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At least 487 records · Page 27

P69 Using the NASA-Unified WRF to Assess the Impacts of Real-Time Vegetation on Simulations of Severe Weather

Since June 2010, the NASA Short-term Prediction Research and Transition (SPoRT; Goodman et al. 2004; Darden et al. 2010; Stano et al. 2012; Fuell et al. 2012) Center has been generating a real-time Normalized Difference Vegetation Index (NDVI) and corresponding Green Vegetation Fraction (GVF) composite based on reflectances from NASA s Moderate Resolution Imaging Spectroradiometer (MODIS) instrument. This dataset is generated at 0.01 resolution across the Continental United States (CONUS), and updated daily. The goal of producing such a vegetation dataset is to improve over the default climatological GVF dataset in land surface and numerical weather prediction models, in order to have better simulations of heat and moisture exchange between the land surface and the planetary boundary layer. Details on the SPoRT/MODIS vegetation composite algorithm are presented in Case et al. (2011). Vegetation indices such as GVF and Leaf Area Index (LAI) are used by land surface models (LSMs) to represent the horizontal and vertical density of plant vegetation (Gutman and Ignatov 1998), in order to calculate transpiration, interception and radiative shading. Both of these indices are related to the NDVI; however, there is an inherent ambiguity in determining GVF and LAI simultaneously from NDVI, as described in Gutman and Ignatov (1998). One practice is to specify the LAI while allowing the GVF to vary both spatially and temporally, as is done in the Noah LSM (Chen and Dudhia 2001; Ek et al. 2003). Operational versions of Noah within several of the National Centers for Environmental Prediction (NCEP) global and regional modeling systems hold the LAI fixed, while the GVF varies according to a global monthly climatology. This GVF climatology was derived from NDVI data on the NOAA Advanced Very High Resolution Radiometer (AVHRR) polar orbiting satellite, using information from 1985 to 1991 (Gutman and Ignatov 1998; Jiang et al. 2010). Representing data at the mid-point of every month, the climatological dataset is on a grid with 0.144 (~16 km) spatial resolution and is distributed with the community WRF model (Ek et al. 2003; Jiang et al. 2010; Skamarock et al. 2008).

Case, Jonathan L.↗

Direct observations of field-induced assemblies in magnetite ferrofluids

Evolution of microstructures in magnetite-based ferrofluids with weak dipolar moments (particle size ≤ 10 nm) is studied with an emphasis on examining the effects of particle concentration (ϕ) and magnetic field strength (H) on the structures. Nanoparticles are dispersed in water at three different concentrations, ϕ = 0.15%, 0.48%, and 0.59% (w/v) [g/ml%] and exposed to uniform magnetic fields in the range of H = 0.05–0.42 T. Cryogenic transmission electron microscopy is employed to provide in-situ observations of the field-induced assemblies in such systems. As the magnetic field increases, the Brownian colloids are observed to form randomly distributed chains aligned in the field direction, followed by head-to-tail chain aggregation and then lateral aggregation of chains termed as zippering. By increasing the field in low concentration samples, the number of chains increases, though their length does not change dramatically. Increasing concentration increases the length of the linear particle assemblies in the presence of a fixed external magnetic field. Thickening of the chains due to zippering is observed at relatively high fields. Through a systematic variation of concentration and magnetic field strength, this study shows that both magnetic field strength and change in concentration can strongly influence formation of microstructures even in weak dipolar systems. Additionally, the results of two commonly used support films on electron microscopy grids, continuous carbon and holey carbon films, are compared. Holey carbon film allows us to create local regions of high concentrations that further assist the development of field-induced assemblies. The experimental observations provide a validation of the zippering effect and can be utilized in the development of models for thermophysical properties such as thermal conductivity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques

The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic, and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching step sizes with the implicit shock fitting procedure. A correlation is found between the marching step size, Reynolds number, and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.

