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DOE OSTI2022

Fourth Generation MPDV and MBR at DARHT

A new experimental setup for diagnosing hydrotest performance was designed, built, and implemented at DARHT. The setup consists of 128 points of fourth generation (Gen4) multiplexed photonic Doppler velocimetry (MPDV) and 128 separate points of modulation based ranging (MBR) to serve as a direct complement to the MPDV. The diagnostics were designed to overcome limitations in the third generation of the MPDV diagnostic that limited laser launch power to ~10 mW per point. As the main failure mechanism identified in the third generation MPDV system arose from stimulated Brillouin scattering, a nonlinear optical phenomenon inherent in standard single mode fiber, the fourth generation MPDV system reduced the number of time-multiplexed channels by a factor of two. This has allowed laser launch power to be increased to as much as 200 mW per channel which is a 20 times increase in the signal to noise ratio (SNR) as compared with the third generation system. This document will first discuss the previous limitations and describe the design of the system. This will be followed by the results of a simple flyer plate experiment used to demonstrate the improved SNR as well as calibrate the phase errors in the system that MBR is sensitive to.

42 ENGINEERING↗

DOE OSTI2020

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

SU-G-TeP3-01: A New Approach for Calculating Variable Relative Biological Effectiveness in IMPT Optimization

Purpose: To investigate the impact of a new approach for calculating relative biological effectiveness (RBE) in intensity-modulated proton therapy (IMPT) optimization on RBE-weighted dose distributions. This approach includes the nonlinear RBE for the high linear energy transfer (LET) region, which was revealed by recent experiments at our institution. In addition, this approach utilizes RBE data as a function of LET without using dose-averaged LET in calculating RBE values. Methods: We used a two-piece function for calculating RBE from LET. Within the Bragg peak, RBE is linearly correlated to LET. Beyond the Bragg peak, we use a nonlinear (quadratic) RBE function of LET based on our experimental. The IMPT optimization was devised to incorporate variable RBE by maximizing biological effect (based on the Linear Quadratic model) in tumor and minimizing biological effect in normal tissues. Three glioblastoma patients were retrospectively selected from our institution in this study. For each patient, three optimized IMPT plans were created based on three RBE resolutions, i.e., fixed RBE of 1.1 (RBE-1.1), variable RBE based on linear RBE and LET relationship (RBE-L), and variable RBE based on linear and quadratic relationship (RBE-LQ). The RBE weighted dose distributions of each optimized plan were evaluated in terms of different RBE values, i.e., RBE-1.1, RBE-L and RBE-LQ. Results: The RBE weighted doses recalculated from RBE-1.1 based optimized plans demonstrated an increasing pattern from using RBE-1.1, RBE-L to RBE-LQ consistently for all three patients. The variable RBE (RBE-L and RBE-LQ) weighted dose distributions recalculated from RBE-L and RBE-LQ based optimization were more homogenous within the targets and better spared in the critical structures than the ones recalculated from RBE-1.1 based optimization. Conclusion: We implemented a new approach for RBE calculation and optimization and demonstrated potential benefits of improving tumor coverage and normal sparing in IMPT planning.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

Four-dimensional dynamics of multirotational transition stimulated rotational Raman scattering in air

Stimulated rotational Raman scattering in air is a powerful parasitic process that degrades high intensity laser beams and pulses propagated over significant distances. Conversely, it is used beneficially in the context of Raman lasers. Through this inelastic scattering process, laser photons are converted to higher (anti-Stokes) or lower (Stokes) energies, according to rotational mode transitions in nitrogen and oxygen diatomic molecules. The full wave-mixing problem involves numerous frequencies, and it is consistently assumed that only one rotational mode contributes to the conversion process. We instead present a dynamic 4D multirotational model that is implemented in a parallelized manner within the Virtual Beamline++ optical modeling package allowing high-resolution 4D studies. We highlight the effect that spontaneous emission plays in large and small beam-width setups, even in the highly saturating regime. The weaker transition modes play a large role in the persistent dynamics and can lead to complex spatiotemporal coupling through nonlinear competition of the modes. We highlight how and why these weaker modes persist, how the size and shape of speckle patterns depends highly on the initial beam profile, and how weaker modes can transiently become stronger as a result of such competition.

