Results for “Programming Models” — Page 71

DOE OSTI2021

Enabling Pulse-level Programming, Compilation, and Execution in XACC

Noisy gate-model quantum processing units (QPUs) are currently available from vendors over the cloud, and digital quantum programming approaches exist to run low-depth circuits on physical hardware. These digital representations are ultimately lowered to pulse-level instructions by vendor quantum control systems to affect unitary evolution representative of the submitted digital circuit. Vendors are beginning to open this pulse-level control system to the public via specified interfaces. Robust programming methodologies, software frameworks, and backend simulation technologies for this analog model of quantum computation will prove critical to advancing pulse-level control research and development. Prototypical use cases for this include error mitigation, optimal pulse control, and physics-inspired pulse construction. Here we present an extension to the XACC quantum-classical software framework that enables pulse-level programming for superconducting, gate-model quantum computers, and a novel, general, and extensible pulse-level simulation backend for XACC that scales on classical compute clusters via MPI. Our work enables custom backend Hamiltonian definitions and gate-level compilation to available pulses with a focus on performance and scalability. We end with a demonstration of this capability, and show how to use XACC for pertinent pulse-level programming tasks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Economic Optimal Control for Minimizing Fuel Consumption of Heavy-Duty Trucks in a Highway Environment

This paper provides a comparative assessment of three economic optimal control strategies, aimed at minimizing the fuel consumption of heavy-duty trucks in a highway environment, under a representative lead vehicle model informed by traffic data. These strategies fuse a global, offline dynamic programming (DP) optimization with online model predictive control (MPC). We then show how two of the three strategies can be adapted to accommodate the presence of traffic and optimally navigate signalized intersections using infrastructure-to-vehicular (I2V) communication. The MPC optimization, which is local in nature, makes refinements to a coarsely (but globally, subject to grid resolution) optimized target velocity profile from the DP optimization. The three candidate economic MPC formulations that are evaluated include: a nonlinear time-based formulation that directly penalizes predicted fuel consumption, a nonlinear time-based formulation that penalizes braking effort as a surrogate for fuel consumption, and a linear distance-based convex formulation that maintains a tradeoff between energy expenditure and tracking of the coarsely optimized velocity profile obtained from DP. Using a medium-fidelity Simulink model, based on a Volvo truck's longitudinal and engine dynamics, we analyze the optimization's performance on four highway routes under various traffic scenarios. Results demonstrate 3.7-8.3% fuel economy improvement on highway routes without traffic and 6.5-10% on the same routes with traffic included. Furthermore, we present a detailed analysis of energy usage by "type" (aerodynamic losses, braking losses, and comparison of brake-specific fuel consumption), under each candidate control strategy.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2022

Grid-Supportive Loads - A New Approach to Increasing Renewable Energy in Power Systems

This paper demonstrates the potential of inverter-based loads to support grid reliability during power system transients thereby enabling reliable integration of renewable energy in power systems. Such loads are referred to in this paper as grid-supportive loads (GSLs). A new GSL model is developed that simulates the transient response capabilities that can be programmed in electronic loads. The model’s design enables it to be easily integrated in widely used commercial power system transient analysis software. Theoretical expressions are derived that explain the workings of the GSL model. The performance, numerical stability, and impact of the GSL model is validated on 9-bus and 2000-bus synthetic power system models using generator tripping and bus fault disturbances. Results on the 2000 bus system show that in the absence of frequency support from wind/solar generation resources, just 20% of loads with grid-supportive capabilities can improve frequency response by up to 2000 MW/0.1 Hz and reduce deviation in frequency at nadir by up to 60% compared to the situation when GSLs are absent. Power system reliability also improves under fault events. Here, it is further shown that GSLs can aid in integrating more renewable generation without degrading the overall transient response of the power system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2017

CICE, The Los Alamos Sea Ice Model

The Los Alamos sea ice model (CICE) is the result of an effort to develop a computationally efficient sea ice component for a fully coupled atmosphere–land–ocean–ice global climate model. It was originally designed to be compatible with the Parallel Ocean Program (POP), an ocean circulation model developed at Los Alamos National Laboratory for use on massively parallel computers. CICE has several interacting components: a vertical thermodynamic model that computes local growth rates of snow and ice due to vertical conductive, radiative and turbulent fluxes, along with snowfall; an elastic-viscous-plastic model of ice dynamics, which predicts the velocity field of the ice pack based on a model of the material strength of the ice; an incremental remapping transport model that describes horizontal advection of the areal concentration, ice and snow volume and other state variables; and a ridging parameterization that transfers ice among thickness categories based on energetic balances and rates of strain. It also includes a biogeochemical model that describes evolution of the ice ecosystem. The CICE sea ice model is used for climate research as one component of complex global earth system models that include atmosphere, land, ocean and biogeochemistry components. It is also used for operational sea ice forecasting in the polar regions and in numerical weather prediction models.

