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DOE OSTI2023

A Testing Framework for Grid-Forming Resources: Preprint

This paper presents a testing framework for grid-forming (GFM) resources. It first analytically derives in frequency domain the active and reactive power response of an ideal voltage source with a reactor. These transfer functions are then used to quantify the voltage source behavior expected from a GFM inverter within subtransient time scales (5-10 cycles) following a grid disturbance. The paper also shows that the testing of a GFM inverter might require a reactor of an appropriate size between the inverter and the grid simulator used for the inverter testing. Finally, the paper presents a systematic approach for developing specifications for GFM resources using active and reactive power response frequency scans. The testing framework and results presented in this paper are demonstrated using EMT simulations of a 1-MW GFM inverter.

frequency scans↗

DOE OSTI2026

Ether of Orbifolds

The orbifold lattice has been proposed as a route to practical quantum simulation of Yang--Mills theory, with claims of exponential speedup over all known approaches. Through analytical derivations, Monte Carlo simulation, and explicit circuit construction, we identify compounding costs entirely absent in Kogut--Susskind formulations: a mass-dependent Trotter overhead that scales as $m^4$, non-singlet contamination that grows as $m^2$ and worsens with penalty terms, and a mandatory mass extrapolation. Monte Carlo simulations of SU(3) establish a universal scaling: the continuum limit forces $m^2 \propto 1/a$, binding the Trotter step to the lattice spacing through a cost unique to orbifolds. For a fiducial $10^3$ calculation, the orbifold is $10^4$--$10^{10}$ times more expensive than every published alternative. These results indicate that the claimed computational advantages do not at present survive quantitative scrutiny.

Lamm, Henry [Fermilab] (ORCID:0000000330330791)↗

DOE OSTI2026

Strong-Drive Limits in Josephson Circuits: From Chaos to an Unbound-Resonance Threshold

Strong microwave drives enable fast measurement and parametric control in superconducting circuits but can induce transitions out of the intended low-energy manifold. We develop a unified description of strong-drive limits in flux- and charge-driven Josephson circuits across drive frequency and dc flux bias. Using classical phase-space analysis and Floquet--Markov simulations, we identify distinct low- and high-frequency mechanisms. At low frequency, we characterize bound-state resonances and separatrix chaos and find that the flux-drive chaos threshold depends strongly on dc flux bias. At high frequency, these mechanisms are suppressed, and the dissipative steady state transfers from the central bound-state sector to outer resonances formed by above-barrier running trajectories. The resulting unbound-resonance threshold is nearly independent of drive frequency and circuit parameters over the regime studied and is controlled primarily by dc flux bias. Coherent simulations show that parametric operation persists beyond this threshold, but at a reduced rate, setting an effective upper bound on the achievable operation speed. We derive analytical criteria for both thresholds, validate them numerically, and experimentally confirm the predicted dc-bias dependence of the low-frequency threshold in a flux-driven SQUID. We also determine the timescales for transfer into the unbound-resonance regime and relaxation back to the bound-state manifold after the drive is removed. Finally, we relate the stability limits to a complementary picture based on the junction critical current and extend the framework to multitone drives and inductively shunted circuits. Together, these results identify the mechanisms limiting strong driving and suggest routes to extend the stable operating range of Josephson circuits.

