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DOE OSTI2014

Interaction-induced backscattering in short quantum wires

We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here in this paper we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is reminiscent to the first passage problem of a Brownian particle and, regardless of the interaction strength, can be described by an inhomogeneous Fokker-Planck equation. From general solutions of the latter we calculate the hole backscattering rate for different wire lengths and discuss the resulting length dependence of interaction-induced correction to the conductance of a clean single channel quantum wire.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Real-Time Control of an Ensemble of Heterogeneous Resources

This paper focuses on the problem of controlling an ensemble of heterogeneous resources connected to an electrical grid at the same point of common coupling (PCC). The controller receives an aggregate power setpoint for the ensemble in real time and tracks this setpoint by issuing individual optimal setpoints to the resources. The resources can have continuous or discrete nature (e.g., heating systems consisting of a finite number of heaters that each can be either switched on or off) and/or can be highly uncertain (e.g., photovoltaic (PV) systems or residential loads). A naive approach would lead to a stochastic mixed-integer optimization problem to be solved at the controller at each time step, which might be infeasible in real time. Instead, we allow the controller to solve a continuous convex optimization problem and compensate for the errors at the resource level by using a variant of the well-known error diffusion algorithm. We give conditions guaranteeing that our algorithm tracks the power setpoint at the PCC on average while issuing optimal setpoints to individual resources. We illustrate the approach numerically by controlling a collection of batteries, PV systems, and discrete loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2017

Features of the structural states of KNbO{sub 3} single crystals before and after fast-neutron irradiation

Neutron irradiation is a unique tool for forming new structural states of ferroelectrics, which cannot be obtained by conventional methods. The inf luence of the irradiation by two doses of fast neutrons (F = 1 × 10{sup 17} and 3 × 10{sup 17} cm{sup –2}) on the structure and properties of KNbO{sub 3} single crystals has been considered for the first time. The developed method for taking into account the experimental correction to the diffuse scattering has been used to analyze the structural changes occurring in KNbO{sub 3} samples at T = 295 K and their correlations with the behavior of dielectric and nonlinear optical characteristics. The irradiation to the aforementioned doses retains the KNbO{sub 3} polar structure, shifting Ð¢{sub Ð}¡ to lower temperatures and significantly affecting only the thermal parameters and microstructure of single crystals. Neutron irradiation with small atomic displacements provides a structure similar to the high-temperature modification of an unirradiated KNbO{sub 3} crystal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Specificities of one-dimensional dissipative magnetohydrodynamics

One-dimensional dynamics of a plane slab of cold (β ≪ 1) isothermal plasma accelerated by a magnetic field is studied in terms of the MHD equations with a finite constant conductivity. The passage to the limit β → 0 is analyzed in detail. It is shown that, at β = 0, the character of the solution depends substantially on the boundary condition for the electric field at the inner plasma boundary. The relationship between the boundary condition for the pressure at β > 0 and the conditions for the electric field at β = 0 is found. The stability of the solution against one-dimensional longitudinal perturbations is analyzed. It is shown that, in the limit β → 0, the stationary solution is unstable if the time during which the acoustic wave propagates across the slab is longer than the time of magnetic field diffusion. The growth rate and threshold of instability are determined, and results of numerical simulation of its nonlinear stage are presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Density-Equalizing Maps for Simply Connected Open Surfaces

Here in this paper, we are concerned with the problem of creating flattening maps of simply connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing maps with any prescribed density distribution. By varying the initial density distribution, a large variety of flattening maps with different properties can be achieved. For instance, area-preserving parameterizations of simply connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Light Water Reactor Sustainability Program Modeling of Cu Precipitate Contributions to Reactor Pressure Vessel Steel Microstructure Evolution and Embrittlement

