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Results for “Perturbative methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Efficacy of the Cell Perturbation Method in Large-Eddy Simulations of Boundary Layer Flow over Complex Terrain

A challenge to simulating turbulent flow in multiscale atmospheric applications is the efficient generation of resolved turbulence motions over an area of interest. One approach is to apply small perturbations to flow variables near the inflow planes of turbulence-resolving simulation domains nested within larger mesoscale domains. While this approach has been examined in numerous idealized and simple terrain cases, its efficacy in complex terrain environments has not yet been fully explored. Here, we examine the benefits of the stochastic cell perturbation method (CPM) over real complex terrain using data from the 2017 Perdigão field campaign, conducted in an approximately 2-km wide valley situated between two nearly parallel ridges. Following a typical configuration for multiscale simulation using nested domains within the Weather Research and Forecasting (WRF) model to downscale from the mesoscale to a large-eddy simulation (LES), we apply the CPM on a domain with horizontal grid spacing of 150 m. At this resolution, spurious coherent structures are often observed under unstable atmospheric conditions with moderate mean wind speeds. Results from such an intermediate resolution grid are often nested down for finer, more detailed LES, where these spurious structures adversely affect the development of turbulence on the subsequent finer grid nest. We therefore examine the impacts of the CPM on the representation of turbulence within the nested LES domain under moderate mean flow conditions in three different stability regimes: weakly convective, strongly convective, and weakly stable. In addition, two different resolutions of the underlying terrain are used to explore the role of the complex topography itself in generating turbulent structures. We demonstrate that the CPM improves the representation of turbulence within the LES domain, relative to the use of high-resolution complex terrain alone. During the convective conditions, the CPM improves the rate at which smaller-scales of turbulence form, while also accelerating the attenuation of the spurious numerically generated roll structures near the inflow boundary. During stable conditions, the coarse mesh spacing of the intermediate LES domain used herein was insufficient to maintain resolved turbulence using CPM as the flow develops downstream, highlighting the need for yet higher resolution under even weakly stable conditions, and the importance of accurate representation of flow on intermediate LES grids.

17 WIND ENERGY↗
DOE OSTI2023

Porting fragmentation methods to GPUs using an OpenMP API: Offloading the resolution-of-the-identity second-order Møller–Plesset perturbation method

Here, using an OpenMP Application Programming Interface, the resolution-of-the-identity second-order Møller–Plesset perturbation (RI-MP2) method has been off-loaded onto graphical processing units (GPUs), both as a standalone method in the GAMESS electronic structure program and as an electron correlation energy component in the effective fragment molecular orbital (EFMO) framework. First, a new scheme has been proposed to maximize data digestion on GPUs that subsequently linearizes data transfer from central processing units (CPUs) to GPUs. Second, the GAMESS Fortran code has been interfaced with GPU numerical libraries (e.g., NVIDIA cuBLAS and cuSOLVER) for efficient matrix operations (e.g., matrix multiplication, matrix decomposition, and matrix inversion). The standalone GPU RI-MP2 code shows an increasing speedup of up to 7.5× using one NVIDIA V100 GPU with one IBM 42-core P9 CPU for calculations on fullerenes of increasing size from 40 to 260 carbon atoms using the 6-31G(d)/cc-pVDZ-RI basis sets. A single Summit node with six V100s can compute the RI-MP2 correlation energy of a cluster of 175 water molecules using the correlation consistent basis sets cc-pVDZ/cc-pVDZ-RI containing 4375 atomic orbitals and 14 700 auxiliary basis functions in ~0.85 h. In the EFMO framework, the GPU RI-MP2 component shows near linear scaling for a large number of V100s when computing the energy of an 1800-atom mesoporous silica nanoparticle in a bath of 4000 water molecules. The parallel efficiencies of the GPU RI-MP2 component with 2304 and 4608 V100s are 98.0% and 96.1%, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Electronic excitation spectra of molecular hydrogen in phase I from quantum Monte Carlo and many-body perturbation methods

Here, we study the electronic excitation spectra in solid molecular hydrogen (phase I) at ambient temperature and 5- to 90-GPa pressures using quantum Monte Carlo methods and many-body perturbation theory. In this range, the system changes from a wide-gap molecular insulator to a semiconductor, altering the nature of the excitations from localized to delocalized. Computed gaps and spectra agree with experiments, proving the ability to predict accurately band gaps of many-body systems in the presence of nuclear quantum and thermal effects.

