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At least 1,639 records · Page 91

DISP: Optimizations towards Scalable MPI Startup

Despite the popularity of MPI for high performance computing, the startup of MPI programs faces a scalability challenge as both the execution time and memory consumption increase drastically at scale. We have examined this problem using the collective modules of Cheetah and Tuned in Open MPI as representative implementations. Previous improvements for collectives have focused on algorithmic advances and hardware off-load. In this paper, we examine the startup cost of the collective module within a communicator and explore various techniques to improve its efficiency and scalability. Accordingly, we have developed a new scalable startup scheme with three internal techniques, namely Delayed Initialization, Module Sharing and Prediction-based Topology Setup (DISP). Our DISP scheme greatly benefits the collective initialization of the Cheetah module. At the same time, it helps boost the performance of non-collective initialization in the Tuned module. We evaluate the performance of our implementation on Titan supercomputer at ORNL with up to 4096 processes. The results show that our delayed initialization can speed up the startup of Tuned and Cheetah by an average of 32.0% and 29.2%, respectively, our module sharing can reduce the memory consumption of Tuned and Cheetah by up to 24.1% and 83.5%, respectively, and our prediction-based topology setup can speed up the startup of Cheetah by up to 80%.

Fu, Huansong↗

IGMS: An Integrated ISO-to-Appliance Scale Grid Modeling System

This paper describes the Integrated Grid Modeling System (IGMS), a novel electric power system modeling platform for integrated transmission-distribution analysis that co-simulates off-the-shelf tools on high performance computing (HPC) platforms to offer unprecedented resolution from ISO markets down to appliances and other end uses. Specifically, the system simultaneously models hundreds or thousands of distribution systems in co-simulation with detailed Independent System Operator (ISO) markets and AGC-level reserve deployment. IGMS uses a new MPI-based hierarchical co-simulation framework to connect existing sub-domain models. Our initial efforts integrate opensource tools for wholesale markets (FESTIV), bulk AC power flow (MATPOWER), and full-featured distribution systems including physics-based end-use and distributed generation models (many instances of GridLAB-D[TM]). The modular IGMS framework enables tool substitution and additions for multi-domain analyses. This paper describes the IGMS tool, characterizes its performance, and demonstrates the impacts of the coupled simulations for analyzing high-penetration solar PV and price responsive load scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗

OmniFed: A Modular Framework for Configurable Federated Learning from Edge to HPC

Federated Learning (FL) is critical for edge and High Performance Computing (HPC) where data is not centralized and privacy is crucial. We present OmniFed, a modular framework designed around decoupling and clear separation of concerns for configuration, orchestration, communication, and training logic. Its architecture supports configuration-driven prototyping and code-level override-what-you-need customization. We also support different topologies, mixed communication protocols within a single deployment, and popular training algorithms. It also offers optional privacy mechanisms including Differential Privacy (DP), Homomorphic Encryption (HE), and Secure Aggregation (SA), as well as compression strategies. These capabilities are exposed through well-defined extension points, allowing users to customize topology and orchestration, learning logic, and privacy/compression plugins, all while preserving the integrity of the core system. We evaluate multiple models and algorithms to measure various performance metrics. By unifying topology configuration, mixed-protocol communication, and pluggable modules in one stack, OmniFed streamlines FL deployment across heterogeneous environments. Github repository is available at https://github.com/at-aaims/OmniFed.

Tyagi, Sahil [ORNL] (ORCID:0009000783144745)↗

Enhanced Performance Assessment Models for Generic Deep Geologic Repositories for High-Level Waste and Spent Nuclear Fuel - 16223

