1) traditional constrained van Genuchten model (“vG_constrained”), (2) traditional unconstrained van Genuchten model (“vG_unconstrained”), (3) PDI-variant of the constrained van Genuchten model (“vG_constrained_PDI”), and (4) PDI-variant of the unconstrained van Genuchten model (“vG_unconstrained_PDI”). The difference between the constrained (1: n) and the unconstrained (2: n, m) van Genuchten models is the number of pore-size distribution parameters in the model equations, giving the unconstrained model more degrees of freedom when fitting the data. Between the traditional and the PDI-variant models, model fitting differs the most at the dry end of the measurements. The traditional models allow infinite suction at the residual water content (water content does not drop below residual water content), and the PDI-variant models enforce a soil water potential value of pF=6.8 (~ -630 MPa) at oven-dryness (water content reaches 0). The inclusion of the van-Genuchten-type models is due to their common application. If other retention models are required, users can access the data in data.csv for further data fitting. More information about the models can be found in the Methods section below. Fitting Tasks The model fitting can be categorized into three levels of tasks (specified by “fitting_task” column in the files). Level 1 (“fit_retention”) only includes retention data fitting (the only level available for the in-situ method). Level 2 (“fit_retention_conductivity”) includes both retention and hydraulic conductivity data fitting, and the saturated hydraulic conductivity (Ks, a parameter of the hydraulic conductivity functions) is fixed by the measurements from KSAT. Level 3 (“fit_retention_conductivity_Ks”) also includes both retention and hydraulic conductivity data fitting, but Ks is a fitted parameter without the constraints from KSAT measurements. Among the same retention models (e.g. vG_constrained models of the same sample), level 1 should produce the best retention data fitting. Level 2 should have the highest misfit of the retention and hydraulic conductivity data, because the retention and hydraulic conductivity functions share common model parameters, and the unsaturated hydraulic conductivity (HYPROP) data fitting is subject to Ks measured independently by KSAT. Level 3 should have mid-level misfits of the retention and hydraulic conductivity data. While level 3 fits the hydraulic conductivity data better than level 2, the fitted Ks value might be unreasonable due to the lack of constraints at the wet end of the measurements. General recommendation when using this data package: (1) Choice of sampling methods: Intact cores and in-situ soil sensors could be prioritized because these sampling methods are less destructive. While the repacked samples were packed to the target bulk density (estimated post-sampling, when sample volume was known), these samples had altered pore structures. Nevertheless, intact cores might suffer from sample gaps that would lead to overestimation of Ks (sample gaps can be inferred from the “soil_sample_volume” column in metadata.csv when the value is < 249). In-situ method also has higher uncertainty in characterizing the wet end of the SWRC because of sensor limitations and the difficulty in reaching full saturation under natural conditions. (2) Choice of fitting tasks: When only retention data is needed, level 1 (“fit_retention”) should be prioritized. When both retention and hydraulic conductivity data are needed, level 2 (“fit_retention_conductivity”) could be prioritized. (3) Choice of models: This could depend on what the downstream models call for. If no specific model is required, model misfit could be used as a ranking criterion. Model misfit values in terms of RMSE can be found in model_parameters.csv. The following files are included in this data package: (1) metadata.csv – This file includes the general information of each sample, including location (description, geocoordinates, elevation), sampling and measurements details (method, depth, time or period, volume, instruments), and soil physical properties (bulk density, saturated hydraulic conductivity, only applicable to physical soil samples). (2) data.csv – This file includes soil water potential, volumetric water content, and unsaturated hydraulic conductivity data of each sample. Column “instrument” specifies the instrument (HYPROP, WP4C, or TEROS) used to perform the measurements. (3) model_fit.csv – This file includes soil water potential, volumetric water content, and unsaturated hydraulic conductivity fitted from the four models and three fitting tasks. Column “model_name” specifies the retention model used, and “fitting_task” specifies the level of data fitting. Missing values indicate that the variable does not apply to that fitting task. (4) model_parameters.csv – This file includes the fitted model parameters, model misfits, and conventional water content thresholds (field capacity and wilting point) from the four models and three fitting tasks. Column “model_name” specifies the retention model used, and “fitting_task” specifies the level of data fitting. Missing values indicate that the parameter does not apply to that model and/or that fitting task. (5) data_Ks.csv – This file includes the saturated hydraulic conductivity measurements from KSAT. (6) /figure/*.png – This folder includes three quick visualizations of the data, retention model fitting results and misfits, and hydraulic conductivity model fitting results, misfits, and parameters. The model fitting results are separated by samples and fitting tasks and colored by models. Zoom-in required. (7) /hyprop/*.bdhx – This folder includes proprietary hyprop files that require the free Labros SoilView-Analysis (METER) to open. Users can explore data fitting using other retention models (i.e. Brooks-Corey, Fredlund-Xing, Kosugi, bimodal models). Be aware that Ks value is pre-entered under “Fitting tab, Conductivity functions parameters” for level 2 fitting. If the value is lost, please refer to metadata.csv under “Ks” column. (8) Six file-level metadata that summarize file, header, column, and variable information of all files. This work was supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231.

