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Comparing computational times for simulations when using PBPK model template and stand-alone implementations of PBPK models

Introduction We previously developed a PBPK model template that consists of a single model “superstructure” with equations and logic found in many physiologically based pharmacokinetic (PBPK) models. Using the template, one can implement PBPK models with different combinations of structures and features. Methods To identify factors that influence computational time required for PBPK model simulations, we conducted timing experiments using various implementations of PBPK models for dichloromethane and chloroform, including template and stand-alone implementations, and simulating four different exposure scenarios. For each experiment, we measured the required computational time and evaluated the impacts of including various model features (e.g., number of output variables calculated) and incorporating various design choices (e.g., different methods for estimating blood concentrations). Results We observed that model implementations that treat body weight and dependent quantities as constant (fixed) parameters can result in a 30% time savings compared with options that treat body weight and dependent quantities as time-varying. We also observed that decreasing the number of state variables by 36% in our PBPK model template led to a decrease of 20–35% in computational time. Other factors, such as the number of output variables, the method for implementing conditional statements, and the method for estimating blood concentrations, did not have large impacts on simulation time. In general, simulations with PBPK model template implementations of models required more time than simulations with stand-alone implementations, but the flexibility and (human) time savings in preparing and reviewing a model implemented using the PBPK model template may justify the increases in computational time requirements. Conclusion Our findings concerning how PBPK model design and implementation decisions impact computational speed can benefit anyone seeking to develop, improve, or apply a PBPK model, with or without the PBPK model template.

Bernstein, Amanda S.

A mathematical approach to using the forgetting curve to evaluate experience and training factors in human reliability analysis

Traditional human reliability analysis (HRA) methods have difficulty dealing with the dynamic nature of factors such as time and rely on static and expert-judgment-based assessments of performance-shaping factors (PSFs) across limited levels. In this study, we introduce a mathematical approach for dynamically evaluating the experience and training PSF. Our proposed method integrates the psychological concept of the “forgetting curve” to evaluate how PSFs are impacted by the number of trainings and the time elapsed since training. To confirm the validity of the model, we provide experimental data fitted by identifying the quantitative relationship between training and human performance. This research enables dynamic and objective assessments, thus reducing reliance on subjective expert judgment and improving the accuracy of HRA.

99 - GENERAL AND MISCELLANEOUS

Transmon Qubit Using Sn as a Junction Superconductor

Superconductor qubits typically use aluminum–aluminum oxide tunnel junctions to provide the nonlinear inductance. Junctions with semiconductor barriers make it possible to vary the superconductor material and explore beyond aluminum. We use InAs semiconductor nanowires coated with thin superconducting shells of β-Sn to realize transmon qubits. By tuning the Josephson energy with a gate voltage, we adjust the qubit frequency over a range of 3 GHz. The longest energy relaxation time, T 1 = 27 μs, is obtained at the lowest qubit frequencies, while the longest echo dephasing time, T 2 = 1.8 μs, is achieved at higher frequencies. Finally, we assess the possible factors limiting coherence times in these devices and discuss steps to enhance performance through improvements in materials fabrication and circuit design.

B-Sn

Scalable Circuit Cutting and Scheduling in a Resource-constrained and Distributed Quantum System

Despite quantum computing's rapid development, current systems remain limited in practical applications due to their limited qubit count and quality. Various technologies, such as superconducting, trapped ions, and neutral atom quantum computing technologies are progressing towards a fault tolerant era, however they all face a diverse set of challenges in scalability and control. Recent efforts have focused on multi-node quantum systems that connect multiple smaller quantum devices to execute larger circuits. Future demonstrations hope to use quantum channels to couple systems, however current demonstrations can leverage classical communication with circuit cutting techniques. This involves cutting large circuits into smaller subcircuits and reconstructing them post-execution. However, existing cutting methods are hindered by lengthy search times as the number of qubits and gates increases. Additionally, they often fail to effectively utilize the resources of various worker configurations in a multi-node system. To address these challenges, we introduce FitCut, a novel approach that transforms quantum circuits into weighted graphs and utilizes a community-based, bottom-up approach to cut circuits according to resource constraints, e.g., qubit counts, on each worker. FitCut also includes a scheduling algorithm that optimizes resource utilization across workers. Implemented with Qiskit and evaluated extensively, FitCut significantly outperforms the Qiskit Circuit Knitting Toolbox, reducing time costs by factors ranging from 3 to 2000 and improving resource utilization rates by up to 3.88 times on the worker side, achieving a system-wide improvement of 2.86 times.

