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Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Large Primtive Asteroids: Thermal and Dynamical Context

Primitiveasteroids, most of which are located in the outer belt and Jupiter’s Trojan clouds, provide information related to the origin and evolution of the solar system and the conditions in which the solar nebula was formed. These asteroids are widely thought to be the origin of the least-altered car-bonaceous chondrite that allow us to put crucial con-straints on the current dynamical and thermal theories of the formation and evolution of the early solar sys-tem. The nature of surface composition of large and low-albedo asteroids, like (1) Ceres, (10) Hygiea and (52) Europa, is still under intense debate and different interpretations have beenput forth to explain the ab-sorption features in these objects (e.g.,[1, 2, 3,4,5,6]). Laboratory and spectroscopic experiments on me-teorites that represent all nine carbonaceous chondrite types also found no spectral matches for these large asteroids (e.g.,[7]). Previous studies of asteroid Ceres (the largest primitive asteroid in the solar system) have been conducted to constrain and estimate its surface composition (e.g., [2, 5]). Using linear mixing,[2]found hydroxide brucite, serpentines, and carbonates, to be consistent with Ceres’ ground-based spectra.[5]estimated the surface composition of Ceres and found evidence of widespread NH3-phyllosilicates across its surface using best-fit solutions to Dawn’s NIR spectra. The presence of NH3-phyllosilicates implies that mate-rial from the outer solar system was incorporated into large primitive asteroids, either during their formation at great heliocentric distance or by incorporation of material transported into the Main Belt region. Here we presentnew largeand primitive asteroidsthat share the same spectral similaritieswith the largest asteroid in the solar system, Ceres.We also present the context of these new observations in terms oftheirthermal and dynamicalevolution.Large Primitive Asteroids: Dynamical and Thermal Context:Orbital Distribution of LargePrimitiveAsteroids: Constraining the mineralogy and surface composition of large primitive asteroids will place crucial con-straints on existing dynamical and thermal theories of the formation of the early solar system. We identified several additional asteroids in the Europa-like group in addition to asteroids Europa, Euphrosyne, and Patien-tia, that wereidentified in [8]using NASA IRTFtele-scope (e.g.,Figure 1). These new asteroids along with the already-observed Ceres-and Europa-like group members are localized in the 2.8 < a < 3.4 AU region and characterized by larger sizes, showing an interest-ing orbital distribution (Figure 2). Ceres-likeand Eu-ropa-like groups, which include the largest asteroids in the solar system, show an interesting orbital distribu-tion. These groups are located in the 2.6 < a < 3.6 AU region that contains the snow-line. The snow-line’s location may have been driftedinwards due to the disk’s cooling and evolution[9,10]. Recent dynamical models[11,12]suggested that a substantial fraction of primitive asteroids originated between or beyond the giant planets (a > 5 AU), where water ice would have been stable, and then implanted in the outer Main Belt region because of the giant planets’ growth.Figure 1. Two asteroids, 94 Aurora and 423 Diotima, showing spectra similar to asteroids (1)Ceres and (52)Europa.Thermal modeling and evolution of primitive aster-oids:Primitive water-rich asteroids are thought to be originally composed of mixtures of anhydrous materi-als and water ice that waslater melted by heating sources such as the decay of 26Al, reacting with anhy-drous materials to form H2O/OH-rich minerals. Calcu-lations of the evolution of the temperature and struc-ture of icy planetesimals were performedusing a 1D finite differences thermal evolution model[13, 14] for 26Al-heated planetesimals. In particular, thermally activated compaction due to hot pressing of bodies with an initially unconsolidated porous structure is included. An ice-rich initial composition that leads to a material dominated by phyllosilicates upon aqueous alteration (with 25 vol% H2O and a rock fraction that contains 85 vol% phyllosilicates and 15 vol% olivine upon aque-ous alteration, similar to CIand CM chondrites) was assumed. Atypical initial porosity of 40%[15] is re-duced following the change of the strain rate that is calculated as Voigt approximation from the strain rates of components[16]. Material properties (thermal con-ductivity, density, heat capacity, etc.) correspond to the composition assumed and are adjusted with tempera-ture and porosity. Melting of the water ice as well as water-rock separation are included[14]. Both short-and long-lived radionuclides are consideredas heat sources. Figure 3 shows the maximum temperature calculated as a function of radius and accretion time. A variety of internal structures is obtained, ranging from primordial (no melting of water ice) over partially melted or partially differentiated (melting of water ice, hydration, formation of a rocky core and water ocean below an undifferentiated layer) to completely differ-entiated ones (rocky core, water mantle, Enceladus-like case). The heating and differentiation of planetesi-mals is determined by the availability of 26Al, i.e., by the accretion time t0 relative to the formation of the calcium-aluminum-rich inclusions (CAIs), such that maximum temperatures and structures vary stronglyfor t0< 6 Myr rel. to CAIs. However, for a later accre-tion only the size of the body determines its maximum tempera-ture and structure due to the nearly constant heating by long-lived radionuclides. Average densities of Ceres-and Europa-like group membersimply high-ly porous interiors and, consequently, relatively late accretion at t0> 3 Myr rel. to CAIs with a maximum temperature of < 600 K (Figure3)

