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At least 1,333 records · Page 74

CoSim: A Simulator for Co-Scheduling of Batch and On-Demand Jobs in HPC Datacenters

The increasing scale and complexity of scientific applications are rapidly transforming the ecosystem of tools, methods, and workflows adopted by the high-performance computing (HPC) community. Big data analytics and deep learning are gaining traction as essential components in this ecosystem in a variety of scenarios, such as, steering of experimental instruments , acceleration of high-fidelity simulations through surrogate computations, and guided ensemble searches. In this context, the batch job model traditionally adopted by the supercomputing in-frastructures needs to be complemented with support to schedule opportunistic on-demand analytics jobs, leading to the problem of efficient preemption of batch jobs with minimum loss of progress. In this paper, we design and implement a simulator, CoSim, that enables on-the-fly analysis of the trade-offs arising between delaying the start of opportunistic on-demand jobs, which leads to longer analytics latency, and loss of progress due to preemption of batch jobs, which is necessary to make room for on-demand jobs. To this end, we propose an algorithm based on dynamic programming with predictable performance and scalability that enables supercomputing infrastructure schedulers to analyze the aforementioned trade-off and take decisions in near real-time. Compared with other state-of-art approaches using traces of the Theta pre-Exascale machine, our approach is capable of finding the optimal solution, while achieving high performance and scalability.

batch job preemption↗

Integrated Effects of Site Hydrology and Vegetation on Exchange Fluxes and Nutrient Cycling at a Coastal Terrestrial‐Aquatic Interface

Abstract The complex interactions among soil, vegetation, and site hydrologic conditions driven by precipitation and tidal cycles control the biogeochemical transformations and bi‐directional exchange of carbon and nutrients across the terrestrial–aquatic interfaces (TAIs) in coastal regions. This study uses a highly mechanistic model, Advanced Terrestrial Simulator (ATS)‐PFLOTRAN, to explore how these interactions affect exchanges of materials and carbon and nitrogen cycling. We used a transect in the Chesapeake Bay region that spans zones of open water, coastal wetland, transition, and upland forest. We designed several simulation scenarios to parse the effects of the individual controlling factors and the sensitivity of carbon cycling to reaction rate parameters derived from laboratory experiments. Our simulations reveal an active zone for carbon cycling under the transition zones between the wetland and the upland. Evapotranspiration is found to enhance the exchange fluxes between the surface and subsurface domains, resulting in a higher dissolved oxygen concentration in the TAIs. The transport of organic carbon derived from plant leaves and roots provide an additional source of organic carbon needed for the aerobic respiration and denitrification processes in the TAIs. The variability in reaction rate parameters associated with microbial activities is also found to play a dominant role in controlling the heterogeneity and dynamics of the simulated redox conditions. This modeling‐focused exploratory study enabled us to better understand the complex interactions among soil, water and microbes that govern the hydro‐biogeochemical processes at the TAIs, which is an important step toward representing coastal ecosystems in larger‐scale Earth system models.

54 ENVIRONMENTAL SCIENCES↗

A machine learning approach targeting parameter estimation for plant functional type coexistence modeling using ELM-FATES (v2.0)