Kan, Shuwen [Fordham University]

Introducing a Markov chain-based time calibration procedure for multi-channel particle detectors: application to the SuperFGD and ToF detectors of the T2K experiment

Inter-channel mis-synchronisation can be a limiting factor to the time resolution of high performance timing detectors with multiple readout channels and independent electronics units. In these systems, time calibration methods employed must be able to efficiently correct for minimal mis-synchronisation between channels and achieve the best detector performance. We present an iterative time calibration method based on Markov Chains, suitable for detector systems with multiple readout channels. Starting from correlated hit pairs alone, and without requiring an external reference time measurement, the method solves for fixed per-channel offsets, with precision limited only by the intrinsic single-channel resolution. A mathematical proof that the method is able to find the correct time offsets to be assigned to each detector channel in order to achieve inter-channel synchronisation is given, and it is shown that the number of iterations to reach convergence within the desired precision is controllable with a single parameter. Numerical studies are used to confirm unbiased recovery of true offsets. Finally, the application of the calibration method to the Super Fine-Grained Detector (SuperFGD) and the Time of Flight (TOF) detector at the upgraded T2K near detector (ND280) shows good improvement in overall timing resolution, demonstrating the effectiveness in a real-world scenario and scalability.

calibration and fitting methods

MicroBooNE investigations on the photon interpretation of the MiniBooNE low energy excess

The MicroBooNE experiment is a liquid argon time projection chamber with 85-ton active volume at Fermilab, operated from 2015 to 2020 to collect neutrino data from Fermilab's Booster Neutrino Beam. One of MicroBooNE's physics goals is to investigate possible explanations of the low-energy excess observed by the MiniBooNE experiment in $\nu_{\mu}\rightarrow \nu_{e}$ neutrino oscillation measurements. MicroBooNE has performed searches to test hypothetical interpretations of the MiniBooNE low-energy excess, including the underestimation of the photon background or instrinic $\nu_{e}$ background. This thesis presents MicroBooNE's searches for two neutral current (NC) single-photon production processes that contribute to the photon background of the MiniBooNE measurement: NC $\Delta$ resonance production followed by $\Delta$ radiative decay: $\Delta \rightarrow N\gamma$, and NC coherent single-photon production. Both searches take advantage of boosted decision trees to yield efficient background rejection, and a high-statistic NC $\pi^0$ measurement to constrain dominant background, and make use of MicroBooNE's first three years of data. The NC $\Delta \rightarrow N\gamma$ measurement yielded a bound on the $\Delta$ radiative decay process at 2.3 times the predicted nominal rate at 90\% confidence level(C.L.), disfavoring a candidate photon interpretation of the MiniBooNE low-energy excess as a factor of 3.18 times the nominal NC Δ radiative decay rate at the 94.8\% C.L. The NC coherent single photon measurement leads to the world's first experimental limit on the cross-section of this process below 1 GeV, of $1.49 \times 10^{-41} \text{cm}^2$ at 90\% C.L., corresponding to 24.0 times the nominal prediction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Tomography of pions and kaons in the QCD vacuum: Transverse momentum dependent parton distribution functions

We evaluate the pion and kaon transverse momentum dependent parton distribution functions in the instanton liquid model, a model of the QCD vacuum at low resolution. The relevant transverse momentum distributions (TMDs) are factored into a constituent quark distribution times a rapidity dependent soft factor from staple-shaped Wilson lines, for fixed parton longitudinal momentum and transverse separation. The results are evolved to higher rapidities using the Collins-Soper kernel and higher resolution using renormalization group evolution. The comparison to existing extractions of pion TMDs from Drell-Yan data is briefly discussed.

classical solutions in field theory

Timing based clustering of childhood BMI trajectories reveals differential maturational patterns; Study in the Northern Finland Birth Cohorts 1966 and 1986