D Takir↗

Electrode and Microstructure Dependence of Oxygen Diffusion in Ferroelectric Hafnium Zirconium Oxide Thin Films

Hafnia-based ferroelectrics hold promise to reduce energy demand for computing by enabling compute-in-memory and as non-volatile memories. The ferroelectric phase in this material system is, in part, stabilized by oxygen vacancies. While oxygen vacancies may be a necessity for phase stability, they limit device endurance through diffusion and accumulation into conducting channels. Herein, it is shown that oxygen diffusion is spatially variable within individual grains of ferroelectric hafnium zirconium oxide (HZO). Using 18 O tracers and finite difference modeling, it is shown that grain boundaries and regions near electrode interfaces allow for relatively rapid oxygen diffusion, with values as much as 10 4 larger than the grain cores. Further, the selection of electrode material affects the diffusion coefficients across all microstructural regions. HZO films in contact with TiN electrodes result in more oxygen-deficient HZO films and higher oxygen diffusion coefficients. Tungsten electrodes result in fewer vacancies and lower diffusion coefficients. Diffusion activation energy differences between the HZO with the two electrodes is reconciled by differing populations of charged and uncharged oxygen vacancies. This insight into the local vacancy populations and diffusion pathways provides a platform for designing hafnia-based films, deposition processes, and integration strategies to reduce vacancy gradients and improve performance.

36 MATERIALS SCIENCE↗

Structural Color Production in Melanin-Based Disordered Colloidal Nanoparticle Assemblies in Spherical Confinement

Melanin is a ubiquitous natural pigment that exhibits broadband absorption and high refractive index. Despite its widespread use in structural color production, how the absorbing material, melanin, affects the generated color is unknown. Using a combined molecular dynamics and finite-difference time-domain computational approach, here we investigates structural color generation in one-component melanin nanoparticle-based supraparticles (called supraballs) as well as binary mixtures of melanin and silica (nonabsorbing) nanoparticle-based supraballs. Experimentally produced one-component melanin and one-component silica supraballs, with thoroughly characterized primary particle characteristics using neutron scattering, produce reflectance profiles similar to the computational analogs, confirming that the computational approach correctly simulates both absorption and multiple scattering from the self-assembled nanoparticles. These combined approaches demonstrate that melanin's broadband absorption increases the primary reflectance peak wavelength, increases saturation, and decreases lightness factor. Additionally, the dispersity of nanoparticle size more strongly influences the optical properties of supraballs than packing fraction, as evidenced by the production of a larger range of colors when size dispersity is varied versus packing fraction. For binary melanin and silica supraballs, the chemistry-based stratification allows for more diverse color generation and finer saturation tuning than does the degree of mixing/demixing between the two chemistries.

broadband absorption↗

Imaging Photonic Resonances within an All‐Dielectric Metasurface via Photoelectron Emission Microscopy