Tropical forest dynamics play a crucial role in the global carbon, water, and energy cycles. However, realistically simulating the dynamics of competition and coexistence between different plant functional types (PFTs) in tropical forests remains a significant challenge. This study aims to improve the modeling of PFT coexistence in the Functionally Assembled Terrestrial Ecosystem Simulator (FATES), a vegetation demography model implemented in the Energy Exascale Earth System Model (E3SM) land model (ELM), ELM-FATES. Specifically, we explore (1) whether plant trait relationships established from field measurements can constrain ELM-FATES simulations and (2) whether machine learning (ML)-based surrogate models can emulate the complex ELM-FATES model and optimize parameter selections to improve PFT coexistence modeling. We conducted three ensembles of ELM-FATES experiments at a tropical forest site near Manaus, Brazil. By comparing the ensemble experiments without (Exp-CTR) and with (Exp-OBS) consideration of observed trait relationships, we found that accounting for these relationships slightly improves the simulations of water, energy, and carbon variables when compared to observations but degrades the simulation of PFT coexistence. Using ML-based surrogate models trained on Exp-CTR, we optimized the trait parameters in ELM-FATES and conducted another ensemble of experiments (Exp-ML) with these optimized parameters. The proportion of PFT coexistence experiments significantly increased from 21 % in Exp-CTR to 73 % in Exp-ML. After filtering the experiments that allow for PFT coexistence to agree with observations (within 15 % tolerance), 33 % of the Exp-ML experiments were retained, which is a significant improvement compared to the 1.4 % in Exp-CTR. Exp-ML also accurately reproduces the annual means and seasonal variations in water, energy, and carbon fluxes and the field inventory of aboveground biomass. This study represents a reproducible method that utilizes machine learning to identify parameter values that improve model fidelity against observations and PFT coexistence in vegetation demography models for diverse ecosystems. Our study also suggests the need for new mechanisms to enhance the robust simulation of coexisting plants in ELM-FATES and has significant implications for modeling the response and feedbacks of ecosystem dynamics to climate change.

54 ENVIRONMENTAL SCIENCES↗

Quantum utility in simulating the real-time dynamics of the Fermi–Hubbard model using superconducting quantum computers

The Fermi–Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi–Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi–Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi–Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Lastly, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.

97 MATHEMATICS AND COMPUTING↗

MLEC-Sim: A Simulator for Evaluating Multi-Level Erasure Coding

We present MLEC-Sim, a sophisticated simulator for Multi-Level Erasure Coding (MLEC), developed in approximately 13 KLOC. The simulator is engineered to analyze the impact of various system configurations and erasure coding policies on system durability and network overhead. It supports a comprehensive range of parameters including disk capacity, disk I/O bandwidth, failure rates, network bandwidth, and system scale, accommodating various erasure coding approaches such as Single-Level Erasure Coding (SLEC), Multi-Level Erasure Coding (MLEC), and Local Reconstruction Codes (LRC). MLEC-Sim provides support for multiple chunk placement policies, including clustered parity and declustered parity, and encompasses a variety of repair methods like Repair-ALL, Repair-FCO, Repair-HYB, and Repair-MIN. It is capable of simulating disk failures through a variety of means, including distribution-based or trace-based mechanisms, and can handle complex multi-level (de)clustered placements and repair processes. A key feature of MLEC-Sim is its adoption of the splitting simulation method for evaluating system durabilities at extremely high levels, which are challenging to assess with traditional simulation approaches. This feature allows for a detailed evaluation of system resilience under a range of conditions, aiding in the selection of appropriate erasure coding solutions for enhancing system durability. MLEC-Sim contributes to the field of data storage and reliability by providing a tool for the detailed evaluation of the durability and efficiency of erasure coding configurations, intended for use by researchers and practitioners in the design and optimization of storage systems.

Wang, Meng↗

Modeling thin layers of analytes on substrates for spectral analysis: use of solid/liquid n and k values to model reflectance spectra

Since solids are only sometimes seen en masse in a pure bulk form, and for liquids other than water almost never, a capability to model reflectance spectra from analytes deposited on various substrates would be highly advantageous. If available, the real, n ( ν ) , and imaginary, k ( ν ) , components of the complex refractive index, n n + i k , can be used to simulate infrared spectra, accounting for reflection, refraction, and absorption phenomena as a function of wavelength. We focus on using the Pacific Northwest National Laboratory (PNNL) derived n / k vectors for solid and liquid analytes deposited as thin layers on different types of substrates including conductors, such as aluminum, and inorganic dielectrics, such as glass. The model is an adaptation of the Monte Carlo ray trace modeling program, TracePro, extended through the use of its macrolanguage. The model is tested using thin films of organic liquids including silicone oil and no. 2 diesel fuel, as well as organic solids such as caffeine and acetaminophen on aluminum and glass. The predicted spectra for the solid films were compared to experimental hemispherical reflectance data measured using a Fourier transform spectrometer with an integrating sphere. The thickness of the calculated layer is a parameter for predicting the (transflectance) spectra and is obtained using the areal density measured from gravimetric methods to generate the thin-layer samples. Comparison of the calculated spectra with experimental hemispherical reflectance data shows excellent agreement, indicating promise for the use of measured n / k data to synthesize reference spectral data. In particular, accounting for the inhomogeneity of the deposits greatly improved the match with experimental data. Finally, the theoretical modeling shows that for thicker layers (ca. 20 to 100 μm) of typical organics possessing moderately strong k values, the longwave infrared features are often saturated and better spectral contrast is obtained from the overtone/combination bands in the shortwave infrared.