EARTH SCIENCE > LAND SURFACE > SOILS↗

Soil Water Retention and Hydraulic Conductivity Data and Model at Trail Creek in Taylor River Watershed, Colorado 2024-2025

This data package includes soil water retention and hydraulic conductivity data and model fitting results from measurements of ex-situ soil samples and in-situ soil sensors near Trail Creek. Soil water retention curves (SWRC) characterize soil water content as a function of soil water potential. SWRC depends on soil texture and pore structure and can be used to describe the constraints on biogeochemical processes in terms of soil water availability. In this data package, the sample identification follows the format TR-X-Y, where TR refers to Trail Creek, X is the treatment block identifier, and Y is the location identifier. Specifically, TR-ASCC1 is the control treatment block under the Adaptive Silviculture for Climate Change (ASCC) project, and TR-ASCC2 is the clear-cut treatment block. TR-ASCC-EHSn is associated with ecohydrology sites under the East-Taylor Watershed Community Observatory Sites directory, and TR-ASCC-ERTn (upslope n=1) are ecohydrology sites along the electrical resistivity tomography transects. The sample and location information can be found in metadata.csv, and the data from the soil sensors will be included in a future data version when the observation period becomes sufficiently long for data analysis. Sampling and Measurements Each sample falls into one of the two sampling methods – (1) intact cores or (2) soil sensors – and one of the two measurement methods – (a) laboratory or (b) in-situ. The intact cores were measured using the laboratory methods, which include measurements of soil water potential (HYPROP & WP4C, METER), saturated (KSAT, METER) and unsaturated hydraulic conductivity (HYPROP). The in-situ method uses a pair of co-located soil sensors to measure volumetric water content (TEROS12, METER) and soil water potential (TEROS21, METER), and the hydraulic conductivity was not measured. In comparison, the laboratory methods progress from full saturation to dry conditions, and the in-situ method includes both dry-to-wet and wet-to-dry cycles. The sampling and measurement methods for each sample can be found in metadata.csv, and more information about the measurements is detailed in the Methods section below. Models Retention and hydraulic conductivity data were fitted with four van-Genuchten-type models (specified by “model_name” column in the files): (1) traditional constrained van Genuchten model (“vG_constrained”), (2) traditional unconstrained van Genuchten model (“vG_unconstrained”), (3) PDI-variant of the constrained van Genuchten model (“vG_constrained_PDI”), and (4) PDI-variant of the unconstrained van Genuchten model (“vG_unconstrained_PDI”). The difference between the constrained (1: n) and the unconstrained (2: n, m) van Genuchten models is the number of pore-size distribution parameters in the model equations, giving the unconstrained model more degrees of freedom when fitting the data. Between the traditional and the PDI-variant models, model fitting differs the most at the dry end of the measurements. The traditional models allow infinite suction at the residual water content (water content does not drop below residual water content), and the PDI-variant models enforce a soil water potential value of pF=6.8 (~ -630 MPa) at oven-dryness (water content reaches 0). The inclusion of the van-Genuchten-type models is due to their common application. If other retention models are required, users can access the data in data.csv for further data fitting. More information about the models can be found in the Methods section below. Fitting Tasks The model fitting can be categorized into three levels of tasks (specified by “fitting_task” column in the files). Level 1 (“fit_retention”) only includes retention data fitting (the only level available for the in-situ method). Level 2 (“fit_retention_conductivity”) includes both retention and hydraulic conductivity data fitting, and the saturated hydraulic conductivity (Ks, a parameter of the hydraulic conductivity functions) is fixed by the measurements from KSAT. Level 3 (“fit_retention_conductivity_Ks”) also includes