Development of an enhanced performance assessment (PA) capability for geologic disposal of spent nuclear fuel and high-level waste has been ongoing for several years in the U.S. repository program. The new Generic Disposal System Analysis (GDSA) modeling and software framework is intended to be flexible enough to evolve through the various phases of repository activities, beginning with generic PA activities in the current Concept Evaluation phase to site-specific PA modeling in the Repository Development phase. The GDSA Framework utilizes modern software and hardware capabilities by being based on open-source software architecture and being configured to run in a massively parallel, high-performance computing (HPC) environment. It consists of two main components, the open-source Dakota uncertainty sampling and analysis software and the PFLOTRAN reactive multi-phase flow and transport simulator. Reference cases or 'generic repositories' have been, and are being developed, based on typical properties for potential salt, clay, and granite host-rock formations and corresponding engineered design concepts for each medium. Past simulations have focused on a generic repository in bedded-salt host rock, while the most recent research has focused on a reference case for a typical clay/shale host rock. A variety of single-realization (i.e., deterministic) and multi-realization (probabilistic) results for the new clay reference case are presented, including an analysis of the effects of heat generation on repository performance, assuming a 100-year out-of-reactor commercial SNF waste form. Order-of-magnitude differences between predicted radionuclide concentrations in thermal versus isothermal simulations imply that mechanistic, coupled-process modeling in three-dimensional (3-D) domains can be important for building confidence in post-closure performance assessments. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

GraphMeta: Managing HPC Rich Metadata in Graphs

High-performance computing (HPC) systems face increasingly critical metadata management challenges, especially in the approaching exascale era. These challenges arise not only from exploding metadata volumes, but also from increasingly diverse metadata, which contains data provenance and arbitrary user-defined attributes in addition to traditional POSIX metadata. This ‘rich’ metadata is becoming critical to supporting advanced data management functionality such as data auditing and validation. In our prior work, we identified a graph-based model as a promising solution to uniformly manage HPC rich metadata due to its flexibility and generality. However, at the same time, graph-based HPC rich metadata anagement also introduces significant challenges to the underlying infrastructure. In this study, we first identify the challenges on the underlying infrastructure to support scalable, high-performance rich metadata management. Based on that, we introduce GraphMeta, a graphbased engine designed for this use case. It achieves performance scalability by introducing a new graph partitioning algorithm and a write-optimal storage engine. We evaluate GraphMeta under both synthetic and real HPC metadata workloads, compare it with other approaches, and demonstrate its advantages in terms of efficiency and usability for rich metadata management in HPC systems.

Dai, Dong↗

Distributed-Memory Sparse Deep Neural Network Inference Using Global Arrays

Partitioned Global Address Space (PGAS) models exhibit tremendous promise in developing efficient and productive distributed-memory parallel applications. They have been used extensively in scientific computations due to conveniently offering a ``shared-memory''-like model and convenient interfaces that separate communication with synchronization. Traditionally, PGAS communication models have been applied to dense/contiguously distributed data, but most modern applications depict varied levels of sparsity. Existing PGAS models require certain adaptations to support distributed sparse computations, since associated computations often require matrix arithmetic, in addition to data movement. The Global Arrays toolkit from Pacific Northwest National Laboratory (PNNL) is one of the earliest PGAS models to combine one-sided data communication and distributed matrix operations and is still used in the popular NWChem quantum chemistry suite. Recently, we have expanded the Global Arrays toolkit to support common sparse operations, like sparse matrix-dense matrix multiplies (SpMM), sparse matrix-sparse matrix multiplication (SpGEMM) and Sampled Dense-Dense Matrix Multiplication (SDDMM). As it turns out, these operations are the bedrock of sparse Deep Learning (DL); sparse deep neural networks and Graph Neural Networks (GNNs) have gained increasing attention recently in achieving speedups on training and inference with reduced memory footprints. Unlike scientific applications in High Performance Computing (HPC), modern (distributed-memory capable) DL toolkits often rely on non-standardized and closed-source vendor software optimizations, creating challenges in software-hardware co-design at scale. Our goal is to support a variety of distributed-memory sparse matrix operations and helper functions in the newly created Sparse Global Arrays (SGA), such that it is possible to build portable and productive Machine Learning scenarios for algorithm/software and hardware codesign purposes. Contemporary data-parallel schemes for training/inference are undergoing a major overhaul since model replication limits scalability and causes resource inefficiencies. As such, we have adopted tensor parallelism in decomposing the model and inputs, to mitigate memory issues. Current implementation is built on top of MPI and uses CPUs to maximize the portability across the platforms.