08 HYDROGEN↗
DOE OSTI2022

Investigations of plasma response associated with resonant magnetic perturbation fields using perturbation method in KSTAR H-mode plasmas

Abstract The plasma response associated with the resonant magnetic perturbation (RMP) field was investigated using the small edge perturbations induced by a modulated supersonic molecular beam injection (SMBI) in KSTAR. The modulated SMBI provides a time-varying perturbation of the plasma density source in the region just inside the last closed flux surface and a modulated flow damping rate. Radial propagation of the toroidal rotation perturbation induced by SMBI from the q = 3 surface to the q = 2 surface was observed. Theoretical analysis using the general perturbed equilibrium code of the RMP intensity profiles of the RMP field is consistent with the phase profile of the toroidal rotation perturbation.

Physics↗
DOE OSTI2023

Toward perturbation theory methods on a quantum computer

Perturbation theory, used in a wide range of fields, is a powerful tool for approximate solutions to complex problems, starting from the exact solution of a related, simpler problem. Advances in quantum computing, especially over the past several years, provide opportunities for alternatives to classical methods. Here, we present a general quantum circuit estimating both the energy and eigenstates corrections that is far superior to the classical version when estimating second-order energy corrections. We demonstrate our approach as applied to the two-site extended Hubbard model. In addition to numerical simulations based on qiskit, results on IBM’s quantum hardware are also presented. Our work offers a general approach to studying complex systems with quantum devices, with no training or optimization process needed to obtain the perturbative terms, which can be generalized to other Hamiltonian systems both in chemistry and physics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Implementation of Perturbation Theory and Sensitivity Capabilities in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor Multiphysics analysis application, jointly developed by Argonne and Idaho National Laboratories under the DOE-NE NEAMS program. This fiscal year, capabilities for reactivity and sensitivity evaluation using perturbation methods were implemented and verified. The First Order Perturbation Method (FOPT) was employed to compute reactivity worth resulting from small perturbations in input parameters, while the Generalized Perturbation Theory (GPT) was used to evaluate sensitivities of a range of response types, including reaction rate ratio, k-eigenvalue, neutron generation time, and effective delayed neutron fraction. These perturbation methods enable users to quantify how response quantities change due to a perturbation in a input parameter without explicitly performing an additional transport simulation for each perturbed state. In particular, the GPT formulation accounts for indirect effects arising from flux changes by solving generalized inhomogeneous equations, for which a Neumann series-based iterative solution method was developed and implemented in Griffin. The implemented reactivity and sensitivity evaluation capabilities were verified using two test problems: an infinite homogeneous system and a two-dimensional hexagonal core. The results showed excellent agreement with reference solutions obtained by a direct method based on finite difference approximation as well as GPT-based results from the PERSENT code, confirming the accuracy of both reactivity and sensitivity evaluations. Additionally, preliminary uncertainty quantification (UQ) results were obtained by combining the sensitivity values computed using GPT and external covariance data, demonstrating that the implemented sensitivity results can be reliably used for uncertainty calculations. To further demonstrate the generality and practical strength of the implementation, the sensitivity evaluation capability was successfully applied to the Empire microreactor with a geometrically complex design that poses significant modeling challenges. The results confirm that Griffin enables sensitivity evaluations even for irregular and highly heterogeneous reactor configurations, thereby establishing a foundation for UQ applications in advanced reactor designs and analyses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

The DESC stellarator code suite. Part 2. Perturbation and continuation methods

A new perturbation and continuation method is presented for computing and analysing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $\boldsymbol {F} \equiv \boldsymbol {J}\times \boldsymbol {B} - \boldsymbol {\nabla } p = 0$ , and an efficient algorithm for computing solutions to second- and third-order perturbations is developed. The method has been implemented in the DESC stellarator equilibrium code, using automatic differentiation to compute the required derivatives. Examples are shown demonstrating its use for computing complicated equilibria, perturbing a tokamak into a stellarator and performing parameter scans in pressure, rotational transform and boundary shape in a fraction of the time required for a full solution.

