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At least 217 records · Page 12

Verification of Floating Offshore Wind Linearization Functionality in OpenFAST

The wind engineering community relies on multiphysics engineering software to run nonlinear time-domain simulations, e.g., for design standards-based loads analysis. Although most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear system equations is often advantageous to understand the system properties and exploit well-established methods and tools for analyzing linear systems. Previous work in this area has focused on the development of the new linearization functionality of the open-source engineering tool OpenFAST for floating offshore wind turbines, as well as the concepts and mathematical background needed to understand and apply it correctly. This paper focuses on the verification of this new linearization functionality, which is carried out by comparing results to previous stable versions of FAST. A nonlinear time-domain simulation for a floating offshore platform is also compared to the time-domain response of the linearized state-space model. The linearized results show good alignment between OpenFAST and previous versions of FAST, as well as with the time-domain simulations, thereby showing the accuracy of the new features in OpenFAST.

17 WIND ENERGY↗

SU-E-T-136: Assessment of Seasonal Linear Accelerator Output Variations and Associated Impacts

Purpose: Application of process control theory in quality assurance programs promises to allow earlier identification of problems and potentially better quality in delivery than traditional paradigms based primarily on tolerances and action levels. The purpose of this project was to characterize underlying seasonal variations in linear accelerator output that can be used to improve performance or trigger preemptive maintenance. Methods: Review of runtime plots of daily (6 MV) output data acquired using in house ion chamber based devices over three years and for fifteen linear accelerators of varying make and model were evaluated. Shifts in output due to known interventions with the machines were subtracted from the data to model an uncorrected scenario for each linear accelerator. Observable linear trends were also removed from the data prior to evaluation of periodic variations. Results: Runtime plots of output revealed sinusoidal, seasonal variations that were consistent across all units, irrespective of manufacturer, model or age of machine. The average amplitude of the variation was on the order of 1%. Peak and minimum variations were found to correspond to early April and September, respectively. Approximately 48% of output adjustments made over the period examined were potentially avoidable if baseline levels had corresponded to the mean output, rather than to points near a peak or valley. Linear trends were observed for three of the fifteen units, with annual increases in output ranging from 2–3%. Conclusion: Characterization of cyclical seasonal trends allows for better separation of potentially innate accelerator behaviour from other behaviours (e.g. linear trends) that may be better described as true out of control states (i.e. non-stochastic deviations from otherwise expected behavior) and could indicate service requirements. Results also pointed to an optimal setpoint for accelerators such that output of machines is maintained within set tolerances and interventions are required less frequently.

07 ISOTOPE AND RADIATION SOURCES↗

TU-H-BRA-06: Characterization of a Linear Accelerator Operating in a Compact MRIGuided Radiation Therapy System

Purpose: To describe the performance of a linear accelerator operating in a compact MRI-guided radiation therapy system. Methods: A commercial linear accelerator was placed in an MRI unit that is employed in a commercial MR-based image guided radiation therapy (IGRT) system. The linear accelerator components were placed within magnetic field-reducing hardware that provided magnetic fields of less than 40 G for the magnetron, gun driver, and port circulator, with 1 G for the linear accelerator. The system did not employ a flattening filter. The test linear accelerator was an industrial 4 MV model that was employed to test the ability to run an accelerator in the MR environment. An MR-compatible diode detector array was used to measure the beam profiles with the accelerator outside and inside the MR field and with the gradient coils on and off to examine if there was any effect on the delivered dose distribution. The beam profiles and time characteristics of the beam were measured. Results: The beam profiles exhibited characteristic unflattened Bremsstrahlung features with less than ±1.5% differences in the profile magnitude when the system was outside and inside the magnet and less than 1% differences with the gradient coils on and off. The central axis dose rate fluctuated by less than 1% over a 30 second period when outside and inside the MRI. Conclusion: A linaccompatible MR design has been shown to be effective in not perturbing the operation of a commercial linear accelerator. While the accelerator used in the tests was 4MV, there is nothing fundamentally different with the operation of a 6MV unit, implying that the design will enable operation of the proposed clinical unit. Research funding provided by ViewRay, Inc.