You, Xinyuan [Fermilab] (ORCID:0000000291789419)↗

DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

FLOWERS AEP: An Analytical Model for Wind Farm Layout Optimization

Annual energy production (AEP) is commonly used in objective functions for wind farm layout optimization. AEP is proportional to wind farm power production integrated over an annual distribution of free-stream wind conditions. Physics-based estimates of wind farm power production typically rely on low-fidelity engineering wake models that approximate the steady-state wind farm flow field. AEP estimates are then obtained by performing independent simulations for discrete wind conditions and using rectangular quadrature to account for each condition's expected frequency of occurrence. Depending on the number of simulated discrete wind conditions, this numerical integral could be hampered by poor accuracy or high computational costs. The FLOWERS AEP model instead poses an analytical integral of the engineering wake model over the variable wind conditions, yielding a closed-form, analytical function for wind farm AEP. This paper derives the analytical functions for FLOWERS AEP and its derivatives with respect to turbine position, which are useful for gradient-based wind farm layout optimization, in nondimensional form. We then analyze the benefits of the FLOWERS AEP model over conventional reference models, focusing on its low cost, adequate wake loss predictions, and smooth design space. Although the FLOWERS approach is found to predict the exact value of AEP with some error relative to the reference model (within 14% on average), it dramatically reduces computation time by an order of magnitude, produces a qualitatively similar design space at relatively low resolution, and yields comparable optimal layouts. This significant speed improvement is critical in layout optimization applications, where determining an optimal layout in an efficient manner is more important than precise AEP prediction.

17 WIND ENERGY↗

DOE OSTI2019

Chapter Six - Derivation, cross-validation, and comparison of analytic formulas for electrostatic deflector aberrations

Here, we derived first and second order analytic aberration formulas in the horizontal transverse plane for an electrostatic deflector specified by the reference orbit radius, the central angle spanning the deflector, and its inhomogeneity coefficients. The derivation was performed using an iterative order-by-order perturbation method in a Frenet–Serret beamline coordinate system. We produced a C program edabrt for calculation of the first and second order aberrations using the formulas that we derived. The electrostatic deflector aberration formulas from Wollnik (1965) disagree with COSY INFINITY and the aberration formulas that we derived here, and they also deviate from the first and second order symplecticity conditions. The reason for this discrepancy is that the aberration formulas from Wollnik (1965) consider only motion in the main field of the deflector and do not properly account for fringe field effects, in particular the necessarily occurring change of kinetic energy due to the change in potential. The code GIOS uses electrostatic aberration formulas from Wollnik (1965) and exhibits the same discrepancy. We performed a comparison of first and second order electrostatic deflector aberrations for (1) the analytic formulas derived in this work, (2) differential-algebraic (DA) numerical integration of the equations of motion using the code COSY INFINITY, (3) the aberration formulas from Wollnik (1965), (4) aberrations computed using the code GIOS, and (5) the aberration formulas from Wollnik (1965) adjusted to account for the occurring change in potential. An electrostatic spherical deflector and an electrostatic cylindrical deflector were used as test cases for this comparison. There is excellent agreement between methods (1), (2), and (5), and these three methods satisfy the first and second order symplecticity conditions.

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

Analytical Modeling of Exoplanet Transit Spectroscopy with Dimensional Analysis and Symbolic Regression

Abstract The physical characteristics and atmospheric chemical composition of newly discovered exoplanets are often inferred from their transit spectra, which are obtained from complex numerical models of radiative transfer. Alternatively, simple analytical expressions provide insightful physical intuition into the relevant atmospheric processes. The deep-learning revolution has opened the door for deriving such analytical results directly with a computer algorithm fitting to the data. As a proof of concept, we successfully demonstrate the use of symbolic regression on synthetic data for the transit radii of generic hot-Jupiter exoplanets to derive a corresponding analytical formula. As a preprocessing step, we use dimensional analysis to identify the relevant dimensionless combinations of variables and reduce the number of independent inputs, which improves the performance of the symbolic regression. The dimensional analysis also allowed us to mathematically derive and properly parameterize the most general family of degeneracies among the input atmospheric parameters that affect the characterization of an exoplanet atmosphere through transit spectroscopy.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Analytic evaluation of energy first derivatives for spin–orbit coupled-cluster singles and doubles augmented with noniterative triples method: General formulation and an implementation for first-order properties

