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At least 973 records · Page 54

Comparison of Conservation Behavior in Several Variationally Derived Implementations for Simulating Electromagnetic Plasmas

Variational techniques based on Low's Lagrangian formulation have demonstrated significant improvement in conservation properties as compared to traditional particle-in-cell (PIC) algorithms. Previous work showed that equations derived from a discretized Lagrangian preserve a discretized version of the connection between Lagrangian symmetries and conservation laws, i.e., Noether's theorem. Specifically, a thorough analysis of energy conservation within the new system explained the absence of “grid heating” phenomena. In the present work, variationally derived implementations in a gridded periodic domain were compared to analogous implementations using Fourier bases. Since the Fourier basis allows for exact momentum conservation, this approach enables us to compare the relative merits of exact and approximate momentum conservation. Furthermore, to establish a tangible comparison for numerical methods, we investigate two simple physical examples; (1) the coupling of an electrostatic and electromagnetic plasma wave and (2) an equilibrium supporting Weibel instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Multi-Federate Co-Convergence with HELICS

In co-simulation studies, convergence refers to the ability of different simulation tools involved to achieve a consistent and stable solution. Convergence is a critical aspect of co-simulation as it determines the accuracy of the results obtained from the simulation. Convergence in co-simulation studies depends on several factors, this includes system complexity, the accuracy of the models used, and the numerical methods employed by the simulation tools. It is essential to ensure that the coupling interfaces between the different tools are designed to allow for data exchange in a consistent and accurate manner. Hierarchical Engine for Large-scale Infrastructure Co-Simulation (HELICS) is an open-source co-simulation framework developed for the energy domain. This paper explores the convergence performance of a set of co-simulation use cases. We further explore the use of a co-convergence helper federate to help with co-simulation convergence. The convergence efficacy of several algorithms (both gradient-based and gradient-free) is tested against these use cases. Finally, the sensitivity of these algorithms to several factors, such as system scaling and others, is tested and detailed in this paper. Our results show that for a subset of use cases, the co-convergence helper federate is able to improve co-simulation convergence significantly.

co-convergence↗

A Semi-Analytical Approach for State-Space Electromagnetic Transient Simulation

Here, this paper proposes a semi-analytical approach for efficient and accurate electromagnetic transient (EMT) simulation of a power grid. The approach first derives a high-order semi-analytical solution (SAS) of the grid’s state-space EMT model using the differential transformation (DT), and then evaluates the solution over enlarged, variable time steps to significantly accelerate the simulations while maintaining its high accuracy on detailed fast EMT dynamics. The approach also addresses switches during large time steps by using a limit violation detection algorithm with a binary search-enhanced quadratic interpolation. Case studies are conducted on EMT models of the IEEE 39-bus system and large-scale systems to demonstrate the merits of the new simulation approach against traditional numerical methods.

electromagnetic transient↗

Structure-Informed Graph Learning of Networked Dependencies for Online Prediction of Power System Transient Dynamics

Online transient analysis plays an increasingly important role in dynamic power grids as the renewable generation continues growing. Traditional numerical methods for transient analysis not only are computationally intensive but also require precise contingency information as input, and therefore, are not suitable for online applications. Existing online transient assessment studies focus on the determination of post-contingency system stability or stability margin. Here, this paper develops a novel graph-learning framework, Deep-learning Neural Representation or DNR, for online prediction, of the time-series trajectories of the system states using initial system responses that can be measured by phasor measurement units (PMUs). The proposed DNR framework consists of two sequential modules: a Network Constructor that captures network dependencies among generators, and a Dynamics Predictor that predicts the system trajectories. The key to improved prediction performance is the introduction of the spatio-temporal message-passing operations into graph neural networks with structural knowledge. Its effectiveness and scalability are validated through comparative studies, demonstrating the prediction performance under different contingency scenarios for systems of different sizes. This framework provides a solution to online predicting post-fault system dynamics based on real-time PMU measurements. Additionally, it can also be applied to facilitate the offline transient simulation without simulating the entire trajectories.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Ensuring Transient Stability With Guaranteed Region of Attraction in DC Microgrids

DC microgrids have promising applications in renewable integration due to their better energy efficiency when connecting DC components. However, they might be unstable since many loads in a DC microgrid are regulated as constant power loads (CPLs) that have a destabilizing negative impedance effect. As a result, the state trajectory displacement caused by abrupt load changes or contingencies can easily lead to instability. Many existing works have been devoted to studying the region of attraction (ROA) of a DC microgrid, in which the system is guaranteed to be asymptotically stable. Nevertheless, existing work either focuses on using numerical methods for ROA approximations that generally have no performance guarantees or cannot ensure a desired ROA for a general DC microgrid. To close this gap, this paper develops an innovative control synthesis algorithm to make a general DC microgrid have a theoretically guaranteed ROA, for example, to cover the entirety of its operating range regarding state trajectories. Here, we first study the nonlinear dynamics of a DC microgrid to derive a novel transient stability condition to rigorously certify whether a given operating range is a subset of the ROA; then, we formulate a control synthesis optimization problem to guarantee the condition’s satisfaction. This condition is a linear constraint, and the optimization problem resembles an optimal power flow problem and has a good computational behavior. Simulation case studies verify the validity of the proposed work.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Verification, Validation, and Uncertainty Quantification in Thermal Hydraulics, Freeman Scholar Lecture (2019)

