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At least 1,225 records · Page 68

A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method that maintains high-order temporal accuracy in both velocity and pressure for steady and unsteady velocity boundary conditions. Fourth order spatial accuracy is achieved through a novel fifth order IIM discretization scheme for the advection term, as well as existing high-order interface-corrected finite difference schemes for the other differential operators. Using a set of manufactured flow problems with stationary and moving boundaries, we demonstrate fourth order convergence of velocity and pressure in the infinity norm, both inside the domain and on the immersed boundaries. The solver’s performance is further validated through a range of practical flow simulations, highlighting its efficiency over a second order scheme. Finally, we showcase the ability of our immersed discretization scheme to handle interface-coupled multiphysics problems by solving a conjugate heat transfer problem with multiple immersed solids. Overall, the proposed approach robustly combines the efficiency of high order discretization schemes with the flexibility of immersed discretizations for flow problems with complex, moving boundaries and interfaces.

42 ENGINEERING↗

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗

A channel flow cell with double disk electrodes for oxygen electroreduction study at elevated temperatures and pressures: Theory

We report a new double-disk-electrode channel flow cell has been designed, constructed and tested. A theoretical treatment and implicit finite difference numerical simulations are presented, which permit the computation of the hydrodynamic behavior of this cell under steady state conditions, i.e., the diffusion limited current at the working electrode and the collection efficiency of the detector. The simulated results are consistent with those measured experimentally, indicating that our simulations appropriately describe the hydrodynamic behavior of this cell. The oxygen reduction reaction (ORR) on a carbon-supported nanoparticle Pt catalyst at both room temperature and 110 °C were preliminarily studied with this cell.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Validation and moisture content sensitivity analysis of cross-laminated timber wall assemblies in EnergyPlus

Cross-laminated timber buildings are becoming more common in North America, with many numerical studies showing potential energy savings. However, no studies have validated any EnergyPlus heat transfer algorithms or quantified their accuracy in simulating CLT in building envelopes. This study empirically validates the heat flux predictions for each of EnergyPlus's heat transfer algorithms (Conduction Transfer Functions (CTF), Effective Moisture Penetration Depth (EMPD), Conduction Finite Difference (CondFD), and Heat and Moisture Transfer (HAMT)) for two different CLT ply thicknesses with both summer and winter boundary conditions measured in controlled lab experiments. It also evaluates the model sensitivity of heat flux and heating and cooling loads to moisture content. The 1D validation shows that the HAMT model is the most accurate among all algorithms. All EnergyPlus's heat flux predictions are accurate independent of CLT plate thickness for summer conditions. However, the three constant property algorithms (CTF, EMPD, and CondFD) underpredict heat flux throughout the whole day during winter conditions. The 1D sensitivity analysis indicates that elevated moisture content can increase peak heat fluxes through the material by up to 20 %. Finally, the whole building model sensitivity analysis shows increased heating load and slight cooling load variation due to increased moisture content when using constant property models. The analysis shows significantly lower peak thermal demand (7 % lower heating and 6 % lower cooling) and monthly thermal load (8 % less cooling and 6 % less heating) predictions when using HAMT vs a constant property model.

42 ENGINEERING↗

Fast GPU 3D diffeomorphic image registration

3D image registration is one of the most fundamental and computationally expensive operations in medical image analysis. Here, we present a mixed-precision, Gauss–Newton–Krylov solver for diffeomorphic registration of two images. Our work extends the publicly available CLAIRE library to GPU architectures. Despite the importance of image registration, only a few implementations of large deformation diffeomorphic registration packages support GPUs. Our contributions are new algorithms to significantly reduce the run time of the two main computational kernels in CLAIRE: calculation of derivatives and scattered-data interpolation. Additionally, we deploy (i) highly-optimized, mixed-precision GPU-kernels for the evaluation of scattered-data interpolation, (ii) replace Fast-Fourier-Transform (FFT)-based first-order derivatives with optimized 8th-order finite differences, and (iii) compare with state-of-the-art CPU and GPU implementations. As a highlight, we demonstrate that we can register clinical images in less than 6 s on a single NVIDIA Tesla V100. This amounts to over 20 speed-up over the current version of CLAIRE and over 30 speed-up over existing GPU implementations.