42 ENGINEERING↗

Lie-algebraic classical simulations for quantum computing

The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for Clifford circuits, tensor networks for low entanglement-generating circuits, or Wick's theorem for fermionic Gaussian states have become central tools in quantum computing. In this work, we contribute to this body of knowledge by presenting a framework for classical simulations, dubbed “𝔤-sim”, which is based on the underlying Lie algebraic structure of the dynamical process. When the dimension of the algebra grows at most polynomially in the system size, there exist observables for which the simulation is efficient. Indeed, we show that 𝔤-sim enables new regimes for classical simulations, is able to deal with certain forms of noise in the evolution, as well as can be used to tackle several paradigmatic variational and nonvariational quantum computing tasks. For the former, we perform Lie-algebraic simulations to train and optimize parametrized quantum circuits (thus effectively showing that some variational models can be dequantized), design enhanced parameter initialization strategies, solve tasks of quantum circuit synthesis, and train a quantum-phase classifier. For the latter, we report large-scale noiseless and noisy simulations on benchmark problems. By comparing the limitations of 𝔤-sim and certain Wick's theorem-based simulations, we find that the two methods become inefficient for different types of states or observables, hinting at the existence of distinct, nonequivalent resources for classical simulation.

97 MATHEMATICS AND COMPUTING↗

Insights into lithium ion deposition on lithium metal surfaces

Lithium metal is among the most promising anodes for the next generation of batteries due to its high theoretical energy density and high capacity. Challenges such as extreme reactivity and lithium dendrite formation have kept lithium metal anodes away from practical applications. However, the underlying mechanisms of Li ion deposition from the electrolyte solution onto the anode surface are still poorly understood due to their inherent complexity. In this work, density functional theory calculations and thermodynamic integration via constrained molecular dynamics simulations are conducted to study the electron and ion transfer between lithium metal slab and the electrolyte in absence of an external field. Here, we explore the effect of the solvent chemistry and structure, distance of the solvated complex from the surface, anion–cation separation, and concentration of Li-salts on the deposition of lithium ions from the electrolyte phase onto the surface. Ethylene carbonate (EC), 1,2-dimethoxyethane (DME), 1,3-dioxolane (DOL), and mixtures of them are used as solvents. These species compete with the salt anion and the Li cation for electron transfer from the surface. It is found that the structure and properties of the solvation shell around the lithium cation has a great influence on the ability of the cation to diffuse as well as on its surrounding electron environment. DME molecules allow easier motion of the lithium ion compared with EC and DOL molecules. The slow growth approach allows the study of energy barriers for the ion diffusion and desolvation during the deposition pathway. This method helps elucidating the underlying mechanisms on lithium-ion deposition and provides a better understanding of the early stages of Li nucleation.

25 ENERGY STORAGE↗

Ra-226 extraction and purification from simulated uranium tailings

Growing demand for Ac-225 has outstripped current production, increasing interest in alternative production routes. Furthermore, these often rely on irradiations of Ra-226, yet Ra-226 supplies are also limited. Uranium tailings provide an abundant source of Ra-226, though separation from these complex matrices remains challenging. A laboratory-scale process was developed to recover Ra-226 from simulated U-tailings. After acid leaching, Ra remained adsorbed on refractory oxides and silicates. An additional CaCl₂ leach of the residue raised recovery to ~ 64%. Subsequent purifications, including precipitation, ion-exchange, and extraction chromatography (TK101), achieved chemical yields up to 73 ± 7%, producing 7.68 ± 0.1 µCi of high-purity Ra-226.