47 OTHER INSTRUMENTATION↗

DOE OSTI2016

Formulation And Implementation of A 1.75D Streamer Model

Streamers are a type of ionization wave occurring during the early time phase of a gas discharge. They are typically launched when the evolving space charge of an electron avalanche reaches a certain critical level, beyond which the field of the space charge itself is sufficient to drive further evolution of the ionization process. One of the most common ways to model streamers is known as a 1.5D model where the field of a uniformly charged set of discs of chosen radius is evaluated along the cylinder axis. This field drives a one-dimensional kinetic ionization process, which results in the nonlinear evolution of the streamer. This model is efficient, but has the drawback of fixing the radius and requiring it as an input parameter. Previously, we tried to extend the 1.5D model to include evolution of its radius by developing a two-step process of axial and radial expansion but we encountered stability issues with the model that we thought could have been due to decoupling the two steps. In this report we introduce a new formulation of a streamer model that includes radial expansion. The goal is to take radial moments of the starting axisymmetric fluid equations and thereby include the radial evolution of the streamer naturally and self-consistently from the beginning. We first develop the fluid model moments without electron attachment. We review the calculation of the electric fields required for the model and investigate approximations to improve computational efficiency. We discuss the code implementation of the model and finally, we add attachment to allow the treatment of electronegative gases.

42 ENGINEERING↗

DOE OSTI2014

Elastically Cooperative Activated Hopping Theory of Relaxation in Viscous Liquids. I. General Formulation and Application to Hard Sphere Fluids.

We generalize the force-level nonlinear Langevin equation theory of single particle hopping to includecollective effects associated with long range elastic distortion of the liquid. The activated alpharelaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collectivebarriers. There are no divergences at volume fractions below jamming or temperatures abovezero Kelvin. The ideas are first developed and implemented analytically and numerically in the contextof hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage processis dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collectivebarrier is more strongly dependent on volume fraction, dominates the highly viscous regime,and is well described by a nonsingular law below jamming. The increase of the collective barrieris determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transientlocalization length, and a growing microscopic jump length. Alpha relaxation time calculations arein good agreement with recent experiments and simulations on dense fluids and suspensions of hardspheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. Thepresent work provides a foundation for constructing a quasi-universal, fit-parameter-free theory forrelaxation in thermal molecular liquids over 14 orders of magnitude in time.

Mirigian, Stephen↗

DOE OSTI2014

Applying Nonlinear Diffusion Acceleration to Fixed-Source Problems with Anisotropic Scattering - Paper 15

Work over the last several years has demonstrated the impressive performance gains that can be attained by using Moment-Based Acceleration (MBA), or High-Order/Low-Order (HOLO), methods in a variety of transport applications. In the field of neutronics, Nonlinear Diffusion Acceleration (NDA) has been used to accelerate the solution to the fixed-source problem and the k-eigenvalue problem. These methods efficiently move a major portion of the computational work out of the full phase-space (high-order (HO)) domain into a reduced phase-space (low-order (LO)) setting. In previous implementations, NDA has only been applied to isotropic scattering problems. In this paper, we will extend this methodology to anisotropic scattering. This initial work on anisotropic scattering will focus on the 1-D multi-group neutron transport equation. This summary focuses on a fixed-source problem, but the extension to criticality problems is straight-forward via NDA-NCA. Within this paper, we have described a method for extending Nonlinear Diffusion Acceleration to solve problems with anisotropic scattering. We demonstrated that a consistent low-order system, resembling the low-order system from, could be constructed. We demonstrated that the NDA method performed exceptionally in the presence of anisotropic scattering. NDA reduced the number of iterations required to meet the convergence tolerance by a factor of 500 over source iteration for a one fixed-source problem and by 3.5-50 x for the Henyey-Greenstein problems. This method is equally well-suited for eigenvalue problems. The NDA method allows us to transition the eigenvalue iteration to the low-order domain.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2017

Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. Particularly, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. Our paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Improving signal strength in serial crystallography with DIALS geometry refinement