60 APPLIED LIFE SCIENCES↗

Radiocarbon Suggests the Hemiparasitic Annual Melampyrum Lineare Desr. May Acquire Carbon from Stressed Hosts

Abstract Hemiparasitic plants obtain water and solutes from their hosts, but much remains to be learned about these transfers. We used a forest girdling experiment to investigate how leaf gas exchange, carbon and nitrogen cycling in the root hemiparasite Melampyrum lineare Desr. responded to disturbance and changes in physiology of potential host trees. By preventing belowground C allocation by 35% of the canopy, girdling decreased the starch and soluble sugar contents of bulk forest floor fine roots. Photosynthetic rates of M. lineare were statistically significantly lower in the girdled plot, but their hypothesized drivers (foliar N, stomatal conductance and transpiration) had no statistically significant differences between girdled and non-girdled plots. However, M. lineare in the girdled plot had higher foliar C concentrations and Δ 14 C than in the control plot, suggesting possible photosynthetic down-regulation in the girdled plot due to influx of older (e.g., host-derived) C into the leaves of M. lineare . Within the girdled plot (but not the control plot), M. lineare foliar C concentrations were positively correlated with foliar Δ 14 C and δ 15 N, suggesting that M. lineare may respond to changes in both C and N biogeochemistry during the decline of dominant canopy species.

Geochemistry & Geophysics↗

Gelation and Re-entrance in Mixtures of Soft Colloids and Linear Polymers of Equal Size

Liquid mixtures composed of colloidal particles and much smaller non-adsorbing linear homopolymers can undergo a gelation transition due to polymer-mediated depletion forces. We now show that the addition of linear polymers to suspensions of soft colloids having the same hydrodynamic size yields a liquid-togel-to-re-entrant liquid transition. In particular, the dynamic state diagram of 1,4-polybutadiene star-linear polymer mixtures was determined with the help of linear viscoelastic and small-angle Xray scattering experiments. While keeping the star polymers below their nominal overlap concentration, a gel was formed upon increasing the linear polymer content. Further addition of linear chains yielded a re-entrant liquid. This unexpected behavior was rationalized by the interplay of three possible phenomena: (i) depletion interactions, driven by the size disparity between the stars and the polymer length scale which is the mesh size of its entanglement network; (ii) colloidal deswelling due to the increased osmotic pressure exerted onto the stars; and (iii) a concomitant progressive suppression of the depletion efficiency on increasing the polymer concentration due to reduced mesh size, hence a smaller range of attraction. Our results unveil an exciting new way to tailor the flow of soft colloids and highlight a largely unexplored path to engineer soft colloidal mixtures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The effect of changes in sea surface temperature on linear growth of Porites coral in Ambon Bay

Coral is one of the most important organisms in the coral reef ecosystem. There are several factors affecting coral growth, one of them is changes in sea surface temperature (SST). The purpose of this research is to understand the influence of SST variability on the annual linear growth of Porites coral taken from Ambon Bay. The annual coral linear growth was calculated and compared to the annual SST from the Extended Reconstructed Sea Surface Temperature version 3b (ERSST v3b) model. Coral growth was calculated by using Coral X-radiograph Density System (CoralXDS) software. Coral sample X-radiographs were used as input data. Chronology was developed by calculating the coral’s annual growth bands. A pair of high and low density banding patterns observed in the coral’s X-radiograph represent one year of coral growth. The results of this study shows that Porites coral extents from 2001-2009 and had an average growth rate of 1.46 cm/year. Statistical analysis shows that the annual coral linear growth declined by 0.015 cm/year while the annual SST declined by 0.013°C/year. SST and the annual linear growth of Porites coral in the Ambon Bay is insignificantly correlated with r=0.304 (n=9, p>0.05). This indicates that annual SST variability does not significantly influence the linear growth of Porites coral from Ambon Bay. It is suggested that sedimentation load, salinity, pH or other environmental factors may affect annual linear coral growth.

54 ENVIRONMENTAL SCIENCES↗

The origin of linear scaling Fock matrix calculation with density prescreening

A theorem was proven, which reads that the number of nonzero two-electron integrals scales linearly with respect to the number of basis functions for large molecular systems. This permits to show that linear scaling property of the Fock matrix calculation with using density prescreening arises due to linear scaling properties of the number of nonzero two-electron integrals and the number of leading matrix elements of density matrix. This property is reinforced by employing the density prescreening technique. The use of the density difference prescreening further improves the linear scaling property of the Fock matrix calculation method. As a result, the linear scaling regime of the Fock matrix calculation can begin from the number of basis functions of 2000–3000 in dependence on the basis function type in molecular calculations. It was also shown that the conventional algorithm of Fock matrix calculation from stored nonzero two-electron integrals with density prescreening possesses linear scaling property.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Non-Condon equilibrium Fermi’s golden rule electronic transition rate constants via the linearized semiclassical method