The paper reports a formulation of analytic energy first derivatives for the coupled-cluster singles and doubles augmented with noniterative triples [CCSD(T)] method with spin–orbit coupling included at the orbital level and an implementation for evaluation of first-order properties. Here, the new development extends the applicability of relativistic coupled cluster methods for heavy-element chemistry and spectroscopy. Benchmark calculations of first-order properties including dipole moments and electric-field gradients using the corresponding exact two-component property integrals are presented for heavy-element containing molecules to demonstrate the usefulness of the present analytic scheme.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Eddy Current Shielding of the Magnetic Field Ripple in the EIC Electron Storage Ring Vacuum Chambers

The EIC electron storage ring (ESR) has very tight tolerances for the beam position and size stability at the interaction point. The oscillations at the proton betatron frequency and its harmonics are the most dangerous because, for instance, they could lead to unacceptable proton emittance growth from the oscillating beam-beam kick from the electrons at the amplitude of the positional oscillations as low as 10 -4 of the beam size. Even at much lower frequencies, down to the single Hz range, the position oscillations at a few percent level of the nominal beam size were found to be dangerous. These oscillations could have different causes including magnet power supply ripple, mag net vibration, noise in the main and crab RF systems, and some collective instabilities. To specify the acceptable level of the current ripple and noise of the magnet power supplies we need to accurately account for the eddy current shielding by the vacuum chamber, as well as, potentially, by the laminated magnet yokes (considered elsewhere). With some ap proximations, the chamber shielding can be described analytically. The main objective of this note is to derive these analytical expressions and to document the resulting shielding performance of the ESR chamber.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Dispersion formulas in QFTs, CFTs and holography

We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n -points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Analytical models of the strength and ductility of CNT reinforced metal matrix nano composites under elevated temperatures

Carbon nanotubes (CNTs) can greatly enhance the strength of metal matrix composites while resulting in ductility loss. This strength-ductility tradeoff dilemma always confines the development of material design and real-life applications. Here in this work, a temperature dependent strengthening analytical model is proposed for CNT reinforced metal matrix composites which considers three common strengthening mechanisms: Orowan looping effect, thermal expansion mismatch effect, and load bearing effect. The proposed model can predict composite material strength with different volume fractions of CNTs and under different temperatures. Combining the strengthening model with the stress based modified Mohr-Coulomb (sMMC) ductile fracture model, a ductility analytical model is then derived. This ductility analytical model includes the influences of temperature, multi-axial stress loading conditions, as well as the aforementioned three strengthening mechanisms. A good agreement has been achieved between literature published experimental data and analytical predictions for both composite material strength and ductility loss. The proposed two analytical models can provide a straightforward way to study the strength-ductility relationship for CNT reinforced metal matrix composites over a wide range of temperatures and different stress states, and then provide guidance on new material design and processing.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Isotherm Model for Moisture-Controlled CO 2 Sorption

Moisture-controlled sorption of CO 2 , the basis for moisture-swing CO 2 capture from air, is a novel phenomenon observed in strong-base anion exchange materials. Prior research has shown that Langmuir isotherms provide an approximate fit to moisture-controlled CO 2 sorption isotherm data. However, this fit still lacks a governing equation derived from an analytic model. As such, in this paper we derive an analytic form for an isotherm equation from a bottom-up approach, starting with a fundamental theory for an alkali liquid. In the range of interest relevant to CO 2 capture from air, an isotherm equation for an alkali liquid reduces to a simple analytic form with a single parameter, $K_{\text{eq}}$. In the limit $K_{\text{eq}} \gg 1$, a 2nd order approximation simplifies to a Langmuir isotherm that, however, deviates from experimental data. The isotherm theory for an alkali liquid has been generalized to a strong-base anion exchange material. In a strong-base anion exchange material, water concentration inside a sorbent, [H 2 O], is not large enough to be regarded as constant, which allows us to extend $K_{\text{eq}}$ to $K_{\text{eq(AEM)eff}} = K_{\text{eq(AEM)}} \times$ [H 2 O]$^{–n}$ according to the law of mass action. The final isotherm formula has been validated by experimental data from the literature. For a moisture-controlled CO 2 sorbent, $K_{\text{eq(AEM)eff}}$ varies significantly with moisture content of the sorbent. Depending on moisture level, the observed $K_{\text{eq(AEM)eff}}$ in a specific sorbent ranges from a few times to a few thousand times the value of $K_{\text{eq}}$ of a 2 mol L –1 alkali liquid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Hybrid Dynamic Modeling of Smart Inverter