The DIALS diffraction-modeling software package has been applied to serial crystallography data. Diffraction modeling is an exercise in determining the experimental parameters, such as incident beam wavelength, crystal unit cell and orientation, and detector geometry, that are most consistent with the observed positions of Bragg spots. These parameters can be refined by nonlinear least-squares fitting. In previous work, it has been challenging to refine both the positions of the sensors (metrology) on multipanel imaging detectors such as the CSPAD and the orientations of all of the crystals studied. Since the optimal models for metrology and crystal orientation are interdependent, alternate cycles of panel refinement and crystal refinement have been required. To simplify the process, a sparse linear algebra technique for solving the normal equations was implemented, allowing the detector panels to be refined simultaneously against the diffraction from thousands of crystals with excellent computational performance. Separately, it is shown how to refine the metrology of a second CSPAD detector, positioned at a distance of 2.5 m from the crystal, used for recording low-angle reflections. With the ability to jointly refine the detector position against the ensemble of all crystals used for structure determination, it is shown that ensemble refinement greatly reduces the apparent nonisomorphism that is often observed in the unit-cell distributions from still-shot serial crystallography. In addition, it is shown that batching the images by timestamp and re-refining the detector position can realistically model small, time-dependent variations in detector position relative to the sample, and thereby improve the integrated structure-factor intensity signal and heavy-atom anomalous peak heights.

36 MATERIALS SCIENCE↗

DOE OSTI2020

GFiRe—Gauge Field integrator for Reheating

We present a new numerical algorithm and code, GFiRe, for solving the nonlinear evolution of Abelian gauge fields coupled to complex scalar fields in homogeneous and isotropic spacetimes. We adopt a hybrid approach to solving the system: the spatial derivatives are discretized using standard Lattice Gauge Field Theory techniques, whereas the time evolution of the fields and scale factor is implemented with explicit, composite, symplectic integrators. An important property of our compound algorithm is that the discretized Gauss constraint is respected exactly, regardless of the order of the symplectic integrator. This remains true even when the background expansion is computed “self-consistently”; that is, when the expansion history is computed using spatial averaged components of the energy momentum tensor in the simulation volume. Hence, our code can also be used in cases where the fields dominate the energy density of the universe, for example, during reheating after inflation. We test the algorithm in scenarios of reheating where the inflaton is a complex scalar field with a potential ∝(2|Φ| 2 - v 2 ) 2 and is coupled to an Abelian gauge field. Tracing the evolution of the system through complex dynamics (including resonant excitation of fields, backreaction, formation of solitons, and changes in the equation of state) in a self-consistently expanding universe, we find the energy conservation violation (<10 -4 ) to be very stable and the Gauss constraint violation (<10 -6 ) to be dominated by differencing noise.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Impedance‐matching model‐in‐the‐loop simulation

Abstract Impedance matching is a novel approach to executing model‐in‐the‐loop (MIL) simulations. The concept, key features, and sample applications of this approach have been described in a series of publications. This paper advances theory and implementation for impedance‐matching MIL by: (1) developing a feedback linearization technique for implementing MIL for nonlinear virtual systems, (2) systematically characterizing MIL performance‐stability tradeoffs using three design‐oriented criteria—performance: defined as closeness of the controlled‐actuator impedance to the virtual‐boundary impedance;control effort: low controller response at high frequencies to reduce sensitivity to measurement noise and uncertainties in the actuator model; andstability: pursued using passivity of the controlled actuator system, and (3) assessing, through experimentation, the robustness of two ways to estimate feedback reaction force from the test article. These fundamental advancements to MIL are described using a one‐dimensional configuration consisting of a fluid‐filled cylindrical vessel as the physical test article and a uniaxial hydraulic shake table controlled to imitate different seismic isolation systems at the base of the vessel.

Engineering↗

DOE OSTI2019

Best Practices for Wake Model and Optimization Algorithm Selection in Wind Farm Layout Optimization

This paper presents the results of two case studies regarding the wind farm layout optimization problem. We asked a general audience to take part in the studies that we designed, and nine individuals participated. Case study 1 considered variations in optimization strategies for a given simple Gaussian wake model. Participants were provided with a wake model that outputs annual energy production (AEP) for an input set of wind turbine locations. Participants used an optimization method of their choosing to find an optimal wind farm layout. Case study 2 looked at trade-offs in performance resulting from variation in both physics model and optimization strategy. For case study 2, participants calculated AEP using a wake model of their choice while also implementing their chosen optimization method. Participants then used their wake model to calculate the AEP all other participant submitted turbine configurations produce for cross-comparison results. for optimized turbine locations were then cross-compared by recalculating the AEP using every other participant's wake model. Results for case study 1 show that the best optimal wind farm layouts in this study were achieved by participants who used gradient-based optimization methods. A front-runner emerged with the Sparse Nonlinear OPTimizer plus Wake Expansion Continuation (SNOPTplusWEC) optimization method, which consistently discovered a higher AEP for each scenario. Results for case study 2 show that for small wind farms with few turbines, turbine placement on the wind farm boundary is superior. Conclusions for case study 2 were drawn from participant cross-comparison of results.