In this paper, we test the accuracy of the linearized semiclassical (LSC) expression for the equilibrium Fermi’s golden rule rate constant for electronic transitions in the presence of non-Condon effects. We do so by performing a comparison with the exact quantum-mechanical result for a model where the donor and acceptor potential energy surfaces are parabolic and identical except for shifts in the equilibrium energy and geometry, and the coupling between them is linear in the nuclear coordinates. Since non-Condon effects may or may not give rise to conical intersections, both possibilities are examined by considering: (1) A modified Garg-Onuchic-Ambegaokar model for charge transfer in the condensed phase, where the donor-acceptor coupling is linear in the primary mode coordinate, and for which non-Condon effects do not give rise to a conical intersection; (2) the linear vibronic coupling model for electronic transitions in gas phase molecules, where non-Condon effects give rise to conical intersections. We also present a comprehensive comparison between the linearized semiclassical expression and a progression of more approximate expressions. The comparison is performed over a wide range of frictions and temperatures for model (1) and over a wide range of temperatures for model (2). The linearized semiclassical method is found to reproduce the exact quantum-mechanical result remarkably well for both models over the entire range of parameters under consideration. In contrast, more approximate expressions are observed to deviate considerably from the exact result in some regions of parameter space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Non-Condon nonequilibrium Fermi’s golden rule rates from the linearized semiclassical method

The nonequilibrium Fermi’s golden rule describes the transition between a photoexcited bright donor electronic state and a dark acceptor electronic state, when the nuclear degrees of freedom start out in a nonequilibrium state. In a previous paper [X. Sun and E. Geva, J. Chem. Theory Comput. 12, 2926 (2016)], we proposed a new expression for the nonequilibrium Fermi’s golden rule within the framework of the linearized semiclassical approximation and based on the Condon approximation, according to which the electronic coupling between donor and acceptor is assumed constant. In this paper we propose a more general expression, which is applicable to the case of non-Condon electronic coupling. We test the accuracy of the new non-Condon nonequilibrium Fermi’s golden rule linearized semiclassical expression on a model where the donor and acceptor potential energy surfaces are parabolic and identical except for shifts in the equilibrium energy and geometry, and the coupling between them is linear in the nuclear coordinates. Since non-Condon effects may or may not give rise to conical intersections, both possibilities are examined by considering the following: (1) A modified Garg-Onuchic-Ambegaokar model for charge transfer in the condensed phase, where the donor-acceptor coupling is linear in the primary-mode coordinate, and for which non-Condon effects do not give rise to a conical intersection; (2) the linear vibronic coupling model for electronic transitions in gas phase molecules, where non-Condon effects give rise to conical intersections. We also present a comprehensive comparison between the linearized semiclassical expression and a progression of more approximate expressions, in both normal and inverted regions, and over a wide range of initial nonequilibrium states, temperatures, and frictions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The linearized LLGE is obtained by assuming a small deviation around the equilibrium state of the magnetic system. Inserting such expansion into LLGE and keeping only first order terms gives the linearized LLGE, which gives a frequency domain solution for the complex magnetization amplitudes under an external time-harmonic applied field of a given frequency. We solve the linear system with an iterative solver using generalized minimal residual method. We construct a preconditioner matrix to effectively solve the linear system. The validity, effectiveness, speed, and scalability of the linear solver are demonstrated via numerical examples.

36 MATERIALS SCIENCE↗

MULTI-SPACECRAFT OBSERVATIONS OF LINEAR MODES AND SIDEBAND WAVES IN ION-SCALE SOLAR WIND TURBULENCE

In the scenario of weak turbulence, energy is believed to be cascaded from smaller to larger wave numbers and frequencies due to weak wave-wave interactions. Based on its perturbative treatment one may regard plasma turbulence as a superposition of linear modes (or normal modes) and sideband waves (or nonlinear modes). In this study, we use magnetic field and plasma measurements of nine solar wind events obtained by the Cluster spacecraft and make extensive use of a high-resolution wave vector analysis method, the Multi-point Signal Resonator technique, to find frequencies and wave vectors of discrete modes on ion kinetic scales in the plasma rest frame. The primarily unstructured wave observations in the frequency-wave number diagram are classified into three distinct linear modes (proton Bernstein modes, helium-alpha Bernstein modes, and kinetic Alfvén waves) and the sideband waves by comparing with the dispersion relations derived theoretically from linear Vlasov theory using observational values of the plasma parameter beta and the propagation angle from the mean magnetic field. About 60% of the observed discrete modes can be explained by the linear modes, primarily as the proton Bernstein and the kinetic Alfvén waves, within the frequency uncertainties, while the rest of the population (about 40%) cannot be classified as linear modes due to the large deviation from dispersion relations. We conclude that both the linear modes and sideband wave components are needed to construct the wave picture of solar wind turbulence on ion-kinetic scales.