Hunke, Elizabeth↗

DOE OSTI2017

FY17 Status Report on the Computing Systems for the Yucca Mountain Project TSPA-LA Models.

Sandia National Laboratories (SNL) continued evaluation of total system performance assessment (TSPA) computing systems for the previously considered Yucca Mountain Project (YMP). This was done to maintain the operational readiness of the computing infrastructure (computer hardware and software) and knowledge capability for total system performance assessment (TSPA) type analysis, as directed by the National Nuclear Security Administration (NNSA), DOE 2010. This work is a continuation of the ongoing readiness evaluation reported in Lee and Hadgu (2014), Hadgu et al. (2015) and Hadgu and Appel (2016). The TSPA computing hardware (CL2014) and storage system described in Hadgu et al. (2015) were used for the current analysis. One floating license of GoldSim with Versions 9.60.300, 10.5, 11.1 and 12.0 was installed on the cluster head node, and its distributed processing capability was mapped on the cluster processors. Other supporting software were tested and installed to support the TSPA- type analysis on the server cluster. The current tasks included preliminary upgrade of the TSPA-LA from Version 9.60.300 to the latest version 12.0 and address DLL-related issues observed in the FY16 work. The model upgrade task successfully converted the Nominal Modeling case to GoldSim Versions 11.1/12. Conversions of the rest of the TSPA models were also attempted but program and operational difficulties precluded this. Upgrade of the remaining of the modeling cases and distributed processing tasks is expected to continue. The 2014 server cluster and supporting software systems are fully operational to support TSPA-LA type analysis.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Multiphysics Simulations of MSRE with NEAMS Thermal Hydraulics Tools

This report documents the benchmarks being developed and simulations performed using tools and codes developed under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, utilizing MSRE experimental data. In FY23, three main work scopes were investigated under the NEAMS MSR work package at ANL. The first scope investigated the Griffin-SAM coupling model for simulating the pump startup transient experiment of MSRE. The analyses start with a simple model (single-channel, single-lattice), gradually adding more details (multi-channel, full-core) into the model. The results show that the reactivity loss curve is very sensitive to the axial boundary conditions and the radial core discretization. The simple model can predict a similar reactivity trend as that of the more sophisticated model, which is likely due to error cancellation. Accurately modeling the axial boundary condition may further improve the reactivity trend but would require significant efforts to generate the mesh of the MSRE inlet and upper plenum. The core channel radial discretization for the Griffin-SAM coupled model also depends on the flow distribution. Given the complex geometry in the inlet plenum, the flow distribution needed to be calculated from CFD analysis, which was performed using the NekRS code. This analysis employed a MSRE CAD model developed by Copenhagen Atomics. The CAD model was disassembled to keep the inlet plenum region only, which was subsequently cleaned and modified so that the mesh generated is under the memory limit. The results are merged to a few radial regions to show that the flow rate is highest in the central region. This would be useful for future improvement of the Griffin-SAM coupling model of the MSRE core. The last task investigated is tritium transport modeling using the standalone SAM code. This task aimed to initiate the effort to demonstrate and validate the tritium transport model implemented in SAM. The preliminary investigation employed an MSRE model consisting of the primary loop. Three tritium transport pathways were examined including the retention in the graphite, the permeation through the HX tube wall, and the removal from the off-gas system. The results compare well with the MSRE data, but improvements are still needed on the initial conditions (i.e., the present state may not have reached equilibrium), the boundary conditions, the off-gas system modeling, and a better numerical strategy to reach the equilibrium state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

CICE, The Los Alamos Sea Ice Model

The Los Alamos sea ice model (CICE) is the result of an effort to develop a computationally efficient sea ice component for a fully coupled atmosphere–land–ocean–ice global climate model. It was originally designed to be compatible with the Parallel Ocean Program (POP), an ocean circulation model developed at Los Alamos National Laboratory for use on massively parallel computers. CICE has several interacting components: a vertical thermodynamic model that computes local growth rates of snow and ice due to vertical conductive, radiative and turbulent fluxes, along with snowfall; an elastic-viscous-plastic model of ice dynamics, which predicts the velocity field of the ice pack based on a model of the material strength of the ice; an incremental remapping transport model that describes horizontal advection of the areal concentration, ice and snow volume and other state variables; and a ridging parameterization that transfers ice among thickness categories based on energetic balances and rates of strain. It also includes a biogeochemical model that describes evolution of the ice ecosystem. The CICE sea ice model is used for climate research as one component of complex global earth system models that include atmosphere, land, ocean and biogeochemistry components. It is also used for operational sea ice forecasting in the polar regions and in numerical weather prediction models.