17 WIND ENERGY↗

DOE OSTI2019

Best Practices for Wake Model and Optimization Algorithm Selection in Wind Farm Layout Optimization: Preprint

17 WIND ENERGY↗

DOE OSTI2012

Development of a fully-consistent reduced order model to study instabilities in boiling water reactors

A simple nonlinear Reduced Order Model to study global, regional and local instabilities in Boiling Water Reactors is described. The ROM consists of three submodels: neutron-kinetic, thermal-hydraulic and heat-transfer models. The neutron-kinetic model allows representing the time evolution of the three first neutron kinetic modes: the fundamental, the first and the second azimuthal modes. The thermal-hydraulic model describes four heated channels in order to correctly simulate out-of-phase behavior. The coupling between the different submodels is performed via both void and Doppler feedback mechanisms. After proper spatial homogenization, the governing equations are discretized in the time-domain. Several modifications, compared to other existing ROMs, have been implemented, and are reported in this paper. One novelty of the ROM is the inclusion of both azimuthal modes, which allows to study combined instabilities (in-phase and out-of-phase), as well as to investigate the corresponding interference effects between them. The second modification concerns the precise estimation of so-called reactivity coefficients or C{sub mn}{sup *V,D} - coefficients by using direct cross-section data from SIMULATE-3 combined with the CORE SIM core simulator in order to calculate Eigenmodes. Furthermore, a non-uniform two-step axial power profile is introduced to simulate the separate heat production in the single and two-phase regions, respectively. An iterative procedure was developed to calculate the solution to the coupled neutron-kinetic/thermal-hydraulic static problem prior to solving the time-dependent problem. Besides, the possibility of taking into account the effect of local instabilities is demonstrated in a simplified manner. The present ROM is applied to the investigation of an actual instability that occurred at the Swedish Forsmark-1 BWR in 1996/1997. The results generated by the ROM are compared with real power plant measurements performed during stability tests and show a good qualitative agreement. The present study provides some insight in a deeper understanding of the physical principles which drive both core-wide and local instabilities. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

A DEEP SEARCH FOR ADDITIONAL SATELLITES AROUND THE DWARF PLANET HAUMEA

Haumea is a dwarf planet with two known satellites, an unusually high spin rate, and a large collisional family, making it one of the most interesting objects in the outer solar system. A fully self-consistent formation scenario responsible for the satellite and family formation is still elusive, but some processes predict the initial formation of many small moons, similar to the small moons recently discovered around Pluto. Deep searches for regular satellites around Kuiper belt objects are difficult due to observational limitations, but Haumea is one of the few for which sufficient data exist. We analyze Hubble Space Telescope (HST) observations, focusing on a 10-consecutive-orbit sequence obtained in 2010 July, to search for new very small satellites. To maximize the search depth, we implement and validate a nonlinear shift-and-stack method. No additional satellites of Haumea are found, but by implanting and recovering artificial sources, we characterize our sensitivity. At distances between ∼10,000 and ∼350,000 km from Haumea, satellites with radii as small as ∼10 km are ruled out, assuming an albedo (p≃0.7) similar to Haumea. We also rule out satellites larger than ≳40 km in most of the Hill sphere using other HST data. This search method rules out objects similar in size to the small moons of Pluto. By developing clear criteria for determining the number of nonlinear rates to use, we find that far fewer shift rates are required (∼35) than might be expected. The nonlinear shift-and-stack method to discover satellites (and other moving transients) is tractable, particularly in the regime where nonlinear motion begins to manifest itself.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solved efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Validity of the Born approximation for beyond Gaussian weak lensing observables

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O(Φ 3 ) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O(Φ 4 ) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5σ. Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

97 MATHEMATICS AND COMPUTING↗