Distributed computing, machine learning↗

High Energy Physics Exascale Requirements Review. An Office of Science review sponsored jointly by Advanced Scientific Computing Research and High Energy Physics, June 10-12, 2015, Bethesda, Maryland

The U.S. Department of Energy (DOE) Office of Science (SC) Offices of High Energy Physics (HEP) and Advanced Scientific Computing Research (ASCR) convened a programmatic Exascale Requirements Review on June 10–12, 2015, in Bethesda, Maryland. This report summarizes the findings, results, and recommendations derived from that meeting. The high-level findings and observations are as follows. Larger, more capable computing and data facilities are needed to support HEP science goals in all three frontiers: Energy, Intensity, and Cosmic. The expected scale of the demand at the 2025 timescale is at least two orders of magnitude — and in some cases greater — than that available currently. The growth rate of data produced by simulations is overwhelming the current ability of both facilities and researchers to store and analyze it. Additional resources and new techniques for data analysis are urgently needed. Data rates and volumes from experimental facilities are also straining the current HEP infrastructure in its ability to store and analyze large and complex data volumes. Appropriately configured leadership-class facilities can play a transformational role in enabling scientific discovery from these datasets. A close integration of high-performance computing (HPC) simulation and data analysis will greatly aid in interpreting the results of HEP experiments. Such an integration will minimize data movement and facilitate interdependent workflows. Long-range planning between HEP and ASCR will be required to meet HEP’s research needs. To best use ASCR HPC resources, the experimental HEP program needs (1) an established, long-term plan for access to ASCR computational and data resources, (2) the ability to map workflows to HPC resources, (3) the ability for ASCR facilities to accommodate workflows run by collaborations potentially comprising thousands of individual members, (4) to transition codes to the next-generation HPC platforms that will be available at ASCR facilities, (5) to build up and train a workforce capable of developing and using simulations and analysis to support HEP scientific research on next-generation systems.

97 MATHEMATICS AND COMPUTING↗

Addressing GPU memory limitations for Graph Neural Networks in High-Energy Physics applications

Introduction Reconstructing low-level particle tracks in neutrino physics can address some of the most fundamental questions about the universe. However, processing petabytes of raw data using deep learning techniques poses a challenging problem in the field of High Energy Physics (HEP). In the Exa.TrkX Project, an illustrative HEP application, preprocessed simulation data is fed into a state-of-art Graph Neural Network (GNN) model, accelerated by GPUs. However, limited GPU memory often leads to Out-of-Memory (OOM) exceptions during training, due to the large size of models and datasets. This problem is exacerbated when deploying models on High-Performance Computing (HPC) systems designed for large-scale applications. Methods We observe a high workload imbalance issue during GNN model training caused by the irregular sizes of input graph samples in HEP datasets, contributing to OOM exceptions. We aim to scale GNNs on HPC systems, by prioritizing workload balance in graph inputs while maintaining model accuracy. Our paper introduces diverse balancing strategies aimed at decreasing the maximum GPU memory footprint and avoiding the OOM exception, across various datasets. Results Our experiments showcase memory reduction of up to 32.14% compared to the baseline. We also demonstrate the proposed strategies can avoid OOM in application. Additionally, we create a distributed multi-GPU implementation using these samplers to demonstrate the scalability of these techniques on the HEP dataset. Discussion By assessing the performance of these strategies as data loading samplers across multiple datasets, we can gauge their effectiveness in both single-GPU and distributed environments. Our experiments, conducted on datasets of varying sizes and across multiple GPUs, broaden the applicability of our work to various GNN applications that handle input datasets with irregular graph sizes.