both retention and hydraulic conductivity data fitting, but Ks is a fitted parameter without the constraints from KSAT measurements. Among the same retention models (e.g. vG_constrained models of the same sample), level 1 should produce the best retention data fitting. Level 2 should have the highest misfit of the retention and hydraulic conductivity data, because the retention and hydraulic conductivity functions share common model parameters, and the unsaturated hydraulic conductivity (HYPROP) data fitting is subject to Ks measured independently by KSAT. Level 3 should have mid-level misfits of the retention and hydraulic conductivity data. While level 3 fits the hydraulic conductivity data better than level 2, the fitted Ks value might be unreasonable due to the lack of constraints at the wet end of the measurements. General recommendation when using this data package: (1) Choice of sampling methods: Intact cores might suffer from sample gaps that would lead to overestimation of Ks (sample gaps can be inferred from the “soil_sample_volume” column in metadata.csv when the value is < 249). In-situ method has higher uncertainty in characterizing the wet end of the SWRC because of sensor limitations and the difficulty in reaching full saturation under natural conditions. (2) Choice of fitting tasks: When only retention data is needed, level 1 (“fit_retention”) should be prioritized. When both retention and hydraulic conductivity data are needed, level 2 (“fit_retention_conductivity”) could be prioritized. (3) Choice of models: This could depend on what the downstream models call for. If no specific model is required, model misfit could be used as a ranking criterion. Model misfit values in terms of RMSE can be found in model_parameters.csv. The following files are included in this data package: (1) metadata.csv – This file includes the general information of each sample, including location (description, geocoordinates, elevation), sampling and measurements details (method, depth, time or period, volume, instruments), and soil physical properties (bulk density, saturated hydraulic conductivity, only applicable to physical soil samples). (2) data.csv – This file includes soil water potential, volumetric water content, and unsaturated hydraulic conductivity data of each sample. Column “instrument” specifies the instrument (HYPROP, WP4C, or TEROS) used to perform the measurements. (3) model_fit.csv – This file includes soil water potential, volumetric water content, and unsaturated hydraulic conductivity fitted from the four models and three fitting tasks. Column “model_name” specifies the retention model used, and “fitting_task” specifies the level of data fitting. Missing values indicate that the variable does not apply to that fitting task. (4) model_parameters.csv – This file includes the fitted model parameters, model misfits, and conventional water content thresholds (field capacity and wilting point) from the four models and three fitting tasks. Column “model_name” specifies the retention model used, and “fitting_task” specifies the level of data fitting. Missing values indicate that the parameter does not apply to that model and/or that fitting task. (5) data_Ks.csv – This file includes the saturated hydraulic conductivity measurements from KSAT. (6) /figure/*.png – This folder includes three quick visualizations of the data, retention model fitting results and misfits, and hydraulic conductivity model fitting results, misfits, and parameters. The model fitting results are separated by samples and fitting tasks and colored by models. Zoom-in required. (7) /hyprop/*.bdhx – This folder includes proprietary hyprop files that require the free Labros SoilView-Analysis (METER) to open. Users can explore data fitting using other retention models (i.e. Brooks-Corey, Fredlund-Xing, Kosugi, bimodal models). Be aware that Ks value is pre-entered under “Fitting tab, Conductivity functions parameters” for level 2 fitting. If the value is lost, please refer to metadata.csv under “Ks” column. (8) Six file-level metadata that summarize file, header, column, and variable information of all files. This work was supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231.