and nuclear chemistry↗

Nucleosynthetic Analysis of Three-dimensional Core-collapse Supernova Simulations

Abstract We study in detail the ejecta conditions and theoretical nucleosynthetic results for 18 three-dimensional core-collapse supernova (CCSN) simulations done by F ornax . Most of the simulations are carried out to at least 3 s after bounce, which allows us to follow their longer-term behaviors. We find that multidimensional effects introduce many complexities into the ejecta conditions. We see a stochastic electron fraction evolution, complex peak temperature distributions and histories, and long-tail distributions of the time spent within nucleosynthetic temperature ranges. These all lead to substantial variation in CCSN nucleosynthetic yields and differences from 1D results. We discuss the production of lighter α -nuclei, radioactive isotopes, heavier elements, and a few isotopes of special interest. Comparing pre-CCSN and CCSN contributions, we find that a significant fraction of elements between roughly Si and Ge are generally produced in CCSNe. We find that 44 Ti exhibits an extended production timescale as compared to 56 Ni, which may explain its different distribution and higher than previously predicted abundances in supernova remnants such as Cas A and SN1987A. We also discuss the morphology of the ejected elements. This study highlights the high-level diversity of ejecta conditions and nucleosynthetic results in 3D CCSN simulations and emphasizes the need for additional long-term (∼10 s) 3D simulations to properly address such complexities.

Astronomy & Astrophysics↗

In-Transit Data Transport Strategies for Coupled AI-Simulation Workflow Patterns

Coupled AI-Simulation workflows are becoming the major workloads for HPC facilities, and their increasing complexity necessitates new tools for performance analysis and prototyping of new in-situ workflows. We present SimAI-Bench, a tool designed to both prototype and evaluate these coupled workflows. In this paper, we use SimAI-Bench to benchmark the data transport performance of two common patterns on the Aurora supercomputer: a one-to-one workflow with co-located simulation and AI training instances, and a many-to-one workflow where a single AI model is trained from an ensemble of simulations. For the one-to-one pattern, our analysis shows that node-local and DragonHPC data staging strategies provide excellent performance compared Redis and Lustre file system. For the many-to-one pattern, we find that data transport becomes a dominant bottleneck as the ensemble size grows. Our evaluation reveals that file system is the optimal solution among the tested strategies for the many-to-one pattern.

Tummalapalli, Harikrishna [Argonne National Labora↗

The Virtual Blast Furnace - An Integrated High Performance Computing Modeling, Simulation, and Visualization Capability for Steel Manufacturing (Final Report)

Many manufacturing industries require substantial capital and utilize energy intensive processes that involve complex phenomena. One example of such an industry is the steel industry, which is the fourth largest energy consuming industry in the U.S. By harnessing the power of High-Performance Computing (HPC) to enhance current simulation and visualization methods in the steel industry, it should be possible to increase resolution and/or decrease time of these methods by a factor of 1000. In this way, information can be obtained in a time frame that is useful for making business and engineering decisions, optimizing manufacturing processes and, ultimately, improving the completeness of U.S. industries. For example, if coke usage in blast furnaces were optimized such that the average coke rate was reduced from 797 lb/net tonne of hot metal (NTHM) to 604 lb/NTHM, costs could be reduced by $894 million/year. Additionally, members of the steel industry need the flexibility to efficiently operate blast furnaces at a range of production rates in order to meet fluctuating market demands. Large scale parameter studies can be utilized to discover workable operating parameters at a range of production rates.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Analysis of secondary organic aerosol simulation bias in the Community Earth System Model (CESM2.1)