Lee, Claire Songhyun↗

NSRD-06. Computational Capability to Substantiate DOE-HDBK-3010 Data

Safety basis analysts throughout the U.S. Department of Energy (DOE) complex rely heavily on the information provided in the DOE Hand book, DOE-HDBK-3010, Airborne Release Fractions/Rates and Resp irable Fractions for Nonreactor Nuclear Facilities , to determine source terms. In calcula ting source terms, analysts tend to use the DOE Handbook's bounding values on airbor ne release fractions (ARFs) and respirable fractions (RFs) for various cat egories of insults (representing potential accident release categories). This is typica lly due to both time constraints and the avoidance of regulatory critique. Unfort unately, these bounding ARFs/RFs represent extremely conservative values. Moreover, th ey were derived from very limited small- scale table-top and bench/labo ratory experiments and/or fr om engineered judgment. Thus the basis for the data may not be re presentative to the actual unique accident conditions and configura tions being evaluated. The goal of this res earch is to develop a more ac curate method to identify bounding values for the DOE Handbook using the st ate-of-art multi-physics-based high performance computer codes. This enable s us to better understand the fundamental physics and phenomena associated with the ty pes of accidents for the data described in it. This research has examined two of the DOE Handbook's liquid fire experiments to substantiate the airborne release frac tion data. We found th at additional physical phenomena (i.e., resuspension) need to be included to derive bounding values. For the specific cases of solid powder under pre ssurized condition and mechanical insult conditions the codes demonstrated that we can simulate the phenomena. This work thus provides a low-cost method to establis h physics-justified sa fety bounds by taking into account specific geometri es and conditions that may not have been previously measured and/or are too costly to do so.

97 MATHEMATICS AND COMPUTING↗

Generation and characterization of carbon fiber microstructure in atomistic simulations

A clear understanding of carbon fiber (CF) microstructure is necessary for the development of high strength CFs. Here, we present an atomistic approach for generating and characterizing realistic mi- crostructures of CFs. Large-scale reactive molecular dynamics simulations are used to generate a set of distinct CF microstructures. Comprehensive characterization of the simulated microstructures is enabled by the development of a suite of computational structural analysis tools capable of evaluation of hy- bridization states of carbon atoms, populations and orientations of individual carbon rings, degree of graphitization, and pore size distribution. The calculation of X-ray diffraction profiles provides a direct link between the structural features of simulated samples and experimental data available for CFs. The CF generation algorithm is shown to produce microstructures with experimental densities and with structural characteristics matching those of PAN-based CFs. The key structural features affecting the properties of CFs, such as the relative fractions of graphitic, turbostratic and amorphous micro- constituents, degree of alignment, pore size distributions, and chemical cross-linking can be effectively controlled in simulations, thus enabling efficient exploration of structureeproperties relationships in CFs. The capabilities of the developed approach are illustrated by performing computational analysis of the mechanical deformation and fracture of CFs under axial tensile loading.

36 MATERIALS SCIENCE↗

Inference-Engine v0.1.0

Given a pre-trained neural network, Inference-Engine performs maps network inputs to outputs by executing the forward pass through the provided network. Although the predominant programming language for machine-learning is Python, most high-performance computing (HPC) applications are written in Fortran, C, or C++. Inference-Engine aims to support HPC programs and is written in Fortran, a language with a large feature set supporting interoperability with C. This software exposes concurrency in a portable way by using standard language features that some modern Fortran compilers can exploit with various optimizations, including offloading computation to a Graphics Processing Unit (GPU). In particular, this software makes extensive use of Fortran's "do concurrent" parallel loop construct, implicitly parallel array statements, and pure procedures that can be invoked inside "do concurrent" blocks. Inference-Engine also supports dynamic choice of inference methods at runtime. Two current options include one method that uses Fortran's "dot_product" intrinsic function inside "do concurrent" blocks and another method that instead uses Fortran' "matmul" array intrinsic function. We plan to investigate automatic compiler offloading of "do concurrent" calculations to GPUs and compile-time substitution of optimized libraries such as the Basic Linear Algebra Library (BLAS) for "matmul" invocations. We also envision the potential for the choice of which method to use could happen at program launch based on in situ performance measurements on any given platform.