This letter proposes a novel hybrid method for assessing grid-connected three-phase converter interfaced resources (CIR) dynamics with the IEEE standard 1547-2018 grid support functions (GSFs), which blends physics and data-driven techniques. First, the letter derives an analytical model of a CIR to represent the internal physics and data-driven model (DDM) using a system identification algorithm to represent the rest of the dynamics, including the GSF. The derived hybrid model combines the analytical model of CIR and DDM, which balances accuracy and flexibility and is compared with the detailed switched model. Furthermore, the efficacy of the proposed approach to represent the advanced CIR dynamics is substantiated by power hardware-in-the-loop experiment data where real measurements from a commercial CIR are used to cross-validate the proposed approach. Furthermore, the results indicate that despite simple, the hybrid model accurately reproduces the dynamics of the detailed CIR model with an acceptable accuracy.

Data-driven model↗

DOE OSTI2022

Collective effect of thermal plumes on temperature fluctuations in a closed Rayleigh–Benard convection cell

Here, we report a systematic study of the collective effect of thermal plumes on the probability density function (PDF) P(δT) of temperature fluctuations δT(t) in turbulent Rayleigh-Benard convection. By decomposing δT(t) into four basic fluctuation modes associated with single and multiple warm and cold plumes and a turbulent background, we derive an analytic form of P(δT) based on the convolutions of the five independent modes. To test the derived form of P(δT) in the multiple-plume regions, where the thermal plumes are heavily populated, we conduct time series measurements of temperature fluctuations in two convection cells; one is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. For a given normalized position in most regions of the convection cell, all of the measured PDFs P(δT) for different Rayleigh numbers fall onto a single master curve, once δT is normalized by its rms value σ T . It is found that the measured P(δT / σT ) at different locations along the symmetric horizontal and vertical axes of the convection cells can all be well described by the derived form of P(δT / σT ). The fitted values of the parameters associated with the number of plumes in multiple plume clusters and their relative strengths and degrees of intermittency are closely linked to the spatial distribution of thermal plumes and local dynamics of the large-scale circulation in a closed convection cell. Our work thus provides a unified theoretical approach for understanding scalar PDFs in a turbulent field, which is very useful not only for the present study but also for the study of many turbulent mixing problems of practical interest.

42 ENGINEERING↗

DOE OSTI2022

Novel nonwetting solid-infused surfaces for superior fouling mitigation

Fouling is a ubiquitous issue in several environmental and energy applications. Here we introduce novel nonwetting solid-infused surfaces (SIS) with superior anti-fouling characteristics that are durable than conventional nonwetting surfaces in a dynamic flow environment. A systematic study is presented to elucidate the fouling mitigation performance of SIS in comparison to lubricant-infused surface (LIS) and conventional smooth surface. Copper tubes with SIS, LIS or smooth inner walls are fabricated and subjected to accelerated calcium sulfate fouling in a flow fouling experimental setup. Fouling on the various surface types is quantified in terms of asymptotic fouling resistance, and the fundamental morphological differences in the interactions of the foulant and the various surface types are analyzed. Based on a systematic sweep of the parameter combinations using design of experiments and Taguchi analysis, an analytical dependence of asymptotic fouling resistance on the governing parameters namely, Reynolds number, foulant concentration and temperature is derived. The analytical model is shown to predict the asymptotic fouling resistance to within 20% accuracy with a 95% confidence. In addition, for the first time, the effects of shear durability on the fouling mitigation performance of LIS vis-à-vis SIS are studied. It is shown that the novel nonwetting SIS offers a robust option for superior fouling mitigation over LIS in the long run.