EARTH SCIENCE > LAND SURFACE > SOILS↗

Soil Water Retention and Hydraulic Conductivity Data and Model at Snodgrass Mountain in East River Watershed, Colorado 2020-2025

This data package includes soil water retention and hydraulic conductivity data and model fitting results from measurements of ex-situ soil samples and in-situ soil sensors at Snodgrass Mountain. Soil water retention curves (SWRC) characterize soil water content as a function of soil water potential. SWRC depends on soil texture and pore structure and can be used to describe the constraints on biogeochemical processes in terms of soil water availability. In this data package, the sample identification follows the format SG-X-Y, where SG refers to Snodgrass Mountain, X is the location identifier, and Y is the depth identifier at the same X (shallow Y=1). Specifically, SG-EHS is associated with ecohydrology sites under the East-Taylor Watershed Community Observatory Sites directory, and SG-ERTn (upslope n=1) are points along the Snodgrass electrical resistivity tomography transect not associated with the existing site names in the directory. The sample and location information can be found in metadata.csv. Sampling and Measurements Each sample falls into one of the three sampling methods – (1) intact cores, (2) repacked samples, or (3) soil sensors – and one of the two measurement methods – (a) laboratory or (b) in-situ. Both intact cores and repacked samples were measured using the laboratory methods, which include measurements of soil water potential (HYPROP & WP4C, METER), saturated (KSAT, METER) and unsaturated hydraulic conductivity (HYPROP). The in-situ method uses a pair of co-located soil sensors to measure volumetric water content (TEROS12, METER) and soil water potential (TEROS21, METER), and the hydraulic conductivity was not measured. In comparison, the laboratory methods progress from full saturation to dry conditions, and the in-situ method includes both dry-to-wet and wet-to-dry cycles. The sampling and measurement methods for each sample can be found in metadata.csv, and more information about the measurements is detailed in the Methods section below. Models Retention and hydraulic conductivity data were fitted with four van-Genuchten-type models (specified by “model_name” column in the files): (1) traditional constrained van Genuchten model (“vG_constrained”), (2) traditional unconstrained van Genuchten model (“vG_unconstrained”), (3) PDI-variant of the constrained van Genuchten model (“vG_constrained_PDI”), and (4) PDI-variant of the unconstrained van Genuchten model (“vG_unconstrained_PDI”). The difference between the constrained (1: n) and the unconstrained (2: n, m) van Genuchten models is the number of pore-size distribution parameters in the model equations, giving the unconstrained model more degrees of freedom when fitting the data. Between the traditional and the PDI-variant models, model fitting differs the most at the dry end of the measurements. The traditional models allow infinite suction at the residual water content (water content does not drop below residual water content), and the PDI-variant models enforce a soil water potential value of pF=6.8 (~ -630 MPa) at oven-dryness (water content reaches 0). The inclusion of the van-Genuchten-type models is due to their common application. If other retention models are required, users can access the data in data.csv for further data fitting. More information about the models can be found in the Methods section below. Fitting Tasks The model fitting can be categorized into three levels of tasks (specified by “fitting_task” column in the files). Level 1 (“fit_retention”) only includes retention data fitting (the only level available for the in-situ method). Level 2 (“fit_retention_conductivity”) includes both retention and hydraulic conductivity data fitting, and the saturated hydraulic conductivity (Ks, a parameter of the hydraulic conductivity functions) is fixed by the measurements from KSAT. Level 3 (“fit_retention_conductivity_Ks”) also includes both retention and hydraulic conductivity data fitting, but Ks is a fitted parameter without the constraints from KSAT measurements. Among the same retention models (e.g. vG_constrained models of the same sample), level 1 should produce