Rouson, Damian↗

Development and Validation of a Two-Phase Thermal-Hydraulic CFD Code NEK-2P

A project is underway to develop, verify and validate an advanced two-phase flow modeling capability for the highly-scalable, high-performance Computational Fluid Dynamics (CFD) code NEK5000. The goal of this work is to verify and validate the two-phase version of the NEK5000 code, named NEK-2P, to simulate the two-phase flow and heat transfer phenomena that occur in a Boiling Water Reactor (BWR) fuel bundle under various operating conditions. The NEK-2P two-phase flow models follow the approach used for the Extended Boiling Framework (EBF) previously developed at Argonne but include more fundamental physical models of boiling phenomena and advanced numerical algorithms for improved computational accuracy, robustness, and computational speed. The development of the NEK-2P two-phase solver and the implementation of the Extended Boiling Framework two-phase models were initially supported by Argonne National Laboratory (Argonne) through a Laboratory Directed Research and Development (LDRD) project during FY2014-2016. The development and validation of the two-phase models through analyses of selected two-phase boiling flow experiments was supported by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in FY2017-2020. This report focuses on verification and validation of the water-steam boiling model NEK-2P Two-Phase, CFD code. The NEK-2P was validated with Nuclear Power Engineering Corporation (NUPEC) Pressurized Water Reactor (PWR) Sub-channel and Bundle Test (PSBT) void distribution benchmark. Three different simulations were performed and analyzed for various operating conditions such as wall-heat flux and sub-cooled inlet temperatures. Reasonably good agreement with measured data was obtained in predicting the measured void distributions. Simulations were performed for Virginia Tech. (VT) 3x3 rod bundle geometry with and without spacers. The preliminary results were presented for Simplified Spacer Grid (SSG). In addition, the implementation of interface reconstruction model was tested with one of the Becker benchmark Critical Heat Flux (CHF) experiments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DenKv: Addressing Design Trade-offs of Key-value Stores for Scientific Applications

High-performance computing (HPC) facilities have employed flash-based storage tier near to compute nodes to absorb high I/O demand by HPC applications during periodic system-level checkpoints. To accelerate these checkpoints, proxy-based distributed key-value stores (PD-KVS) gained particular attention for their flexibility to support multiple backends and different network configurations. PD-KVS rely internally on monolithic KVS, such as LevelDB or RocksDB, to exploit the KV interface and query support. However, PD-KVS are unaware of the high redundancy factor in checkpoint data, which can be up to GBs to TBs, and therefore, tend to generate high write and space amplification on these storage layers. In this paper, we propose DenKv which is deduplication-extended node-local LSM-tree-based KVS. DenKv employs asynchronous partially inline dedup (APID) and aims to maintain the performance characteristics of LSM-tree-based KVS while reducing the write and space amplification problems. We implemented DenKv atop BlobDB and showed that our proposed solution maintains performance while reducing write amplification up to 2× and space amplification by 4× on average.

Khan, Awais↗

Distributionally Robust Partially Observable Markov Decision Process with Moment-Based Ambiguity

In this paper, we consider a distributionally robust partially observable Markov decision process (DR-POMDP), where the distribution of the transition-observation probabilities is unknown at the beginning of each decision period, but their realizations can be inferred using side information at the end of each period after an action being taken. We build an ambiguity set of the joint distribution using bounded moments via conic constraints and seek an optimal policy to maximize the worst-case (minimum) reward for any distribution in the set. We show that the value function of DR-POMDP is piecewise linear convex with respect to the belief state and propose a heuristic search value iteration method for obtaining lower and upper bounds of the value function. We conduct numerical studies and demonstrate the computational performance of our approach via testing instances of a dynamic epidemic control problem. Our results show that DR-POMDP can produce more robust policies under misspecified distributions of transition-observation probabilities as compared to POMDP but has less costly solutions than robust POMDP. The DR-POMDP policies are also insensitive to varying parameter in the ambiguity set and to noise added to the true transition-observation probability values obtained at the end of each decision period.

97 MATHEMATICS AND COMPUTING↗

A Case Study of Multimodal, Multi-institutional Data Management for the Combinatorial Materials Science Community

Although the convergence of high-performance computing, automation, and machine learning has significantly altered the materials design timeline, transformative advances in functional materials and acceleration of their design will require addressing the deficiencies that currently exist in materials informatics, particularly a lack of standardized experimental data management. The challenges associated with experimental data management are especially true for combinatorial materials science, where advancements in automation of experimental workflows have produced datasets that are often too large and too complex for human reasoning. The data management challenge is further compounded by the multimodal and multi-institutional nature of these datasets, as they tend to be distributed across multiple institutions and can vary substantially in format, size, and content. Furthermore, modern materials engineering requires the tuning of not only composition but also of phase and microstructure to elucidate processing–structure–property–performance relationships. To adequately map a materials design space from such datasets, an ideal materials data infrastructure would contain data and metadata describing (i) synthesis and processing conditions, (ii) characterization results, and (iii) property and performance measurements. In this work, we present a case study for the low-barrier development of such a dashboard that enables standardized organization, analysis, and visualization of a large data lake consisting of combinatorial datasets of synthesis and processing conditions, X-ray diffraction patterns, and materials property measurements generated at several different institutions. While this dashboard was developed specifically for data-driven thermoelectric materials discovery, we envision the adaptation of this prototype to other materials applications, and, more ambitiously, future integration into an all-encompassing materials data management infrastructure.

