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At least 1,405 records · Page 78

Monte Carlo/CFD Coupling for Accurate Modeling of the Delayed Neutron Precursors and Compressibility Effects in Molten Salt Reactors

Multiphysics reactor analysis has become one of the leading activities of most nuclear engineering research groups. Coupled neutronics and thermal/hydraulics (T/H) simulations have traditionally been performed by adopting deterministic transport tools and reactor system T/H codes. The main reason for avoiding higher fidelity numerical methods like continuous-energy Monte Carlo analysis has been the high computational cost of coupled, full-scale simulations. Nowadays, high fidelity multiphysics simulations represent a hot research topic, with several applications involving advanced nuclear systems. Liquid fuel Molten Salt Reactors (MSRs) feature peculiar physical phenomena that are not present in solid fuel reactors. Some of these phenomena are not correctly resolved by legacy reactor physics tools, and require specific treatments. This work focuses in particular on the analysis of the effect of the delayed neutron precursors drift and the impact of liquid fluid thermal expansion and compressibility in postulated criticality excursion transients in fast-spectrum MSRs. A new modeling tool based on a Monte Carlo approach for neutronics (Serpent code) coupled to a Computational Fluid Dynamic (CFD) analysis (OpenFOAM) was developed to obtain accurate modeling and simulation of these phenomena. The development of the Serpent Monte Carlo code [1] at VTT in the past few years has made this code particularly attractive for performing multiphysics studies. The availability of a flexible multiphysics interface, on-the-fly Doppler broadening and density-based collision rejection, and Delta-tracking, proved of paramount importance for the computationally efficient performance of coupled Monte Carlo/CFD calculations [2]. OpenFOAM is a C++ multiphysics toolkit featured by automatic matrix construction and solution capabilities for scalar and vector partial differential equations (PDEs), adopting several possible differencing and interpolation schemes, based on the Finite-Volume method. The ease of implementing the constitutive equations of different physical phenomena makes OpenFOAM particularly suitable for the modeling of complex coupled phenomena. In the past, several research activities proposed the adoption of both Serpent and OpenFOAM for the modeling and simulation of MSRs and the associated fuel cycles. In this work, these tools have been internally coupled for the steady-state and transient analysis of fast-spectrum systems, accounting for the effect of delayed neutron precursors transport and the salt thermal expansion and compressibility.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Neural message-passing for objective-based uncertainty quantification and optimal experimental design

Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be high. In such cases, based on a Bayesian paradigm, we can design robust operators retaining the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to enhance the performance of such operators maximally. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) provides an effective means for quantifying uncertainty in complex systems, the high computational cost of estimating MOCU has been a challenge in applying it to real-world scientific/engineering problems. In this work, we propose a novel scheme to reduce the computational cost for objective-UQ via MOCU based on a data-driven approach. We adopt a neural message-passing model for surrogate modeling, incorporating a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance robust synchronization performance through uncertainty reduction. We show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, without any visible performance loss compared to the state-of-the-art. The proposed approach applies to general OED tasks, beyond the Kuramoto model.

97 MATHEMATICS AND COMPUTING↗

Regional-scale fault-to-structure earthquake simulations with the EQSIM framework: Workflow maturation and computational performance on GPU-accelerated exascale platforms

Continuous advancements in scientific and engineering understanding of earthquake phenomena, combined with the associated development of representative physics-based models, is providing a foundation for high-performance, fault-to-structure earthquake simulations. However, regional-scale applications of high-performance models have been challenged by the computational requirements at the resolutions required for engineering risk assessments. The EarthQuake SIMulation (EQSIM) framework, a software application development under the US Department of Energy (DOE) Exascale Computing Project, is focused on overcoming the existing computational barriers and enabling routine regional-scale simulations at resolutions relevant to a breadth of engineered systems. This multidisciplinary software development—drawing upon expertise in geophysics, engineering, applied math and computer science—is preparing the advanced computational workflow necessary to fully exploit the DOE’s exaflop computer platforms coming online in the 2023 to 2024 timeframe. Achievement of the computational performance required for high-resolution regional models containing upward of hundreds of billions to trillions of model grid points requires numerical efficiency in every phase of a regional simulation. This includes run time start-up and regional model generation, effective distribution of the computational workload across thousands of computer nodes, efficient coupling of regional geophysics and local engineering models, and application-tailored highly efficient transfer, storage, and interrogation of very large volumes of simulation data. This article summarizes the most recent advancements and refinements incorporated in the workflow design for the EQSIM integrated fault-to-structure framework, which are based on extensive numerical testing across multiple graphics processing unit (GPU)-accelerated platforms, and demonstrates the computational performance achieved on the world’s first exaflop computer platform through representative regional-scale earthquake simulations for the San Francisco Bay Area in California, USA.