the best retention data fitting. Level 2 should have the highest misfit of the retention and hydraulic conductivity data, because the retention and hydraulic conductivity functions share common model parameters, and the unsaturated hydraulic conductivity (HYPROP) data fitting is subject to Ks measured independently by KSAT. Level 3 should have mid-level misfits of the retention and hydraulic conductivity data. While level 3 fits the hydraulic conductivity data better than level 2, the fitted Ks value might be unreasonable due to the lack of constraints at the wet end of the measurements. General recommendation when using this data package: (1) Choice of sampling methods: Intact cores and in-situ soil sensors could be prioritized because these sampling methods are less destructive. While the repacked samples were packed to the target bulk density (estimated post-sampling, when sample volume was known), these samples had altered pore structures. Nevertheless, intact cores might suffer from sample gaps that would lead to overestimation of Ks (sample gaps can be inferred from the “soil_sample_volume” column in metadata.csv when the value is < 249). In-situ method also has higher uncertainty in characterizing the wet end of the SWRC because of sensor limitations and the difficulty in reaching full saturation under natural conditions. (2) Choice of fitting tasks: When only retention data is needed, level 1 (“fit_retention”) should be prioritized. When both retention and hydraulic conductivity data are needed, level 2 (“fit_retention_conductivity”) could be prioritized. (3) Choice of models: This could depend on what the downstream models call for. If no specific model is required, model misfit could be used as a ranking criterion. Model misfit values in terms of RMSE can be found in model_parameters.csv. The following files are included in this data package: (1) metadata.csv – This file includes the general information of each sample, including location (description, geocoordinates, elevation), sampling and measurements details (method, depth, time or period, volume, instruments), and soil physical properties (bulk density, saturated hydraulic conductivity, only applicable to physical soil samples). (2) data.csv – This file includes soil water potential, volumetric water content, and unsaturated hydraulic conductivity data of each sample. Column “instrument” specifies the instrument (HYPROP, WP4C, or TEROS) used to perform the measurements. (3) model_fit.csv – This file includes soil water potential, volumetric water content, and unsaturated hydraulic conductivity fitted from the four models and three fitting tasks. Column “model_name” specifies the retention model used, and “fitting_task” specifies the level of data fitting. Missing values indicate that the variable does not apply to that fitting task. (4) model_parameters.csv – This file includes the fitted model parameters, model misfits, and conventional water content thresholds (field capacity and wilting point) from the four models and three fitting tasks. Column “model_name” specifies the retention model used, and “fitting_task” specifies the level of data fitting. Missing values indicate that the parameter does not apply to that model and/or that fitting task. (5) data_Ks.csv – This file includes the saturated hydraulic conductivity measurements from KSAT. (6) /figure/*.png – This folder includes three quick visualizations of the data, retention model fitting results and misfits, and hydraulic conductivity model fitting results, misfits, and parameters. The model fitting results are separated by samples and fitting tasks and colored by models. Zoom-in required. (7) /hyprop/*.bdhx – This folder includes proprietary hyprop files that require the free Labros SoilView-Analysis (METER) to open. Users can explore data fitting using other retention models (i.e. Brooks-Corey, Fredlund-Xing, Kosugi, bimodal models). Be aware that Ks value is pre-entered under “Fitting tab, Conductivity functions parameters” for level 2 fitting. If the value is lost, please refer to metadata.csv under “Ks” column. (8) Six file-level metadata that summarize file, header, column, and variable information of all files. This work was supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231.

