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At least 55 records · Page 3

$T\overline{T}$ deformations of supersymmetric quantum mechanics

We define a manifestly supersymmetric version of the $T\overline{T}$ deformation appropriate for a class of (0 + 1)-dimensional theories with $\mathcal{N}$ = 1 or $\mathcal{N}$ = 2 supersymmetry, including one presentation of the super-Schwarzian theory which is dual to JT supergravity. These deformations are written in terms of Noether currents associated with translations in superspace, so we refer to them collectively as f($\mathcal{Q}$) deformations. We provide evidence that the f($\mathcal{Q}$) deformations of $\mathcal{N}$ = 1 and $\mathcal{N}$ = 2 theories are on-shell equivalent to the dimensionally reduced supercurrent-squared deformations of 2d theories with $\mathcal{N}$ = (0, 1) and $\mathcal{N}$ = (1, 1)supersymmetry, respectively. In the $\mathcal{N}$ = 1 case, we present two forms of the f($\mathcal{Q}$) deformation which drive the same flow, and clarify their equivalence by studying the analogous equivalent deformations in the non-supersymmetric setting.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Neutrino masses from low scale partial compositeness

We consider a class of models in which the neutrinos acquire Majorana masses through mixing with singlet neutrinos that emerge as composite states of a strongly coupled hidden sector. In this framework, the light neutrinos are partially composite particles that obtain their masses through the inverse seesaw mechanism. We focus on the scenario in which the strong dynamics is approximately conformal in the ultraviolet, and the compositeness scale lies at or below the weak scale. The small parameters in the Lagrangian necessary to realize the observed neutrino masses can naturally arise as a consequence of the scaling dimensions of operators in the conformal field theory. We show that this class of models has interesting implications for a wide variety of experiments, including colliders and beam dumps, searches for lepton flavor violation and neutrinoless double beta decay, and cosmological observations. At colliders and beam dumps, this scenario can give rise to striking signals involving multiple displaced vertices. The exchange of hidden sector states can lead to observable rates for flavor violating processes such as μ → eγ and μ → e conversion. If the compositeness scale lies at or below a hundred MeV, the rate for neutrinoless double beta decay is suppressed by form factors and may be reduced by an order of magnitude or more. The late decays of relic singlet neutrinos can give rise to spectral distortions in the cosmic microwave background that are large enough to be observed in future experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Surrogate Constructed Scalable Circuits ADAPT-VQE in the Schwinger model

Inspired by recent advancements of simulating periodic systems on quantum computers, we develop a new approach, (SC)$^2$-ADAPT-VQE, to further advance the simulation of these systems. Our approach extends the scalable circuits ADAPT-VQE framework, which builds an ansatz from a pool of coordinate-invariant operators defined for arbitrarily large, though not arbitrarily small, volumes. Our method uses a classically tractable ``Surrogate Constructed'' method to remove irrelevant operators from the pool, reducing the minimum size for which the scalable circuits are defined. Bringing together the scalable circuits and the surrogate constructed approaches forms the core of the (SC)$^2$ methodology. Our approach allows for a wider set of classical computations, on small volumes, which can be used for a more robust extrapolation protocol. While developed in the context of lattice models, the surrogate construction portion is applicable to a wide variety of problems where information about the relative importance of operators in the pool is available. As an example, we use it to compute properties of the Schwinger model - quantum electrodynamics for a single, massive fermion in $1+1$ dimensions - and show that our method can be used to accurately extrapolate to the continuum limit.

Gustafson, Erik [RIACS, Mtn. View] (ORCID:00000001↗

Uniform-in-phase-space data selection with iterative normalizing flows

Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that are routinely generated. In applications that are constrained by memory and computational intensity, excessively large datasets may hinder scientific discovery, making data reduction a critical component of data-driven methods. Datasets are growing in two directions: the number of data points and their dimensionality. Whereas dimension reduction typically aims at describing each data sample on lower-dimensional space, the focus here is on reducing the number of data points. A strategy is proposed to select data points such that they uniformly span the phase-space of the data. The algorithm proposed relies on estimating the probability map of the data and using it to construct an acceptance probability. An iterative method is used to accurately estimate the probability of the rare data points when only a small subset of the dataset is used to construct the probability map. Instead of binning the phase-space to estimate the probability map, its functional form is approximated with a normalizing flow. Therefore, the method naturally extends to high-dimensional datasets. The proposed framework is demonstrated as a viable pathway to enable data-efficient machine learning when abundant data are available.

