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At least 1,621 records · Page 90

Modeling and simulation of a turbulent far wake

Work continued on two projects which had been started during previous years. Both projects involve calculations of the subsonic, turbulent far wake of a two-dimensional object at a Reynolds number of 1000 (based on wake momentum thickness). This flow was used as a test case for direct comparison of various turbulence models and a direct numerical simulations (DNS) of this flow were undertaken. In the turbulence model comparison studies, for any particular model tested, a unique self-similar solution was obtained far enough downstream, regardless of inlet conditions. Furthermore, different turbulence models led to different far-wake equilibrium solutions. No turbulence model could correctly predict all features of the turbulent far wake. For example, the spreading rate and turbulent shear stresses were underpredicted by all the standard models (both two-equation and full Reynolds stress models). In cases where a more correct spreading rate was achieved, it was at the expense of the turbulent kinetic energy, which was overpredicted. In general, the Algebraic Dissipation Rate Model of Gatski and Speziale, 1992, when added to any of the standard models, improved the results dramatically. Also, full Reynolds stress closure models did a much better job at predicting the shapes of both the mean and turbulence profiles, but the spreading rate was not significantly improved over that predicted by the simpler two-equation models. There are two main conclusions from these studies: First, in a comparison such as this, it is not enough to compare just one parameter, like the spreading rate. A good prediction for one parameter does not necessarily imply good predictions for all parameters in a flow. Second, since no turbulence model could correctly predict the turbulent far wake, much of the important physics of turbulent free shear flows is apparently lost by the assumptions inherent in today's methods of turbulence modeling; turbulence models must be improved. Direct simulations of this flow were begun last year in order to provide a data base through which some of the deficiencies of the existing turbulence models could be identified. Quantities such as the pressure-strain correlation, turbulent diffusion, and the dissipation rate tensor can be easily calculated from the DNS results, whereas these quantities are nearly impossible to measure experimentally. Improvements to existing turbulence models (and development of new models) require knowledge about flow quantities such as these. During this summer, diagnostics codes were written which will calculate the parameters mentioned above, along with other single-point and multi-point statistics. The DNS calculations are still in progress at the time of this writing. When these calculations are complete, the diagnostics codes will be applied so that the results can aid turbulence modelers. In addition, the results will show whether or not there exists a universal equilibrium turbulent far wake, independent of initial conditions.

Cimbala, John M.↗

A new look at ocean ventilation time scales and their uncertainties

Abstract A suite of eddy‐resolving ocean transient tracer model simulations are first compared to observations. Observational and model pCFC‐11 ages agree quite well, with the eddy‐resolving model adding detail. The CFC ages show that the thermocline is a barrier to interior ocean exchange with the atmosphere on time scales of 45 years, the measureable CFC transient, although there are exceptions. Next, model simulations are used to quantify effects on tracer ages of the spatial dependence of internal ocean tracer variability due to stirring from eddies and biases from nonstationarity of the atmospheric transient when there is mixing. These add to tracer age uncertainties and biases, which are large in frontal boundary regions, and small in subtropical gyre interiors. These uncertainties and biases are used to reinterpret observed temporal trends in tracer‐derived ventilation time scales taken from observations more than a decade apart, and to assess whether interpretations of changes in tracer ages being due to changes in ocean ventilation hold water. For the southern hemisphere subtropical gyres, we infer that the rate of ocean ventilation 26–27.2 σ θ increased between the mid‐1990s and the decade of the 2000s. However, between the mid‐1990s and the decade of the 2010s, there is no significant trend—perhaps except for South Atlantic. Observed age/AOU/ventilation changes are linked to a combination of natural cycles and climate change, and there is regional variability. Thus, for the future it is not clear how strong or steady in space and time ocean ventilation changes will be.

