Accurate and Numerically Efficient r 2 SCAN Meta-Generalized Gradient Approximation
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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
SEARCH · Engineering Papers
Results for “Numerical approximations”
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Dual-map framework for noise characterization of quantum computers
In order to understand the capabilities and limitations of quantum computers, it is necessary to develop methods that efficiently characterize and benchmark error channels present on these devices. In this paper, we present a method that faithfully reconstructs a marginal (local) approximation of the effective noise (MATEN) channel, that acts as a single layer at the end of the circuit. We first introduce a dual-map framework that allows us to analytically derive expectation values of observables with respect to noisy circuits. These findings are supported by numerical simulations of the quantum approximate optimization algorithm (QAOA) that also justify the MATEN, even in the presence of nonlocal errors that occur during a circuit. Finally, we demonstrate the performance of the method on Rigetti's Aspen-11 quantum computer for QAOA circuits up to six qubits, successfully predicting the observed measurements on a majority of the qubits.
Sud, James↗
Computational capacity in hydrodynamic real-time hybrid simulation applied to simulate the dynamic response of floating offshore wind turbines
Real-time hybrid simulation (RTHS) mitigates similitude distortions in model-scale tests of floating offshore wind turbines (FOWTs) by coupling physical experiments with numerical models in real time. The coupling requires faster-than-real-time numerical computations to satisfy temporal similitude with the physical experiment, presenting a bottleneck for using more complex numerical models in RTHS. This paper presents a hydrodynamic-RTHS (hydro-RTHS) framework for FOWTs that simulates the hydrodynamics physically and the aerodynamics numerically with sensor feedback from the physical testing. The framework adapts the three-loop hardware architecture to leverage greater computational resources and mitigate strict temporal requirements, enabling more computationally demanding numerical analyses in hydro-RTHS. The three-loop hardware architecture integrates multiple machines, each dedicated to either numerical analysis or RTHS controls, with a rate-transition algorithm to synchronize the tasks executed across the different machine processors. Virtual and physical tests verified and validated the hydro-RTHS framework, respectively. The ”virtual” tests, which approximates the physical domain numerically, verified the RTHS framework with respect to a numerical full-scale complete FOWT model simulated in the open-source software, OpenFAST. The virtual tests were able to maintain comparable control signals while enabling greater computational resources for the numerical calculations. Real-world physical tests demonstrated that the hydro-RTHS framework computes aerodynamic forces similar to the complete OpenFAST model, validating the hydro-RTHS framework using the three-loop hardware architecture. Findings show that the hydro-RTHS framework with the three-loop hardware architecture is computationally efficient, with reserve capacity to simulate more complex problems due to the customized software, hardware, and rate-transition algorithm.
17 WIND ENERGY↗
Computational modelling and experimental tank testing of the multi float WaveSub under regular wave forcing
A submerged wave device generates energy from the relative motion of floating bodies. In WaveSub, three floats are joined to a reactor; each connected to a spring and generator. Electricity generated damps the orbital movements of the floats. The forces are non-linear and each float interacts with the others. Tuning to the wave climate is achieved by changing the line lengths, so there is a need to understand the performance trade-offs for a large number of configurations. This requires an efficient, large displacement, multidirectional, multi-body numerical scheme. Results from a 1/25 scale wave basin experiment are described. Here, we show that a time domain linear potential flow formulation (Nemoh, WEC-Sim) can match the tank testing provided that suitably tuned drag coefficients are employed. Inviscid linear potential models can match some wave device experiments; however, additional viscous terms generally provide better accuracy. Scale experiments are also prone to mechanical friction, and we estimate friction terms to improve the correlation further. The resulting error in mean power between numerical and physical models is approximately 10%. Predicted device movement shows a good match. Overall, drag terms in time domain wave energy modelling will improve simulation accuracy in wave renewable energy device design. to understand the performance trade-offs for a large number of configurations. This requires an efficient, large displacement, multidirectional, multi-body numerical scheme. Results from a 1/25 scale wave basin experiment are described. Here, we show that a time domain linear potential flow formulation (Nemoh, WEC-Sim) can match the tank testing provided that suitably tuned drag coefficients are employed. Inviscid linear potential models can match some wave device experiments; however, additional viscous terms generally provide better accuracy. Scale experiments are also prone to mechanical friction, and we estimate friction terms to improve the correlation further. The resulting error in mean power between numerical and physical models is approximately 10%. Predicted device movement shows a good match. Overall, drag terms in time domain wave energy modelling will improve simulation accuracy in wave renewable energy device design.