Conlin, Rory (ORCID:0000000183662111)↗
DOE OSTI2020

Efficient perturbation-tracking method for directly probing the spectral phonon properties from molecular dynamics simulations

Existing methods for directly extracting the spectral phonon properties from molecular dynamics (MD) simulations, like the normal mode analysis (NMA) and spectral energy density analysis, all require a very long simulation time to produce reliable results with good convergence. So far, these methods are mainly applied in studies using small systems and with empirical potentials, as the heavy computational load has greatly hindered their further applications. Here we propose a perturbation-tracking (PT) method for directly probing the mode-wise phonon anharmonic frequencies and lifetimes. We show that results obtained from our method are in excellent agreement with those from the conventional NMA approach, using Si as the model material system. Comparing with the NMA approach, the PT method offers a greater accuracy and significant improvement of efficiency. It takes an average of two orders of magnitude and up to three orders of magnitude less simulation time to obtain the same lifetime result of a phonon mode with intermediate to high accuracy. Meanwhile, our method preserves all the dynamics of probed phonon mode from a particular state, which means it is capable of studying the transient thermal transport processes in a nonequilibrium system. Besides the exceptional efficiency, our method also comes with freedom to choose to probe only those modes of interest. This makes it ideal for use with large systems and in computationally demanding applications, such as ab initio MD simulations. Moreover, the PT method we propose here is very straightforward and easy to implement.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Impact of Momentum Perturbation on Convective Boundary Layer Turbulence

Mesoscale-to-microscale coupling is an important tool for conducting turbulence-resolving multiscale simulations of realistic atmospheric flows, which are crucial for applications ranging from wind energy to wildfire spread studies. Different techniques are used to facilitate the development of realistic turbulence in the large-eddy simulation (LES) domain while minimizing computational cost. Here, we explore the impact of a simple and computationally efficient Stochastic Cell Perturbation method using momentum perturbation (SCPM-M) to accelerate turbulence generation in boundary-coupled LES simulations using the Weather Research and Forecasting model. We simulate a convective boundary layer (CBL) to characterize the production and dissipation of turbulent kinetic energy (TKE) and the variation of TKE budget terms. Furthermore, we evaluate the impact of applying momentum perturbations of three magnitudes below, up to, and above the CBL on the TKE budget terms. Momentum perturbations greatly reduce the fetch associated with turbulence generation. When applied to half the vertical extent of the boundary layer, momentum perturbations produce an adequate amount of turbulence. However, when applied above the CBL, additional structures are generated at the top of the CBL, near the inversion layer. The magnitudes of the TKE budgets produced by SCPM-M when applied at varying heights and with different perturbation amplitudes are always higher near the surface and inversion layer than those produced by No-SCPM, as are their contributions to the TKE. This study provides a better understanding of how SCPM-M reduces computational costs and how different budget terms contribute to TKE in a boundary-coupled LES simulation.

17 WIND ENERGY↗
DOE OSTI2024

Perturbative diffraction methods resolve a conformational switch that facilitates a two-step enzymatic mechanism

Enzymes catalyze biochemical reactions through precise positioning of substrates, cofactors, and amino acids to modulate the transition-state free energy. However, the role of conformational dynamics remains poorly understood due to poor experimental access. This shortcoming is evident with Escherichia coli dihydrofolate reductase (DHFR), a model system for the role of protein dynamics in catalysis, for which it is unknown how the enzyme regulates the different active site environments required to facilitate proton and hydride transfer. Here, we describe ligand-, temperature-, and electric-field-based perturbations during X-ray diffraction experiments to map the conformational dynamics of the Michaelis complex of DHFR. We resolve coupled global and local motions and find that these motions are engaged by the protonated substrate to promote efficient catalysis. This result suggests a fundamental design principle for multistep enzymes in which pre-existing dynamics enable intermediates to drive rapid electrostatic reorganization to facilitate subsequent chemical steps.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Measurement of the proton spin structure at long distances

