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Non-linear MHD modelling of edge localized modes suppression by resonant magnetic perturbations in ITER
Edge localized modes (ELMs) suppression by resonant magnetic perturbations (RMPs) was studied with the non-linear magneto-hydro-dynamic (MHD) code JOREK for the ITER H-mode scenarios at 15 MA, 12.5 MA, 10 MA/5.3 T. In this study, the main aim was to demonstrate that ELMs can be suppressed by RMPs while the divertor 3D footprints of heat and particle fluxes remain within divertor material limits. The unstable peeling–ballooning modes responsible for ELMs without RMPs were modelled first for each scenario using numerically accessible parameters for ITER. Then the stabilization of ELMs by RMPs was modelled with the same parameters. RMP spectra, optimized by the linear MHD MARS-F code, with main toroidal harmonics N = 2, N = 3, N = 4 have been used as boundary conditions of the computational domain of JOREK, including realistic RMP coils, main plasma, scrape off layer (SOL) divertor and realistic first wall. The model includes all relevant plasma flows: toroidal rotation, two fluid diamagnetic effects and neoclassical poloidal friction. With RMPs, the main toroidal harmonic and the non-linearly coupled harmonics remain dominant at the plasma edge, producing saturated modes and a continuous MHD turbulent transport thereby avoiding ELM crashes in all scenarios considered here. The threshold for ELM suppression was found at a maximum RMP coils current of 45 kAt–60 kAt compared to the coils maximum capability of 90 kAt. In the high beta poloidal steady-state 10 MA/5.3 T scenario, a rotating QH-mode without ELMs was observed even without RMPs. In this scenario with RMPs N = 3, N = 4 at 20 kAt maximum current in RMP coils, similar QH-mode behaviour was observed however with dominant edge harmonic corresponding to the main toroidal number of RMPs. The present MHD modelling was limited in time by few tens of ms after RMPs were switched on until the magnetic energy of the modes saturates. As a consequence the thermal energy was still evolving on this time scale, far from the ITER confinement time scale and hence only the form of 3D footprints on the divertor targets can be indicated within this set-up. Also note, that the divertor physics was missing in this model, so realistic values of fluxes are out of reach in this modelling. However the stationary 3D divertor and particle fluxes could be simply extrapolated from these results to the stationary situation considering that a large power fraction should be radiated in the core and SOL and only about 50 MW power is going to the divertor, which is an arbitrary, but reasonable number used here. The 3D footprints with RMPs show the characteristic splitting with the main RMP toroidal symmetry. The maximum radial extension of the footprints typically was ~20 cm in inner divertor and ~40 cm in outer divertor with stationary heat fluxes decreasing further out from the initial strike point from ~5 MW m ₋2 to ~1 MW m ₋2 assuming a total power in the divertor and walls is 50 MW. The heat fluxes remain within the divertor target and baffle areas, however with rather small margin in the outer divertor which could be an issue for the first wall especially in transient regimes when part of the plasma thermal energy is released due to switching on the RMP coils. This fact should be considered when RMPs are applied with a more favorable application before or soon after the L–H transition, although optimization is required to avoid increasing the L–H power threshold with RMPs.
Harnessing Machine Learning to Predict MoS 2 Solid Lubricant Performance
Physical vapor deposited (PVD) molybdenum disulfide (MoS 2 ) solid lubricant coatings are an exemplar material system for machine learning methods due to small changes in process variables often causing large variations in microstructure and mechanical/tribological properties. Here, in this work, a gradient boosted regression tree machine learning method is applied to an existing experimental data set containing process, microstructure, and property information to create deeper insights into the process-structure–property relationships for molybdenum disulfide (MoS 2 ) solid lubricant coatings. The optimized and cross-validated models show good predictive capabilities for density, reduced modulus, hardness, wear rate, and initial coefficients of friction. The contribution of individual deposition variables (i.e., argon pressure, deposition power, target conditioning) on coating properties is highlighted through feature importance. The process-property relationships established herein show linear and non-linear relationships and highlight the influence of uncontrolled deposition variables (i.e., target conditioning) on the tribological performance.