Kaul, U. K.↗

An Overset Grid Motion Driver for Resolving Entry Vehicle CFD Simulations with Large Changes in Wake Orientation

Time-accurate computational fluid dynamics (CFD) simulations using overset meshes can enable reduced computational cost compared to a rigid, monolithic mesh for blunt-body atmospheric entry vehicles. If the vehicle has a significant change in attitude, the high-density region of the overset mesh designed for resolving the subsonic wake can be kept in position as the wake orientation changes relative to the body. Current simulations generally keep the wake mesh fixed in attitude while the body rotates, assuming the wake orientation remains relatively constant. However, changes in the relative velocity over a long-duration simulation or effects of the body geometry can invalidate this assumption. This work presents a method for calculating the desired mesh orientation to resolve a blunt body wake using the atmosphere-relative velocity of the vehicle. A motion driver using these calculations is implemented in a CFD-in-the-loop flight model bridging the FUN3D flow solver and POST2 trajectory propagator. Overset meshing is performed using the Yoga extension for FUN3D. Results are presented for simulations with both overset and monolithic meshes under large changes in relative velocity (and therefore wake orientation). The results demonstrate that the motion driver successfully orients an overset wake mesh to capture the subsonic wake with sufficient resolution despite variable body rotation and body-relative freestream velocity.

CFD↗

An Overset Grid Motion Driver for Resolving Entry Vehicle CFD Simulations with Large Changes in Wake Orientation

Time-accurate computational fluid dynamics (CFD) simulations using overset meshes can enable reduced computational cost compared to a rigid, monolithic mesh for blunt-body atmospheric entry vehicles. If the vehicle has a significant change in attitude, the high-density region of the overset mesh designed for resolving the subsonic wake can be kept in position as the wake orientation changes relative to the body. Current simulations generally keep the wake mesh fixed in attitude while the body rotates, assuming the wake orientation remains relatively constant. However, changes in the relative velocity over a long-duration simulation or effects of the body geometry can invalidate this assumption. This work presents a method for calculating the desired mesh orientation to resolve a blunt body wake using the atmosphere-relative velocity of the vehicle. A motion driver using these calculations is implemented in a CFD-in-the-loop flight model bridging the FUN3D flow solver and POST2 trajectory propagator. Overset meshing is performed using the Yoga extension for FUN3D. Results are presented for simulations with both overset and monolithic meshes under large changes in relative velocity (and therefore wake orientation). The results demonstrate that the motion driver successfully orients an overset wake mesh to capture the subsonic wake with sufficient resolution despite variable body rotation and body-relative freestream velocity.

Computational Fluid Dynamics↗

Adaptive PV Frequency Control Strategy Based on Real-time Inertia Estimation

The declining cost of solar Photovoltaics (PV) generation is driving its worldwide deployment. As conventional generation with large rotating masses is being replaced by renewable energy such as PV, the power system’s inertia will be affected. As a result, the system’s frequency may vary more dramatically in the case of a disturbance, and the frequency nadir may be low enough to trigger protection relays such as under-frequency load shedding. The existing frequency-watt function mandated in power inverters cannot provide grid frequency support in a loss-of-generation event, as PV plants usually do not have power reserves. Here, a novel adaptive PV frequency control strategy is proposed to reserve the minimum power required for grid frequency support. A machine learning model is trained to predict system frequency response under varying system conditions, and an adaptive allocation of PV headroom reserves is made based on the machine learning model as well as real-time system conditions including inertia. Case studies show the proposed control method meets the frequency nadir requirements using minimal power reserves compared to a fixed headroom control approach.

14 SOLAR ENERGY↗

The RealGas and RealGasH2O Options of the TOUGH+ Code for the Simulation of Coupled Fluid and Heat Flow in Tight/Shale Gas Systems