Organic aerosol (OA) has been considered as one of the most important uncertainties in climate modeling due to the complexity in presenting its chemical production and depletion mechanisms. To better understand the capability of climate models and probe into the associated uncertainties in simulating OA, we evaluate the Community Earth System Model version 2.1 (CESM2.1) configured with the Community Atmosphere Model version 6 (CAM6) with comprehensive tropospheric and stratospheric chemistry representation (CAM6-Chem) through a long-term simulation (1988–2019) with observations collected from multiple datasets in the United States. We find that CESM generally reproduces the interannual variation and seasonal cycle of OA mass concentration at surface layer with a correlation of 0.40 compared to ground observations and systematically overestimates (69%) in summer and underestimates (-19%) in winter. Through a series of sensitivity simulations, we reveal that modeling bias is primarily related to the dominant fraction of monoterpene-formed secondary organic aerosol (SOA), and a strong positive correlation of 0.67 is found between monoterpene emission and modeling bias in the eastern US during summer. In terms of vertical profile, the model prominently underestimates OA and monoterpene concentrations by 37%–99% and 82%–99%, respectively, in the upper air (>500 m) as validated against aircraft observations. Our study suggests that the current volatility basis set (VBS) scheme applied in CESM might be parameterized with monoterpene SOA yields that are too high, which subsequently results in strong SOA production near the emission source area. We also find that the model has difficulty in reproducing the decreasing trend of surface OA in the southeastern US probably because of employing pure gas VBS to represent isoprene SOA which is in reality mainly formed through multiphase chemistry; thus, the influence of aerosol acidity and sulfate particle change on isoprene SOA formation has not been fully considered in the model. This study reveals the urgent need to improve the SOA modeling in climate models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Machine Learning Driven Sensitivity Analysis of E3SM Land Model Parameters for Wetland Methane Emissions

Methane (CH 4 ) is globally the second most critical greenhouse gas after carbon dioxide, contributing to 16%–25% of the observed atmospheric warming. Wetlands are the primary natural source of methane emissions globally. However, wetland methane emission estimates from biogeochemistry models contain considerable uncertainty. One of the main sources of this uncertainty arises from the numerous uncertain model parameters within various physical, biological, and chemical processes that influence methane production, oxidation, and transport. Sensitivity Analysis (SA) can help identify critical parameters for methane emission and achieve reduced biases and uncertainties in future projections. This study performs SA for 19 selected parameters responsible for critical biogeochemical processes in the methane module of the Energy Exascale Earth System Model (E3SM) land model (ELM). The impact of these parameters on various CH 4 fluxes is examined at 14 FLUXNET- CH 4 sites with diverse vegetation types. Given the extensive number of model simulations needed for global variance-based SA, we employ a machine learning (ML) algorithm to emulate the complex behavior of ELM methane biogeochemistry. We found that parameters linked to CH 4 production and diffusion generally present the highest sensitivities despite apparent seasonal variation. Comparing simulated emissions from perturbed parameter sets against FLUXNET-CH 4 observations revealed that better performances can be achieved at each site compared to the default parameter values. This presents a scope for further improving simulated emissions using parameter calibration with advanced optimization techniques.

54 ENVIRONMENTAL SCIENCES↗

Elucidating the Atomic Structures of the Gel Layer Formed during Aluminoborosilicate Glass Dissolution: An Integrated Experimental and Simulation Study

The altered glasses produced during aqueous dissolution of silicate and borosilicate glasses are among the most complex structures to understand at the atomic level due to their amorphous nature, random porosity and various levels of hydration. In this study, we gained insights of the complex atomic structures of altered aluminoborosilicate glasses by combining a range of experimental and computational approaches. The altered glasses were prepared by dissolution of three glasses with varying level of alumina in acid for 7 days. A comprehensive set of experimental [elemental analysis, high-energy X-ray diffraction, 29 Si and 27 Al solid-state nuclear magnetic resonance (NMR), and O 1s X-ray photoelectron spectroscopy (XPS)] and modeling (molecular dynamics (MD) simulations using non-reactive and reactive force fields) were used to study the atomic structures of these altered glasses. Elemental analysis showed that most of the B in the pristine glasses was leached into the solution and was not contained in the altered glass. The 29 Si and 27 Al solid-state NMR spectra revealed that the altered glasses have more polymerized silicate network as compared to those in the pristine glasses due to the reformation of linkages among Si and Al oxygen polyhedral in the altered glasses. The bridging and non-bridging (or hydroxyl O) atoms in the altered glasses were also quantified from their O 1s XPS spectra. Atomic structure models of the altered glasses were constructed by using MD simulations using the reactive force field based on the compositional information obtained from experiments. Various pore structures were generated using the charge-scaling (CS) method by using different initial densities and CS temperatures; the best CS parameters of each alternated glass were then determined by comparing with the experimental structure factors obtained from high energy X-ray diffraction. Pore and the atomic structures and vibrational properties around these pore surfaces were analyzed. Furthermore, these results from this comprehensive study thus provides a realistic insight into the pore morphology, atomic structure, and vibrational properties of altered glasses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dissociative electron attachment to 5-bromo-uracil: non-adiabatic dynamics on complex-valued potential energy surfaces