This report summarizes the lower-length-scale effort during FY 2017 in developing simulation capabilities for the mesoscale: models for microstructure evolution and plasticity in reactor pressure vessel steels. During operation, reactor pressure vessels undergo hardening and embrittlement caused by irradiation induced defect accumulation and irradiation enhanced solute precipitation. Both defect production and solute precipitation initiate on the atomic scale and manifest their eventual effects as degradation in the engineering scale properties. To predict the engineering scale property degradation, multiscale modeling and simulation capabilities are needed to better understand the microstructure evolution and to connect the microstructure feature evolution to the engineering scale material properties. In this report the development of coupling across different length scale models to understand the multi-physics property dedgration problem is discussed. The development of coupling a lattice kinetic Monte Carlo code to cluster dynamics to capture irradiation enhanced diffusion in the formation of defects is summarized. The implementation of a cluster dynamics model with Grizzly to predict Cu percipitate formation is discussed. A summary of the coupling of crystal plasticity and cluster dynamics to predict the effect on reactor pressure steel hardening is given.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

Cosmic-Ray Diffusion Coefficients throughout the Inner Heliosphere from a Global Solar Wind Simulation

We use a three-dimensional magnetohydrodynamic simulation of the solar wind to calculate cosmic-ray diffusion coefficients throughout the inner heliosphere (2 R{sub ⊙}−3 au). The simulation resolves large-scale solar wind flow, which is coupled to small-scale fluctuations through a turbulence model. Simulation results specify background solar wind fields and turbulence parameters, which are used to compute diffusion coefficients and study their behavior in the inner heliosphere. The parallel mean free path (mfp) is evaluated using quasi-linear theory, while the perpendicular mfp is determined from nonlinear guiding center theory with the random ballistic interpretation. Several runs examine varying turbulent energy and different solar source dipole tilts. We find that for most of the inner heliosphere, the radial mfp is dominated by diffusion parallel to the mean magnetic field; the parallel mfp remains at least an order of magnitude larger than the perpendicular mfp, except in the heliospheric current sheet, where the perpendicular mfp may be a few times larger than the parallel mfp. In the ecliptic region, the perpendicular mfp may influence the radial mfp at heliocentric distances larger than 1.5 au; our estimations of the parallel mfp in the ecliptic region at 1 au agree well with the Palmer “consensus” range of 0.08–0.3 au. Solar activity increases perpendicular diffusion and reduces parallel diffusion. The parallel mfp mostly varies with rigidity (P) as P{sup .33}, and the perpendicular mfp is weakly dependent on P. The mfps are weakly influenced by the choice of long-wavelength power spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

An Integrated Approach to Parameter Learning in Infinite-Dimensional Space

The availability of sophisticated modern physics codes has greatly extended the ability of domain scientists to understand the processes underlying their observations of complicated processes, but it has also introduced the curse of dimensionality via the many user-set parameters available to tune. Many of these parameters are naturally expressed as functional data, such as initial temperature distributions, equations of state, and controls. Thus, when attempting to find parameters that match observed data, being able to navigate parameter-space becomes highly non-trivial, especially considering that accurate simulations can be expensive both in terms of time and money. Existing solutions include batch-parallel simulations, high-dimensional, derivative-free optimization, and expert guessing, all of which make some contribution to solving the problem but do not completely resolve the issue. In this work, we explore the possibility of coupling together all three of the techniques just described by designing user-guided, batch-parallel optimization schemes. Our motivating example is a neutron diffusion partial differential equation where the time-varying multiplication factor serves as the unknown control parameter to be learned. We find that a simple, batch-parallelizable, random-walk scheme is able to make some progress on the problem but does not by itself produce satisfactory results. After reducing the dimensionality of the problem using functional principal component analysis (fPCA), we are able to track the progress of the solver in a visually simple way as well as viewing the associated principle components. This allows a human to make reasonable guesses about which points in the state space the random walker should try next. Thus, by combining the random walker's ability to find descent directions with the human's understanding of the underlying physics, it is possible to use expensive simulations more efficiently and more quickly arrive at the desired parameter set.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Accelerated coupled Monte Carlo-Thermal hydraulic calculations using a hybrid GTF-diffusion-based prediction block: first results