Engineering problems are generally solved by analytical models or computer codes. These models, in addition to conservation equations, also include many empirical relationships and approximate numerical methods. Each of these components contributes to the uncertainty in the prediction. A systematic approach to judge the applicability of the code to the intended application is needed. It starts from verification of implementation of formulation in the code, identification of important phenomena, finding relevant tests with quantified uncertainty for these phenomena, and validation of the code by comparing predictions with the relevant test data. The relevant tests must address phenomena as expected in the intended application. In case of small size or limited condition tests, the scaling analyses are needed to assess the relevancy of the tests. Finally, a statement of uncertainty in the prediction is needed. Systematic approaches are described to aggregate uncertainties from different components of the code for intended application. Here, verification, validation, and uncertainty quantifications (VVUQs) are briefly described.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to reduce classical computations and state preparation at every time step. For this, the algorithm approximates the qubit relative phases and subtracts them at the end of each time step. Phases are evaluated using the iterative phase estimation algorithm and subtracted using single-qubit rotation phase gates. Further, this method optimizes the quantum resource required and makes it more appropriate for near-term quantum hardware. We also demonstrate how the checkerboard deficiency that the D1Q2 scheme presents can be resolved using the D1Q3 scheme. The algorithm is validated by simulating two canonical partial differential equations: the diffusion and Burgers' equations on different quantum simulators. We find good agreement between quantum simulations and classical solutions for the presented algorithm.

97 MATHEMATICS AND COMPUTING↗

Sinusoidal Siemens star spatial frequency response measurement errors due to misidentified target centers

Numerous methods are available to measure the spatial frequency response (SFR) of an optical system. A recent change to the ISO 12233 photography resolution standard includes a sinusoidal Siemens star test target. We take the sinusoidal Siemens star proposed by the ISO 12233 standard, measure system SFR, and perform an analysis of errors induced by incorrectly identifying the center of a test target. We show a closed-form solution for the radial profile intensity measurement given an incorrectly determined center and describe how this error reduces the measured SFR of the system. As a result, using the closed-form solution, we propose a two-step process by which test target centers are corrected and the measured SFR is restored to the nominal, correctly centered values.

79 ASTRONOMY AND ASTROPHYSICS↗

Ex situ metrology and data processing techniques developed at the ALS for optimization of beamline performance of bendable x-ray mirrors

We discuss experimental, analytical, and numerical methods recently developed at the Advanced Light Source (ALS) X?Ray Optics Laboratory (XROL) for calibration and precision shaping of bendable x-ray mirrors. The methods are based on ex situ measurements with the mirrors using surface slope profilers available at the ALS XROL. The first realization of methods and dedicated software has allowed the optimization of the beamline performance of bendable mirrors by adjustment of the mirror shape to minimize the root-mean-square variation of residual (after subtraction of the ideal desired shape) slope deviations from ideal (specified) surface figure. Here, we further develop the methods that in application to elliptically bent mirrors adapt as a figure of merit the minimum of the rms size of the focused beam. The efficacy of the developed methods is demonstrated with examples of optimal tuning of an elliptically bendable cylindrical mirror designed for the ALS beamline 10.3.2.

Yashchuk, VV↗

Quantum phase transition dynamics in the two-dimensional transverse-field Ising model

The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical behavior near the quantum phase transitions (QPTs). It is now well understood for the one-dimensional quantum matter. Higher-dimensional systems, however, remain a challenge, complicated by the fundamentally different character of the associated QPTs and their underlying conformal field theories. In this work, we take the first steps toward theoretical exploration of the QKZM in two dimensions for interacting quantum matter. We study the dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort of modern state-of-the-art numerical methods, including artificial neural networks and tensor networks. As a central result, we quantify universal QKZM behavior close to the QPT. We also note that, upon traversing further into the ferromagnetic regime, deviations from the QKZM prediction appear. We explain the observed behavior by proposing an extended QKZM taking into account spectral information as well as phase ordering. Our work provides a testing platform for higher-dimensional quantum simulators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Establishing gold and platinum standards to 1 terapascal using shockless compression

New techniques are advancing the frontier of high-pressure physics beyond 1 terapascal, leading to new discoveries and offering stringent tests for condensed-matter theory and advanced numerical methods. However, the ability to absolutely determine the pressure state remains challenging, and well-calibrated pressure-density reference materials are required. We conducted shockless dynamic compression experiments at the National Ignition Facility and the Z machine to obtain quasi-absolute, high-precision, pressure-density equation-of-state data for gold and platinum. We derived two experimentally constrained pressure standards to terapascal conditions. Establishing accurate experimental determinations of extreme pressure will facilitate better connections between experiments and theory, paving the way toward improving our understanding of material response to these extreme conditions.