EARTH SCIENCE > LAND SURFACE > SOILS↗

Lunar rovers and local positioning system

Telerobotic rovers equipped with adequate actuators and sensors are clearly necessary for extraterrestrial construction. They will be employed as substitutes for humans, to perform jobs like surveying, sensing, signaling, manipulating, and the handling of small materials. Important design criteria for these rovers include versatility and robustness. They must be easily programmed and reprogrammed to perform a wide variety of different functions, and they must be robust so that construction work will not be jeopardized by parts failures. The key qualities and functions necessary for these rovers to achieve the required versatility and robustness are modularity, redundancy, and coordination. Three robotic rovers are being built by CSC as a test bed to implement the concepts of modularity and coordination. The specific goal of the design and construction of these robots is to demonstrate the software modularity and multirobot control algorithms required for the physical manipulation of constructible elements. Each rover consists of a transporter platform, bus manager, simple manipulator, and positioning receivers. These robots will be controlled from a central control console via a radio-frequency local area network (LAN). To date, one prototype transporter platform frame was built with batteries, motors, a prototype single-motor controller, and two prototype internal LAN boards. Software modules were developed in C language for monitor functions, i/o, and parallel port usage in each computer board. Also completed are the fabrication of half of the required number of computer boards, the procurement of 19.2 Kbaud RF modems for inter-robot communications, and the simulation of processing requirements for positioning receivers. In addition to the robotic platform, the fabrication of a local positioning system based on infrared signals is nearly completed. This positioning system will make the rovers into a moving reference system capable of performing site surveys. In addition, a four degree mechanical manipulator especially suited for coordinated teleoperation was conceptually designed and is currently being analyzed. This manipulator will be integrated into the rovers as their end effector. Twenty internal LAN cards fabricated by a commercial firm are being used, a prototype manipulator and a range finder for a positioning system were built, a prototype two-motor controller was designed, and one of the robots is performing its first telerobotic motion. In addition, the robots' internal LAN's were coordinated and tested, hardware design upgrades based on fabrication and fit experience were completed, and the positioning system is running. The rover system is able to perform simple tasks such as sensing and signaling; coordination systems which allow construction tasks to begin were established, and soon coordinated teams of robots in the laboratory will be able to manipulate common objects.

Avery, James↗

Cryogenic Thermal Emittance Measurements on Small-Diameter Stainless Steel Tubing

The Mid Infrared Instrument aboard the James Webb Space Telescoep includes a mechanical cryocooler which cools its detectors to their 6 K operating temperature. The refrigerant flows through several meters of approximately 2 mm diameter 304L stainless steel tubing, with some sections gold plated, and some not, which are exposed to their environment. An issue of water freezing onto the tube surfaces is mitigated by a running a warm gas through the lines to sublimate the water. To model the effect of this process on nearby instruments, an accurate measure of the tube emittance is needed. Previously we reported the abosprtance of the gold plated stainless steel tubing as a function of source temperature (i.e. its environment). In this work the thermal emittance of the uncoated tubing is measured as a function of its temperature between 100 and 300 K. This value leads to an accurate prediction of the minimum length of time required to thermally recycle the system. We report the technique and present the results.

cryogenic↗

Cryogenic Thermal Emittance Measurements on Small-Diameter Stainless Steel Tubing

The Mid Infrared Instrument aboard the James Webb Space Telescope includes a mechanical cryocooler which cools its detectors to their 6 K operating temperature. The refrigerant flows through several meters of 2 mm diameter 304L stainless steel tubing, with some sections gold plated, and some not, which are exposed to their environment. An issue of water freezing onto the tube surfaces is mitigated by running a warm gas through the lines to sublimate the frozen water. To model the effect of this process on nearby instruments, an accurate measure of the tube emittance is needed. Previously we reported the absorptance of the gold plated stainless steel tubing as a function of source temperature (i.e. its environment). In this work the thermal emittance of the uncoated tubing is measured as a function of its temperature between 100 and 280 K. These values lead to an accurate prediction of the minimum length of time required to thermally recycle the system. We report the technique and present the results.