Sequence of polyhedral relaxations for nonlinear univariate functions
Here, given a nonlinear, univariate, bounded, and differentiable function f(x), this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of f(x) and its convex hull, respectively. Theoretical convergence of the sequence of relaxations to the graph of the function and its convex hull is established. For nonlinear non-convex optimization problems, the relaxations presented in this article can be used to construct tight MILP and LP relaxations. These MILP and the LP relaxations can also be used with MILP-based and spatial branch-and-bound based global optimization algorithms, respectively.
On unifying randomized methods for inverse problems
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems with Gaussian priors by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a sample average approximation (SAA). More importantly, we are able to prove a single theoretical result that guarantees the asymptotic convergence for a variety of randomized methods. Additionally, viewing randomized methods as an SAA enables us to prove, for the first time, a single non-asymptotic error result that holds for randomized methods under consideration. Another important consequence of our unified framework is that it allows us to discover new randomization methods. Here, we present various numerical results for linear, nonlinear, algebraic, and PDE-constrained inverse problems that verify the theoretical convergence results and provide a discussion on the apparently different convergence rates and the behavior for various randomized methods.
ELSI — An open infrastructure for electronic structure solvers
Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with different structures. The ELectronic Structure Infrastructure (ELSI) project provides an open-source software interface to facilitate the implementation and optimal use of high-performance solver libraries covering cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between. In this paper, we present recent improvements and developments inside ELSI, mainly covering (1) new solvers connected to the interface, (2) matrix layout and communication adapted for parallel calculations of periodic and/or spin-polarized systems, (3) routines for density matrix extrapolation in geometry optimization and molecular dynamics calculations, and (4) general utilities such as parallel matrix I/O and JSON output. The ELSI interface has been integrated into four electronic structure code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on results of a systematic set of large-scale benchmarks performed with Kohn–Sham density-functional theory and density-functional tight-binding theory, we identify factors that strongly affect the efficiency of the solvers, and propose a decision layer that assists with the solver selection process. As a result, we describe a reverse communication interface encoding matrix-free iterative solver strategies that are amenable, e.g., for use with planewave basis sets.
Tech-X contributions to the Center for Tokamak Transients (CTTS) Scientific Discovery through Advanced Computing (SciDAC) project (Final Report)
The Center for Tokamak Transients Simulations (CTTS) consists of computational plasma physicists, computer scientists, and applied mathematicians who are together developing and applying simulation software to improve our understanding of and ability to predict and control transient events in tokamak discharges, particularly those that lead to violent disruptions. We have major simulation activities concerning disruptions that are caused by violating ideal MHD stability criteria, vertical displacement events, resistive wall modes, and tearing modes. We are performing comprehensive modeling of disruption mitigation techniques, particularly by shattered pellet injection (SPI). The Center is built around two mature extended MHD codes: NIMROD and M3D-C1. These codes are being extended in a number of ways as required by the demands of disruption modeling, and are being optimized to work well for larger problem size and modern computer architectures as required to model tokamak plasmas with realistic parameters over the required timescales. The codes will be coupled to the FronTier code for state-of-the-art modeling of SPI. Validation with experimental data on DIII-D, NSTX, and JET is being facilitated by rigorous uncertainty quantification (UQ). The high-level objectives of the center are to: (1) Develop better understanding and improved predictive capability of when crossing a linear stability boundary will likely lead to a disruption, (2) Provide a tool for calculating vessel forces, both axisymmetric and non-axisymmetric, for worst case VDE and other disruptions in tokamaks, (3) Develop increased understanding and improved predictive capability for locked mode disruptions and how best to avoid them, (4) Develop, verify, and validate 3D models for disruption mitigation by shattered pellets that can be used to design and optimize a system for future tokamaks, and (5) Increase the efficiency and scalability of the M3D-C1 and NIMROD codes so that they can model disruptions in ITER scale devices using the most powerful DOE HPC hardware, and (6) Demonstrate code-coupling via FronTier coupling with NIMROD and M3D-C1 and by interfacing these codes within a WDM framework.