97 MATHEMATICS AND COMPUTING↗

Aeroelastic oscillations of a pitching flexible wing with structural geometric nonlinearities: Theory and numerical simulation

In this paper, we focus on the derivation of an analytical model of the aeroelastic dynamics of an elastically mounted flexible wing. This equations of motion obtained serve to help understand the behaviour of the aeroelastic wind tunnel setup in question, which consists of a rectangular wing with a uniform NACA 0012 airfoil profile, whose base is free to rotate rigidly about a longitudinal axis. Of particular interest are the structural geometric nonlinearities primarily introduced by the coupling between the rigid body pitch degree-of-freedom and the continuous system. A coupled system of partial differential equations (PDEs) coupled with an ordinary differential equation (ODE) describing axial-bending-bending-torsion-pitch motion is derived using Hamilton's principle. A finite dimensional approximation of the system of coupled differential equations is obtained using the Galerkin method, leading to a system of coupled nonlinear ODEs. Subsequently, these nonlinear ODEs are solved numerically using Houbolt's method. The results that are obtained are verified by comparison with the results obtained by direct integration of the equations of motion using a finite difference scheme. Adopting a linear unsteady aerodynamic model, it is observed that the system undergoes coalescence flutter due to coupling between the rigid body pitch rotation dominated mode and the first flapwise bending dominated mode. Finally, the behaviour of the limit cycle oscillations is primarily influenced by the structural geometric nonlinear terms in the coupled system of PDEs and ODE.

42 ENGINEERING↗

Characterization of high-temperature figure of merit for solar-thermal absorbers

The figure of merit (FOM) is a widely used metric to characterize the solar-thermal conversion performance of solar absorber layers. Many of previous works have reported FOMs estimated from the radiative properties measured at room temperature. However, advanced concentrated solar power (CSP) plants operate at very high temperatures (~750°C), which can strongly affect the absorber’s radiative properties. Here, the present work proposes using a 1-D conduction-based reference bar technique to directly measure the converted thermal energy to determine the FOM at high absorber temperatures (≳ 750°C) while operating under a large solar concentration (~ 1200 x suns). Using the finite difference method, we carefully analyze several key parameters influencing the design of the experimental setup, such as temperature distribution, material properties, heat loss, and sensor accuracy. In addition, a rigorous uncertainty analysis is incorporated into the FOM to ascertain the confidence level of the result. We validate this new technique on a custom-built tungsten reference bar with an oxidized Inconel 625 solar-thermal absorber. A good agreement between the model and the experiment shows the reliability of the FOM measurement with a well-defined uncertainty. The same method can be implemented to measure the high-temperature FOM of most surface or volumetric solar absorbers for CSP.

14 SOLAR ENERGY↗

Hybrid SERS platform by adapting both chemical mechanism and electromagnetic mechanism enhancements: SERS of 4-ATP and CV by the mixture with GQDs on hybrid PdAg NPs

Surface-enhanced Raman spectroscopy (SERS) is a versatile analytical technique widely adapted for the identification of target analytes even at an extremely low concentration. Herein, a unique hybrid SERS platform is demonstrated by utilizing the graphene quantum dots (GQDs) and hybrid PdAg NPs for the detection of 4-amino-thiophenol (4-ATP) and crystal violet (CV). GQDs offer the rich charge transfer to the LUMO and HOMO of 4-ATP and CV by the CM enhancement. A significant EM enhancement is achieved by the strong localized surface plasmon resonance (LSPR) of uniquely designed hybrid core-shell PdAg NP, possessing the narrow nano-gaps with the highly dense small Ag NPs and Pd core Ag shell configuration. As a result, orders of enhancement of originally weak 4-ATP and CV Raman signal is witnessed by the combination of electromagnetic mechanism (EM) and chemical mechanism (CM) enhancements on a single SERS substrate. The hybrid GQD/HNP SERS substrate demonstrates significantly improved hot spots and strongly localized electromagnetic fields as confirmed by the finite-difference time-domain (FDTD) simulations. There for a proper mixture ratio of GQDs and probe molecules presents largely enhanced SERS signals by a strong adsorption of probe molecules through π - π interaction and the enhancement factors vary by the mixture ratio depending on the adsorption kinetics and Raman cross-section of molecules.