16 TIDAL AND WAVE POWER↗
Modeling the small-scale deposition of snow onto structured Arctic sea ice during a MOSAiC storm using snowBedFoam 1.0.
The remoteness and extreme conditions of the Arctic make it a very difficult environment to investigate. In these polar regions covered by sea ice, the wind is relatively strong due to the absence of obstructions and redistributes a large part of the deposited snow mass, which complicates estimates for precipitation hardly distinguishable from blowing or drifting snow. Moreover, the snow mass balance in the sea ice system is still poorly understood, notably due to the complex structure of its surface. Quantitatively assessing the snow distribution on sea ice and its connection to the sea ice surface features is an important step to remove the snow mass balance uncertainties (i.e., snow transport contribution) in the Arctic environment. In this work we introduce snowBedFoam 1.0., a physics-based snow transport model implemented in the open-source fluid dynamics software OpenFOAM. We combine the numerical simulations with terrestrial laser scan observations of surface dynamics to simulate snow deposition in a MOSAiC (Multidisciplinary Drifting Observatory for the Study of Arctic Climate) sea ice domain with a complicated structure typical for pressure ridges. The results demonstrate that a large fraction of snow accumulates in their vicinity, which compares favorably against scanner measurements. However, the approximations imposed by the numerical framework, together with potential measurement errors (precipitation), give rise to quantitative inaccuracies, which should be addressed in future work. The modeling of snow distribution on sea ice should help to better constrain precipitation estimates and more generally assess and predict snow and ice dynamics in the Arctic.
54 ENVIRONMENTAL SCIENCES↗
Quantum Control Landscapes Beyond the Dipole Approximation: Controllability, Singular Controls, and Resources
We investigate the control landscapes of closed n-level quantum systems beyond the dipole approximation by including a polarizability term in the Hamiltonian. The latter term is quadratic in the control field. Theoretical analysis of singular controls is presented, which are candidates for producing landscape traps. The results for considering the presence of singular controls are compared to their counterparts in the dipole approximation (i.e., without polarizability). A numerical analysis of the existence of traps in control landscapes for generating unitary transformations beyond the dipole approximation is made upon including the polarizability term. An extensive exploration of these control landscapes is achieved by creating many random Hamiltonians which include terms linear and quadratic in a single control field. The discovered singular controls are all found not to be local optima. This result extends a great body of recent work on typical landscapes of quantum systems where the dipole approximation is made. We further investigate the relationship between the magnitude of the polarizability and the fluence of the control resulting from optimization. It is also shown that including a polarizability term in an otherwise uncontrollable dipole coupled system removes traps from the corresponding control landscape by restoring controllability. We numerically assess the effect of a polarizability term on a known example of a particular three-level Λ-system with a second order trap in its control landscape. It is found that the addition of the polarizability removes the trap from the landscape. The general practical control implications of these simulations are discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Inelastic Triatom-Atom Quantum Close-Coupling Dynamics in Full Dimensionality: All Rovibrational Mode Quenching of Water Due to the H Impact on a Six-Dimensional Potential Energy Surface
The rovibrational level populations, and subsequent emission in various astrophysical environments, are driven by inelastic collision processes. The available rovibrational rate coefficients for water have been calculated using a number of approximations. We present a numerically exact calculation for the rovibrational quenching for all water vibrational modes due to collisions with atomic hydrogen. The scattering theory implements a quantum close-coupling (CC) method on a high level ab initio six-dimensional (6D) potential energy surface (PES). Total rovibrational quenching cross sections for excited bending levels were compared with earlier results on a 4D PES with the rigid-bender closecoupling (RBCC) approximation. General agreement between 6D-CC and 4DRBCC calculations are found, but differences are evident including the energy and amplitude of low-energy orbiting resonances. Quenching cross sections from the symmetric and asymmetric stretch modes are provided for the first time. The current 6D-CC calculation provides accurate inelastic data needed for astrophysical modeling.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Approximation of periodic Green's operator in real space using numerical integration and its use in fast Fourier transform-based micromechanical models
In this work, we propose an expression for the periodic first derivative of Green's function in real space. The proposed expression allows an alternative way of computing the periodic Green's operator based on periodically summing the free-space Green's operator in terms of an appropriate quadrature rule. We provide computational examples, which show the accuracy of the proposed approach, together with reduced spurious oscillations in the solution fields.