58 GEOSCIENCES↗

Predicting beam transmission using 2-dimensional phase space projections of hadron accelerators

We present a method to compress the 2D transverse phase space projections from a hadron accelerator and use that information to predict the beam transmission. This method assumes that obtaining at least three projections of the 4D transverse phase space is possible and that an accurate simulation model is available for the beamline. Using a simulated model, we show that—a computer can train a convolutional autoencoder to reduce phase-space information which can later be used to predict the beam transmission. Finally, we argue that although using projections from a realistic nonlinear distribution produces less accurate results, the method still generalizes well.

43 PARTICLE ACCELERATORS↗

An ultrahigh-accuracy body pointing system for the Large Space Telescope

The Large Space Telescope (LST) program is aimed at placing a three-meter diffraction-limited telescope in a 270-nm orbit to perform astronomical observations that are not possible with earth-based telescopes. A complex simulation model is described which was developed to determine whether the stringent pointing stability requirements could be met. The model (programmed on a hybrid computer) included detailed dynamic representation of control moment gyros (CMGs) and reaction wheels (RWs), including their noise characteristics; dynamic sensor representation (including noise); shockmounts for the CMG actuators; detailed representation of an image motion compensation system; and a detailed flexible body vehicle model. Stability and performance studies based on the simulation model showed that the body pointing system will meet LST requirements in the presence of CMG vibrational disturbances and sensor noise. The recommended system consists of three orthogonally mounted RWs for primary short-term control, and a cluster of CMG actuators for continuous RW desaturation and vehicle maneuvering.

Rybak, S. C.↗

Revisiting the Potential of Melt Pond Fraction as a Predictor for the Seasonal Arctic Sea Ice Extent Minimum

The rapid change in Arctic sea ice in recent decades has led to a rising demand for seasonal sea ice prediction. A recent modeling study that employed a prognostic melt pond model in a stand-alone sea ice model found that September Arctic sea ice extent can be accurately predicted from the melt pond fraction in May. Here we show that satellite observations show no evidence of predictive skill in May. However, we find that a significantly strong relationship (high predictability) first emerges as the melt pond fraction is integrated from early May to late June, with a persistent strong relationship only occurring after late July. Our results highlight that late spring to mid summer melt pond information is required to improve the prediction skill of the seasonal sea ice minimum. Furthermore, satellite observations indicate a much higher percentage of melt pond formation in May than does the aforementioned model simulation, which points to the need to reconcile model simulations and observations, in order to better understand key mechanisms of melt pond formation and evolution and their influence on sea ice state.

sea ice↗

An Evaluation of Co-Simulation for Modeling Coupled Natural Gas and Electricity Networks

Reliance on natural gas for power generation has increased the coupling between gas and power networks. While this coupling can bring operational and economic benefits, it can also yield challenges, as the constraints in one system can impact the other. Co-simulation can capture the constraints and interactions between these systems, but so far, there has been limited comparison of co-simulation results to those of an integrated model. In this work, we develop a new co-simulation framework using the HELICS platform and the SAInt tool for modeling transient gas and AC optimal power flow. We evaluate this co-simulation framework against a fully integrated version of the SAInt power and gas simulators, thus providing a benchmarking of the co-simulation approach. We compare results across the two approaches for two test networks and a network representing the Belgian power and gas networks, testing both normal operating conditions and cases with compressor disruptions. In each of the cases tested, we find nearly identical results from the two approaches across various metrics of interest, such as nodal pressure, gas flow rates, and active power generation. This alignment suggests that co-simulation can yield comparable results to fully integrated models for modeling coupled gas and electricity networks.