Measuring the spin structure of protons and neutrons tests our understanding of how they arise from quarks and gluons, the fundamental building blocks of nuclear matter. At long distances, the coupling constant of the strong interaction becomes large, requiring non-perturbative methods to calculate quantum chromodynamics processes, such as lattice gauge theory or effective field theories. In this work, we report proton spin structure measurements from scattering a polarized electron beam off polarized protons. The spin-dependent cross-sections were measured at large distances, corresponding to the region of low momentum transfer squared between 0.012 and 1.0GeV 2 . This kinematic range provides unique tests of chiral effective field theory predictions. Our results show that a complete description of the nucleon spin remains elusive, and call for further theoretical works, for example, in lattice quantum chromodynamics. Finally, our data extrapolated to the photon point agree with the Gerasimov–Drell–Hearn sum rule, a fundamental prediction of quantum field theory that relates the anomalous magnetic moment of the proton to its integrated spin-dependent cross-sections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Shock wave formation in radiative plasmas

The temporal evolution of weak shocks in radiative media is theoretically investigated in this work. The structure of radiative shocks has traditionally been studied in a stationary framework. Their systematic classification is complex because layers of optically thick and thin regions alternate to form a radiatively-driven precursor and a temperature-relaxation layer, between which the hydrodynamic shock is embedded. In this work, we analyze the formation of weak shocks when two radiative plasmas with different pressures are put in contact. Applying a reductive perturbative method yields a Burgers-type equation that governs the temporal evolution of the perturbed variables including the radiation field. The conditions upon which optically thick and thin solutions exist have been derived and expressed as a function of the shock strength and Boltzmann number. Below a certain Boltzmann number threshold, weak shocks always become optically thick asymptotically in time, while thin solutions appear as transitory structures. The existence of an optically thin regime is related to the presence of an overdense layer in the compressed material. Scaling laws for the characteristic formation time and shock width are provided for each regime. The theoretical analysis is supported by FLASH simulations, and a comprehensive testcase has been designed to benchmark radiative hydrodynamic codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Design and fabrication of a four-rod radio frequency quadrupole with a variable aperture

Radiofrequency quadrupole (RFQ) linear accelerators with variable aperture cell parameters offer an effective means of accelerating high-intensity ion beams exceeding 100 mA and have been implemented in various RFQ designs. However, in a four-rod RFQ, the use of dielectric perturbation methods to measure the voltage distribution behind the rod electrodes is not applicable when implementing variable aperture geometries, because changes in the rod shape influence the electric field at the location of the perturbation element. Therefore, it was necessary to design the rod profile for each cell such that the electric field distribution behind the rods remains unaffected by changes in the aperture. In this study, we present a method to adjust the voltage distribution by modifying the geometry of the rod electrodes according to each cell's aperture parameters. This design approach enables the integration of variable aperture cells into a four-rod RFQ linac, significantly enhancing the achievable beam current. To ensure uniform capacitance and maintain a constant rod-electrode voltage despite variations in the average aperture radius, we developed a systematic method for shaping the rod electrodes. This method was refined using two-dimensional (2D) and three-dimensional (3D) electromagnetic field simulations to optimize the electrode cross-sectional profiles. The fabricated rod electrodes were then installed in a four-rod RFQ, and the electric field distribution was measured using the perturbation method and tuned by adjusting the base plates. As a result, the measured variation of ±1.1 % confirms that this design methodology can produce a sufficiently uniform voltage distribution for high-current beam acceleration. These results demonstrate the practical feasibility of a variable-aperture four-rod RFQ linac.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

DQ Admittance Model Extraction for IBRs via Gaussian Pulse Excitation

While $dq$ admittance models have shown to be very useful for stability analysis, extracting admittance models of inverter-based resources (IBRs) from the electromagnetic transient (EMT) simulation environment using frequency scans takes time. In this letter, a new perturbation method based on Gaussian pulses in combination with the system identification algorithms shows great promise for parametric $dq$ admittance model extraction. We present the $dq$ admittance model extracting method for a type-4 wind turbine. Challenges in implementing Gaussian pulse excitation are also pointed out. In conclusion, the extracted $dq$ admittance model via the new method shows to have a high matching degree with the measurements obtained from frequency scans.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics

We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) based on the ensemble normal ordering of Mukherjee and Kutzelnigg (1997). This ensemble averages over all microstates of a given total spin quantum number, and therefore, it is invariant with respect to SU(2) transformations. As such, all equations may be reformulated in terms of spin-free quantities and they closely resemble those of spin-adapted closed-shell coupled cluster (CC) theory. The current implementation is used to assess the accuracy of various truncated MR-DSRG methods (perturbation theory up to third order and iterative methods with single and double excitations) in computing the constants of 33 first-row diatomic molecules. The accuracy trends for these first-row diatomics are consistent with our previous benchmark on a small subset of closed-shell diatomic molecules. We then present the first MR-DSRG application on transition-metal complexes by computing the spin splittings of the [Fe(H 2 O) 6 ] 2+ and [Fe(NH 3 ) 6 ] 2+ molecules. A focal point analysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. The FPA based on the linearized MR-DSRG theory with one- and two-body operators and up to a quintuple- ζ basis set predicts the spin splittings of [Fe(H 2 O) 6 ] 2+ and [Fe(NH 3 ) 6 ] 2+ to be –35.7 and –17.1 kcal mol –1 , respectively, showing good agreement with the results of local CC theory with singles, doubles, and perturbative triples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Analytic Nuclear Gradients for Complete Active Space Linearized Pair-Density Functional Theory

Accurately modeling photochemical reactions is difficult due to the presence of conical intersections and locally avoided crossings, as well as the inherently multiconfigurational character of excited states. As such, one needs a multistate method that incorporates state interaction in order to accurately model the potential energy surface at all nuclear coordinates. The recently developed linearized pair-density functional theory (L-PDFT) is a multistate extension of multiconfiguration PDFT, and it has been shown to be a cost-effective post-MCSCF method (as compared to more traditional and expensive multireference many-body perturbation methods or multireference configuration interaction methods) that can accurately model potential energy surfaces in regions of strong nuclear–electronic coupling in addition to accurately predicting Franck–Condon vertical excitations. Here, in this paper, we report the derivation of analytic gradients for L-PDFT and their implementation in the PySCF-forge software, and we illustrate the utility of these gradients for predicting ground- and excited-state equilibrium geometries and adiabatic excitation energies for formaldehyde, s-trans-butadiene, phenol, and cytosine.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A static quantum embedding scheme based on coupled cluster theory

Here, we develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment problem using a high-level CC method and address the environment problem with a lower-level Møller–Plesset (MP) perturbative method. This embedding approach inherits many conceptual developments from the hybrid second-order Møller–Plesset (MP2) and CC works by Nooijen [J. Chem. Phys. 111, 10815 (1999)] and Bochevarov and Sherrill [J. Chem. Phys. 122, 234110 (2005)]. We go beyond those works here by primarily targeting a specific localized fragment of a molecule and also introducing an alternative mechanism to relax the environment within this framework. We will call this approach MP-CC. We demonstrate the effectiveness of MP-CC on several potential energy curves and a set of thermochemical reaction energies, using CC with singles and doubles as the fragment solver, and MP2-like treatments of the environment. The results are substantially improved by the inclusion of orbital relaxation in the environment. Using localized bonds as the active fragment, we also report results for N=N bond breaking in azomethane and for the central C–C bond torsion in butadiene. We find that when the fragment Hilbert space size remains fixed (e.g., when determined by an intrinsic atomic orbital approach), the method achieves comparable accuracy with both a small and a large basis set. Additionally, our results indicate that increasing the fragment Hilbert space size systematically enhances the accuracy of observables, approaching the precision of the full CC solver.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Hamiltonian formulations for perturbed dissipationless plasma equations

The Hamiltonian formulations for the perturbed Vlasov–Maxwell equations and the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms of the perturbation derivative ∂ F / ∂ ϵ ≡ [ F , S ] of an arbitrary functional F [ ψ ] of the Vlasov–Maxwell fields ψ = ( f , E , B ) or the ideal MHD fields ψ = ( ρ , u , s , B ) , which are assumed to depend continuously on the (dimensionless) perturbation parameter ϵ . In this study, [ , ] denotes the functional Poisson bracket for each set of plasma equations and the perturbation action functional S is said to generate dynamically accessible perturbations of the plasma fields. The new Hamiltonian perturbation formulation introduces a framework for functional perturbation methods in plasma physics and highlights the crucial roles played by polarization and magnetization in Vlasov–Maxwell and ideal MHD perturbation theories. One application considered in this paper is a formulation of plasma stability that guarantees dynamical accessibility and leads to a natural generalization to higher-order perturbation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