Children’s biological age does not always correspond to their chronological age. In the case of BMI trajectories, this can appear as phase variation, which can be seen as shift, stretch, or shrinking between trajectories. With maturation thought of as a process moving towards the final state - adult BMI, we assessed whether children can be divided into latent groups reflecting similar maturational age of BMI. The groups were characterised by early factors and time-related features of the trajectories. We used data from two general population birth cohort studies, Northern Finland Birth Cohorts 1966 and 1986 (NFBC1966 and NFBC1986). Height (n = 6329) and weight (n = 6568) measurements were interpolated in 34 shared time points using B-splines, and BMI values were calculated between 3 months to 16 years. Pairwise phase distances of 2999 females and 3163 males were used as a similarity measure in k-medoids clustering. We identified three clusters of trajectories in females and males (Type 1: females, n = 1566, males, n = 1669; Type 2: females, n = 1028, males, n = 973; Type 3: females, n = 405, males, n = 521). Similar distinct timing patterns were identified in males and females. The clusters did not differ by sex, or early growth determinants studied. Trajectory cluster Type 1 reflected to the shape of what is typically illustrated as the childhood BMI trajectory in literature. However, the other two have not been identified previously. Type 2 pattern was more common in the NFBC1966 suggesting a generational shift in BMI maturational patterns.

60 APPLIED LIFE SCIENCES

Tundra Vegetation Community Type, Not Microclimate, Controls Asynchrony of Above‐ and Below‐Ground Phenology

The below-ground growing season often extends beyond the above-ground growing season in tundra ecosystems and as the climate warms, shifts in growing seasons are expected. However, we do not yet know to what extent, when and where asynchrony in above- and below-ground phenology occurs and whether variation is driven by local vegetation communities or spatial variation in microclimate. Here, we combined above- and below-ground plant phenology metrics to compare the relative timings and magnitudes of leaf and fine-root growth and senescence across microclimates and plant communities at five sites across the Arctic and alpine tundra biome. We observed asynchronous growth between above- and below-ground plant tissue, with the below-ground season extending up to 74% (~56 days) beyond the onset of above-ground leaf senescence. Plant community type, rather than microclimate, was a key factor controlling the timing, productivity, and growth rates of fine roots, with graminoid roots exhibiting a distinct ‘pulse’ of growth later into the growing season than shrub roots. Our findings indicate the potential of vegetation change to influence below-ground carbon storage as the climate warms and roots remain active in unfrozen soils for longer. Taken together, our findings of increased root growth in soils that remain thawed later into the growing season, in combination with ongoing tundra vegetation change including increased shrub and graminoid abundance, indicate increased below-ground productivity and altered carbon cycling in the tundra biome.

below-ground

Millisecond lifetimes and coherence times in 2D transmon qubits

Materials improvement is a powerful approach to reducing loss and decoherence in superconducting qubits, because such improvements can be readily translated to large-scale processors. Recent work improved transmon coherence by using tantalum as a base layer and sapphire as a substrate. The losses in these devices are dominated by two-level systems with comparable contributions from both the surface and bulk dielectrics, indicating that both must be tackled to achieve substantial improvements in the state of the art. Here we show that replacing the substrate with high-resistivity silicon markedly decreases the bulk substrate loss, enabling 2D transmons with time-averaged quality factors (Q avg ) of 9.7 × 10 6 across 45 qubits. For our best qubit, we achieve a Q avg of 1.5 × 10 7 , reaching a maximum Q of 2.5 × 10 7 , corresponding to a lifetime (T 1 ) up to 1.68 ms. This low loss also allows us to observe decoherence effects related to the Josephson junction, and we use an improved, low-contamination junction deposition to achieve Hahn echo coherence times (T 2E ) exceeding T 1 . We achieve these materials improvements without any modifications to the qubit architecture, allowing us to readily incorporate standard quantum control gates. Here, we demonstrate single-qubit gates with 99.994% fidelity. The tantalum-on-silicon platform comprises a simple material stack that can potentially be fabricated at the wafer scale and therefore can be readily translated to large-scale quantum processors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Modeling glass degradation and release of radionuclides from vitrified waste for performance assessment simulations