Dielectric metasurfaces, through volume‐type photonic resonances, enable precise control of light‐matter interactions for applications including imaging, holography, and sensing. The application space of dielectric metasurfaces has extended from infrared to visible wavelengths by incorporating high refractive index materials, such as titanium dioxide (TiO 2 ). Understanding the fundamental and fabrication limits for these applications requires metrology with nanoscale resolution, sensitivity to electromagnetic fields within the meta‐atom volume, and far‐field excitation. In this work, photoelectron emission microscopy (PEEM) is used to image field distributions of photonic resonances in a TiO 2 metasurface excited with far‐field, visible‐wavelength illumination. The local volumetric field variations within the meta‐atoms are analyzed as a function of illumination angle and polarization by comparing photoelectron images to finite‐difference time‐domain simulations. This study determines the inelastic mean free path of very low‐energy (<1 eV) photoelectrons to be 35 ± 10 nm, which is comparable to the meta‐atom height thereby highlighting PEEM sensitivity to resonances within the volume. Additionally, the simulations reveal high sensitivity of PEEM images to an in‐plane component of the illumination k ‐vector. These results demonstrate that photoelectron imaging with subwavelength resolution offers unique advantages for examining light‐matter interactions in volume‐type (as opposed to surface) photonic modes within dielectric nanophotonic structures.

electron inelastic mean free path↗

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Abstract Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [ Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

Silva, Goncalo↗

Photonic devices fabricated from (111)‐oriented single crystal diamond

Abstract Diamond is a material of choice in the pursuit of integrated quantum photonic technologies. So far, the majority of photonic devices fabricated from diamond are made from (100)‐oriented crystals. In this work, we demonstrate a methodology for the fabrication of optically active membranes from (111)‐oriented diamond. We use a liftoff technique to generate membranes, followed by chemical vapor deposition of diamond in the presence of silicon to generate homogenous silicon vacancy color centers with emission properties that are superior to those in (100)‐oriented diamond. We further use the diamond membranes to fabricate microring resonators with quality factors exceeding ~ 3000. Supported by finite‐difference time‐domain calculations, we discuss the advantages of (111)‐oriented structures as building blocks for quantum nanophotonic devices. image

Regan, Blake↗

Determining the twist angle of stacked MoS 2 layers using machine learning-assisted low-frequency interlayer Raman fingerprints

The investigation of twisted stacked few-layer MoS 2 has revealed novel electronic, optical, and vibrational properties over an extended period. For the successful integration of twisted stacked few-layer MoS 2 into a wide range of applications, it is crucial to employ a noninvasive, versatile technique for characterizing the layered architecture of these complex structures. Here, in this work, we introduce a machine learning-assisted low-frequency Raman spectroscopy method to characterize the twist angle of few-layer stacked MoS 2 samples. A feedforward neural network (FNN) is utilized to analyze the low-frequency breathing mode as a function of the twist angle. Moreover, using finite difference method (FDM) and density functional theory (DFT) calculations, we show that the low-frequency Raman spectra of MoS 2 are mainly influenced by the effect of the nearest and second nearest layers. A new improved linear chain model (TA-LCM) with taking the twist angle into the consideration is developed to understand the interlayer breathing modes of stacked few-layer MoS 2 . This approach can be extended to other 2D materials systems and provides an intelligent way to investigate naturally stacked and twisted interlayer interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of XC functionals and dispersion corrections on the DFT‐computed structural and vibrational properties of SrCl 2 –NaCl and ZrF 4 –LiF

Density functional theory (DFT) calculations were performed to examine the impact of exchange–correlation (XC) functionals and van der Waals corrections (specifically the D3 method) on the structural and vibrational properties of the SrCl 2 –NaCl and ZrF 4 –LiF salt systems. Multiple XC functionals, including the local density approximation (LDA), the generalized gradient approximation using the Perdew–Burke–Ernzerhof (PBE) model, and its modified form suitable for solids (PBEsol), the dispersion-corrected PBE-D3 and PBEsol-D3, were considered. Of these functionals, LDA was found to exhibit the highest degree of error, while PBEsol and PBE-D3 displayed the least error. Underestimated lattice parameters compared with experimental values were observed to result in higher force constants, leading to an overprediction of vibrational frequencies. Conversely, an overestimation of lattice parameters was associated with lower vibrational frequencies. The methodology presented in this study yielded results that are in good agreement with experiment, irrespective of the method (finite differences vs. density functional perturbation theory) employed for calculating infrared and Raman spectra. It was further demonstrated that for alkali halides with weak Raman scattering, utilizing a supercell constructed from primitive cells better predicts Raman features than does the use of conventional cells.