36 MATERIALS SCIENCE↗

Thermal Spectrum Molten Salt-Fueled Reactor Reference Plant Model

This report details a fully coupled neutronics thermal hydraulics reference plant model for a thermal spectrum molten salt-fueled reactor. The Multiphysics model is developed on the Nuclear Regulatory Commission's Comprehensive Reactor Analysis Bundle available on the Idaho National Laboratory high-performance computer, which natively and seamlessly couples Griffin and Sam codes of the Multiphysics Object-Oriented Simulation Environment (MOOSE) based applications. Griffin provides the reactor physics capabilities, k-eigenvalue, delayed neutron precursor concentrations, and transient solutions for stationary and flowing fuels. Sam provides the solution of mass, momentum, and energy conservation equations of the whole system with a set of system components for one-dimensional single-phase flow. The neutronics feedback model relies primarily on fuel and moderator temperatures, fuel salt density, and delayed neutron precursors distributions. This report presents our results for the coupled steady state core and an unprotected loss of flow event. Although this model is prototypical regarding capabilities in the Comprehensive Reactor Analysis Bundle, its results are consistent with experimental data of the pump transient tests that were performed at zero power of the Molten Salt Reactor Experiment (MSRE).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Enabling parallel simulation of large-scale HPC network systems

Here, with the increasing complexity of today’s high-performance computing (HPC) architectures, simulation has become an indispensable tool for exploring the design space of HPC systems—in particular, networks. In order to make effective design decisions, simulations of these systems must possess the following properties: (1) have high accuracy and fidelity, (2) produce results in a timely manner, and (3) be able to analyze a broad range of network workloads. Most state-of-the-art HPC network simulation frameworks, however, are constrained in one or more of these areas. In this work, we present a simulation framework for modeling two important classes of networks used in today’s IBM and Cray supercomputers: torus and dragonfly networks. We use the Co-Design of Multi-layer Exascale Storage Architecture (CODES) simulation framework to simulate these network topologies at a flit-level detail using the Rensselaer Optimistic Simulation System (ROSS) for parallel discrete-event simulation. Our simulation framework meets all the requirements of a practical network simulation and can assist network designers in design space exploration. First, it uses validated and detailed flit-level network models to provide an accurate and high-fidelity network simulation. Second, instead of relying on serial time-stepped or traditional conservative discrete-event simulations that limit simulation scalability and efficiency, we use the optimistic event-scheduling capability of ROSS to achieve efficient and scalable HPC network simulations on today’s high-performance cluster systems. Third, our models give network designers a choice in simulating a broad range of network workloads, including HPC application workloads using detailed network traces, an ability that is rarely offered in parallel with high-fidelity network simulations

97 MATHEMATICS AND COMPUTING↗

Reaction Mechanism Generator v3.0: Advances in Automatic Mechanism Generation

In chemical kinetics research, kinetic models containing hundreds of species and tens of thousands of elementary reactions are commonly used to understand and predict the behavior of reactive chemical systems. Reaction Mechanism Generator (RMG) is a software suite developed to automatically generate such models by incorporating and extrapolating from a database of known thermochemical and kinetic parameters. Here, we present the recent version 3 release of RMG and highlight improvements since the previously published description of RMG v1.0. Most notably, RMG can now generate heterogeneous catalysis models in addition to the previously available gas- and liquid-phase capabilities. For model analysis, new methods for local and global uncertainty analysis have been implemented to supplement first-order sensitivity analysis. The RMG database of thermochemical and kinetic parameters has been significantly expanded to cover more types of chemistry. The present release includes parallelization for faster model generation and a new molecule isomorphism approach to improve computational performance. RMG has also been updated to use Python 3, ensuring compatibility with the latest cheminformatics and machine learning packages. Overall, RMG v3.0 includes many changes which improve the accuracy of the generated chemical mechanisms and allow for exploration of a wider range of chemical systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