The release of radionuclides initially encapsulated in a slowly degrading solid waste form and contained in an eventually corroding canister defines the source term for numerical simulations for the assessment of a geologic repository for high-level radioactive waste. While the details of waste degradation, canister corrosion, and dissolution and mobilization of the radionuclides in pore water include complex chemical reaction and transport processes that are coupled to the thermal, hydrological, microbiological, and mechanical conditions in the repository, the source-term model suitable for use in a numerical performance assessment model should be a defensible abstraction of these mechanisms. We developed a radiological source-term model and implemented it into a non-isothermal flow and transport simulator. While the proposed source-term model is applicable to various waste forms, canister systems, and disposal concepts, we specifically considered radionuclide releases from vitrified high-level waste placed in a cylindrical canister disposed in a deep vertical borehole repository. In this model, waste degradation is a function of temperature, and it can be adjusted to evaluate the influence of and propagate uncertainties in pH, passivation reactions, and chemical conditions as well as geometrical factors. The time-dependent, congruent release of safety-relevant radionuclides present in the decaying inventory is then calculated. Finally, the radionuclides are mobilized by diffusive and advective transport according to the thermo-hydraulic conditions prevailing in the near field of the repository, from where they migrate through the geosphere to the accessible environment. We examine the influence of the source-term model’s parameters on performance assessment calculations through sensitivity and uncertainty propagation analyses, identifying influential factors and confirming the upper bound of their impact. These considerations align with the overarching goal of repository design, which is to demonstrate that engineered and natural barriers can collectively delay radionuclide migration for timescales far exceeding human planning, thereby providing multiple, redundant barriers against environmental contamination.

iTOUGH2

Measuring the neutrino-oxygen neutral current quasielastic cross section using the accelerator neutrino neutron interaction experiment

The Accelerator Neutrino Neutron Interaction Experiment (ANNIE) is a 26-ton gadolinium-doped water Cherenkov detector located on-axis to Fermilab’s Booster Neutrino Beam (BNB). ANNIE is uniquely positioned to perform high-statistics measurements of neutrino-nucleus interactions in water, benefiting from a large neutrino flux due to a short (100-meter) baseline. A central focus of ANNIE’s physics program is the measurement of both charged current (CC) and neutral current (NC) cross sections on water, including neutral current quasielastic (NCQE) and CC-inclusive channels. The NCQE measurement is particularly critical for constraining uncertainties in rare-event searches such as the Diffuse Supernova Neutrino Background (DSNB), where atmospheric $\nu$NCQE interactions constitute a significant and poorly constrained background. This dissertation presents a measurement of the flux-averaged neutrino-oxygen neutral current quasielastic ($\nu$NCQE) cross section using $2.573 \times 10^{20}$~POT of BNB exposure from the 2022 and 2023 beam years. The $\nu$NCQE interaction is identified through the primary $\gamma$-rays produced by nuclear de-excitation of the residual $^{15}$N$^*$ or $^{15}$O$^*$ nucleus following nucleon knockout from $^{16}$O. A dedicated Monte Carlo (MC) re-tuning campaign was conducted using an americium-beryllium (AmBe) calibration source, Michel electrons from stopped muons, and throughgoing dirt muons originating upstream of the detector. This multi-sample approach provided a wide-ranging $\mathcal{O}(\text{MeV})$--$\mathcal{O}(\text{GeV})$ dataset for tuning the simulated detector response, which was subsequently validated against AmBe neutron and Michel electron data for use in the $\nu$NCQE analysis. A dedicated laser calibration campaign was carried out to reduce timing uncertainties across the PMT system, enabling reconstruction of the BNB bunch substructure with sufficient resolution to serve as a background rejection tool. By selecting events in-time with individual neutrino bunches, beam-correlated $\nu$NCQE events are separated from diffuse and accelerator-induced backgrounds, notably skyshine neutrons and externally-originating events, that would otherwise dominate traditional charge-based selections within a small-scale, surface-level, short-baseline detector. A data-driven estimation of the skyshine neutron and external background rates was performed and incorporated into the systematic uncertainty budget. The flux-averaged $\nu$NCQE cross section on oxygen is measured to be $1.57 \pm 0.06\,(\text{stat.})$ $^{+0.91}_{-0.67}\,(\text{syst.})$ $\times 10^{-38}\ \text{cm}^{2}$. A full systematic budget is constructed by propagating uncertainties in the secondary hadronic interaction modeling, background cross section normalizations, detector response, neutrino flux, and the primary $\gamma$-ray emission probabilities from oxygen nuclear de-excitation. An idealized de-excitation model, constructed from existing measurements in the literature is developed to benchmark the predictions of the \textsc{GENIE} event generator. A comparison reveals that \textsc{GENIE} systematically overpredicts the primary $\gamma$-ray emission probability from oxygen de-excitation by a factor of $1.49\times$ for $E_\gamma > 6$~MeV and $3.07\times$ in the $3$--$6$~MeV band. This comparison motivates the dominant systematic uncertainty in this analysis, where a conservative uncertainty of $^{+39.9\%}_{-0\%}$ on the primary $\gamma$-ray signal prediction is assigned. The ANNIE result is consistent with and complementary to existing flux-averaged $\nu$NCQE cross section measurements from T2K and Super-Kamiokande, providing an independent measurement with a different detector, neutrino beam, and analysis methodology. Looking ahead, an upgrade to the ANNIE DAQ infrastructure enabling continuous extended readout will allow a complementary $\nu$NCQE neutron multiplicity measurement, directly relevant to constraining the NCQE background in DSNB searches, competitive with the recent T2K measurement at SK-Gd. The planned Super-SANDI upgrade, deploying a large Water-based Liquid Scintillator (WbLS) volume, will further extend ANNIE's reach to hadronic final states and exclusive NC channels, and enable joint measurements with liquid argon detectors sharing the BNB beamline ahead of DUNE and Hyper-Kamiokande.