We developed two new EOS additions to the TOUGH+ family of codes, the RealGasH2O and RealGas . The RealGasH2O EOS option describes the non-isothermal two-phase flow of water and a real gas mixture in gas reservoirs, with a particular focus in ultra-tight (such as tight-sand and shale gas) reservoirs. The gas mixture is treated as either a single-pseudo-component having a fixed composition, or as a multicomponent system composed of up to 9 individual real gases. The RealGas option has the same general capabilities, but does not include water, thus describing a single-phase, dry-gas system. In addition to the standard capabilities of all members of the TOUGH+ family of codes (fully-implicit, compositional simulators using both structured and unstructured grids), the capabilities of the two codes include: coupled flow and thermal effects in porous and/or fractured media, real gas behavior, inertial (Klinkenberg) effects, full micro-flow treatment, Darcy and non-Darcy flow through the matrix and fractures of fractured media, single- and multi-component gas sorption onto the grains of the porous media following several isotherm options, discrete and fracture representation, complex matrix-fracture relationships, and porosity-permeability dependence on pressure changes. The two options allow the study of flow and transport of fluids and heat over a wide range of time frames and spatial scales not only in gas reservoirs, but also in problems of geologic storage of greenhouse gas mixtures, and of geothermal reservoirs with multi-component condensable (H2O and CH4) and non-condensable gas mixtures. The codes are verified against available analytical and semi-analytical solutions. Their capabilities are demonstrated in a series of problems of increasing complexity, ranging from isothermal flow in simpler 1D and 2D conventional gas reservoirs, to non-isothermal gas flow in 3D fractured shale gas reservoirs involving 4 types of fractures, micro-flow, non-Darcy flow and gas composition changes during production.

03 NATURAL GAS↗

California Price Response Potential Study

California's energy landscape is undergoing a significant transformation, driven by the increasing integration of renewable energy sources, the increased adoption of distributed energy resources, the electrification of end-use loads, and the growing need for grid efficiency. To address these challenges, recent revisions to the State’s Load Management Standards (LMS) require all of California’s large utilities and community choice aggregators (CCAs) to offer dynamic electricity pricing options to customers by 2027. Dynamic pricing, which involves varying electricity rates based on real-time supply and demand conditions, offers a promising solution for optimizing grid operations, reducing costs, and incentivizing efficient use of grid capacity. Effective implementation of dynamic pricing requires understanding the potential impacts on customer bills, system load, and the cost-effectiveness of automation technologies. This study aims to evaluate the load response of various end-use devices to hourly dynamic prices. The end-uses studied here are space cooling, space heating, water heating, crop irrigation, pool and spa pumps, and electric vehicle (EV) charging, all for both residential and commercial applications, except for crop irrigation. In 2030, these end uses are forecasted to account for 18% of annual electricity demand in the state, but 40% of demand in the peak net load hour. By modeling possible price-responsive load dispatch algorithms and assessing the resulting impacts on both individual bills and the overall grid, we seek to inform policymakers and utilities about the potential benefits and challenges associated with dynamic pricing, and considerations for the design of dynamic pricing tariffs. Additionally, we will explore the cost effectiveness of adopting automation technologies to enable devices to respond more effectively to real-time price signals. This study considers a range of price profiles, accounting for differences across utilities and customer classes, and presents scenarios for dynamic price design via variation in the percentage of total customer electric costs that are allocated dynamically (versus constituting a fixed portion of the hourly volumetric price). We present results focused primarily on 2030, forecasting electricity prices under both low and high-cost scenarios, to inform longer-term tariff design considerations. We design tariffs by starting with 2019 prices that were calculated according to CalFUSE guidance (CPUC, 2022) and that have been used in recent studies; these prices are all-in volumetric rates that vary by utility and are revenue-neutral to each customer class. They are developed by considering six electricity cost components that are allocated hourly based on system load indicators (gross and net load, and wholesale prices). These prices are forecasted to 2030 for low and high cost scenarios, considering recent trends in total electricity costs with and without years of substantial wildfire mitigation investments. These tariffs, which allocate all costs on an hourly basis, are considered our “Full” dynamic tariff design scenario, while two additional scenarios explore allocating a portion of costs as a flat volumetric charge: the “Medium” scenario allocates 50% of revenue dynamically (and keeps 50% flat), while the “Mild” scenario allocates 20% of revenue dynamically. The 20% dynamic allocation on the Mild scenario aims to represent a case where only the marginal operating costs of the grid are included in the dynamic price.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A Consistent Representation of Cloud Overlap and Cloud Subgrid Vertical Heterogeneity