Accurate predictions of spatial power and temperature distributions require the coupling of a neutron transport solver with a thermal-hydraulic (TH) feedback. Nowadays, Monte Carlo (MC) codes are widely coupled to TH solvers, typically via a Picard iteration (PI) method, due to the higher fidelity that such frameworks can produce. To speed up a PI, a prediction step can produce an improved initial guess for a source distribution and feed it to the MC code. Recent work investigated a prediction step that uses generalized transfer functions (GTFs) to predict the macroscopic cross sections' variations following a perturbation in TH properties, such as coolant density. The previous method also relied on first order perturbation (FOP) theory to predict perturbed power profiles, rather than using an expensive MC iterate. The implemented FOP method relied on generating a fission matrix from which the forward and adjoint Eigenmodes were extracted and later used to for power calculations. The generation of the fission matrix can introduce a significant computational overhead, therefore undermining the performance of the proposed hybrid technique when applied to high-dimensional problems, e.g., full core calculations. This work attempts to improve the GTF-FOP prediction step by replacing the FOP solver with a nodal diffusion solver, thus eliminating the need to calculate a fission matrix. The GTF-diffusion step was tested for various moderator density perturbations. In each case, the predicted power distribution showed good agreement with the reference case. The latter is attributed to the generally good prediction of most spatially distributed macroscopic cross sections, except the transport cross section, which will become the focus of future work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

A multi-probe thermophoretic soot sampling system for high-pressure diffusion flames

Optical diagnostics and physical probing of the soot processes in high pressure combustion pose challenges that are not faced in atmospheric flames. One of the preferred methods of studying soot in atmospheric flames is in situ thermophoretic sampling followed by transmission electron microscopy imaging and analysis for soot sizing and morphology. The application of this method of sampling to high pressures has been held back by various operational and mechanical problems. In this work, we describe a rotating disk multi-probe thermophoretic soot sampling system, driven by a microstepping stepper motor, fitted into a high-pressure chamber capable of producing sooting laminar diffusion flames up to 100 atm. Innovative aspects of the sampling system design include an easy and precise control of the sampling time down to 2.6 ms, avoidance of the drawbacks of the pneumatic drivers used in conventional thermophoretic sampling systems, and the capability to collect ten consecutive samples in a single experimental run. Proof of principle experiments were performed using this system in a laminar diffusion flame of methane, and primary soot diameter distributions at various pressures up to 10 atm were determined. High-speed images of the flame during thermophoretic sampling were recorded to assess the influence of probe intrusion on the flow field of the flame.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Accelerated Coupled Monte Carlo-Thermal Hydraulic Calculations using a Hybrid GTF-Diffusion-based Prediction Block: First Results

Accurate predictions of spatial power and temperature distributions require the coupling of a neutron transport solver with a thermal-hydraulic (TH) feedback. Nowadays, Monte Carlo (MC) codes are widely coupled to TH solvers, typically via a Picard iteration (PI) method, due to the higher fidelity that such frameworks can produce. To speed up a PI, a prediction step can produce an improved initial guess for a source distribution and feed it to the MC code. Recent work [1, 2] investigated a prediction step that uses generalized transfer functions (GTFs) to predict the macroscopic cross sections’ variations following a perturbation in TH properties, such as coolant density. The previous method also relied on first order perturbation (FOP) theory to predict perturbed power profiles, rather than using an expensive MC iterate. The implemented FOP method relied on generating a fission matrix from which the forward and adjoint eigenmodes were extracted and later used to for power calculations. The generation of the fission matrix can introduce a significant computational overhead, therefore undermining the performance of the proposed hybrid technique when applied to high-dimensional problems, e.g., full core calculations. This work attempts to improve the GTF-FOP prediction step by replacing the FOP solver with a nodal diffusion solver, thus eliminating the need to calculate a fission matrix. The GTF-diffusion step was tested for various moderator density perturbations. In each case, the predicted power distribution showed good agreement with the reference case. The latter is attributed to the generally good prediction of most spatially distributed macroscopic cross sections, except the transport cross section, which will become the focus of future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Molecular Viscosity and Diffusivity Effects in Transitional and Shock-Driven Mixing Flows