42 ENGINEERING↗
Large-d phase transitions in holographic mutual information
In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in G N in the holographic limit. Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations. Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in 3 spacetime dimensions. Inspired by recent explorations of general relativity at large- d , we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory. We interpret this result as illustrating the spatial decoupling of holographic correlations in the large- d limit, and provide intuition for this phenomenon using results from quantum information theory. We also compute the phase transition separation numerically for a range of bulk spacetime dimensions from 4 to 21, where analytic results are intractable but numerical results provide insight into the dimension-dependence of holographic correlations. For bulk dimensions above 5, our exact numerical results are well approximated analytically by working to next-to-leading order in the large- d expansion.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A parametric study of slow dynamic nonlinear elasticity with comparisons to models
Several phenomenological models that aspire to quantitative description of anomalous nonlinear mesoscopic elasticity are reviewed and compared with laboratory measurements. This class of nonlinearity, best known perhaps for slow dynamics and aging, is seen widely in imperfectly consolidated granular solids but is not well understood. Typical slow dynamic tests show that a modest conditioning oscillatory "pump" strain depresses material stiffness, which then recovers like the logarithm of time after conditioning ceases. Several phenomenological models based on physical arguments have been proposed that predict the material stiffness response to arbitrary pump strain histories during conditioning and recovery. Approximate closed form and numerical solutions to the models are presented that predict the quantitative influence of three key pump parameters: the pump's strain amplitude, the pump's strain rate, and the pump’s duration. Laboratory measurements on Berea sandstone, concrete and a confined single aluminum bead find that slow dynamic responses are linear in pump strain and independent of pump frequency. Measurements also show that, after pump-off, stiffness recovers over times far longer than the pump duration. These observations and others are compared to model predictions. One of the considered models, based on a picture of fast brittle damage and slow healing, successfully matches all these behaviors.
36 MATERIALS SCIENCE↗
Numerical assessment of the impact of the guiding-centre approximation on fast ion simulations in NSTX
Guiding-centre (GC) and full-orbit (FO) simulations of the beam-injected fast ion distribution and the corresponding neutron emissivity have been carried out for magnetohydrodynamics-quiescent National Spherical Torus eXperiment (NSTX) plasmas, using a combination of ASCOT5 and DRESS, to assess the suitability of the GC approximation for fast ions in NSTX. It was found that GC and FO simulations predicted substantially different steady-state distributions in both position and velocity space and different neutron emissivity profiles, leading to a 15% reduction in the predicted global neutron rate for FO relative to GC. These changes accompany a higher magnetic moment in FO, and correspond to a change in particle orbits from co-passing to trapped and stagnation orbits. ASCOT5 was also benchmarked against TRANSP/NUBEAM with input loaded entirely from TRANSP/NUBEAM output files, with agreement found between the GC simulations when finite Larmor radius (FLR) corrections were omitted. ASCOT5 FO and TRANSP/NUBEAM with FLR produced fast ion distributions which differed in localised regions, but predicted global neutron rates which agree within 3%.
ASCOT↗
Analytical WKB theory for high-harmonic generation and its application to massive Dirac electrons
Here we propose an analytical approach to high-harmonic generation (HHG) for nonperturbative low-frequency and high-intensity fields based on the (Jeffreys-)Wentzel-Kramers-Brillouin (WKB) approximation. By properly taking into account Stokes phenomena of WKB solutions, we obtain wave functions that systematically include the repetitive dynamics of production and acceleration of electron-hole pairs and quantum interference due to phase accumulation between different pair production times (Stückelberg phase). Using the obtained wave functions without relying on any phenomenological assumptions, we explicitly compute electric current (including intra- and interband contributions) as the source of HHG for a massive Dirac system in (1+1) dimensions under an ac electric field. We demonstrate that the WKB approximation agrees well with numerical results obtained by solving the time-dependent Schrödinger equation and point out that the quantum interference is important in HHG. We also predict in the deep nonperturbative regime that (1) harmonic intensities oscillate with respect to electric-field amplitude E 0 and frequency Ω with a period determined by the Stückelberg phase, (2) the cutoff order of HHG is determined by 2eE 0 ℏΩ 2 , with e being the electron charge, and that (3) noninteger harmonics, controlled by the Stückelberg phase, appear as a transient effect. Our WKB theory is particularly suited for a parameter regime, where the Keldysh parameter γ = (Δ/2)Ω/eE 0 ,with Δ being the gap size, is small. This parameter regime corresponds to intense lasers in the terahertz regime for realistic massive Dirac materials. Our analysis implies that the so-called HHG plateau can be observed at the terahertz frequency within the current technology.