Raman↗

Tailored Frequency Conversion in Nonlinear Subwavelength Grating Metaslabs

The use of metaslab waveguides consisting of subwavelength gratings (SWGs) is proposed as a highly flexible approach to obtain phase‐matched frequency conversion in nonlinear integrated devices. Control over the phase matching (PM) condition is achieved through modification of the linear modal propagation constants by the SWG. The method is experimentally demonstrated by fabrication of 0.4 mm‐long GaAs metaslabs designed for second harmonic generation of near‐infrared light. A controlled spectral shift of up to 100 nm in the PM condition, relative to a uniform slab is observed. Excellent agreement is found between the experimental results and finite‐difference eigenmode simulations, which predict a tunable frequency conversion bandwidth of ∼300 nm for the design parameters. The different regimes of PM control supported by the structure are discussed. This work highlights the potential of SWGs as building blocks for tailored frequency conversion in nonlinear integrated devices.

Form birefringence↗

Optimizing multigrid reduction-in-time and Parareal coarse-grid operators for linear advection

Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent partial differential equations (PDEs) in modern high-performance computing environments. While these techniques have been very successful for parabolic equations, it has often been observed that their performance suffers dramatically when applied to advection-dominated problems or purely hyperbolic PDEs using standard rediscretization approaches on coarse grids. In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically nonscalable or even divergent behavior of these solvers for this problem. To overcome these failings, we replace rediscretization on coarse grids with improved coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory. Therefore, one of our main findings is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behavior of the hyperbolic problem by tracking the characteristic curves. Our approach is tested for schemes of various orders using explicit or implicit Runge–Kutta methods combined with upwind-finite-difference spatial discretizations. In all cases, we obtain scalable convergence in just a handful of iterations, with parallel tests also showing significant speed-ups over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗

Optimal Polynomial Smoothers and One‐Sided V‐Cycles for Poisson Problems

The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier‐Stokes equations needs robust preconditioning strategies. One such strategy is multigrid. To realize the potential of multigrid methods, effective smoothing strategies are needed. Chebyshev polynomial smoothers, in conjunction with pointwise Jacobi or additive Schwarz methods (ASMs), prove to be an effective smoother. Other polynomial smoothers, however, may provide superior convergence to the multigrid preconditioner. The authors compare the standard Chebyshev polynomial smoothers to both the novel fourth‐kind Chebyshev polynomial smoothers proposed by Lottes as well as smoothers based on the polynomial of best uniform approximation to as proposed by Kraus, Vassilevski, and Zikatanov. At the cost of symmetry, further improvements may be made. For example, a order polynomial smoother on both sides of the V‐cycle may be substituted with an order polynomial smoother on one side at no additional cost. The choice of omitting the postsmoother in favor of higher‐order polynomial presmoothing is advantageous in cases where the multigrid approximation property constant is large. The authors consider a 2D model problem based on finite differences to motivate the choice of polynomial smoother, order, and whether to apply postsmoothing for the target application of high‐order ‐geometric multigrid methods for GPU architectures. Results from both domains demonstrate the substantial improvement of these approaches over the standard Chebyshev polynomial smoother with a symmetric V‐cycle.