03 NATURAL GAS↗

Evaluation of CMIP6 models in simulating the statistics of extreme precipitation over Eastern Africa

We report the Eastern Africa region experiences frequent extreme precipitation events that can cause destruction of property and environment, and loss of lives. Thus, there is a need to understand how these events may change in the future and how well the global climate models that are used to make projections can simulate precipitation extremes in this region before they can be used in downscaling or flood and drought impact assessment studies. In this work, we evaluated the ability of sixteen Coupled Model Intercomparison Project Phase 6 (CMIP6) models to simulate present-day precipitation extremes over the Eastern Africa region during the two rainy seasons (March–May and September–November). We used nine extreme precipitation indices (including seven (one) indices of wet (dry) extremes) defined by the Expert Team on Climate Change Detection and Indices. The CMIP6 models were evaluated against two gridded observation datasets: Global Precipitation Climatology Project One-Degree Daily Dataset and Tropical Rainfall Measuring Mission Multi-satellite Precipitation Analysis 3B42. Three model performance metrics (percentage bias, normalized root-mean-square error, and pattern correlation coefficient) were employed to further assess the strengths and weakness of the models. Our results show that the multi-model ensemble mean generally provides a better representation of observed precipitation and related extremes compared to individual models when considering all metrics and seasons. Several consistent biases are evident across CMIP6 models, which tend to overestimate the total-wet day precipitation and consecutive wet days, and underestimate very wet days and maximum 5-day precipitation in both seasons. Furthermore, no single model consistently performs best, model performance varies with the season and index under consideration and is generally independent of horizontal resolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Using Transport Diagnostics to Understand Chemistry Climate Model Ozone Simulations

We demonstrate how observations of N2O and mean age in the tropical and midlatitude lower stratosphere (LS) can be used to identify realistic transport in models. The results are applied to 15 Chemistry Climate Models (CCMs) participating in the 2010 WMO assessment. Comparison of the observed and simulated N2O/mean age relationship identifies models with fast or slow circulations and reveals details of model ascent and tropical isolation. The use of this process-oriented N2O/mean age diagnostic identifies models with compensating transport deficiencies that produce fortuitous agreement with mean age. We compare the diagnosed model transport behavior with a model's ability to produce realistic LS O3 profiles in the tropics and midlatitudes. Models with the greatest tropical transport problems show the poorest agreement with observations. Models with the most realistic LS transport agree more closely with LS observations and each other. We incorporate the results of the chemistry evaluations in the SPARC CCMVal Report (2010) to explain the range of CCM predictions for the return-to-1980 dates for global (60 S-60 N) and Antarctic column ozone. Later (earlier) Antarctic return dates are generally correlated to higher (lower) vortex Cl(sub y) levels in the LS, and vortex Cl(sub y) is generally correlated with the model's circulation although model Cl(sub y) chemistry or Cl(sub y) conservation can have a significant effect. In both regions, models that have good LS transport produce a smaller range of predictions for the return-to-1980 ozone values. This study suggests that the current range of predicted return dates is unnecessarily large due to identifiable model transport deficiencies.

Strahan, S. E.↗

Accelerated Fuel Qualification of Fast Modular Reactor Fuel in a Thermal Reactor: Modeling and Simulation Paired with Irradiation Testing

The accelerated fuel qualification (AFQ) methodology is applied by simulating accelerated fuel tests of the General Atomics Electromagnetic Systems’ fuel system for its 44-MW(electric) gas-cooled, fast-spectrum fast modular reactor (FMR). This fuel is comprised of UO 2 pellets in SiGA® cladding, a silicon carbide ceramic matrix composite. Fast reactors, like the FMR, offer many benefits, including high fuel utilization and flexibility, but may require a lengthy material design process if tests are performed using fast neutron irradiation alone. A thermal neutron irradiation can instead be used to rapidly test how well key components of the current material models extend to high burnup. Thermal neutrons produce a different radial power distribution within the pin than fast neutrons. However, the temperature and burnup values for the two neutron types are comparable, and the differences between the simulated fuel responses are relatively small, demonstrating the weak sensitivity of the physics-based fuel model calculations on the neutron type and the irradiation rate. Furthermore, the deformation of the SiGA cladding saturates after about 1 displacement per atom for both neutron spectra. In an accelerated fuel test, the irradiation time required to reach the target fuel burnup can be reduced by a factor of 3 by using a small rodlet with a 45% smaller pellet diameter while maintaining the same linear power. Therefore, the time for data collection up to high burnup can be significantly reduced while maintaining the same temperature profile, which largely determines the material response. Tests of fuel rodlets of standard and compact size will be carried out in the Idaho National Laboratory’s Advanced Test Reactor (ATR), including full size and compact rodlets with varying gap sizes. By applying physics-based mechanistic modeling and simulation in accordance with the AFQ methodology, this type of compact rodlet testing in a thermal test reactor captures the necessary phenomena to test fuel material models up to high burnup and to simulate the expected impact of fast neutron radiation on the fuel in FMR operations. Finally, this approach to testing fast reactor fuels in existing thermal test reactors, paired with advanced physics-based mechanistic modeling and simulation, is expected to be applicable to a range of advanced fuels and will decrease the overall fuel qualification timeframe from decades to years.