79 ASTRONOMY AND ASTROPHYSICS↗

Linear magnetoresistance with a universal energy scale in the strong-coupling superconductor Mo8Ga41 without quantum criticality

The recent discovery of a nonsaturating linear magnetoresistance in several correlated electron systems near a quantum critical point has revealed an interesting interplay between the linear magnetoresistance and the zero-field linear-in-temperature resistivity. These studies suggest a possible role of quantum criticality on the observed linear magnetoresistance. Here we report our discovery of a nonsaturating, linear magnetoresistance in Mo 8 Ga 41 , a nearly isotropic strong electron-phonon coupling superconductor with a linear-in-temperature resistivity from the transition temperature to ~ 55 K. The growth of the resistivity in field is comparable to that in temperature, provided that both quantities are measured in the energy unit. Overall, our data sets are remarkably similar to magnetoresistance data of the optimally doped La 2 - x Sr x CuO 4 , despite the clearly different crystal and electronic structures, and the apparent absence of quantum critical physics in Mo 8 Ga 41 . A new empirical scaling formula is developed, which is able to capture the key features of the low-temperature magnetoresistance data of Mo 8 Ga 41 , as well as the data of La 2 - x Sr x CuO 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

SU-E-T-475: An Accurate Linear Model of Tomotherapy MLC-Detector System for Patient Specific Delivery QA

Purpose: An accurate leaf fluence model can be used in applications such as patient specific delivery QA and in-vivo dosimetry for TomoTherapy systems. It is known that the total fluence is not a linear combination of individual leaf fluence due to leakage-transmission, tongue-and-groove, and source occlusion effect. Here we propose a method to model the nonlinear effects as linear terms thus making the MLC-detector system a linear system. Methods: A leaf pattern basis (LPB) consisting of no-leaf-open, single-leaf-open, double-leaf-open and triple-leaf-open patterns are chosen to represent linear and major nonlinear effects of leaf fluence as a linear system. An arbitrary leaf pattern can be expressed as (or decomposed to) a linear combination of the LPB either pulse by pulse or weighted by dwelling time. The exit detector responses to the LPB are obtained by processing returned detector signals resulting from the predefined leaf patterns for each jaw setting. Through forward transformation, detector signal can be predicted given a delivery plan. An equivalent leaf open time (LOT) sinogram containing output variation information can also be inversely calculated from the measured detector signals. Twelve patient plans were delivered in air. The equivalent LOT sinograms were compared with their planned sinograms. Results: The whole calibration process was done in 20 minutes. For two randomly generated leaf patterns, 98.5% of the active channels showed differences within 0.5% of the local maximum between the predicted and measured signals. Averaged over the twelve plans, 90% of LOT errors were within +/−10 ms. The LOT systematic error increases and shows an oscillating pattern when LOT is shorter than 50 ms. Conclusion: The LPB method models the MLC-detector response accurately, which improves patient specific delivery QA and in-vivo dosimetry for TomoTherapy systems. It is sensitive enough to detect systematic LOT errors as small as 10 ms.

60 APPLIED LIFE SCIENCES↗

Fast and Robust Linear Solvers based on Hierarchical Matrices (LDRD Final Report)

This report is the final report for the LDRD project "Fast and Robust Linear Solvers using Hierarchical Matrices". The project was a success. We developed two novel algorithms for solving sparse linear systems. We demonstrated their effectiveness on ill-conditioned linear systems from ice sheet simulations. We showed that in many cases, we can obtain near-linear scaling. We believe this approach has strong potential for difficult linear systems and should be considered for other Sandia and DOE applications. We also report on some related research activities in dense solvers and randomized linear algebra.