stainless steel↗

Experimental realization of Feynman’s ratchet

Feynman's ratchet is a microscopic machine in contact with two heat reservoirs, at temperatures T A and T B , that was proposed by Richard Feynman to illustrate the second law of thermodynamics. In equilibrium (T A = T B ), thermal fluctuations prevent the ratchet from generating directed motion. When the ratchet is maintained away from equilibrium by a temperature difference (T A ≠T B ), it can operate as a heat engine, rectifying thermal fluctuations to perform work. While it has attracted much interest, the operation of Feynman's ratchet as a heat engine has not been realized experimentally, due to technical challenges. In this work, we realize Feynman's ratchet with a colloidal particle in a one dimensional optical trap in contact with two heat reservoirs: one is the surrounding water, while the effect of the other reservoir is generated by a novel feedback mechanism, using the Metropolis algorithm to impose detailed balance. We verify that the system does not produce work when T A = T B , and that it becomes a microscopic heat engine when T A ≠T B . We analyze work, heat and entropy production as functions of the temperature difference and external load. As a result, our experimental realization of Feynman's ratchet and the Metropolis algorithm can also be used to study the thermodynamics of feedback control and information processing, the working mechanism of molecular motors, and controllable particle transportation.

42 ENGINEERING↗

Impact of Functionally Graded Cylinders: Theory

This final report summarizes the work funded under the Grant NAG3-2411 during the 04/05/2000-04/04/2001 period. The objective of this one-year project was to generalize the theoretical framework of the two-dimensional higher-order theory for the analysis of cylindrical functionally graded materials/structural components employed in advanced aircraft engines developed under past NASA Glenn funding. The completed generalization significantly broadens the theory's range of applicability through the incorporation of dynamic impact loading capability into its framework. Thus, it makes possible the assessment of the effect of damage due to fuel impurities, or the presence of submicron-level debris, on the life of functionally graded structural components. Applications involving advanced turbine blades and structural components for the reusable-launch vehicle (RLV) currently under development will benefit from the completed work. The theory's predictive capability is demonstrated through a numerical simulation of a one-dimensional wave propagation set up by an impulse load in a layered half-plane. Full benefit of the completed generalization of the higher-order theory described in this report will be realized upon the development of a related computer code.

Aboudi, Jacob↗

PI-in-a-box: Intelligent onboard assistance for spaceborne experiments in vestibular physiology

In construction is a knowledge-based system that will aid astronauts in the performance of vestibular experiments in two ways: it will provide real-time monitoring and control of signals and it will optimize the quality of the data obtained, by helping the mission specialists and payload specialists make decisions that are normally the province of a principal investigator, hence the name PI-in-a-box. An important and desirable side-effect of this tool will be to make the astronauts more productive and better integrated members of the scientific team. The vestibular experiments are planned by Prof. Larry Young of MIT, whose team has already performed similar experiments in Spacelab missions SL-1 and D-1, and has experiments planned for SLS-1 and SLS-2. The knowledge-based system development work, performed in collaboration with MIT, Stanford University, and the NASA-Ames Research Center, addresses six major related functions: (1) signal quality monitoring; (2) fault diagnosis; (3) signal analysis; (4) interesting-case detection; (5) experiment replanning; and (6) integration of all of these functions within a real-time data acquisition environment. Initial prototyping work has been done in functions (1) through (4).

Colombano, Silvano↗

Coupled Cluster Green's function formulations based on the effective Hamiltonians

In this work, we demonstrate that the effective Hamiltonians obtained with the downfolding procedure based on double unitary coupled cluster (DUCC) ansatz can be used in the context of Green’s function coupled cluster (GFCC) formalism to calculate spectral functions of molecular systems. This combined approach (DUCC-GFCC) provides a significant reduction of numerical effort and good agreement with the corresponding all-orbital GFCC methods in energy windows that are consistent with the choice of active space. These features are demonstrated on the example of two benchmark systems: H 2 O and N 2 , where DUCC-GFCC calculations were performed for active spaces of various sizes.

74 ATOMIC AND MOLECULAR PHYSICS↗

Heisenberg-scaling measurement protocol for analytic functions with quantum sensor networks

Here we generalize past work on quantum sensor networks to show that, for d input parameters, entanglement can yield a factor O(d) improvement in mean-squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and we conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