Many global climate models underestimate the cloud cover and overestimate the cloud albedo, especially for low-level clouds. We determine how a correct representation of the vertical structure of clouds can fix part of this bias. We use the 1D McICA framework and focus on low-level clouds. Using Large Eddy Simulations results as reference, we propose a method based on exponential-random overlap that represents the cloud overlap between layers and the subgrid cloud properties over several vertical scales, with a single value of the overlap parameter. Starting from a coarse vertical grid, representative of atmospheric models, this algorithm is used to generate the vertical profile of the cloud fraction with a finer vertical resolution, or to generate it on the coarse grid but with subgrid heterogeneity and cloud overlap that ensures a correct cloud cover. Doing so we find decorrelation lengths are dependent on the vertical resolution, except if the vertical subgrid heterogeneity and interlayer overlap are taken into account coherently. We confirm that the frequently used maximum-random overlap leads to a significant error by underestimating the low-level cloud cover with a relative error of about 50%, that can lead to an error of SW cloud albedo as big as 70%. Not taking into account the subgrid vertical heterogeneity of clouds can cause a relative error of 20% in brightness, assuming the cloud cover is correct.

54 ENVIRONMENTAL SCIENCES↗

A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques

The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching-step sizes with the implicit shock fitting procedure. A correlation is found between the marching-step size, Reynolds number and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.

Kaul, U. K.↗

The System Modeling and Analysis of Resiliency in STEReO (SMARt-STEReO)

Wildfire emergency response has remained rooted in relatively low-tech solutions for coordination between ground and aerial assets. These low-tech solutions are robust for the remote environments in which wildfires are usually fought, but limit strategic cross-organizational support and the ability to deploy and effectively utilize aerial assets. As aircraft become more advanced and new technology, including drones, become available to firefighters, a new, more modern method of asset coordination is needed. NASA is working on a project called ‘Scalable Traffic Management for Emergency Response Operations’ (STEReO) to integrate unmanned aerial systems (UAS)and UAS traffic management (UTM)into wildfire response. STEReO’s goals include simplifying the coordination of aerial assets, improving the existing UAS framework, and increasing the role of additional autonomous systems to reduce human risk and to increase system resilience. This paper describes the development of the ‘System Modeling and Analysis of Resiliency in STEReO’ (SMARt-STEReO) project, which aims to model wildfire response and to quantify the additional system resilience that STEReO technology provides firefighters. This paper verifies SMARt-STEReO and defines its scope; it includes experimental and statistical analysis of the impact that the addition of UAS has on both performance metrics and also on performance resiliency response to a given fault. SMARt-STEReO is a grid-based model of fire propagation that incorporates varying crew responses. Through the use of a Python package called ‘fmdtools’, the model easily allows for the addition of faults to the system. These faults allow analysts to investigate various response parameters. Factors including terrain, fuel type and wind speed can be modified to affect the fire propagation; additionally, the number of ground crews, engines, fixed wing aircraft, helicopters, and UAS can be changed to affect the crew response. The communication lines between actors mimic those used in real life situations. This paper explains the development of SMARt-STEReO including background research, verification and validation, and preliminary experimental analysis of system resilience to both a minor and major fault in systems with and without UAS.