Hunke, Elizabeth↗

DOE OSTI2023

Code for the manuscript "Lagrangian Large Eddy Simulations vis Physics-informed Machine Learning"

We would like to disclose a code based on Python/Pytorch, in which we implement the data-driven physics-informed machine learning of Lagrangian large eddy simulation that is described in the manuscript "Lagrangian Large Eddy Simulations via Physics-Informed Machine Learning ". High-Reynolds number Homogeneous Isotropic Turbulence is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as Large Eddy Simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about the effects of sub-grid scales on the resolved scales. Here, we take an alternative approach and design novel LES heuristics stated in terms of Lagrangian particles moving with the flow. Our \emph{Lagrangian LES}, thus L-LES, is described by equations generalizing the weakly compressible Smoothed Particle Hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from Direct Numerical Simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The sub-grid scale contributions are modeled separately with physical constraints to account for the effects from un-resolved scales. We build the resulting model under the Differentiable Programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our Lagrangian LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

Tian, Yifeng↗

DOE OSTI2020

Developing Decommissioning Cost Estimating Relationships and the Decommissioning Estimate Analysis Library Estimating System - 20423

DOE-EM's Consolidated Business Center (EM-CBC) Office of Cost Estimating has developed a system of Decommissioning Cost Estimating Relationships (CERs) and Models to improve the reliability and efficiency of its estimates. The development builds on the multi-year process of collecting and organizing historical cost data from DOEEMs decommissioning projects and estimate model development to support project and program-level decommissioning estimates. The latest work has extended these models down to project scope element and component building area levels, allowing the actual costs of work for these estimate components to be assembled into estimates that reflect specific projects. The CERs have been incorporated into two estimator-friendly products - as cost libraries in the MII estimating program and as an MS Excel-based model, and are available for DOE federal staff use. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

$\mathrm{PPT}$-Multicore: performance prediction of Open$\mathrm{MP}$ applications using reuse profiles and analytical modeling

In this report we present PPT-Multicore, an analytical model embedded in the Performance Prediction Toolkit (PPT) to predict parallel applications’ performance running on a multicore processor. PPT-Multicore builds upon our previous work towards a multicore cache model. We extract LLVM basic block labeled memory trace using an architecture-independent LLVM-based instrumentation tool only once in an application’s lifetime. The model uses the memory trace and other parameters from an instrumented sequentially executed binary. We use probabilistic and computationally efficient reuse profiles to predict the cache hit rates and runtimes of OpenMP programs’ parallel sections. We model Intel’s Broadwell, Haswell, and AMD’s Zen2 architectures and validate our framework using different applications from PolyBench and PARSEC benchmark suites. The results show that PPT-Multicore can predict cache hit rates with an overall average error rate of 1.23% while predicting the runtime with an error rate of 9.08%.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Lagrangian large eddy simulations via physics-informed machine learning

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier–Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Transient Efficiency, Flexibility, and Reliability Optimization of Coal-Fired Power Plants - Final Program Review