58 GEOSCIENCES↗

Comparison Made of Operating Characteristics of Spiral Bevel Gears Manufactured Using Different Methods

Spiral bevel gears are important components on all current rotorcraft drive systems. These components are required to operate at high speeds, high loads, and for an extremely large number of load cycles. In this application, spiral bevel gears are used to redirect the shaft from the horizontal gas turbine engine to the vertical rotor. Because of the high expense of manufacturing these gears, methods that can achieve the same level of performance at reduced cost are highly desirable to aerospace gear manufacturers. Gears manufactured for aerospace applications use high-quality materials and are manufactured to tight tolerances. Special manufacturing machine tools and computer numerically controlled coordinate measurement systems have enabled rotorcraft drive system manufacturers to produce extremely high-quality gears during their normal production. Because of low production rates for rotorcraft, these gears are manufactured in small batches, and thus are unable to benefit from the economics of high production numbers as in other industries. In this investigation, two different manufacturing methods, face-milled and face-hobbed, were used to fabricate spiral bevel gears. For face-milled spiral bevel gears, grinding of the contacting surfaces is the final manufacturing step. At least two different specialty machines are needed to generate the teeth for face-milled spiral bevel gears. For face-hobbed gears, hard cutting is the final manufacturing process. The same machine is used to rough cut and finish cut the gears. This study compared the operational behavior of face-milled spiral bevel gears with that of face-hobbed spiral bevel gears. Test hardware was manufactured to fit within NASA Glenn Research Center's Spiral Bevel Test Facility and to aerospace quality standards. Tests were conducted for stress, vibration, and noise. A comparison of the results attained indicated that the face-hobbed gears had a lower alternating stress level with a more even distribution of loading across the teeth, and slightly reduced levels of vibration and noise. Results of this study show that the face-hobbed method is a viable and lower-cost alternative for producing aerospace-quality spiral-bevel gears.

Handschuh, Robert F.↗

Used Fuel Storage Monitoring Using Helium-4 Scintillation Fast Neutron Detectors and Neutron Spectral Analysis

This project aimed to address the technology gap in the reliable methods to verify contents of sealed dry storage casks for spent nuclear fuel. Helium-4 gas scintillation neutron detectors was proposed to be developed into a neutron spectroscopy and imaging system for nuclear security and safeguards applications. 4 He gas is significantly more available than 3 He gas and it has unique advantages such as low gamma interaction probability and direct detection of fast neutrons. Due to the sheer amount of fissile materials in a single dry cask, there is a significant neutron fluence emitted whose energies range from thermal to uncollided high-energy neutrons suitable for the detection capability of the 4 He detectors. Our project demonstrated the first ever neutron spectroscopic capabilities using 4 He detectors, explored novel detector design and performed detector characterization. It further qualified the detectors for use in various applications including high-flux environments with significant gamma-fluence. Computer simulations were used to test various large cask measurement system designs and tests, beyond the compact prototype system and laboratory measurements exploring the feasibility of the neutron spectroscopic approach. Although some cask-characterization methods proved unfeasible, alternative characterization methods using the He-4 detectors were explored and generated promising results.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Developing and testing capabilities for simulating cases with heterogeneous land/water surfaces in a novel atmospheric large eddy simulation code

Large eddy simulations (LES) are the primary computational tool used to simulate high Reynolds number three-dimensional turbulent flows. In the context of earth system sciences, particularly atmospheric science, LES are uniquely able to resolve the scales of atmospheric motion that are key for building process-level understanding of boundary layer turbulence, atmosphere-surface interaction, clouds, and cloud-aerosol-chemistry interaction, and are a core limited-area modeling capability. Increasing demands are being placed on LES code bases as growing high performance computing resources allow LES to address a wider range of scientific problems. In addition, LES are emerging as a source of high-quality machine learning training data. These demands necessitate an agile and extensible code base that allows the model to quickly adapt to emergent needs. However, LES have largely relied on legacy Fortran code bases that lack flexibility. A new, Python-based LES capability called Predicting INteractions of Aerosol and Clouds in Large Eddy Simulation (PINACLES) has been developed as part of the Department of Energy’s Earth System Model Development (ESMD) program area’s Enabling Aerosol-cloud interactions at Global convection-permitting scalES (EAGLES) project. PINACLES was developed from the ground up with a philosophy of maximizing scientific throughput, by attempting to optimize for both model throughput and software extensibility. The initial development of PINACLES delivered a state-of-the-art idealized LES capability solving the non-hydrostatic anelastic equations of motion with doubly periodic boundary conditions and idealized homogenous surface boundary conditions. Here we provide a final report on the outcomes of a fiscal year 2021 Seed Laboratory Directed Research Project that extended PINACLES in two key ways. First, PINACLES was coupled to a state-of-the-art land surface model enabling it to simulate spatially inhomogeneous land-atmosphere interactions that are known to control key atmospheric processes. Second, the dynamical core of PINACLES was modified to permit non-periodic boundary conditions. This model enhancement enables simulation of realistic cases with boundary conditions prescribed from atmospheric reanalysis and enables nested simulations conducted on a hierarchy of computational domains with increasing resolution. Together, these extensions to PINACLES make it a formidable modeling capability and expand its potential application to diverse components of DOE’s atmospheric science portfolio.