Resiliency↗

Integrated Optimization and Control of a Hybrid Gas Turbine/sCO 2 Power System

During phase-I, the project team led by Echogen Power Systems (EPS) had two primary objectives based on investigating the application of gas turbines with supercritical carbon dioxide (sCO 2 ) power cycles. The first objective was to improve the overall efficiency and performance of a hybrid gas turbine/sCO 2 power system through a joint optimization of the two subsystems (gas turbine and sCO 2 power cycle) using non-linear optimization techniques that simultaneously evaluate thermal performance of the combined cycle. The hybrid power system included several points of interaction, including (but not limited to) gas turbine exhaust, fuel heating, inlet chilling and turbine cooling. The second objective was to establish a baseline transient response model of the hybrid power system and a notional microgrid and begin steps to integrate the control systems of the three major elements (gas turbine, sCO 2 cycle and grid controller). The project team established a baseline performance for a combined cycle power plant using a production gas turbine and scaled sCO 2 power cycle only utilizing exhaust heat recovery. Echogen’s non-linear techno-economic optimization code was extended by adding gas turbine component models derived from a in-house developed gas turbine design code. With the two cycles coupled by the gas turbine exhaust, design parameters of both cycles were allowed to vary simultaneously to determine performance opportunity versus isolated designs. Returning to the baseline gas turbine/sCO 2 power cycle transient models: Echogen had in-house developed sCO 2 cycle transient model in GT-Suite system simulation software, and had partnered with Siemens Finspång for gas turbine transient model, and Siemens PTI group to provide micro-grid load profile as well as hybrid power cycle generated load (power and frequency) analysis. The transient model for the SGT-750 Siemens gas turbine was a “black-box” functional mock-up interface (FMI) model developed by Siemens Industrial Turbomachinery in Finspång, Sweden. The SGT-750 is a twin-shaft gas turbine that produces 40 MW electricity with an efficiency of about 40% at ISO conditions. At 100% gas turbine throttle (load), the SGT-750 has average exhaust conditions of 114.6 kg/s and 469.8°C. The transient model for sCO 2 power cycle was developed by Echogen in GT-SUITE 1D system simulation software platform. The basic CO 2 flow circuit has single-shaft turbomachinery with net 11.5 MW electrical power output at design conditions. The power turbine has a double-ended shaft with one end connected to synchronous generator through a fixed-ratio gearbox. The other end of power turbine is connected to the compressor through a continuously variable transmission. The major components of the sCO 2 power cycle modeled include air cooled condenser/cooler, CO 2 compressor, recuperator, two waste heat exchanger coils, power turbine, continuous variable transmission, gearbox and generator. Integration of SGT-750 transient model and sCO 2 power cycle transient model was done in Matlab Simulink. In the integrated model, the gas turbine and sCO 2 power cycle interacted at two points, first one being the gas turbine exhaust gas flow rate and temperature, which were inputs to sCO 2 power cycle model. The second point was the distribution of micro-grid load demand signal between the SGT-750 generator and sCO 2 cycle generator. For a given combined-cycle load demand, the gas turbine load demand was equal to the total demand minus the sCO 2 cycle power generated. In the present study the integrated model was simulated for two cases of grid load demand: (i) for a step change, both positive-step and negative-step, in grid load demand (ii) for a micro-grid load demand curve provided by Siemens PTI group. Finally, the time series plots representing load demand versus integrated system response were presented including the sCO 2 power cycle control system performance plots. The actual generated power and frequency of both the generators, gas turbine and sCO 2 power cycle, was supplied to Siemens PTI group for dynamic grid assessment, results of which are provided in appendices.

03 NATURAL GAS↗

Characterization of Exoplanet Atmospheres with the Optical Coronagraph on WFIRST

Wide-Field Infrared Survey Telescope (WFIRST)-CGI is a NASA technology demonstration mission that is charged with demonstrating key technologies for future exo-Earth imaging missions in space. In the process, it will obtain images and low-resolution spectra of a handful to a dozen extrasolar planets and possibly protoplanetary disks. Its unprecedented contrast levels in the optical will provide astronomers’ with their first direct look at mature, Jupiter-sized planets at moderate separations. This paper addresses the question: what science can be done with such data? An analytic noise model, which is informed by the ongoing engineering developments, is used to compute maximum achievable signal-to-noise ratios and scientifically viable integration times for hypothetical star–planet systems, as well as to investigate the constraining power of various combinations of WFIRST-CGI photometric and spectral observations. This work introduces two simple models for planetary geometric albedos, which are inspired largely by the solar system’s gas giants. The first planet model is a hybrid Jupiter–Neptune model, which separately treats the short and long wavelengths where chromophores and methane dominate absorption, respectively. The second planet model fixes cloud and haze properties in CoolTLusty to match Jupiter’s albedo spectrum, it then perturbs only the metallicity. MCMC retrievals performed on simulated observations are used to assess the precision with which planet model parameters can be measured subject to different exposure times and observing cases. Planet radius is recovered within ±15% for all observing cases with both the hybrid model and the CoolTLusty metallicity grid. Fit results for both models’ parameterizations of geometric albedo spectra demonstrate that a rough indication of the metallicity or methane content should be possible for some WFIRST-CGI targets. We conclude that real observations will likely be able to differentiate between extreme cases using these models, but will lack the precision necessary to uncover subtle trends.