36 MATERIALS SCIENCE↗
One-dimensional reflection in the quantum mechanical bootstrap
We describe the application of the quantum mechanical bootstrap to the solution of one-dimensional scattering problems. By fixing a boundary and modulating the Robin parameter of the boundary conditions we are able to extract the reflection coefficient for various potentials and compare to physical expectations. This includes an application of semidefinite programming to solving a half line Schrodinger problem with arbitrary Robin boundary conditions. Finally, the WKB approximation is used to numerically determine the scattering behavior of the exponential potential of Liouville theory. Published by the American Physical Society 2024
Astronomy & Astrophysics↗
Dielectric screening at TMD:hBN interfaces: Monolayer-to-bulk transition, local-field effect, and spatial dependence
The dielectric effects of a substrate have been shown to be important for modulating the electronic properties of an adsorbate, especially in van der Waals heterostructures. Here, using the first-principles dielectric embedding GW approach within the framework of many-body perturbation theory, we perform a case study on the dielectric screening effects of hexagonal boron nitride (hBN) on various transition-metal dichalcogenides (TMDs). We consider three systems, monolayer MoS 2 , bilayer MoS 2 , and a mixed WS 2 /MoS 2 bilayer adsorbed on hBN, and examine three aspects of the substrate dielectric screening: (i) the thickness dependence and the monolayer-to-bulk transition, for which we consider the effects of one-, two-, three-, and four-layer hBN; (ii) the local-field effect, for which we numerically assess a common approximation of neglecting the in-plane local-field components of the substrate polarizability; and (iii) the spatial dependence, for which we consider the mixed WS 2 /MoS 2 bilayer adsorbed on hBN with either side facing the substrate. Finally, our results provide quantitative insight into how the substrate screening effects can be leveraged for band structure engineering.
36 MATERIALS SCIENCE↗
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↗
Direct Nonlinear Approximation for Security Region Boundary of Integrated Energy Systems: A Polynomial Chaos Expansion Solution
The strong interdependence of electricity, gas, and heating systems can facilitate fault propagation within integrated energy systems (IESs), posing significant challenges to secure operation. This paper proposes a polynomial chaos expansion (PCE)-based approximation method to accurately characterize the IES security region boundary (IES–SRB). By integrating the Karush-Kuhn-Tucker conditions with PCE theory, the IES-SRB approximation problem is reformulated as a set of nonlinear equations concerning the approximation coefficients. Using the Galerkin projection method, these equations are further transformed into a system of projection equations that govern the polynomial approximation coefficients in the IES-SRB approximation. To reduce computational complexity while maintaining high approximation accuracy, a piecewise polynomial approximation method is proposed. Numerical studies on the E39-G20-H6 and E118-G96-H52 IES test systems demonstrate that the proposed method can accurately and effectively construct IES security regions.
Wu, Chenghao [Northeast Electric Power University]↗
Subcritical Multiplication with a Fixed Source
In a subcritical, multiplying medium, the system multiplication describes the expected total number of neutrons created by a single source neutron. Subcriticality plays a large role in criticality safety and thus it is vital for the subcritical multiplication factor be accurate, especially as a system approaches criticality. This work examines the accuracy of calculating the system multiplication using the MCNP6.2 ® k-eigenvalue power iteration (KCODE) method when a fixed-point source is present in a multiplying medium, for near critical systems. This work compares the standard approach for calculating system multiplication, using the fixed-source calculational approach, to a new, single k-eigenvalue power iteration approach that incorporates a fixed-source component and a fission-source component into a single calculation. For the remainder of this paper, some theoretical background and numerical results for an approximate k eigenvalue approach, an accurate fixed-source approach and a new and more accurate k-eigenvalue approach to computing system multiplication are provided.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Minimally Intrusive Data-Driven Approximation of Schur Complement-based Coupling Operators for Heterogeneous Numerical Methods
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de Castro, Amy Grace [Sandia National Laboratories↗