42 ENGINEERING↗

The role of HiPPI switches in mass storage systems: A five year prospective

New standards are evolving which provide the foundation for multi-gigabit per second data communication structures. The lowest layer protocols are so generalized that they encourage a wide range of application. Specifically, the ANSI High Performance Parallel Interface (HiPPI) is being applied to computer peripheral attachment as well as general data communication networks. The HiPPI Standards suite and technology products which incorporate the standards are introduced. The use of simple HiPPI crosspoint switches to build potentially complex extended 'fabrics' is discussed in detail. Several near term applications of the HiPPI technology are briefly described with additional attention to storage systems. Finally, some related standards are mentioned which may further expand the concepts above.

Gilbert, T. A.↗

Robust computer-aided synthesis and optimization of linear multivariable control systems with varying plant dynamics via AUTOCON

AUTOCON is an automated computer-aided design tool for the synthesis and optimization of linear multivariable control systems based upon user-defined control parameter optimization. Violations in stability and performance requirements are computed from constraints on Single Input/Single Output (SISO) open- and closed-loop transfer function frequency responses, and from constraints on the singular-value frequency responses of Multiple Input/Multiple Output (MIMO) transfer functions, for all critical plant variations. Optimum nonlinear programming algorithms are used in the search for local constrained solutions in which violations in stability and performance are caused either to vanish or be minimized for a proper selection of the control parameters. Classical control system stability and performance design can, in this way, be combined with modern multivariable robustness methods to offer general frequency response loop-shaping via a computer-aided design tool. Complete Nichols, Nyquist, Bode, singular-value Bode magnitude and transient response plots are produced, including user-defined boundary responses. AUTOCON is used to synthesize and optimize the lateral/directional flight control system for a typical high-performance aircraft.

Lefkowitz, C. P.↗

A novel approach to interface high-Q Fabry–Pérot resonators with photonic circuits

The unique benefits of Fabry–Pérot resonators as frequency-stable reference cavities and as an efficient interface between atoms and photons make them an indispensable resource for emerging photonic technologies. To bring these performance benefits to next-generation communications, computation, and time-keeping systems, it will be necessary to develop strategies to integrate compact Fabry–Pérot resonators with photonic integrated circuits. In this paper, we demonstrate a novel reflection cancellation circuit that utilizes a numerically optimized multi-port polarization-splitting grating coupler to efficiently interface high-finesse Fabry–Pérot resonators with a silicon photonic circuit. This circuit interface produces a spatial separation of the incident and reflected waves, as required for on-chip Pound–Drever–Hall frequency locking, while also suppressing unwanted back reflections from the Fabry–Pérot resonator. Using inverse design principles, we design and fabricate a polarization-splitting grating coupler that achieves 55% coupling efficiency. This design realizes an insertion loss of 5.8 dB for the circuit interface and more than 9 dB of back reflection suppression, and we demonstrate the versatility of this system by using it to interface several reflective off-chip devices.

Optics↗

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a set of low-dimensional (latent) descriptors that efficiently parameterize the response of the high-dimensional computational model. To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data. Since operations on the Grassmann require the data to be concentrated, we propose an adaptive algorithm based on Riemannian K-means and the minimization of the sample Fréchet variance on the Grassmann manifold to identify “local” principal geodesic submanifolds that represent different system behavior across the parameter space. Polynomial chaos expansion is then used to construct a mapping between the random input parameters and the projection of the response on these local principal geodesic submanifolds. Here, the method is demonstrated on four test cases, a toy-example that involves points on a hypersphere, a Lotka-Volterra dynamical system, a continuous-flow stirred-tank chemical reactor system, and a two-dimensional Rayleigh-Bénard convection problem.