Adapting Optimal Velocity Tracking Control to Account for WEC Constraints and Power-Take-Off Efficiencies: Preprint
Wave energy converters (WECs) come in many different forms, from point absorbers, oscillating water columns, to bulge wave devices. This paper focuses on the control of point absorber WECs, which typically have a narrow-banded frequency response and, therefore, control is well placed to improve the energy capture of such WECs. The acausal nature of the control problem means that theoretically optimal control is almost impossible to achieve inpractice; however optimal velocity tracking (OVT) offers a simple and robust approximation to optimal control that can achieve better power capture than passive linear damping methods, albeit with necessarily higher force demands. OVT is a form of impedance matching and the magnitude of the power-take off (PTO) force demand is often not linearly proportional to the WEC velocity, which can lead to PTO force and speed combinations far from the optimalPTO efficiency. The highly non-linear PTO force and speed to efficiency mapping can, without remedial measures, severely diminish the effectiveness of OVT techniques. In this paper, limits to the movement and force of the PTO are demonstrated, allowing OVT to be more easily applied in practice. The effect of PTO efficiency is explored, and a potential solution to the problem of adapting control to account for efficiency is presented. Both aspects of the work presented highlight the requirement for co-design of the WEC, PTO, and controller.
Autonomous sputter synthesis of thin film nitrides with composition controlled by Bayesian optimization of optical plasma emission
Autonomous experimentation has emerged as an efficient approach to accelerate the pace of material discovery. Although instruments for autonomous synthesis have become popular in molecular and polymer science, solution processing of hybrid materials, and nanoparticles, examples of autonomous tools for physical vapor deposition are scarce yet important for the semiconductor industry. Here, we report the design and implementation of an autonomous workflow for sputter deposition of thin films with controlled composition, leveraging a highly automated sputtering reactor custom-controlled by Python, optical emission spectroscopy (OES), and a Bayesian optimization algorithm. We modeled film composition, measured by x-ray fluorescence, as a linear function of plasma emission lines monitored during co-sputtering from elemental Zn and Ti targets in an N 2 and Ar atmosphere. A Bayesian control algorithm, informed by OES, navigates the space of sputtering power to fabricate films with user-defined compositions by minimizing the absolute error between desired and measured optical emission signals. We validated our approach by autonomously fabricating Zn x Ti 1-x N y films that deviate from the targeted cation composition by a relative ±3.5%, even for 15 nm thin films, demonstrating that the proposed approach can reliably synthesize thin films with a specific composition and minimal human interference. Moreover, the proposed method can be extended to more difficult synthesis experiments where plasma intensity lines depend non-linearly on pressure, or the elemental sticking coefficients strongly depend on the substrate temperature.
Electrochemical Characterization of Photo-Driven Hole-Scavenging by Cadmium Sulfide Quantum Dot-Nitrogenase Biohybrid Complexes
Light-driven biohybrid systems that couple semiconductor nanocrystals with enzymes offer a promising strategy for solar-to-chemical energy-conserving reduction reactions, yet are often limited by inefficient hole scavenging. Hole scavenging is critical for maintaining charge separation in the light-absorbing electron donor molecule and, thus, for sustaining catalytic turnover, making quantification essential to improving system efficiency. Here, we introduce a photoelectrochemical approach for real-time monitoring of hole scavenging in cadmium sulfide (CdS) quantum dot (QD)-nitrogenase MoFe protein biohybrids that catalyze the reduction of H+ and N2. Using hydroquinone (HQ) as the sacrificial electron donor (SED), oxidation of HQ to benzoquinone (BQ) by photogenerated valence-band holes is coupled to the electrochemical reduction of BQ at an electrode, enabling quantification of the hole-scavenging reaction via chronoamperometry. This approach provides a continuous, real-time readout of charge-transfer dynamics under illumination. Systematic variation of light intensity and donor concentration reveals that hole scavenging scales with photon flux and exhibits a non-linear dependence on SED concentration, with an optimum at intermediate HQ concentrations. These results establish chronoamperometry as a powerful tool for probing photoinduced charge transfer, advancing the quantitative understanding of hole-scavenging in biohybrid systems, and offering a generalizable framework for optimizing solar-driven biocatalysis.