Here, this paper investigates the importance of molecular viscosity and diffusivity for the prediction of transitional and shock-driven mixing flows featuring high and low Reynolds and Mach number regions. Two representative problems are computed with implicit large-eddy simulations using the inviscid Euler equations (EE) and viscous Navier-Stokes equations (NSE): the Taylor-Green vortex at Reynolds number Re = 3000 and initial Mach number Ma = 0.28, and an air- SF 6 -air gas curtain subjected to two shock waves at Ma = 1.2. The primary focus is on differences between NSE and EE predictions due to viscous effects. The outcome of the paper illustrates the advantages of utilizing NSE. In contrast to the EE, where the effective viscosity decreases upon grid refinement, NSE predictions can be assessed for simulations of flows with transition to turbulence at prescribed constant Re. The NSE can achieve better agreement between solutions and reference data, and the results converge upon grid refinement. On the other hand, the EE predictions do not converge with grid refinement, and can only exhibit similarities with the NSE results at coarse grid resolutions. We also investigate the effect of viscous effects on the dynamics of the coherent and turbulent fields, as well as on the mechanisms contributing to the production and diffusion of vorticity. The results show that nominally inviscid calculations can exhibit significantly varying flow dynamics driven by changing effective resolution-dependent Reynolds number, and highlight the role of viscous processes affecting the vorticity field. These tendencies become more pronounced upon grid refinement. The discussion of the results concludes with the assessment of the computational cost of inviscid and viscous computations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Lab-scale Development of a Hybrid Capture System with Advanced Membrane, Solvent system, and Process Integration

The objective of the project is to achieve lab-scale demonstration of a transformational hybrid membrane/solvent system for the capture of CO 2 from flue gas. A novel process integration scheme was proposed to overcome the low partial pressure of CO 2 present in flue gas. This scheme takes advantage of the potential synergies inherent in the membrane and solvent capture systems. The proposed hybrid technology replaces the second-stage membrane with a solvent capture process. The combustion air is used as a sweeping gas in the solvent stripper. This overall configuration has the major advantages of requiring much less air and eliminating the problems associated with oxygen slip in the membrane-based systems. Even more importantly, because of the presence of the air sweep in the stripper, much lower temperatures are required for solvent regeneration, which enables heat integration to the point that no process steam is required. This project was to perform lab-scale demonstration of Liquid Ion Solutions (LIS) transformational hybrid membrane/solvent system for post-combustion CO 2 capture while demonstrating significant progress toward achievement of the overall fossil energy performance goals of 90% CO 2 capture rate with 95% CO 2 purity at a cost of electricity 30% less than baseline capture approaches. This report is written chronologically based on budget periods. Each budget period discusses the work performed and its results. At the end of each budget period the milestone charts are provided to show the progress. This project was not able to meet its stated goals. The performances of the power plant equipped with the hybrid process and Baseline Case B12B were compared. The simulation results showed that the power plant equipped with hybrid CO2 capture process has an improved thermal efficiency of 33.4% compared to the Baseline Case B12B, which is 32.5%. However, the COE for the hybrid process is $146.3/MWh which is higher than the $142.8/MWh for Case B12B. If this process were to be applied as a retrofit, it may make sense to use this configuration as it does not require any change in an existing plant configuration and steam cycle. However, for a new powerplant the capital cost is higher than the Case B12B. On the membrane development side, we successfully showed that interfacially-controlled envelope (ICE) membranes work. The inclusion of surface modified nano-particles results in much higher gas diffusivities. The Gen-1 ICE membrane developed under this project showed exceptional improved permeability for CO 2 . However, we ran into major problems which were associated with the scalability and reproducibility of the poly(phosphozene) polymers. The issues with scale-up are and batch to batch variability is also discussed. At the end of this report we have provided our recommendations on materials development for better membrane materials and alluded to the use of much simpler chemistry while keeping the concept of ICE membrane intact. It is also clear that vacuum and compression equipment is costly. If a process which can eliminate the use of vacuum and compression equipment would significantly decrease the overall cost of capture. Some thoughts regarding such system is also provided in the outlook portion of this report.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2020