42 ENGINEERING↗

DOE OSTI2026

Modification of ion-temperature-gradient turbulence by impurities in stellarator plasmas

Recent nonlinear gyrokinetic simulations have shown that impurities can strongly modify the turbulent heat flux in stellarator plasmas. Here, the ion-temperature-gradient (ITG) dispersion relation in a plasma containing impurities is analytically solved in certain limits and an expression for the modification of the ITG growth rate by impurities is derived. The analytical expression is the sum of three terms corresponding to three different physical causes (impurity density gradient, impurity temperature gradient and dilution) of the change in the growth rate. The scalings predicted analytically for the modification of the growth rate are shown to be reproduced by linear gyrokinetic simulations. The conditions for reduction or increase of the ITG growth by impurities are also correctly predicted by the analytical solution to the dispersion relation. Finally, a remarkable correlation is found between the analytical expression for the modification of the growth rate and the modification of the turbulent heat flux obtained from nonlinear gyrokinetic simulations.

Calvo, Iván [Research Centre for Energy, Environme↗

DOE OSTI2020

Analytical Voltage Sensitivity Analysis for Unbalanced Power Distribution System

Large scale integration of distributed energy resources and electric vehicles in a transactive energy environment present new challenges in terms of voltage stability and fluctuations in a power distribution system. The impact of different level of DER/EV penetration on the voltages across the network is typically quantified through voltage sensitivity analyses. Existing methods of voltage sensitivity analysis are computationally expensive and prior efforts to develop analytical approximation lacks generality and have not been effectively validated. The objective of this work is to provide a new analytical method of voltage sensitivity analysis that has low computational cost and also allows for stochastic analysis of voltage change. This paper first derives an analytical approximation of change in voltage at a particular bus due to change in power consumption at other bus in a radial three phase unbalanced power distribution system. Then, the proposed method is shown to be valid for different load configurations, which demonstrates its generality. The results from our analytical approach is validated via classical load flow simulation of the test system based on IEEE 37 bus network. The proposed method is shown to have good accuracy, and computation complexity is of order O(1), compared to O(n3) in classical sensitivity analysis approaches.

Munikoti, Sai↗

DOE OSTI2022

Entanglement and seniority

In quantum mechanics entanglement is the most striking phenomenon which has no counterpart in classical systems. Although, different approaches have already been developed to study correlations in the case of indistinguishable particles, the exploration of the so-called mode entanglement is still in its initial stage in nuclear physics. Study of mode-entanglement in the seniority model, derivation of analytic formulas for the one-body reduced density matrix of states with seniority $ν$ = 0, 1, 2, and $ν$ = 3, and also determination of the particle number dependence of the one-body reduced density matrix for arbitrary seniority. In addition, comparison of the predictions of the seniority model with the results of the shell model to gain insight into the structure and correlations of the ground and lowest yrast states. In the seniority model the analytic results are calculated using the quasi-spin formalism. The numerical shell model calculations are carried out in the standard shell model framework using an inert core. The applied realistic effective interactions are derived earlier using the $G$-matrix formalism. The density matrix renormalization group method is also applied in order to directly calculate the mode entropies. In the seniority model simple analytical expressions are given for the mode entropies. The peculiar behavior of the half-filled shells and the seniority-zero states are revealed. Numerical results are presented for the lightest stable calcium isotopes and for 94 Ru nucleus. For 94 Ru, the seniority model accounts for the 0$g$ 9/2 mode entropies, but seniority mixing is important for certain yrast states. Furthermore, interaction induced quantum fluctuations decrease the occupation of the 0$f$ 5/2 , 1$p$ 3/2 and 1$p$ 1/2 shells, and amount in non-negligible mode entropies on these shells, too, clearly outside the scope of the simple (0$g$ 9/2 ) 4 seniority model. The 0$f$ 7/2 shell-based seniority model is more accurate for the Ca isotopes, but seniority mixing is substantial for some 44 Ca yrast states, too. Mode and one-body entanglement entropies are useful tools to investigate the structure of quantum correlations in nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