97 MATHEMATICS AND COMPUTING↗

Surrogate-constructed scalable-circuits adaptive variational quantum eigensolver in the Schwinger model

Inspired by recent advancements in simulating periodic systems on quantum computers, we develop an approach to further advance the simulation of these systems, named (SC) 2 -ADAPT-VQE. Our approach extends the scalable-circuits ADAPT-VQE framework, which builds an ansatz from a pool of coordinate-invariant operators defined for arbitrarily large, though not arbitrarily small, volumes. Our method uses a classically tractable “surrogate constructed” method to remove irrelevant operators from the pool, reducing the minimum size for which the scalable circuits are defined. Bringing together the scalable circuits and the surrogate constructed approaches forms the core of the (SC) 2 methodology. Our approach allows for a wider set of classical computations on small volumes, which can be used for a more robust extrapolation protocol. While developed in the context of lattice models, the surrogate construction portion is applicable to a wide variety of problems where information about the relative importance of operators in the pool is available. As an example, we use it to compute the properties of the Schwinger model—quantum electrodynamics for a single, massive fermion in 1 +1 dimensions—and show that our method can be used to accurately extrapolate to the continuum limit.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Dimension Reduction and Redundancy Removal through Successive Schmidt Decompositions

Quantum computers are believed to have the ability to process huge data sizes, which can be seen in machine learning applications. In these applications, the data, in general, are classical. Therefore, to process them on a quantum computer, there is a need for efficient methods that can be used to map classical data on quantum states in a concise manner. On the other hand, to verify the results of quantum computers and study quantum algorithms, we need to be able to approximate quantum operations into forms that are easier to simulate on classical computers with some errors. Motivated by these needs, in this paper, we study the approximation of matrices and vectors by using their tensor products obtained through successive Schmidt decompositions. We show that data with distributions such as uniform, Poisson, exponential, or similar to these distributions can be approximated by using only a few terms, which can be easily mapped onto quantum circuits. The examples include random data with different distributions, the Gram matrices of iris flower, handwritten digits, 20newsgroup, and labeled faces in the wild. Similarly, some quantum operations, such as quantum Fourier transform and variational quantum circuits with a small depth, may also be approximated with a few terms that are easier to simulate on classical computers. Furthermore, we show how the method can be used to simplify quantum Hamiltonians: In particular, we show the application to randomly generated transverse field Ising model Hamiltonians. The reduced Hamiltonians can be mapped into quantum circuits easily and, therefore, can be simulated more efficiently.

97 MATHEMATICS AND COMPUTING↗

Fabrication and Evaluation of Large Alumina Crucibles by Vat Photopolymerization Additive Manufacturing for High-Temperature Actinide Chemistry

Additive manufacturing (AM) offers opportunities to advance the design and function of ceramic tooling in high temperature actinide pyrochemistry. In technical ceramics such as alumina, conventional forming techniques often restrict design flexibility and can limit experimental progress. In this study, we investigate the use of vat photopolymerization (VP) with commercial resins to fabricate large-scale alumina crucibles, reaching dimensions up to 125 mm, which is significantly larger than typically reported for dense VP ceramics. Notably, these additively manufactured components are produced using consumer-grade hardware, which limits process control, but offers significant upside in scalability and accessibility. Using microscopy and X-ray computed tomography, the VP alumina parts have high bulk densities above 95%, but also the prevalence of AM-induced artifacts and surface defects. Mechanical testing showed these defects to significantly reduce flexural strength and compromise part reliability. Electrorefining trials under sustained exposure to molten salts and metals reveal mixed results, with the AM material exhibiting high chemical compatibility, but mechanical failures due to the reduced strength were prevalent. Our findings illustrate both the promise and current limitations of AM ceramics for actinide chemistry, and point toward future improvements in process optimization, design strategies, and part screening to enhance performance and reliability.