Source identification by non-negative matrix factorization combined with semi-supervised clustering

Machine-learning methods and apparatus are provided to solve blind source separation problems with an unknown number of sources and having a signal propagation model with features such as wave-like propagation, medium-dependent velocity, attenuation, diffusion, and/or advection, between sources and sensors. In exemplary embodiments, multiple trials of non-negative matrix factorization are performed for a fixed number of sources, with selection criteria applied to determine successful trials. A semi-supervised clustering procedure is applied to trial results, and the clustering results are evaluated for robustness using measures for reconstruction quality and cluster separation. The number of sources is determined by comparing these measures for different trial numbers of sources. Source locations and parameters of the signal propagation model can also be determined. Disclosed methods are applicable to a wide range of spatial problems including chemical dispersal, pressure transients, and electromagnetic signals, and also to non-spatial problems such as cancer mutation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Source identification by non-negative matrix factorization combined with semi-supervised clustering

Alexandrov, Boian S.↗

DOE OSTI2021

Parallel-In-Time Integration for Hyperbolic Problems (Final Report)

The work for the subcontract was situated in the area of parallel-in-time integration for advection-dominated and hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. Over the past two decades, much progress has been made in this area; however, this progress has largely been limited to non-hyperbolic, diffusion-dominated PDEs. Given the ubiquity of numerical simulations of advection-dominated hyperbolic PDEs throughout the sciences, there is a strong need to develop efficient parallel-in-time techniques for hyperbolic problems, which was the main topic of this subcontract.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

The “Fresnel Equations” for Diffuse radiation on Inclined photovoltaic Surfaces (FEDIS)

Here the well-known Fresnel equations solve for the reflection and transmission of light for precise incident angles. The transmission of diffuse radiation incident on a planar or domed surface is often needed for real-world applications. Due to the complexity of the Fresnel equations, the analytical solution of the integration has hitherto been unobtainable over the last centuries. Therefore, this problem was numerically solved by integrating the angular transmittances in space often leading to substantial computing burden and bias in the results. To efficiently estimate the solar energy resource for a glass-covered photovoltaic (PV) module, we derive an analytical solution of diffuse transmission based on the rigorous integration of an alternate form of the Fresnel equations. The approach leads to a simple yet accurate relative transmittance model that reconciles the solar energy sensed by pyranometers and PV panels. With limited and clearly stated approximations, the complex mathematical derivation resulted in an elegant solution. An experiment using 1-year of data at the National Renewable Energy Laboratory's (NREL's) Solar Radiation Research Laboratory (SRRL) shows that the new model dramatically decreases the disparity between the solar radiation measurements by a Kipp and Zonen CM Pyranometer 22 (CMP22) and an IMT reference cell on a 1-axis tracking system. The solution in this paper can be widely used in scientific and engineering research, development, and applications wherever the Fresnel equations are used.

14 SOLAR ENERGY↗

DOE OSTI2022

FEDIS (The “Fresnel Equations” for Diffuse radiation on Inclined photovoltaic Surfaces) [SWR-22-64]

The well-known Fresnel equations solve for the reflection and transmission of light for precise incident angles. The transmission of diffuse radiation incident on a planar or domed surface is often needed for real-world applications. Due to the complexity of the Fresnel equations, the analytical solution of the integration has hitherto been unobtainable over the last centuries. Therefore, this problem was numerically solved by integrating the angular transmittances in space often leading to substantial computing burden and bias in the results. To efficiently estimate the solar energy resource for a glass-covered photovoltaic (PV) module, we derive an analytical solution of diffuse transmission based on the rigorous integration of an alternate form of the Fresnel equations. The approach leads to a simple yet accurate relative transmittance model that reconciles the solar energy sensed by pyranometers and PV panels. With limited and clearly stated approximations, the complex mathematical derivation resulted in an elegant solution.

Xie, Yu↗