Doran, Steven [Iowa State U.]

A Comprehensive Analysis of Uncertainties in Warm-Rain Parameterizations in Climate Models Based on In Situ Measurements

Abstract Because of the coarse grid size of Earth system models (ESMs), representing warm-rain processes in ESMs is a challenging task involving multiple sources of uncertainty. Previous studies evaluated warm-rain parameterizations mainly according to their performance in emulating collision–coalescence rates for local droplet populations over a short period of a few seconds. The representativeness of these local process rates comes into question when applied in ESMs for grid sizes on the order of 100 km and time steps on the order of 20–30 min. We evaluate several widely used warm-rain parameterizations in ESM application scenarios. In the comparison of local and instantaneous autoconversion rates, the two parameterization schemes based on numerical fitting to stochastic collection equation (SCE) results perform best. However, because of Jessen’s inequality, their performance deteriorates when grid-mean, instead of locally resolved, cloud properties are used in their simulations. In contrast, the effect of Jessen’s inequality partly cancels the overestimation problem of two semianalytical schemes, leading to an improvement in the ESM-like comparison. In the assessment of uncertainty due to the large time step of ESMs, it is found that the rainwater tendency simulated by the SCE is roughly linear for time steps smaller than 10 min, but the nonlinearity effect becomes significant for larger time steps, leading to errors up to a factor of 4 for a time step of 20 min. After considering all uncertainties, the grid-mean and time-averaged rainwater tendency based on the parameterization schemes is mostly within a factor of 4 of the local benchmark results simulated by SCE.

Meteorology & Atmospheric Sciences

Optimizing high energy density sulfur cathodes: A multivariate approach to electrode formulation and processing

Lithium-sulfur (Li-S) batteries involve complex solid-liquid-solid phase transformations during both discharging and charging processes, where cathode materials, formulation, and structure play a crucial role. Here, a design of experiments (DoE) methodology and an empirical model are developed to systematically explore the interactions and trade-offs among cathode factors and process variables, and to obtain generalizable effects estimates for the multivariate system. Compared to the conventional one-factor-at-a-time (OFAT) approach, this work demonstrates advantages in both efficiency and accuracy by allowing the data to guide future research and decisions. Further, an optimized cathode formulation and processing parameters are predicted and validated experimentally, achieving over 1000 mAh g -1 in discharge capacity and improved cycling under practical lean electrolyte (4 µL mg -1 S) and high S-loading cathodes (>4 mg cm -2 ) conditions. The optimized cathode was scaled up and assembled into Li-S pouch cells, achieving 316 Wh kg -1 in cell-level energy, proving that the comprehensive and rigorous framework for optimizing complex systems with DoE leads to improved performance in a practical pouch cell system.