Electron induced dissociation reactions are relevant to many fields, ranging from prebiotic chemistry to cancer treatments. However, the simulation of dissociation electron attachment (DEA) dynamics is very challenging because the auto-ionization widths of the transient negative ions must be accounted for. We propose an adaptation of the ab initio multiple spawning (AIMS) method for complex-valued potential energy surfaces, along the lines of recent developments based on surface hopping dynamics. Our approach combines models for the energy dependence of the auto-ionization widths, obtained from scattering calculations, with survival probabilities computed for the trajectory basis functions employed in the AIMS dynamics. The method is applied to simulate the DEA dynamics of 5-bromouracil in full dimensionality, i.e., taking all the vibrational modes into consideration. The propagation starts on the $π_{2}^{*}$ resonance state and describes the formation of Br - anions mediated by non-adiabatic couplings. The potential energies, gradients and non-adiabatic couplings were computed with the fractional-occupancy molecular orbital complete-active-space configuration-interaction method, and the calculated DEA cross section are consistent with the observed DEA intensities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High pressure/high temperature multiphase simulations of dodecane injection to nitrogen: Application on ECN Spray-A

The present work investigates the complex phenomena associated with pressure/high temperature dodecane injection for the Engine Combustion Network (ECN) Spray-A case, employing more elaborate thermodynamic closures, to avoid well known deficiencies concerning density and speed of sound prediction using traditional cubic models. A tabulated thermodynamic approach is proposed here, based on log 10 (p)-T tables, providing very high accuracy across a large range of pressures, spanning from 0 to 2500 bar, with only a small number of interpolation points. The tabulation approach is directly extensible to any thermodynamic model, existing or to be developed in the future. Here NIST REFPROP properties are used, combined with PC-SAFT Vapor-Liquid-Equilibrium to identify the liquid in mixtures penetration, hence avoiding the use of an arbitrary threshold for mass fraction. Identified liquid and vapour penetration are compared against experimental data from the ECN database showing a good agreement, within approximately 3–8% for axial penetration of liquid, 2% for vapor axial penetration and within experimental uncertainty for radial distribution of mass fraction. Analysis of the vortex evolution indicates that driving mechanisms behind the jet break-up are vortex tilting/stretching, then baroclinic torque, leading to Rayleigh-Taylor instabilities, closely followed by vortex dilation and finally viscous effects.

42 ENGINEERING↗

A synthetic strategy for the preparation of alkoxy‐functionalized bis‐1,2,4‐triazinyl‐2,6‐pyridines

Heteroaryl-1,2,4-triazine complexants are commonly utilized in separation science for the selective chelation of minor An from Ln in simulated high-level waste. Furthermore, to facilitate access to relevant chemical entities for hypothesis-driven inquiry toward improved separations performance, a synthetic method to construct various alkoxy-complexant derivatives was required. In this work, a convergent synthetic strategy for the production of 3,3′- and 4,4′-tetraalkoxy-bis-1,2,4-triazinyl-2,6-pyridines from readily available starting materials via a dealkylation/alkylation/condensation approach is described. Synthetic method development, substrate scope, preliminary solubility, and hydrolytic stability data in various process-relevant diluents are reported herein.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