This program developed an advanced model-based monitoring and model-predictive control algorithms for a coal fired power plant (CFPP), and deployed these algorithms in a real-time platform to demonstrate performance benefits for transient flexibility and plant operation efficiency. More specifically, the objectives were successfully achieved through a combination of (i) developing a high-fidelity transient plant model in Apros, which was used as a high-fidelity plant simulation between $100-50\% TMCR$ where TMCR denotes the turbine maximum continuous rating, i.e., baseload, (ii) developing a very fast physics-based reduced-order model (ROM) of the plant, which ran more than $100\times$ faster than real-time, enabling its use as real-time embedded model for model-based estimation (MBE) and model predictive control (MPC) (iii) implementing a real-time MBE based on ROM using a robust unscented Kalman filter (UKF) to continuously tune the ROM to match the measurements from high-fidelity Apros plant model despite significant plant-model mismatch, and thus, obtain a Digital Twin of the plant (iv) designing and implementing a real-time MPC with dual objectives of transient plant load tracking with high ramp rates and minimizing coal consumption, i.e., improving plant efficiency in the baseload-partload operation range of $100-50\% TMCR$. Each key element above was developed and tested individually, and has been reported in corresponding Topical Reports. Finally, all the individual elements were integrated in an overall closed-loop system, that was successfully tested in desktop Simulink test harness simulations with ROM or high-fidelity model as the plant. Thereafter, the Simulink implementation was used to auto-generate C-code and deploy as real-time Docker microservice containers in Linux, and validate that they can run in real-time in the hardware-in-the loop (HIL) setup and produce the same results as in Simulink. The results of the integrated simulation tests in Simulink as well as the real-time HIL deployment are documented in this final report, showing good load tracking for load ramps at $3-4\%/min$ ramp rates, and achieving up to $5.5\%$ reduction in coal relative to baseline operation at $50\% TMCR$ load. The desktop and HIL simulations show successful performance of the overall model based estimation and control solution and achieve the key objectives of the program for flexible, efficient and reliable operation of sub-critical coal fired power plants.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2023

Transient Efficiency, Flexibility, and Reliability Optimization of Coal-Fired Power Plants - Final Report

This program developed an advanced model-based monitoring and model-predictive control algorithms for a coal fired power plant (CFPP), and deployed these algorithms in a real-time platform to demonstrate performance benefits for transient flexibility and plant operation efficiency. More specifically, the objectives were successfully achieved through a combination of (i) developing a high-fidelity transient plant model in Apros, which was used as a high-fidelity plant simulation between $100-50\% TMCR$ where TMCR denotes the turbine maximum continuous rating, i.e., baseload, (ii) developing a very fast physics-based reduced-order model (ROM) of the plant, which ran more than $100\times$ faster than real-time, enabling its use as real-time embedded model for model-based estimation (MBE) and model predictive control (MPC) (iii) implementing a real-time MBE based on ROM using a robust unscented Kalman filter (UKF) to continuously tune the ROM to match the measurements from high-fidelity Apros plant model despite significant plant-model mismatch, and thus, obtain a Digital Twin of the plant (iv) designing and implementing a real-time MPC with dual objectives of transient plant load tracking with high ramp rates and minimizing coal consumption, i.e., improving plant efficiency in the baseload-partload operation range of $100-50\% TMCR$. Each key element above was developed and tested individually, and has been reported in corresponding Topical Reports. Finally, all the individual elements were integrated in an overall closed-loop system, that was successfully tested in desktop Simulink test harness simulations with ROM or high-fidelity model as the plant. Thereafter, the Simulink implementation was used to auto-generate C-code and deploy as real-time Docker microservice containers in Linux, and validate that they can run in real-time in the hardware-in-the loop (HIL) setup and produce the same results as in Simulink. The results of the integrated simulation tests in Simulink as well as the real-time HIL deployment are documented in this final report, showing good load tracking for load ramps at $3-4\%/min$ ramp rates, and achieving up to $5.5\%$ reduction in coal relative to baseline operation at $50\% TMCR$ load. The desktop and HIL simulations show successful performance of the overall model based estimation and control solution and achieve the key objectives of the program for flexible, efficient and reliable operation of subcritical coal fired power plants.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2015

Computer simulation of nonstationary thermal fields in design and operation of northern oil and gas fields

A mathematical model, numerical algorithm and program code for simulation and long-term forecasting of changes in permafrost as a result of operation of a multiple well pad of northern oil and gas field are presented. In the model the most significant climatic and physical factors are taken into account such as solar radiation, determined by specific geographical location, heterogeneous structure of frozen soil, thermal stabilization of soil, possible insulation of the objects, seasonal fluctuations in air temperature, and freezing and thawing of the upper soil layer. Results of computing are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Modeling, Performance Assessment, and Nodal Data Analysis of TRISO-Fueled Systems with Shift