97 MATHEMATICS AND COMPUTING↗

Compare linear-system solver and preconditioner stacks with emphasis on GPU performance and propose phase-2 NGP solver development pathway

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind project are Nalu-Wind, which is an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, and OpenFAST, which is a whole-turbine simulation code. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and a momentum equation for the velocity. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. In this report we evaluated GPU-performance baselines for the linear solvers in the Trilinos and hypre solver stacks using two representative Nalu-Wind simulations: an atmospheric boundary layer precursor simulation on a structured mesh, and a fixed-wing simulation using unstructured overset meshes. Both strong-scaling and weak-scaling experiments were conducted on the OLCF supercomputer Summit and similar proxy clusters. We focused on the performance of multi-threaded Gauss-Seidel and two-stage Gauss-Seidel that are extensions of classical Gauss-Seidel; of one-reduce GMRES, a communication-reducing variant of the Krylov GMRES; and algebraic multigrid methods that incorporate the afore-mentioned methods. The team has established that AMG methods are capable of solving linear systems arising from the fixed-wing overset meshes on CPU, a critical intermediate result for ExaWind FY20 Q3 and Q4 milestones. For the fixed-wing strong-scaling study (model with 3M grid-points), the team identified that Nalu-Wind simulations with the new Trilinos and hypre solvers scale to modest GPU counts, maintaining above 70% efficiency up to 6 GPUs. However, there still remain significant bottlenecks to performance: matrix assembly (hypre), AMG setup (hypre and Trilinos) In the weak-scaling experiments (going from 0.4M to 211M gridpoints), it's shown that the solver apply phases are faster on GPUs, but that Nalu-Wind simulation times grow, primarily due to the multigrid-setup process. Finally, based on the report outcomes, we propose a linear solver path-forward for the remainder of the ExaWind project. Near term, the NREL team will continue their work on GPU-based linear-system assembly. They will also investigate how the use of alternatives to the NVIDIA UVM (unified virtual memory) paradigm affects performance. Longer term, the NREL team will evaluate algorithmic performance on other types of accelerators and merge their improvements back to the main hypre repository branch. Near term, the Trilinos team will address performance bottlenecks identified in this milestone, such as implementing a GPU-based segregated momentum solve and reusing matrix graphs across linear-system assembly phases. Longer term, the Trilinos team will do detailed analysis and optimization of multigrid setup.

17 WIND ENERGY↗

The impacts of convex piecewise linear cost formulations on AC optimal power flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. Furthermore, these results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, an important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Verification of a quasi-linear model for gyrokinetic turbulent transport

The verification and calibration of a new quasi-linear transport model with a large database of gyrokinetic turbulence simulations is presented in this paper. In a previous paper (Staebler et al 2020 Plasma Phys. Control. Fusion 63 015013), a model for the saturated spectrum of electric potential fluctuations was developed based on the properties of the non-linear 3D spectrum. In this paper, a modification to the overall multiplicative factor in this model is found to be necessary to improve the fit to scans of the temperature and density gradients. The error in the fit of the quasi-linear fluxes of electron and ion energy fluxes is significantly better than for previous saturation models. The spectral shift model for the impact of equilibrium E × B velocity shear (Staebler et al 2013 Phys. Rev. Lett. 110 055003) and the zonal flow mixing model for electron-scale turbulence (Staebler et al 2016 Phys. Plasmas 23 062518) are both revised to be compatible with this new model. Furthermore, the models for the loss of bounce averaging and electron collisions in the TGLF reduced linear equations (Staebler et al 2005 Phys. Plasmas 12 102508) are also changed to improve the linear eigenmodes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Flexible CUDA LU-based Solver for Small, Batched Linear Systems

This chapter presents the implementation of a batched CUDA solver based on LU factorization for small linear systems. This solver may be used in applications such as reactive flow transport models, which apply the Newton-Raphson technique to linearize and iteratively solve the sets of non linear equations that represent the reactions for ten of thousands to millions of physical locations. The implementation exploits somewhat counterintuitive GPGPU programming techniques: it assigns the solution of a matrix (representing a system) to a single CUDA thread, does not exploit shared memory and employs dynamic memory allocation on the GPUs. These techniques enable our implementation to simultaneously solve sets of systems with over 100 equations and to employ LU decomposition with complete pivoting, providing the higher numerical accuracy required by certain applications. Other currently available solutions for batched linear solvers are limited by size and only support partial pivoting, although they may result faster in certain conditions. We discuss the code of our implementation and present a comparison with the other implementations, discussing the various tradeoffs in terms of performance and flexibility. This work will enable developers that need batched linear solvers to choose whichever implementation is more appropriate to the features and the requirements of their applications, and even to implement dynamic switching approaches that can choose the best implementation depending on the input data.

bached linear solvers↗