Materials science↗

Innovations in optimization and control of accelerators using methods of differential geometry and genetic algorithms (Final Report)

Online tuning of particle accelerators is necessary in order to achieve optimal machine performance. However, it is also a major challenge due to the large parameter space which must be searched and the fact that many of the desir- able objectives compete with one another, and so will not reach their optimal values simultaneously. In order to mitigate these issues, we have explored using dimension-reduction techniques to reduce the size of the parameter space which must be searched and multi-objective genetic algorithms to obtain the sets of tuning parameters which provide pareto-optimal values for the objectives. These methods have enabled us to obtain improved values of the vertical emittance at the Cornell Electron Storage Ring (CESR), and to do so with greater control of orbit errors. Algorithmic tuning is a multidisciplinary endeavour, requiring expertise in beam dynamics, diagnostics, control systems and computer science, and thus a key practical problem is to formulate a common language in which experts with different specialties can communicate. We developed a solution to this problem in the form of a generic accelerator software interface that allows for rapid prototyping of optimization and control algorithms. Our interface is built on the Experimental Physics and Industrial Control Systems (EPICS) and makes possible testing control code in simulation before deployment on real accelerators, as well as deployment of third-party optimization code.

43 PARTICLE ACCELERATORS↗

Morphology and chemical behavior of model CsO x /Cu 2 O/Cu(111) nanocatalysts for methanol synthesis: Reaction with CO 2 and H 2

Cs is a promoter of Cu-based catalysts for the synthesis of alcohols from CO 2 hydrogenation. Scanning tunneling microscopy and ambient-pressure x-ray photoelectron spectroscopy were used to study the morphology and chemical properties of surfaces generated by the deposition of cesium on Cu 2 O/Cu(111) and Cu(111) substrates. CsO x nanostructures were formed after Cs metal was deposited on Cu 2 O/Cu(111) at 300 K. The formed CsO x protrude over the surface of copper oxide by 2–4 Å, with the dimension at the base of the nanostructures being in the range of 1–3 nm. Heating to elevated temperature induced significant changes in the size and dispersion of the CsO x nanostructures, and there was a clear reconstruction of the copper oxide substrate, which then exhibited long range order with a hexagonally packed structure. The as-deposited and annealed surfaces of CsO x /Cu 2 O/Cu(111) were more reactive toward CO 2 than plain Cu 2 O/Cu(111) or clean Cu(111). Yet, none of them were stable in the presence of H 2 , which fully reduced the copper oxide at 400–450 K. In CsO x /Cu(111), the CsO x nanoclusters were dispersed all over the metallic copper in no particular order. The CsO x species had an average width of 2 nm and ~1 Å height. The CsO x /Cu(111) systems exhibited the highest activity for the binding and dissociation of CO 2 , indicating that the CsO x -copper interface plays a key role in alcohol synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ceramic Composite Inert Matrix Fuel Forms in High-Temperature Gas-Cooled Microreactors

Here, this work optimizes micro-prismatic high-temperature gas reactor (HTGR) designs to reduce the energy-normalized mass of spent nuclear fuel (SNF) and high-level waste (HLW) produced. The optimization was performed for the current graphite moderator and an inert matrix fuel (IMF) concept employing different composite moderators in a prismatic design architecture. The fuel matrix is magnesium oxide (MgO) with entrained tristructural-isotropic (TRISO) fuel. The moderator materials, including beryllium oxide (MgO-BeO) and beryllium (MgO-Be) at 40 vol % loading and yttrium hydride (MgO-YH x=1.9 ) and zirconium hydride (MgO-ZrH x=1.9 ) at 15 vol % loading, were entrained within the MgO host matrix. A generic graphite micro-prismatic HTGR is used as the baseline point design where the external dimensions are held constant. The composite moderator designs use 19.9% enriched uranium nitride TRISO fuel and hexagonal assemblies. For each IMF concept, an optimization study was performed to maximize the discharge burnup of the fuel by varying the TRISO packing fraction and the lattice pitch of the assemblies. The mass of SNF and HLW, other waste metrics, fuel cost, environmental impact metrics, and the activity of the SNF and HLW at 100 years and 100 000 years were calculated for the optimized IMF and graphite reference designs. The IMF results were subsequently compared to those of the graphite reference and the values for a light water reactor (LWR) and a small modular LWR. For the SNF and HLW, all the IMF concepts and the graphite reference produced less waste compared to the traditional LWR designs. However, the IMF concepts outperformed the graphite reference regarding the mass of SNF and HLW. For the other waste metrics, the IMF concepts showed reductions in fuel cost with improved environmental metrics relative to the graphite reference. Overall, the IMF concepts significantly reduced the SNF and HLW produced per unit of energy generated compared to traditional LWR designs.