36 MATERIALS SCIENCE↗

Gradient-based optimization of 3D MHD equilibria

Using recently developed adjoint methods for computing the shape derivatives of functions that depend on magnetohydrodynamic (MHD) equilibria (Antonsen et al. , J. Plasma Phys. , vol. 85, issue 2, 2019; Paul et al. , J. Plasma Phys. , vol. 86, issue 1, 2020), we present the first example of analytic gradient-based optimization of fixed-boundary stellarator equilibria. We take advantage of gradient information to optimize figures of merit of relevance for stellarator design, including the rotational transform, magnetic well and quasi-symmetry near the axis. With the application of the adjoint method, we reduce the number of equilibrium evaluations by the dimension of the optimization space ( ${\sim }50\text {--}500$ ) in comparison with a finite-difference gradient-based method. We discuss regularization objectives of relevance for fixed-boundary optimization, including a novel method that prevents self-intersection of the plasma boundary. We present several optimized equilibria, including a vacuum field with very low magnetic shear throughout the volume.

Physics↗

Scattering of radiofrequency waves by randomly modulated density interfaces in the edge of fusion plasmas

In the scrape-off layer and the edge region of a tokamak, the plasma is strongly turbulent and scatters the radiofrequency (RF) electromagnetic waves that propagate through this region. It is important to know the spectral properties of these scattered RF waves, whether used for diagnostics or for heating and current drive. The spectral changes influence the interpretation of the obtained diagnostic data, and the current and heating profiles. A full-wave, three-dimensional (3-D) electromagnetic code ScaRF has been developed for studying the RF wave propagation through turbulent plasma. ScaRF is a finite-difference frequency-domain (FDFD) method used for solving Maxwell's equations. The magnetized plasma is defined through the cold plasma by the anisotropic permittivity tensor. As a result, ScaRF can be used to study the scattering of any cold plasma RF wave. It can also be used for the study of the scattering of electron cyclotron waves in ITER-type and medium-sized tokamaks such as TCV, ASDEX-U and DIII-D. For the case of medium-sized tokamaks, there is experimental evidence that drift waves and rippling modes are present in the edge region. Hence, we have studied the scattering of RF waves by periodic density interfaces (plasma gratings) in the form of a superposition of spatial modes with varying periodicity and random amplitudes. The power reflection coefficient (a random variable) is calculated for different realizations of the density interface. In this work, the uncertainty of the power reflection coefficient is rigorously quantified by use of the Polynomial Chaos Expansion method in conjunction with the Smolyak sparse-grid integration, which is known as the PCE-SG method. The PCE-SG method is proven to be accurate and more efficient compared with alternative methods such as the Monte Carlo (MC) approach.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

The development of an implicit, unconditionally stable, numerical method for solving the Vlasov–Poisson system in one dimension using a phase-space grid is presented. The algorithm uses the Crank–Nicolson discretization scheme and operator splitting allowing for direct solution of the finite difference equations. This method exactly conserves particle number, enstrophy and momentum. A variant of the algorithm which does not use splitting also exactly conserves energy but requires the use of iterative solvers. This algorithm has no dissipation and thus fine-scale variations can lead to oscillations and the production of negative values of the distribution function. We find that overall, the effects of negative values of the distribution function are relatively benign. We consider a variety of test cases that have been used extensively in the literature where numerical results can be compared with analytical solutions or growth rates. We examine higher-order differencing and construct higher-order temporal updates using standard composition methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The DESC stellarator code suite. Part 1. Quick and accurate equilibria computations

Three-dimensional equilibrium codes are vital for stellarator design and operation, and high-accuracy equilibria are also necessary for stability studies. This paper details comparisons of two three-dimensional equilibrium codes: VMEC, which uses a steepest-descent algorithm to reach a minimum-energy plasma state, and DESC, which minimizes the magnetohydrodynamic (MHD) force error in real space directly. Accuracy as measured by satisfaction of MHD force balance is presented for each code, along with the computation time. It is shown that DESC is able to achieve more accurate solutions, especially near axis. The importance of higher-accuracy equilibria is shown in DESC's better agreement of stability metrics with asymptotic formulae. DESC's global Fourier–Zernike basis also yields solutions with analytic derivatives explicitly everywhere in the plasma volume, provides improved accuracy in the radial direction versus conventional finite differences and allows for exponential convergence. Further, DESC can compute a solution with the same accuracy as VMEC in order-of-magnitude less time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical methods for nonlocal and fractional models

Partial differential equations (PDEs) are used with huge success to model phenomena across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDEs fail to adequately model observed phenomena, or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. Here, we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis and of specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modelling and algorithmic extensions, which serve to show the wide applicability of nonlocal modelling.