Maximizing dynamic range and performance of anatase TiO 2 ECRAM through structure and programming
Here, in this study, we investigate the structure-dependent modulation characteristics of all-solid-state three-terminal electrochemical random-access memory (ECRAM) based on an anatase Li x TiO 2 channel. By directly comparing “asymmetric” and “symmetric” ECRAM device architectures, we reveal significant insight into the impact of a non-zero gate-drain open-circuit voltage and its influence on voltage vs. current-controlled gating. We also explore the impact of potentiation/depression write parameters on the symmetry, linearity, and dynamic range of the device response. Together, initial results from optimizing structure and programming approaches yielded unprecedented G max /G min ratios of >1,000 for ECRAM and hundreds of tunable memory states with excellent linearity and symmetry. Simulations based on these ECRAM devices further illustrate the promise of this analog memory technology, achieving near 2% classification error in the MNIST digit recognition benchmark for a range of training parameters compared to a theoretical best of 1.66% and outperforming other device models extracted from the literature.
GPAW: An open Python package for electronic structure calculations
We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe–Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn–Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.
A Comparative Study of Model Predictive Control and Optimal Causal Control for Heaving Point Absorbers
Efforts by various researchers in recent years to design simple causal control laws that can be applied to WEC devices suggest that these controllers can yield similar levels of energy output as those of more complex non-causal controllers. However, most studies were established without adequately considering device and power conversion system constraints which are relevant design drivers from a cost and economic point of view. It is therefore imperative to understand the benefits of MPC compared to causal control from a performance and constraint handling perspective. In this paper, we compare linear MPC to a casual controller that incorporates constraint handling to benchmark its performance on a one DoF heaving point absorber in a range of wave conditions. Our analysis demonstrates that MPC provides significant performance advantages compared to an optimized causal controller, particularly if significant constraints on device motion and/or forces are imposed. We further demonstrate that distinct control performance regions can be established that correlate well with classical point absorber and volumetric limits of the wave energy conversion device.
A Distributed Model Identification Algorithm for Multi-Agent Systems: Preprint
In this study, we investigate agent-based approach for system model identification with emphasis on power distribution system applications. Departing from conventional practices of relying on historical data for offline model identification, we adopt online update approach utilizing real-time data by employing the latest data points for gradient computation. This methodology offers advantages including a large reduction in the communication network's bandwidth requirements by minimizing the data exchanged at each iteration and enabling the model to adapt in real-time to disturbances. Furthermore, we extend our model identification process from linear frameworks to more complex non-linear convex models. This extension is validated through numerical studies demonstrating improved control performance for a synthetic IEEE test case.
Phonon-informed Neural Thermal Scattering (NeTS) Optimization for Crystalline Graphite and Beryllium Metal
Fast neutrons born from fission lose energy through scattering interactions in the process of slowing-down. As neutrons thermalize to the order of $k$ $b$ $T$ (where $k$ $b$ is the Boltzmann constant, and $T$ is the temperature of the medium), their de Broglie wavelength and energy approaches the order of inter-atomic spacing and quantized lattice vibrations, i.e., phonons. At thermal energies, the thermal scattering law (TSL), i.e., $S$($α, β$), captures crystal binding contributions to the total reaction rate, or cross section. This dimensionless material property describes the energy ($β$) and momentum ($α$) exchanges available in a medium. Currently, $S$($α, β$) is evaluated in the Full Law Analysis Scattering System Hub (FLASSH) code for discrete inputs and stored as ENDF/B File 7 for 0-phonon elastic (MT 2) and n-phonon inelastic (MT 4) processes. Further processing recasts $S$($α, β$) into cumulative distribution functions for sampling post-collision scattering kinematics. In practice, interpolation schemes are employed to access data between tabulated values. An improvement to this juncture of the nuclear data pipeline is supplying cross sections on-the-fly (OTF), as has been developed for the un-resolved resonance region to minimize non-physical interpolation errors. This capability may improve simulation accuracy for accident and transient analyses, where rapidly varying changes in temperature and pressure are difficult to predict beforehand. To do so, deep artificial neural networks (ANNs) can be employed which collapse non-linear, complex data into a lightweight dictionary of neural weights and biases. This has been successfully demonstrated for the hydrogen in light water $S$($α, β$) dataset in the form of a Neural Thermal Scattering (NeTS) module. In this work, the NeTS framework is extended to consider the impact of material-dependent dynamical features on optimal neural pre-processing and architecture design decisions, such as number of neurons per hidden layer, residual skip connections and neural depth. New NeTS modules for crystalline graphite and beryllium metal illuminate a novel correlation between dynamical nonlinearity and optimal neural parametrization when deploying $S$($α, β$) on-the-fly.