TRISO↗

Quantitative metrics for evaluating thermonuclear design codes and physics models applied to the National Ignition Campaign

In this study, physics models and design codes for hot dense plasmas undergoing thermonuclear burn are evaluated objectively using statistical metrics that compare the difference between calculations and data relative to the experimental uncertainties. The analysis is applied to the National Ignition Campaign (NIC) because it is relevant, comprehensive, and well documented. The statistics confirm that a key process afflicting NIC performance is mix driven by hydrodynamic instabilities as approximated here using the KL model [G. Dimonte and R. Tipton, Phys. Fluids 18, 085101 (2006)]. New physics models are also presented for instability-driven magnetic fields [B. Srinivasan et al., Phys. Rev. Lett. 108, 165002 (2012)] and the Coulomb logarithm for electron–ion thermal relaxation [G. Dimonte and J. Daligault, Phys. Rev. Lett. 101, 135001 (2008)]. The plasma-generated magnetic fields improve the agreement between code and data in a statistically significant manner by reducing the electron thermal conduction in the hot-spot via the Hall term. The Coulomb logarithm is presented in a numerically practical form that incorporates recent theoretical advances. However, it does not improve the agreement between the code and data because the thermal relaxation is so fast in non-ignited NIC plasmas that the typical 20% error does not change the tight coupling between electrons and ions. Even with these improved physics models, the one-dimensional simulations presented here are not able to describe the high-convergence NIC implosions in a statistically acceptable manner. Of the heroic multi-dimensional simulations of Clark et al. [Phys. Plasmas 23, 056302 (2016)], only those in three-dimensions satisfy the statistical acceptance criterion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Symmetric carbon tetramers forming spin qubits in hexagonal boron nitride

Abstract Point defect quantum bits in semiconductors have the potential to revolutionize sensing at atomic scales. Currently, vacancy-related defects are at the forefront of high spatial resolution and low-dimensional sensing. On the other hand, it is expected that impurity-related defect structures may give rise to new features that could further advance quantum sensing in low dimensions. Here, we study the symmetric carbon tetramer clusters in hexagonal boron nitride and propose them as spin qubits for sensing. We utilize periodic-DFT and quantum chemistry approaches to reliably and accurately predict the electronic, optical, and spin properties of the studied defect. We show that the nitrogen-centered symmetric carbon tetramer gives rise to spin state-dependent optical signals with strain-sensitive intersystem crossing rates. Furthermore, the weak hyperfine coupling of the defect to their spin environments results in a reduced electron spin resonance linewidth that can enhance sensitivity.

Chemistry↗

The R-matrix bootstrap for the 2d O( N ) bosonic model with a boundary

The S-matrix bootstrap is extended to a 1+1d theory with O(N) symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space of allowed R-matrices is an infinite dimensional convex space from which we plot a two dimensional section given by a convex domain on a 2d plane. In certain cases, at the boundary of the domain, we find vertices corresponding to integrable R-matrices with no free parameters. In other cases, when there is a one-parameter family of integrable R-matrices, the whole boundary represents integrable theories. We also consider R-matrices which are analytic in an extended region beyond the physical cuts, thus forbidding poles (resonances) in that region. In certain models, this drastically reduces the allowed space of R-matrices leading to new vertices that again correspond to integrable theories. We also work out the dual problem, in particular in the case of extended analyticity, the dual function has cuts on the physical line whenever unitarity is saturated. For the periodic Yang-Baxter solution that has zero transmission, we computed the R-matrix initially using the bootstrap and then derived its previously unknown analytic form.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Tunable room-temperature ferromagnetism in Co-doped two-dimensional van der Waals ZnO

The recent discovery of ferromagnetism in two-dimensional van der Waals crystals has provoked a surge of interest in the exploration of fundamental spin interaction in reduced dimensions. However, existing material candidates have several limitations, notably lacking intrinsic room-temperature ferromagnetic order and air stability. Here, motivated by the anomalously high Curie temperature observed in bulk diluted magnetic oxides, we demonstrate room-temperature ferromagnetism in Co-doped graphene-like Zinc Oxide, a chemically stable layered material in air, down to single atom thickness. Through the magneto-optic Kerr effect, superconducting quantum interference device and X-ray magnetic circular dichroism measurements, we observe clear evidences of spontaneous magnetization in such exotic material systems at room temperature and above. Transmission electron microscopy and atomic force microscopy results explicitly exclude the existence of metallic Co or cobalt oxides clusters. X-ray characterizations reveal that the substitutional Co atoms form Co 2+ states in the graphitic lattice of ZnO. By varying the Co doping level, we observe transitions between paramagnetic, ferromagnetic and less ordered phases due to the interplay between impurity-band-exchange and super-exchange interactions. Our discovery opens another path to 2D ferromagnetism at room temperature with the advantage of exceptional tunability and robustness.

36 MATERIALS SCIENCE↗

Nucleation and growth of blue phase liquid crystals on chemically-patterned surfaces: a surface anchoring assisted blue phase correlation length

In condensed matter, the correlation length is an essential parameter which describes the distance over which a material maintains its structural properties. In liquid crystals, for the orientational order parameter this characteristic length is of the order of nanometers, while in solid crystals it can extend to macroscopic length scales. Here, we report the measurement of the correlation length, or persistence length, of the crystallographic orientation of blue phases (BPs)—chiral liquid crystals with long-range 3D-crystalline structures and submicron-sized lattice-parameters. These materials exhibit phase transformations that have been identified as the liquid analog of crystal-crystal martensitic transformations. In this work, we use liquid epitaxial growth to achieve spontaneous BP-crystal nucleation and subsequent growth. Specifically, we design patterned substrates made of a binary array of regions with different liquid crystal anchoring, which facilitate a uniform nucleation and growth of BP-crystals with (100)-lattice orientation and a simple cubic symmetry. Furthermore, our results indicate that this simple cubic BP, the so-called blue phase II (BPII), forms first on the patterned surface, thereby propagating the growth of domains in directions parallel or perpendicular to the patterned regions. These results are used to understand the emergence of a surface anchoring assisted BPII-correlation length, taken as the distance over which the BP preserves its lattice orientation, as a function of time and pattern characteristics. We found that BPII single crystals can be achieved on patterned regions whose lateral dimensions are equal to or larger than 10 μm, consistent with our measurements of the BPII-correlation length. This newly acquired understanding of the role of surfaces on the formation of BPs is then used to design processes that permit formation of macroscopically large mono-domain, single-crystal BPs by relying on significantly reduced patterned areas (only part of the area is patterned), a feature that could benefit the applications of this intriguing class of materials.

correlation length↗

High Temperature Additive Architectures for 65% Efficiency (Final Technical Report)