42 ENGINEERING↗

PIMS: Memristor-Based Processing-in-Memory-and-Storage.

Continued progress in computing has augmented the quest for higher performance with a new quest for higher energy efficiency. This has led to the re-emergence of Processing-In-Memory (PIM) ar- chitectures that offer higher density and performance with some boost in energy efficiency. Past PIM work either integrated a standard CPU with a conventional DRAM to improve the CPU- memory link, or used a bit-level processor with Single Instruction Multiple Data (SIMD) control, but neither matched the energy consumption of the memory to the computation. We originally proposed to develop a new architecture derived from PIM that more effectively addressed energy efficiency for high performance scientific, data analytics, and neuromorphic applications. We also originally planned to implement a von Neumann architecture with arithmetic/logic units (ALUs) that matched the power consumption of an advanced storage array to maximize energy efficiency. Implementing this architecture in storage was our original idea, since by augmenting storage (in- stead of memory), the system could address both in-memory computation and applications that accessed larger data sets directly from storage, hence Processing-in-Memory-and-Storage (PIMS). However, as our research matured, we discovered several things that changed our original direc- tion, the most important being that a PIM that implements a standard von Neumann-type archi- tecture results in significant energy efficiency improvement, but only about a O(10) performance improvement. In addition to this, the emergence of new memory technologies moved us to propos- ing a non-von Neumann architecture, called Superstrider, implemented not in storage, but in a new DRAM technology called High Bandwidth Memory (HBM). HBM is a stacked DRAM tech- nology that includes a logic layer where an architecture such as Superstrider could potentially be implemented.

97 MATHEMATICS AND COMPUTING↗

Sensitivity analysis of generic deep geologic repository with focus on spatial heterogeneity induced by stochastic fracture network generation

Geologic Disposal Safety Assessment Framework is a state-of-the-art simulation software toolkit for probabilistic post-closure performance assessment of systems for deep geologic disposal of nuclear waste developed by the United States Department of Energy. This paper presents a generic reference case and shows how it is being used to develop and demonstrate performance assessment methods within the Geologic Disposal Safety Assessment Framework that mitigate some of the challenges posed by high uncertainty and limited computational resources. Variance-based global sensitivity analysis is applied to assess the effects of spatial heterogeneity using graph-based summary measures for scalar and time-varying quantities of interest. Behavior of the system with respect to spatial heterogeneity is further investigated using ratios of water fluxes. This analysis shows that spatial heterogeneity is a dominant uncertainty in predictions of repository performance which can be identified in global sensitivity analysis using proxy variables derived from graph descriptions of discrete fracture networks. New quantities of interest defined using water fluxes proved useful for better understanding overall system behavior.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Multidisciplinary analysis and sensitivity derivatives for isolated helicopter rotors in hover

A new method is presented for using Navier-Stokes results in the system analysis and sensitivity derivative computations for a helicopter rotor in hover. The system coupling includes the interactions between rotor performance, rotor structural properties and aerodynamics (i.e., airfoil shape). Emphasis is placed on the use of high fidelity Navier-Stokes algorithms for the aerodynamic problem. The present formulation is chosen to reduce the number of sensitivity derivative equations and their dimensions as much as possible. In addition, an alternative adjoint formulation is presented which dramatically reduces the computational requirement for disciplines in which there may be a large number of design variables (e.g., aerodynamics). The theoretical method makes use of a combination of derivatives from each discipline; the computation of these derivatives has already been shown to be feasible. Sample computations for the aerodynamic-rotor model coupling and an associated sensitivity derivative are also presented.