This technical report documents several enhancements to the Shift Monte Carlo (MC) code under the US Department of Energy (DOE) Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in fiscal year (FY) 2022. Performance enhancements were added to Shift specifically for tristructural isotropic (TRISO)–fueled reactor systems and guided based on performance analysis in FY 2021. For the pebble performance model developed in previous studies, the runtime improved by ~ 91× compared to the original model and ~ 2× compared to the user-optimized model. Compared to Serpent, Shift is ~ 3× slower if Serpent delta-tracking is enabled but ~ 2× faster when delta-tracking is disabled. The multigroup cross section generation was improved through simplifying tally input definitions, porting several post-processing tally operations from Python scripts into the Shift code base, and accounting for production reactions in the scattering multiplicity. Progress was also made on two emerging capabilities: (1) the development of Titan (a Shift reactor physics user interface) and (2) initial investigation into path-length tallies for computing multigroup scattering matrices.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Modeling Radionuclide Vaporization from Sodium Pools for SFR Mechanistic Source Term Analysis

To assist both the advanced reactor industry and U.S. Nuclear Regulatory Commission (NRC) in the pursuit of reactor design and licensing, the U.S. Department of Energy (DOE) Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has established a mechanistic source term (MST) research project under the Multiphysics Applications technical area. As part of this effort, an MST mod/sim development pathway was developed in FY21 under the NEAMS program, which outlines the high-level objectives and near-term tasks necessary to achieve the project objectives. One such recommended task was the assessment of a previously developed thermodynamic database to model radionuclide vaporization from liquid sodium pools (specifically in the context of MST analyses), which is the focus of this topic report. As such, a thermodynamic database was created in FactSage for liquid sodium pools containing oxygen and relevant elements which represent radionuclides pertinent to MST analyses. The database was demonstrated in calculating vapor fraction curves for each element in the system at concentrations relevant to SFR MST.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

HTGR Multiphysics Application Drivers FY26 Updates

This report summarizes FY26 progress under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program's high-temperature gas-cooled reactor (HTGR) application driver work, covering a wide range of activities such as code validation and multi-physics code assessment. 1) A detailed SAM model of the High-Temperature Engineering Test Reactor (HTTR) was developed using a unique-block grouping approach, with an extended parallel thermal network method to capture block-to-block conduction and radiation heat transfer, and applied to steady-state simulations of the HTTR 30~MW and 9~MW cases. 2) In another activity, SAM's newly implemented multi-component gas flow model was validated against the Natural convection Shutdown heat removal Test Facility (NSTF) argon ingress experiment, correctly capturing the density-driven suppression and thermal recovery of natural circulation observed when argon is introduced into the air-cooled Reactor Cavity Cooling System (RCCS) loop. 3) For the OECD/NEA High Temperature Test Facility (HTTF) benchmark, we co-led the international benchmark activities as well as the OECD/NEA final benchmark report to be released at the end of this year. 4) Finally, the coupled Griffin-SAM modeling capability for pebble-bed HTGRs was advanced by verifying the Griffin neutronics solution against Serpent Monte Carlo for a realistic non-uniform temperature distribution, resolving several deficiencies in the SAM-to-Griffin temperature transfer scheme, and enabling distinct fuel kernel, moderator, and coolant temperatures for cross section feedback. These new features were demonstrated in a PBR load-following transient.

Lee, Alvin↗

DOE OSTI2018

Stochastic Simulation of Complex Fluid Flows (Progress Report for period 07/01/2016 - 06/30/2018)

At a microscopic scale, fluids are composed of molecules whose positions and velocities are random. This gives rise to thermal fluctuations that span the whole range of scales from the microscopic through the mesoscopic, and even the macroscopic. The inclusion of thermal fluctuations is crucial in multi-scale models, which are an important theme in the research program of the DOE Office of Science, and in particular the ASCR Applied Mathematics program's priority focus area on modeling of complex systems involving processes that span vastly different time and/or length scales. In this five-year Early Career project, the PI Aleksandar Donev and collaborators developed computational algorithms for modeling complex fluid mixtures at small scales using a formulation based on fluctuating hydrodynamics. Novel computational methods were developed to model complex fluids with increasing physical complexity, starting from binary miscible and immiscible mixtures, going through multispecies non-reactive and reactive mixtures, and culminating with reactive electrolytes mixtures of neutral molecules and ions. In close collaboration with the group of John Bell at Lawrence Berkeley National Laboratory, the methods were implemented in a scalable computational framework suitable for modern parallel supercomputers, and made publicly available on github. A number of physical examples in which giant nonequilibrium fluctuations are improtant were studied, with a special focus on instabilities at a liquid-liquid interface driven by gravity, diffusion, reactions, and/or electric fields. The methods and codes developed in this project are expected to enable other novel applications in the DOE Basic Energy Sciences program, and engineering sciences more broadly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