25 ENERGY STORAGE

Capturing Surface Coverage Effects in Heterogeneous Catalysis

Adsorbate–adsorbate lateral interactions at relevant surface coverages have a significant effect on chemical kinetics, thereby influencing the activity of a heterogeneous catalyst. Coverage-dependent kinetic and thermodynamic parameters therefore must be included in studies of such complex systems to properly predict the turnover frequencies and kinetic trends. Thus, it becomes extremely important to accurately capture the strength of lateral interactions between neighboring species under realistic reaction conditions. In this Perspective, we discuss the various existing computational and experimental methods for determining adspecies coverage and configurational effects. The choice of the tools and methods employed in such studies depends on factors such as time, length scales, computational cost, the presence of solvents, and reaction conditions. The applications of each method and the respective challenges are also discussed here. As a result, we discuss the recent developments and future of the state-of-the-art for inclusion of surface coverage and configuration into a holistic picture for accurate predictions of catalytic behavior.

09 BIOMASS FUELS

Efficient wind farm layout optimization with the FLOWERS AEP model and analytic gradients

Wind farm layout optimization (WFLO) studies often aim to maximize the annual energy production (AEP) of a wind farm by choosing an arrangement of turbines that minimizes wake interactions. One way to reduce the cost of WFLO studies is by using more computationally efficient AEP models. The cost of standard AEP modeling approaches, based on the numerical integration of low-fidelity engineering wake models, scales poorly with the number of simulated discrete wind conditions. A second way to reduce cost when using a gradient-based algorithm is to supply exact gradient information instead of finite-difference estimates. However, analytical functions for the derivatives of AEP with respect to turbine positions are not always available in the conventional modeling approach. FLOWERS is a computationally inexpensive, analytical model for wind farm AEP that is specifically developed for WFLO applications. In this paper, we analyze the performance of the FLOWERS AEP model with analytic gradients in a layout optimization study compared with a reference optimization framework across three wind farm case studies. We find that the FLOWERS-based approach reduces computation time by a factor of 50–4000 and improves optimal AEP by about 0.3% with less than half of the variability in AEP across instances with randomized initial conditions. We also find the optimal layouts to be insensitive to model parameter tuning, making FLOWERS-based layout optimization a streamlined, user-friendly approach.

17 WIND ENERGY

Efficient Optimization of Plasma Radiation Detector Configurations using Imperfect Inference Models

The configurations of instruments fielded on an experiment affect the amount of information captured and the quality of subsequent inference. Here, we investigate the problem of optimizing plasma x-ray radiation detectors in a magneto-inertial fusion experiment at Sandia National Laboratories. It is impossible to directly measure properties such as the temperature of the thermonuclear fusion plasma produced in these experiments because of the extreme environment and destructive nature of the experiment. Among other diagnostics, several detectors are placed with significant standoff from the fusion target to capture the x-rays emitted by the fusion plasma, which can be used to infer some of its properties. To optimize the configuration of these detectors, a high-fidelity model (HFM) is used for simulating outputs and a low-fidelity model (LFM) is used for inference. We develop methods based on A- and L-optimality criteria that are efficient to compute while explicitly accounting for the discrepancy between the HFM and the LFM. The method allows us to find detector configurations that perform similarly to or better than the configuration obtained using an existing sampling-based optimization method while decreasing computational time by a factor of 50. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Bayesian optimization

Enhanced Carbon Dioxide Uptake in Drilled Hollow Core Fibers for Raman Spectroscopy

Fiber-based Raman spectroscopy enhances the Raman signal by maximizing the overlap of the optical field and the gas species. However, filling the hollow-core fiber (HCF) with gas requires time that is dependent on the fiber core diameter, fiber length, and pressure of the gas. At ambient pressure, the fiber gas uptake is driven by diffusion into the fiber ends, severely limiting the response time of the system. By laser drilling access holes to the core along the length of the fiber, the uptake time of the gas is reduced, improving the system response time. In this work, we study the carbon dioxide (CO 2 ) sensor dynamics based on Raman signal intensity generated in HCFs. The signal intensity versus gas concentration is characterized by controlling the CO 2 concentration in the surrounding environment of the fiber. Next, we characterize the gas uptake time in HCFs as a function of fiber length. Finally, we optimize the access hole configuration along the fiber, demonstrating reduced sensor uptake time by a factor of three.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH