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At least 829 records · Page 46

Additional considerations in analytical solution for time-dependent heat conduction in a three-dimensional multilayer sphere

This work presents an analytical method to solve the heat conduction equation in three dimensions for problems consisting of multilayer concentric spheres. The method can be used to treat time-varying heat conduction problems where the heat source that drives the transient is time-invariant. Equally applicable to all Poisson-type problems with concentric spherical geometry, the method consists of representing the solution as a summation of weighted eigenfunctions. The weights for each eigenfunction are computed algebraically. Previous work has already established the core constituents of the methodology. The current work augments the existing methods by including consideration of nonzero interface resistance between layers and explicit discussion on the boundary condition homogenization required to treat inhomogeneous problems. Also, two demonstration problems are presented. One demonstration problem is based on the method of manufactured solutions and therefore allows for comparison with exact expressions for the solution temperature distribution. The second, more complex, demonstration problem relies on the finite element method for comparisons. The expected convergence behavior is observed for both demonstration problems.

97 - MATHEMATICS AND COMPUTING↗

Symmetry structure of a Riccati equation appearing in penetration mechanics

In the design of projectile penetration experiments a matter of considerable interest is scaling: that is, the potential relevance of small-scale experiments to their full-scale counterparts, in a manner analogous to that most often encountered in the context of fluid mechanics. From the theoretical standpoint, phenomena associated with scaling and scalability can be assessed using the well-established tools of dimensional analysis and the Buckingham-Pi Theorem. However, the familiar precepts of dimensional analysis are themselves a specific manifestation of the broader group invariance properties or symmetries of a mathematical model. Here, this work explores these notions – that is, dimensional analysis, the conditions for realizing complete similarity, and any additional symmetry structures – in the context of a Riccati differential equation appearing in the context of penetration mechanics. The aim of the investigation is twofold: 1) to complement existing empirical considerations with a concrete theoretical basis, and 2) to provide a deeper theoretical understanding of the projectile penetration model and its many implications.

97 MATHEMATICS AND COMPUTING↗

Re-investigation of high-temperature phase equilibria in Fe-rich Sm–Fe–Ti alloys

Recently renewed attempts to develop high-performance rare-earth-lean permanent magnets based on the Sm(Fe,Ti) 12 compound have drawn attention to the limited knowledge about the high-temperature phase equilibria in the Sm–Fe–Ti system. Experimental investigation of equilibrated alloys with electron probe microanalysis, X-ray diffraction and thermomagnetic analysis revealed several inaccuracies in the currently accepted phase relations at 1000°C and allowed for a revision of the Fe-rich corner of the Sm–Fe–Ti phase diagram. The Sm(Fe,Ti) 12 and Sm 3 (Fe,Ti) 29 phases were found to have more extended Ti ranges of 5.1–9.7 at% and 2.8–6.9 at%, respectively. With increasing of the Ti content, the Curie temperature of the Sm(Fe,Ti) 12 remains nearly constant at 306–312°C, whereas that of the Sm 3 (Fe,Ti) 29 increases from 188°C to 207°C. The low-titanium Sm 3 (Fe,Ti) 29 phase equilibrates not only with the Sm(Fe,Ti) 12 and Sm2(Fe,Ti) 17 phases, but also with (α-Fe) solid solution. Newly demonstrated equilibrium between Sm 2 (Fe,Ti) 17 and TiFe 2 phases makes impossible the earlier reported equilibrium between the Sm 3 (Fe,Ti) 29 and Sm(Fe,Ti) 11 phases. Because of an invariant reaction at 1000 °C, the revised phase diagram also features a class II four-phase equilibrium Sm 3 (Fe,Ti) 29 + TiFe 2 + Sm(Fe,Ti) 12 + Sm 2 (Fe,Ti) 17 . Peritectic decomposition of the Sm(Fe,Ti) 11 phase, which occurs either at 1075°C or at 1087°C, was found to have among its products the Sm(Fe,Ti) 12 phase. Although no such equilibration was attempted, it must be possible to obtain above 1087°C a two-phase state composed of the Sm(Fe,Ti) 12 phase and a liquid – which is important for manufacturing of the Sm(Fe,Ti) 12 - based permanent magnets via the liquid-phase sintering.

36 MATERIALS SCIENCE↗

Carbidic Mo is the sole kinetically-relevant active site for catalytic methane dehydroaromatization on Mo/H-ZSM-5

Systematic variation of Mo/Al = {0.10, 0.25, 0.35} in Mo/H-ZSM-5 catalysts effects ~20× change of Mo-to-H + ratio during methane dehydroaromatization (DHA) reactions at steady state and on deactivating catalysts. Mo and Brønsted-acid site count, respectively enumerated by ethane hydrogenolysis probe reaction and dimethyl ether chemical titration, evolve disparately during DHA catalysis, indicating the two sites reduce in number by distinct mechanisms. Here, the deactivation of Mo/H-ZSM-5 catalytic activity is uniquely attributed to the loss of active, or accessible, Mo sites, evinced by (i) the non-selective nature of deactivation (i.e. that deactivation occurs without modification of residual active sites), (ii) invariance in product distribution from Mo/H + = 0.10–2.1, and (iii) linear correspondence between Mo-catalyzed ethane hydrogenolysis rate and active site count during DHA on deactivating samples. DHA forward rate – the intrinsic kinetic descriptor of catalyst activity – normalizes by Mo content at steady state and on deactivating catalysts with Mo/Al = 0.10–0.35 for Mo-based contact times in the range τ Mo = 0.79–44 mol Mo s mol –1 C , unequivocally establishing Mo aggregates as the sole kinetically-relevant active site on Mo/H-ZSM-5. Brønsted-acid site content over a ~40× range in τ H+ = 1.4–54 mol H+ s mol –1 C has no discernable correlation with or effect on DHA rate, methane conversion, or product distribution – demonstrating H + does not catalyze any rate- or selectivity-determining steps in the benzene formation pathway and suggesting that the benefits of zeolitic acid sites are only to disperse Mo during catalyst synthesis and, conceivably, to catalyze equilibrated reaction steps.

02 PETROLEUM↗

Rates and reversibility of CO 2 hydrogenation on Cu-based catalysts

Kinetics of reaction pathways involved in the conversion of CO 2 to methanol and CO on Cu/ZnO/Al 2 O 3 are resolved using in situ chemical titration, steady-state kinetic measurements, and mathematical formalisms for reversibility to probe salient species governing methanol selectivity and yield during CO 2 hydrogenation. Across a range of H 2 :CO 2 = 1:1 to H 2 :CO 2 = 80.5:1, active site density determined from in situ chlorine uptake remained invariant; hence, observed trends in rates can be interpreted as only arising from reaction kinetics and not from changing active site density. Kinetic and thermodynamic contributions to rates are decoupled to evaluate forward and reverse rates of methanol synthesis and reverse water-gas shift (RWGS) reactions. These kinetic analyses show that the forward rates of methanol synthesis exhibit persistent first order dependence on hydrogen pressure and are inhibited by water more significantly than the forward rates of RWGS. In contrast, the reverse rates of methanol synthesis and RWGS are both inhibited by H 2 . Consequently, without any modifications to the Cu/ZnO/Al 2 O 3 catalyst formulation, methanol selectivity can be increased to > 80% by increasing inlet H 2 partial pressure and methanol yield can be enhanced by ~20% by adding water adsorbents even under conditions far from equilibrium. Here, the kinetic treatments presented herein demonstrate a dearth of H* species during catalysis, provide thermodynamic constraints precluding sequential RWGS and CO hydrogenation as the pathway for methanol synthesis, reveal P H2 and P H2O as salient in determining methanol selectivity and yield by impacting both the forward and reverse rates of CO 2 hydrogenation on Cu/ZnO/Al 2 O 3 , and explicate the fundamentals of novel sorption-enhanced methanol synthesis, which not only alleviates equilibrium constraints but also alters the intrinsic rate at which the system approaches equilibrium.

42 ENGINEERING↗

Mechanistic and kinetic relevance of hydrogen and water in CO 2 hydrogenation on Cu-based catalysts

Here, we ally steady-state kinetics, kinetic isotope effects, and density functional theory (DFT) calculations to illustrate that Cu-based catalysts remain saturated by H-adatoms (H*) and molecular formic acid (HCOOH**) during CO 2 hydrogenation. High H* coverage under methanol synthesis conditions is evidenced by reverse water-gas shift (RWGS) rates that exhibit positive H 2 reaction orders only at P H2 ≲ 0.5 bar, above which methanol synthesis and RWGS rates exhibit first and zeroth order dependence on P H2 , respectively. HCOOH** also accumulates on the surface with increasing P CO2 as informed by the Langmuir-type dependence on P CO2 (0.25-23 bar) for both methanol synthesis and RWGS. As both HCOOH** and H* have one H-atom per site occupied, the two species share the same P H2 dependence and give rise to CO 2 reaction orders that are independent of P H2 . Surface coverages determined based on kinetic analyses are further corroborated with DFT-derived adsorption energies that show favorable HCOOH** adsorbate-adsorbate interactions as well as repulsive interactions for bidentate formate (HCOO**) on H*-saturated surfaces. Methanol selectivity remains invariant with P CO2 and P CO despite CO inhibiting reaction rates, thereby demonstrating methanol synthesis and RWGS occur on the same active site. In contrast, water preferentially inhibits methanol synthesis rates, increases methanol synthesis H 2 reaction order from 1.0 to 1.5, and alters the methanol synthesis H 2 /D 2 kinetic isotope effect; the inhibitory effect of H 2 O thus cannot be attributed to competitive adsorption alone and instead reflects a change in the rate-determining step for methanol synthesis. The disparate kinetics of methanol synthesis and RWGS evince a branching pathway where methanol is formed from formates and CO is formed from carboxylates. The presented work thus identifies the relevant surface species, underscores the distinct catalytic role of water in branching methanol synthesis and RWGS pathways, and, in doing so, details a mechanistic picture that yields predictable rates and reaction orders for both methanol synthesis and RWGS on Cu-based CO 2 hydrogenation catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids

In this work, we develop a numerical method for solving the acoustic wave equation in covariant form on staggered curvilinear grids in an energy conserving manner. The use of a covariant basis decomposition leads to a rotationally invariant scheme that outperforms a Cartesian basis decomposition on rotated grids. The discretization is based on high order Summation-By-Parts (SBP) operators and preserves both symmetry and positive definiteness of the contravariant metric tensor. To improve accuracy and decrease computational cost, we also derive a modified discretization of the metric tensor that leads to a conditionally stable discretization. Bounds are derived that yield a point-wise condition that can be evaluated to check for stability of the modified discretization. This condition shows that the interpolation operators should be constructed such that their norm is close to one.

97 MATHEMATICS AND COMPUTING↗

Massively parallel transport sweeps on meshes with cyclic dependencies

When solving the first-order form of the linear Boltzmann equation, a common misconception is that the matrix-free computational method of “sweeping the mesh”, used in conjunction with the Discrete Ordinates method, is too complex or does not scale well enough to be implemented in modern high performance computing codes. This has led to considerable efforts in the development of matrix-based methods that are computationally expensive and is partly driven by the requirements placed on modern spatial discretizations. In particular, modern transport codes are required to support higher order elements, a concept that invariably adds a lot of complexity to sweeps because of the introduction of cyclic dependencies with curved mesh cells. In this article we will present a comprehensive implementation of sweeping, to a piecewise-linear DFEM spatial discretization with particular focus on handling cyclic dependencies and possible extensions to higher order spatial discretizations. We find that these methods are implemented in a new C++ simulation framework called Chi-Tech (). We present some typical simulation results with some performance aspects that one can expect during real world simulations, we also present a scaling study to >100k processes where Chi-Tech maintains greater than 80% efficiency solving a total of 87.7 trillion angular flux unknowns for a 116 group simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Active- and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows

Active- and transfer-learning are applied to microscale dynamics of polymer flows for the multiscale discovery of effective constitutive approximations required in viscoelastic flow simulation. The result is macroscopic rheology directly connected to a microstructural model. Micro and macroscale simulations are adaptively coupled by means of Gaussian process regression (GPR) to run the expensive microscale computations only as necessary. This multiscale method is demonstrated with flows of a polymer solution as a model system. At the microscale level dissipative particle dynamics (DPD) is employed to model the fluid as a suspension of bead-spring micro-structures subjected to steady shear flow. The results yield the non-Newtonian viscosity and the first normal stress difference at strain rates as training data used in a GPR model. DPD parameters are calibrated with respect to experimental data for a real polymer solution. Compliance with these data requires adjustment of the DPD model's cutoff radius, which then becomes a function of the second invariant of the strain rate tensor. The FENE-P model is chosen for the macroscale description using the spectral element method (SEM) to simulate channel flow and flow past a circular cylinder. The DPD results at the lowest possible shear strain rate yield an estimate of the zero-shear rate viscosity, which allows the initiation of the macroscale flow by SEM as a Newtonian fluid. The resulting strain-rate field is surveyed to determine additional shear strain rate sampling points for the DPD system. This new information allows an initial fitting of parameters of the constitutive equation followed by new SEM simulations at the macroscale. Additionally, guided by active-learning GPR to select new sampling points, this process continues until convergence is achieved. The effectiveness of this new simulation paradigm for viscoelastic flows is tested with different macroscale operating conditions. The effective closure learned in the channel simulation is then transferred directly to the flow past a circular cylinder at low Reynolds number, where the results show that only two additional DPD simulations are required to achieve a satisfactory constitutive model. With an increase of the Reynolds number, the active-learning scheme automatically detects the inaccuracy of the learned constitutive model, and initiates additional DPD simulations for the extra data needed to once again close the microscale-macroscale coupled system. This new paradigm of active- and transfer-learning for multiscale modeling is readily applicable to other microscale-macroscale coupled simulations of complex fluids and other materials. Furthermore, the coupling between microscale and macroscale solvers can be seamlessly implemented with our open source multiscale universal interface (MUI) library.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations

We propose an unsupervised machine-learning checkpoint-restart (CR) algorithm for particle-in-cell (PIC) algorithms using Gaussian mixtures (GM). The algorithm compresses the particle population per spatial cell by constructing a velocity distribution function using GM. Particles are reconstructed at restart time by local resampling of the Gaussians. To guarantee fidelity of the CR process, we ensure the exact preservation of invariants such as charge, momentum, and energy for both compression and reconstruction stages, everywhere on the mesh. We also ensure the preservation of Gauss' law after particle reconstruction by exactly matching the density profile at restart time. As a result, the GM CR algorithm is shown to provide a clean, conservative restart capability while potentially affording orders of magnitude savings in input/output requirements. Here, we demonstrate the algorithm using a recently developed exactly energy- and charge-conserving PIC algorithm using both electrostatic and electromagnetic tests. The tests demonstrate not only a high-fidelity CR capability, but also its potential for enhancing the fidelity of the PIC solution for a given particle resolution.

97 MATHEMATICS AND COMPUTING↗

Scalable semidefinite programming approach to variational embedding for quantum many-body problems

In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate ‘high-level’ theory and glued together self-consistently by a less accurate ‘low-level’ theory at the global scale. The recently introduced variational embedding approach for quantum many-body problems combines the insights of semidefinite relaxation and quantum embedding theory to provide a lower bound on the ground-state energy that improves as the cluster size is increased. The variational embedding method is formulated as a semidefinite program (SDP), which can suffer from poor computational scaling when treated with black-box solvers. Here, we exploit the interpretation of this SDP as an embedding method to develop an algorithm which alternates parallelizable local updates of the high-level quantities with updates that enforce the low-level global constraints. Moreover, we show how translation invariance in lattice systems can be exploited to reduce the complexity of projecting a key matrix to the positive semidefinite cone.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect to rotations and permutations. Existing methodologies yield sets of symmetrized functions that are over-complete. These methodologies thus require an additional numerical procedure, such as singular value decomposition (SVD), to eliminate redundant functions. In this work, it is shown that analytical linear relationships for subsets of cluster functions may be derived using recursion and permutation properties of generalized Wigner symbols. From these relationships, subsets (blocks) of cluster functions can be selected such that, within each block, functions are guaranteed to be linearly independent. It is conjectured that this block-wise independent set of permutation-adapted rotation and permutation invariant (PA-RPI) functions forms a complete, independent basis for ACE. Along with the first analytical proofs of block-wise linear dependence of ACE cluster functions and other theoretical arguments, numerical results are offered to demonstrate this. The utility of the method is demonstrated in the development of an ACE interatomic potential for tantalum. Using the new basis functions in combination with Bayesian compressive sensing sparse regression, some high degree descriptors are observed to persist and help achieve high-accuracy models.

Angular momentum↗

Quantum mechanical closure of partial differential equations with symmetries

We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a quantum mechanical representation, we use the space of quantum density operators to model the unresolved degrees of freedom of the original dynamics in a statistical sense, and the framework of quantum measurement to predict their contributions to the resolved dynamics. The embedded dynamics is discretized by a positivity preserving process, leading to a compressed representation that is invariant under the dynamical symmetries of the resolved dynamics. We present a data based formulation of the closure scheme and apply it to a closure problem for the shallow water equations. The numerical results demonstrate that our closure model can accurately predict the main features of the true dynamics, including for out of sample initial conditions.

Delay embedding↗

A conservative discontinuous Galerkin algorithm for particle kinetics on smooth manifolds

A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using both canonical and non-canonical Hamiltonian formulations. Our schemes apply to both formulations, but the canonical formulation results in a particularly efficient scheme that also conserves particle density and energy exactly. The collisionless update is coupled to a Bhatnagar-Gross-Krook (BGK) collision operator that provides a simplified model for relaxation to local thermodynamic equilibrium. An iterative scheme is constructed to ensure collisional invariants (density, momentum and energy) are preserved numerically. Rotation of the manifold is incorporated by modifying the Hamiltonian while ensuring a canonical formulation. Several test problems, including a kinetic version of the classical Sod shock problem, Kelvin-Helmholtz instability on the surfaces of a sphere and a hyperboloid, with and without rotations, are presented. A prospectus for further development of this approach to simulation of kinetic theory in general relativity is presented.

Discontinuous Galerkin↗

Structural investigation of the temperature-stable relaxor dielectric Ba 0.8 Ca 0.2 TiO 3 -Bi(Mg 0.5 Ti 0.5 )O 3

Aberration corrected scanning transmission electron microscopy (STEM) and electron diffraction have been used to disclose local structure and nano-chemistry in a Ca modified BaTiO 3 -Bi(Mg 0.5 Ti 0.5 )O 3 relax or dielectric ceramic which exhibits high and near-invariant relative permittivity over a wide temperature range. High resolution, synchrotron X-ray diffraction indicated a globally cubic structure ($Pm$$\overline{3}$$m$), but direct atomic-scale imaging by STEM revealed local tetragonal distortions. Nanopolar clusters were identified from B-site atomic displacement vectors measured relative to oxygen ion positions along < 100 > and < 110 > zone axes of integrated differential phase contrast (iDPC) STEM images, highlighting cluster sizes of 2–5 nm. Chemical analysis by STEM-energy dispersive X-ray spectroscopy and full pattern refinements of X-ray powder diffraction data each implied high levels of Bi vacancies within the matrix. The possibility that these A-site vacancies modulate the nanopolar structure and promote flattening of the permittivity-temperature response in this class of dielectric is discussed.

36 MATERIALS SCIENCE↗

Modeling the processes of soil moisture in regulating microbial and carbon-nitrogen cycling

Soil carbon (C) and nitrogen (N) cycles and their complex responses to hydro-climatic forcing have gained increasing attention. While the temperature effects have been intensively studied, soil moisture response functions (SMRFs) are not well documented for various microbial and enzymatic processes due to the difficulties in directly measuring and differentiating the moisture effects on various processes. In this work we extended our C-only Microbial-ENzyme Decomposition (MEND) model to the C-N coupled MEND model with flexible element stoichiometry. Our model calibration showed good agreement between simulated and observed C:N ratios in soil organic matter and microbial biomass, as well as the ammonium and nitrate concentrations. We show that the selection of SMRFs for specific biogeochemical processes could result in significant differences in model simulated microbial and C-N processes. In particular, it is essential to account for the soil moisture effects on microbial dormancy and resuscitation, as the changes in microbial physiology under favorable or stressful conditions will exert strong controls on soil C and N dynamics. We also advocate the utilization of dynamic (time-variant) data (e.g., litter input, N deposition, soil temperature and moisture), instead of time-invariant data, to drive model simulations and analyses. Dynamic forcing data (particularly dynamic soil moisture) better represent the real-world climate and environmental conditions, which could facilitate more realistic modeling and understanding of soil C and nutrient cycling in a changing world.

54 ENVIRONMENTAL SCIENCES↗

Multi-fidelity Fourier neural operator for fast modeling of large-scale geological carbon storage

Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical simulators are required to train a model to accurately predict the complex physical behaviors associated with this process. In practice, the available training data are always limited in large-scale 3D problems due to the high computational cost. Therefore, we propose to use a multi-fidelity Fourier neural operator (FNO) to solve large-scale GCS problems with more affordable multi-fidelity training datasets. FNO has a desirable grid-invariant property, which simplifies the transfer learning procedure between datasets with different discretization. Here, we first test the model efficacy on a GCS reservoir model being discretized into 110 k grid cells. The multi-fidelity model can predict with accuracy comparable to a high-fidelity model trained with the same amount of high-fidelity data with 81% less data generation costs. We further test the generalizability of the multi-fidelity model on a same reservoir model with a finer discretization of 1 million grid cells. This case was made more challenging by employing high-fidelity and low-fidelity datasets generated by different geostatistical models and reservoir simulators. We observe that the multi-fidelity FNO model can predict pressure fields with reasonable accuracy even when the high-fidelity data are extremely limited. The findings of this study can help for better understanding of the transferability of multi-fidelity deep learning surrogate models.

58 GEOSCIENCES↗

Fatigue of laser powder bed fusion processed 17-4 stainless steel using prior process exposed powder feedstock

The rapid pace of development seen in the metal additive manufacturing (AM) process of laser powder-bed fusion (LPBF) requires in-step advances in processes qualification to enable full-scale adoption. This particularly applies to quantifying how powder feedstock conditions impact end-component quality. Here this study examines how in-machine 17-4 stainless steel powder feedstocks are affected by prior LPBF processes, and how these effects impact subsequent builds. Examinations of powder morphology, chemistry, flowability, and rheology were conducted to characterize the powder conditions. The resultant effects of powder feedstock condition on produced component quasi-static tensile and high-cycle fatigue properties were analyzed. Fatigue life was analyzed using a reliability modeling approach that enabled a robust statistical comparison of life. Powder characteristics were found to evolve with powder exposure to prior LPBF processes, particularly in the extremes of powder size distribution and measures of bulk flow. No significant effects of these changes on tensile properties were observed. Reliability modeling methods, including the lognormal and Weibull distributions as well as the empirical survival function, are shown to be effective tools for modeling fatigue variability in LPBF manufactured components. Through these tools, fatigue life was found to be invariant with changes in powder condition.

42 ENGINEERING↗