97 MATHEMATICS AND COMPUTING↗

Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory

We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting square gradient minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant ΔSCF and spin-purified restricted open-shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the maximum overlap method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ΔSCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer, or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High Resolution Photoelectron Spectroscopy of the Acetyl Anion

High-resolution photoelectron spectra of cryogenically cooled acetyl anions (CH 3 CO - ) obtained using slow photoelectron velocity-map imaging are reported. The high resolution of the photoelectron spectrum yields a refined electron affinity of 0.4352 ± 0.0012 eV for the acetyl radical as well as the observation of a new vibronic structure that is assigned based on ab initio calculations. Three vibrational frequencies of the neutral radical are measured to be 1047 ± 3 cm -1 (ν 6 ), 834 ± 2 cm -1 (ν 7 ), and 471 ± 1 cm -1 (ν 8 ). Here this work represents the first experimental measurement of the ν 6 frequency of the neutral. The measured electron affinity is used to calculate a refined value of 1641.35 ± 0.42 kJ mol -1 for the gas-phase acidity of acetaldehyde. Analysis of the photoelectron angular distributions provides insight into the character of the highest occupied molecular orbital of the anion, revealing a molecular orbital with strong d-character. Additionally, details of a new centroiding algorithm based on finite differences, which has the potential to decrease data acquisition times by an order of magnitude at no cost to accuracy, are provided.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Comparable Enhancement of TERS Signals from WSe 2 on Chromium and Gold

Plasmonic tip-sample junctions, at which the incident and scattered optical fields are localized and optimally enhanced, are often exploited to achieve ultrasensitive and highly spatially localized tip-enhanced Raman scattering (TERS). Recent work has demonstrated that the sensitivity and spatial resolution that are required to probe single molecules are attainable in such platforms. In this work, we observe and rationalize comparable TERS from few-layer WSe 2 single crystals exfoliated onto Au- and Cr-coated Si substrates, using a plasmonic TERS probe excited with a 638-nm laser. Our experimental observations are supported by finite-difference time-domain simulations that illustrate that the attainable field enhancement factors at the Au-Au and Au-Cr tip-sample nanojunctions are comparable in magnitude. Furthermore, through a combined experimental and theoretical analysis, we propose that besides Au/Ag, several metallic substrates may be used to record bright TERS spectral images.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nanoparticle-Enhanced Plasma Discharge Using Nanosecond High-Voltage Pulses

By discharging nanosecond high-voltage (5 kV) pulses across an insulating substrate containing Au, Pt, or Cu nanoparticles, a 3 order of magnitude (1000×) enhancement in the generation of plasma can be achieved through local field enhancement on the surface of the nanoparticles. The low-temperature nature of this transient plasma is crucial to maintaining the structural integrity of these delicate nanoparticles. These nanoparticles provide up to a 1000-fold enhancement in the generation of the plasma, which is localized to the surface of the nanoparticles where it is potentially useful (e.g., for catalysis). Additionally, we performed both time-domain and frequency-domain calculations of the electromagnetic response of the nanoparticles based on high-resolution transmission electron microscope (HRTEM) images, which show local field enhancement of the nanosecond high-voltage pulse on the order of 3×. Since the plasma initiation depends exponentially on the peak electric field strength, this 3-fold increase in the local electric field can result in a several orders of magnitude increases in the generation of plasma at a given applied external field strength. In order to rule out plasmon-resonance enhancement, which is often associated with small metal nanoparticles, we performed finite difference time domain (FDTD) simulations in the optical frequency domain, which show that the effect of plasmon resonance is negligible for Pt nanoparticles. We therefore attribute the nanoparticle-based enhancement to the generation of plasma (an electrostatic effect) rather than enhanced coupling of light from the near field to the far field via the plasmon resonance phenomenon (an optical effect).

36 MATERIALS SCIENCE↗

Tip-Enhanced Raman Nanospectroscopy of Smooth Spherical Gold Nanoparticles

We record nanoscale-resolved chemical images of thiobenzonitrile (TBN)-functionalized smooth gold nanospheres on silicon via tip-enhanced Raman (TER) nano-spectroscopy. The recorded images trace the nascence of the familiar doughnut-shaped scattering profile of nanoparticles on silicon at its origin (the particle surface), which appears as a horseshoe-shaped scattering pattern under our experimental conditions. The local optical field maps are in agreement with their simulated finite-difference time-domain analogues. Analysis of the recorded spectra with the aid of ab initio molecular dynamics-based Raman spectral simulations further suggests that optical rectification and molecular charging take place throughout the course of atomic force microscopy-based TER nanoscale chemical imaging.

Bhattarai, Ashish↗