This project aimed to develop advanced high-temperature additive components that contribute towards the DOE’s goal for advanced gas turbines that are capable of at least 65% efficiency in combined cycle application. The objective was to leverage state-of-the-art additive manufacturing to develop an innovative stage 1 turbine nozzle (S1N) that can provide cooling flow savings while maintaining the component durability expected in today’s gas turbines. The program had two phases. Phase I was a conceptual phase for novel advanced cooling designs enabled by additive manufacturing, as well as proposals for validation. Phase II included execution of the Phase I conceptual design, including manufacturing of prototype hardware and validation within an environment that is similar to engine operation. During Phase I of the program, the team devised a concept to reduce cooling air usage. The cooling air used in the side walls is filmed out along the side walls, while the cooling air used in the airfoil is eventually directed to near-wall channels and exits holes along the airfoil trailing end. During this program, the team performed additive trials to analyze the geometric limitations of additive manufacturing. This helped the team understand minimum wall thicknesses, hole sizes, and cooling channel dimensions among other limits. Phase II of this program pushed GE Vernova beyond its previous experience of designing and manufacturing an additively manufactured hot gas path component. Modern hot gas path components utilize material chemistries that are traditionally hard to weld, such as cast Renè 108, and exhibit solidification cracking when additively manufactured using Direct Metal Laser Melting (DMLM). Note that AM108 is a powder form of Renè 108. A S1N with advanced cooling is larger and more complex than parts previously built by additive manufacturing and required new learnings to resolve risks around solidification cracking. Finally, the team validated the design in a combustion rig that replicated operation in a gas turbine. In order to properly quantify the benefits of the new additive design, a baseline was also tested in the rig and operated under the same conditions. In addition, an uncertainty analysis was done to quantify any sources of error that could impact the results. At the end of the validation effort, it was determined that the additive nozzle exceeded the 15% reduction in cooling flow goal even with the worst-case assumptions for uncertainty.

03 NATURAL GAS↗

Spontaneously Broken Noninvertible Symmetries in Transverse-Field Ising Qudit Chains

Recent developments have revealed that symmetries need not form a group, but instead can be noninvertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a noninvertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group 𝐺 (reducing to ordinary qubits when 𝐺=ℤ 2 ). We construct Ising-type transverse-field Hamiltonians with Rep⁡(𝐺) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group 𝐺 . For non-Abelian 𝐺 , the symmetry is noninvertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain—features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with nontrivial internal Hilbert spaces and fusion rules. Our Letter identifies properties of noninvertible symmetry breaking that existing quantum hardware can probe.

1-dimensional spin chains↗

Chemistry and Dynamics of Supercritical Carbon Dioxide and Methane in the Slit Pores of Layered Silicates

In the mid 2010s, high-pressure diffraction and spectroscopic tools opened a window into the molecular-scale behavior of fluids at the conditions of many CO 2 sequestration and shale/tight gas reservoirs - conditions where CO 2 and CH 4 are present as variably wet supercritical fluids. Integrating high-pressure spectroscopy and diffraction with molecular modeling has revealed much about the ways that supercritical CO 2 and CH 4 behave in reservoir components, particularly in the slit-shaped micro- and meso-pores of layered silicates (phyllosilicates) abundant in caprocks and shales. This Account summarizes how supercritical CO 2 and CH 4 behave in the slit pores of swelling phyllosilicates as functions of the H 2 O activity, framework structural features, and charge-balancing cation properties at 90 bar and 323 K – conditions similar to a reservoir at ~1 km depth. Slit pores containing cations with large radii, low hydration energy, and large polarizability readily interact with CO 2 , allowing CO 2 and H 2 O to adsorb and co-exist in these interlayer pores over a wide range of fluid humidities. In contrast, cations with small radii, high hydration energy, and low polarizability weakly interact with CO 2 leading to reduced CO 2 uptake and a tendency to exclude CO 2 from interlayers when H 2 O is abundant. The reorientation dynamics of confined CO 2 depends on the interlayer pore height, which is strongly influenced by the cation properties, framework properties, and fluid humidity. The silicate structural framework also influences CO 2 uptake and behavior - for example, smectites with increasing F-for-OH substitution in the framework take up greater quantities of CO 2 . Reactions that trap CO 2 in carbonate phases have been observed in thin H 2 O films near smectite surfaces, including a dissolution-reprecipitation mechanism when the edge surface area is high and an ion exchange-precipitation mechanism when the interlayer cation can form a highly insoluble carbonate. In contrast, supercritical CH 4 does not readily associate with cations, does not react with smectites, and is only incorporated into interlayer slit mesopores when (i) the pore has a $z$-dimension large enough to accommodate CH 4 , (ii) the smectite has low charge and (iii) the H 2 O activity is low. In conclusion, the adsorption and displacement of CH 4 by CO 2 and vice-versa have been studied on the molecular scale in one shale, but opportunities remain to examine behavioral details in this more complicated, slit-pore inclusive system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