Jones, Henry E.↗

DESIGN AND EXPERIMENTAL STUDY OF A HIGH PRESSURE AND SUPERCRITICAL METHANE-OXYGEN BURNER

Directly heated supercritical oxy-fuel power cycles have potential to offer a higher thermal efficiency and lower pollutant emissions compared to existing power cycles. Recent thermodynamic analysis of the cycle performed by several groups including the UTEP-Air Liquide research team show that combustion in the vicinity of 300 bar pressure and 1000-1400 K temperature allows for relatively high system efficiencies while operating within the limit of practical combustor materials. However, the realization of directly heated supercritical power cycle requires combustion systems be designed to operate in supercritical conditions and at temperature far below the blowout limit of conventional flames (above 1500 K), where not only the thermodynamic properties but also the combustion properties and kinetics are unexplored. To minimize these knowledge gaps, some intermediate pressure ranges (up to 20 bar) are experimented and modeled using a CFD simulation tool. The knowledge obtained from the high pressure test will assist in understanding the combustion chamber pressurization mechanism, ignition and flame behavior at the elevated pressure. This is a systematic first step in testing at higher pressures of 100 and 300 bar pressures. The primary objective of this dissertation is to perform qualitative analysis on oxy-methane combustion at high pressure (< 20 bar) and compare to CFD model for future scale up to supercritical condition. For modeling of the system, a commercial computational fluid dynamics simulation tool, ANSYS Fluent, is used. The inlet conditions for the CFD analysis are obtained from the experiments. The geometry used for the study is same as the test apparatus and operates at the same power ratings. The expertise gained from this experimental study is important to accurately and safely design combustors at elevated pressures up to 300bar. A high pressure methane-oxygen fuel burner and combustor have been developed to accommodate oxycombustion environment. A detailed CFD analysis is conducted to understand the flame length and cooling phenomenon inside the combustor first at pressures up to 20 bar to compare to experiments then at supercritical pressure. The first part of the dissertation compares CFD results with high pressure burner experiments at pressures up to 20 bar. The test is conducted for 30 s within 150 kW – 250 kW thermal power inputs. Afterwards, based on the simulation results a cooling system is proposed for steady state high pressure combustion experiments. It is observed from the experimental study that the proposed pressurization mechanism able to pressurize the vessel up to 20 bar. It is also determined that the current combustor can operate up to 20 bar for short term. The steady state CFD simulation demonstrates that a cooling system must be incorporated for continuous operation. Additionally, the study focuses on the ignition delay due to added diluent during the combustion process. It is observed that as the carbon dioxide recirculation ratio increases the ignition delay time increases. Later part of the dissertation provides a preliminary guideline for developing a laboratory scale supercritical oxy combustor. The employment of supercritical fluid in gas turbine is fairly a new concept. Hence, there are many questions that need to be answered. During this dissertation study an investigation is performed to understand the impact of equation of state in the supercritical combustion simulation. Finally, a CFD model for developing supercritical oxy-methane burner and the combustor, incorporating real gas model, is presented. Although Lee-Kesler equation of state provides better accuracy than Peng Robinson, due to the computational time Peng Robinson equation of state is used for the simulation. It is found that existing knowledge is not enough to simulate combustion at supercritical phase. Detailed combustion chemistry at the supercritical condition must be developed and should be incorporated to accurately replicate the combustion phenomenon.

Chowdhury, ASM Arifur Rahim↗

Efficient Parallel Kernel Solvers for Computational Fluid Dynamics Applications

Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm and Reduced Parallel Diagonal Dominant (RPDD) algorithm have been carefully studied on different parallel platforms for different applications, and a NASA simulation code developed by Man M. Rai and his colleagues has been parallelized and implemented based on data dependency analysis. These achievements are addressed in detail in the paper.

Sun, Xian-He↗

A Performance Evaluation of the Cray X1 for Scientific Applications

The last decade has witnessed a rapid proliferation of superscalar cache-based microprocessors to build high-end capability and capacity computers because of their generality, scalability, and cost effectiveness. However, the recent development of massively parallel vector systems is having a significant effect on the supercomputing landscape. In this paper, we compare the performance of the recently-released Cray X1 vector system with that of the cacheless NEC SX-6 vector machine, and the superscalar cache-based IBM Power3 and Power4 architectures for scientific applications. Overall results demonstrate that the X1 is quite promising, but performance improvements are expected as the hardware, systems software, and numerical libraries mature. Code reengineering to effectively utilize the complex architecture may also lead to significant efficiency enhancements.

Oliker, Leonid↗

Xenon Recovery at Room Temperature using Metal-Organic Frameworks

Xenon is known to be a very efficient anesthetic gas but its cost prohibits the wider use in medical industry and other potential applications. It has been shown that Xe recovery and recycle from anesthetic gas mixture can significantly reduce its cost as anesthetic. The current technology uses series of adsorbent columns followed by low temperature distillation to recover Xe, which is expensive to use in medical facilities. Herein, we propose much efficient and simpler system to recover and recycle Xe from simulant exhale anesthetic gas mixture at room temperature using metal organic frameworks. Among the MOFs tested, PCN-12 exhibits unprecedented performance with high Xe capacity, Xe/N2 and Xe/O2 selectivity at room temperature. The in-situ synchrotron measurements suggest the Xe is occupied in the small pockets of PCN-12 compared to unsaturated metal centers (UMCs). Computational modeling of adsorption further supports our experimental observation of Xe binding sites in PCN-12.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