36 MATERIALS SCIENCE↗

Resonance compression of an acoustic beam in a crystal

The resonance excitation of an intense acoustic beam in a crystal is described for a special geometry of pump-wave reflection from the crystal surface. The resonance appears in the vicinity of the total internal reflection angle under the condition that the wave field in a compressed reflected beam propagating almost parallel to the surface is close to the volume eigenmode satisfying the free boundary condition. Criteria for the existence of such modes are considered in detail. Conversion conditions are analyzed under which a “parasitic” reflected wave of the same branch as the incident wave is absent and entire energy from the incident wave falls within a narrow intense acoustic beam of another branch. It is shown that, when the surface is chosen parallel to the crystal symmetry plane, the conversion criterion is reduced to the sole condition on the elastic moduli of the medium. Analysis is performed by analytic and numerical methods for skew cuts of monoclinic, rhombic, trigonal, and hexagonal crystals, when the boundary is the symmetry plane, while the sagittal plane has no symmetry. A number of crystals are found in which resonance excitation is very close to conversion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Light Scattering by a Periodically Corrugated Boundary of a Hyperbolic Medium

The scattering features of radiation incident on a periodically modulated boundary of a hyperbolic medium (HM) are studied numerically. An optimal (in a certain class of functions)—sawtooth—profile shape is found that provides minimum reflection in a wide range of wavelengths. It is shown that, for a certain orientation of the optical axes of the HM, “hot points” appear on the sawtooth boundary, that are responsible for the subwavelength field localization. A generalization is implemented of the numerical method based on the Green’s second identity for the field calculation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simulation of perturbation produced by an absorbing spherical body in collisionless plasma

A steady plasma state reached in the course of charging of an absorbing spherical body is found using computational methods. Numerical simulations provide complete information on this process, thereby allowing one to find the spatiotemporal dependences of the physical quantities and observe the kinetic phenomena accompanying the formation of stable electron and ion distributions in phase space. The distribution function of trapped ions is obtained, and their contribution to the screening of the charged sphere is determined. The sphere charge and the charge of the trapped-ion cloud are determined as functions of the unperturbed plasma parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Thermal fluctuations of pair interaction forces in liquid Yukawa systems

The dynamics of charged particles in two- and three-dimensional Yukawa systems is studied using numerical methods. Nonideal systems are simulated in a wide range of their parameters. The density of thermal fluctuations of pair interaction forces in liquid structures is obtained and compared with the internal energy density of the systems under study.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical modeling of the polarization current of geminate pairs in disordered polymers with traps

The time dependences of the polarization current of geminate pairs in disordered media are simulated by the Monte Carlo numerical method. A model of hopping transport with exponential energy distribution of the hopping centers is considered. The dependence of the polarization-current kinetics on the initial geminate-pair separation, the relative concentration of traps, the temperature, and the strength of the applied electric field is investigated. The limits of the applicability of an analytical theory based on the driftdiffusion description of electron and hole motion of the geminate pair in the dispersive-transport mode are discussed. The range of parameters is determined in which the existence of the negative current is possible.

36 MATERIALS SCIENCE↗

Determination of the Parameters of Metal–Insulator–Semiconductor Structures with Ultrathin Insulating Layer from High-Frequency Capacitance–Voltage Measurements

A simple numerical method for processing the data of the high-frequency capacitance–voltage characteristics of metal–insulator–semiconductor structures is proposed. The approach is based on analyzing the experimental characteristics near the flat-band states, where the charge exchange of surface localized electron states is of little importance compared with changes in the near-boundary charged layer in the semiconductor. The developed technique makes it possible, first, to find the necessary parameters of the semiconductor and insulating layer and, second, to obtain the experimental field dependences of the energy-band bending in the semiconductor and the total concentration of the built-in charge, the charge of boundary states and minority charge carriers at the semiconductor–insulator interface in the range from the flat bands to deep depletion. The technique is well applicable to structures with an ultra-thin insulating layer. On n-Si-based metal–oxide–semiconductor samples with an oxide thickness of 39 Å, experimental approbation of the proposed approach is carried out. The accuracy of the obtained results is 2–3%.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Formation of Vortex Flows in Liquid Crystal Phases Encapsulated in Microliter Volumes under the Action of Focused Laser Radiation

A theoretical description of the process of formation of vortex flows v(t, r) and the evolution of the director field n̂ in microliter liquid crystal (LC) volumes with a free surface under the influence of a temperature gradient ∇T(t, r), which is initiated by focused laser radiation, has been proposed. Thermomechanical contributions to both the stress tensor and viscous moment which are acting per unit volume of the LC phase were taken into account in the framework of the nonlinear generalization of the classical Ericksen−Leslie theory, which allowed describing the origin and formation of vortex flows in nematics formed by 4-n-pentyl- 4'-cyanobiphenyl molecules. Various hydrodynamic modes of vortex formation in microsized LC volumes under the action of focused laser radiation have been investigated by numerical methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