79 ASTRONOMY AND ASTROPHYSICS↗

Coarse grained simulation of convectively driven turbulent mixing, transition, and turbulence decay

Accurate predictions with quantifiable uncertainties are essential to many practical turbulent flow applications exhibiting extreme geometrical complexity and broad ranges of length and time scales. Under-resolved computer simulations are typically unavoidable in such applications, and implicit large-eddy simulation (ILES) often becomes the effective strategy. In this work, we focus on assessing ILES initialized with well-characterized 25 6 3 homogeneous isotropic turbulence datasets generated with direct numerical simulation (DNS). ILES solutions based on the LANL xRAGE code are studied as function of resolution for 6 4 3 , 12 8 3 , 25 6 3 , and 51 2 3 grids. ILES performance of new directionally-unsplit high-order numerical hydrodynamics algorithms in xRAGE is examined in this context. Compared to the initial 25 6 3 DNS, we find longer inertial subranges and higher turbulence Reynolds number (Re) for 25 6 3 and 51 2 3 xRAGE — attributed to having linked DNS (Navier–Stokes based) solutions to nominally inviscid (higher Re) Euler based ILES solutions. For fixed 25 6 3 resolution, we find that significantly larger simulated turbulence Re can be achieved with the higher-order unsplit (vs. split) discretizations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

High-energy differential-filtering photon spectrometer for ultraintense laser-matter interactions

Large quantities of ultrahigh-energy x-rays are produced by petawatt-class lasers; however, spectroscopy in this range of 0.1-1 MeV is difficult due to the long photon mean free path. A novel geometry step filter to measure the high-energy bremsstrahlung emission tail has been developed for use in high energy density, short-pulse laser-matter interaction experiments. The grid design of the filters allows for the independent determination of a local background, which reduces systematic errors in the reconstructed spectra. This spectrometer was used to measure x-ray spectra for various laser and target conditions at intensities near 1 × 10 18 W/cm 2 where single-exponential bremsstrahlung spectra were fit to the data and show an increasing photon temperature with pulse duration for a fixed laser intensity.

47 OTHER INSTRUMENTATION↗

Application of a field-based method to spatially varying thermal transport problems in molecular dynamics

This paper derives a methodology to enable spatial and temporal control of thermally inhomogeneous molecular dynamics (MD) simulations. The primary goal is to perform non-equilibrium MD of thermal transport analogous to continuum solutions of heat flow which have complex initial and boundary conditions, moving MD beyond quasi-equilibrium simulations using periodic boundary conditions. In our paradigm, the entire spatial domain is filled with atoms and overlaid with a finite element (FE) mesh. The representation of continuous variables on this mesh allows fixed temperature and fixed heat flux boundary conditions to be applied, non-equilibrium initial conditions to be imposed and source terms to be added to the atomistic system. In effect, the FE mesh defines a large length scale over which atomic quantities can be locally averaged to derive continuous fields. Unlike coupling methods which require a surrogate model of thermal transport like Fourier's law, in this work the FE grid is only employed for its projection, averaging and interpolation properties. Inherent in this approach is the assumption that MD observables of interest, e.g. temperature, can be mapped to a continuous representation in a non-equilibrium setting. This assumption is taken advantage of to derive a single, unified set of control forces based on Gaussian isokinetic thermostats to regulate the temperature and heat flux locally in the MD. Example problems are used to illustrate potential applications. In addition to the physical results, data relevant to understanding the numerical effects of the method on these systems are also presented.

36 MATERIALS SCIENCE↗