97 MATHEMATICS AND COMPUTING↗

Sparsity Applications for Gradient‐Based Optimization of Wind Farms

Optimizing wind farms is essential for designing efficient energy systems, especially as farms grow larger and span multiple sites. However, this optimization becomes increasingly challenging due to the rising computational cost associated with more turbines. Gradient‐based optimization methods scale better than gradient‐free approaches for large problems, but the most computationally expensive component remains the calculation of gradients for the objective function and constraint Jacobians. To address this, we propose leveraging sparsity to accelerate gradient evaluations and reduce the size of the constraint Jacobian. Wind farms naturally exhibit sparsity—many turbines do not influence each other under certain wind directions. However, unlike traditional sparse problems with fixed patterns, wind farm sparsity is dynamic, requiring new strategies to handle changing interactions efficiently. This paper presents a study of sparsity in wind farm optimization and introduces several methods to exploit it. These strategies are tested on multiple farms using the analytic Cumulative Curl model, with gradients computed via automatic differentiation (AD). The same sparsity‐aware techniques are also applicable to finite difference (FD) methods, where they can yield even greater speedups due to the high cost of directional evaluations. Results show that sparse methods achieve up to a 10x speedup with less than ± 5% variance in optimized wake losses compared to traditional methods. These findings suggest that sparsity‐aware optimization not only maintains solution quality but also scales efficiently with farm size, enabling more comprehensive design exploration at reduced computational cost.

17 WIND ENERGY↗

Quantum Spectral Methods for Differential Equations

Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a d-dimensional system of linear equations or linear differential equations with complexity poly(logd). While several of these algorithms approximate the solution to within ϵ with complexity poly(log(1/ϵ)), no such algorithm was previously known for differential equations with time-dependent coefficients. In this work, we develop a quantum algorithm for linear ordinary differential equations based on so-called spectral methods, an alternative to finite difference methods that approximates the solution globally. Using this approach, we give a quantum algorithm for time-dependent initial and boundary value problems with complexity poly(logd, log(1/ϵ)).

97 MATHEMATICS AND COMPUTING↗

Non-close-packed plasmonic Bravais lattices through a fluid interface-assisted colloidal assembly and transfer process

Abstract The assembly of colloids at fluid interfaces followed by their transfer to solid substrates represents a robust bottom-up strategy for creating colloidal monolayers over large, macroscopic areas. In this study, we showcase how subtle adjustments in the transfer process, such as varying the contact angle of the substrate and controlling deposition speed and direction, enable the realization of all five two-dimensional Bravais lattices. Leveraging plasmonic core–shell microgels as the building blocks, we successfully engineered non-close-packed plasmonic lattices exhibiting hexagonal, square, rectangular, centered rectangular, and oblique symmetries. Beyond characterizing the monolayer structures and their long-range order, we employed extinction spectroscopy alongside finite difference time domain simulations to comprehensively investigate and interpret the plasmonic response of these monolayers. Additionally, we probed the influence of the refractive index environment on the plasmonic properties by two methods: first, by plasma treatment to remove the microgel shells, and second, by overcoating the resulting gold nanoparticle lattices with a homogeneous refractive index polymer film. Graphical Abstract

Chemistry↗

Controls on the frequency content of near-source infrasound at open-vent volcanoes: a case study from Volcán Villarrica, Chile

Infrasound signals from open-vent volcanoes can contain information related to that volcano’s eruption dynamics and future activity. Studying a specific volcano’s acoustic signature during periods of relative quiescence is thus important for understanding potential warning signs of impending eruptions. Volcán Villarrica, located in southern Chile, has a long-lived active lava lake that produces continuous infrasound with spectral peaks centered around 1 Hz that vary by + / - ~ 0.2 Hz over day-to-week-long time scales. The infrasound frequency content has been shown to illuminate key volcanic properties such as eruption style and crater shape. Leading up to Villarrica’s most recent paroxysm in 2015, for instance, infrasound spectral changes coincided with a rise in Villarrica’s lava lake level. Quantifying and understanding the regular fluctuation in recorded infrasonic frequencies from Villarrica and other open-vent volcanoes is thus imperative during periods of relative calm. Our experiment entailed a week-long period of crater rim infrasound observations associated with stable, open-vent activity and revealed two independent source processes: spatter bursting events (relatively broadband infrasound) and lava lake-induced tremor (sustained signals peaked at 1 Hz). A comparison of these acoustic signals with results from 3-D finite-difference time-domain wave propagation models shows that while sound speed variability can influence Villarrica’s spectrum, it cannot explain the full extent of the observed frequency excursions. We conclude that source spectrum variability is primarily responsible for the frequency excursions. In conclusion, our work highlights the utility of data collected from a dense distribution of twenty infrasound sensors operating at the summit coupled with numerical modeling of sound radiation.

58 GEOSCIENCES↗

Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations

Abstract In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.

Mathematics↗