Improving wafer-scale Josephson junction resistance variation in superconducting quantum coherent circuits
Quantum bits, or qubits, are an example of coherent circuits envisioned for next-generation computers and detectors. A robust superconducting qubit with a coherent lifetime of O (100 µs) is the transmon: a Josephson junction functioning as a non-linear inductor shunted with a capacitor to form an anharmonic oscillator. In a complex device with many such transmons, precise control over each qubit frequency is often required, and thus variations of the junction area and tunnel barrier thickness must be sufficiently minimized to achieve optimal performance while avoiding spectral overlap between neighboring circuits. Simply transplanting our recipe optimized for single, stand-alone devices to wafer-scale (producing 64, 1x1 cm dies from a 150 mm wafer) initially resulted in global drifts in room-temperature tunneling resistance of ± 30%. Inferring a critical current variation from this resistance distribution, we present an optimized process developed from a systematic 38 wafer study that results in < 3.5% relative standard deviation (RSD) in critical current ( ) for 3000 Josephson junctions (both single-junctions and asymmetric SQUIDs) across an area of 49 cm 2 . Looking within a 1x1 cm moving window across the substrate gives an estimate of the variation characteristic of a given qubit chip. Our best process, utilizing ultrasonically assisted development, uniform ashing, and dynamic oxidation has shown = 1.8% within 1x1 cm, on average, with a few 1x1 cm areas having < 1.0% (equivalent to < 0.5%). Such stability would drastically improve the yield of multi-junction chips with strict critical current requirements.
Modeling Methods for Capturing System Interactions of Combined Technologies: A Study of PV + Battery
The costs of solar photovoltaics (PV) have been dropping in recent years, leading to increasing installations of solar PV systems and growing interest in how the technology will impact the electric grid at higher penetrations. Additionally, as battery costs decline it becomes important to understand the benefits and limitations of battery storage for the grid as well as potential benefits of co-locating battery storage and PV, particularly within the realm of future system planning. However, it is non-trivial to capture these potential benefits within a linearized capacity expansion model (CEM). This paper presents methodological developments to more fully represent the value and limitations of coupled PV and battery systems (PV + Battery) in CEMs using the Resource Planning Model (RPM), which co-optimizes capacity investments, transmission investments, and reduced-order dispatch in the Western Interconnection of North America through 2045. We use the model to simulate the evolution of the generation and transmission system under two core scenarios - a baseline scenario and a high renewable penetration scenario - coupled with sensitivities assuming low and midline PV and battery cost projections. When incorporating PV + battery, we find that it is important for CEMs to capture the ability of the coupled technology to provide firm capacity and reduce expected curtailment, compared to independent systems. These interactions can have even more dramatic impacts at higher solar penetrations.
A meshing framework for digital twins for extrusion based additive manufacturing
Additive manufacturing (AM) allows for manufacturing of complex three-dimensional geometries not typically realizable with standard manufacturing practices. The internal microstructure of AM components has a significant impact on mechanical, vibrational, and shock properties and permits richer design space when this is controllable. Due to complex interactions of internal geometry of an extrusion-based AM component, it is common practice to assume homogeneous behavior or to perform characterization testing on specific toolpath configurations. To avoid testing or material waste, it is necessary to develop a consistently accurate numerical simulation framework with relevant boundary value problems that can handle the complicated geometry of internal material microstructure present in AM components. Herein, a framework is proposed to directly create computational meshes suitable for finite element analysis (FEA) of the fine-scale features generated from extrusion-based AM tool paths to maintain a strong process–structure–property-performance linkage. This mesh can be manually or automatically analyzed using standard FEA simulations such as quasi-static preloading or modal analysis. The framework allows an in-silico assessment of a target AM geometry where fine-scale features greatly impact quantities of design interest such as in soft elastomeric lattices where toolpath infill can greatly influence the self-contact of a structure in compression, which we use as a motivating exemplar. This approach greatly reduces both time and resource waste present in traditional build and test design cycles for non-intuitive design spaces, and acts as a tool for use in the production of a key component of a digital twin, a mesh suitable for finite element analysis. In conclusion, it also further allows for the exploration of toolpath infill to optimize component properties beyond simple linear properties such as density and stiffness.