Advanced test reactor (ATR)↗

NASA ETM Modeling and Simulation Upper E Traffic Management Meeting December 2020

This is a slide set to be used as part of a meeting series with members of a working group aimed at the development of a concept that addresses needs and gaps in the management of high altitude airspace operations. This concept leverages elements developed through the UAS Traffic Management project with respect to a cooperative, service-based approach that provides services and capabilities in areas (e.g., Upper Class E airspace) that currently receive no or limited service from Air Traffic Control. This concept is meant to provide a safe, fair, and scalable approach to management of Upper Class E operations that reduces the burden on ATC while providing the flexibility and access desired by current and new users of the airspace. This set of slides includes an overview of the past accomplishments, current project structure, and a simulation roadmap for planned work ahead.

NASA ETM modeling and simulation↗

A Poisson equation method for prescribing fully developed non-Newtonian inlet conditions for computational fluid dynamics simulations in models of arbitrary cross-section

Prescribing inlet boundary conditions for computational fluid dynamics (CFD) simulations of internal flow in complex geometries such as anatomical vascular models is challenging. In the absence of patient-specific inlet velocity data, a common approach for long blood vessels is to assume that the inlet flow is fully developed. In vessels of irregular cross section, however, prescribing fully developed conditions is complicated due to the lack of a general closed-form analytical solution. In this study, we develop a simple Poisson equation method for prescribing fully developed inlet conditions for the flow of either Newtonian or non-Newtonian fluids in CFD models of arbitrary cross-section. We first derive the generalized Poisson equation for fully developed flow of a non-Newtonian fluid and we then develop and verify a methodology for numerically computing the solution on any planar boundary domain. In addition, we develop a simple extension of the method for prescribing a non-orthogonal inlet velocity that represents fully developed flow from an upstream tube that is connected to the CFD inlet at a non-orthogonal angle. This may be used to investigate a common source of uncertainty in CFD simulations of internal flow that is due to a lack of information concerning the exact streamwise flow direction at the inlets. Comparison to several Newtonian and non-Newtonian benchmark verification solutions shows the method to be extremely accurate. As a practical demonstration case, we use the method to prescribe fully developed conditions on multiple non-circular inlets for the non-Newtonian flow of blood in a patient-specific model of the inferior vena cava (IVC). Finally, we further demonstrate the utility of the method by performing a sensitivity study using the patient-specific IVC model, wherein we investigate the influence of inlet velocity flow direction on the non-Newtonian IVC hemodynamics. Given its simplicity and computational efficiency, the method is shown to be far superior to alternative approaches for prescribing fully developed inlet conditions in such complicated geometries. In conclusion, to facilitate the adoption of our Poisson equation method, we have distributed our OpenFOAM source code and the associated test cases from this study as open-source software.

97 MATHEMATICS AND COMPUTING↗

Modeling and Simulation of Air-Source CO2 Heat Pump Water Heater

Carbon dioxide (CO2) has been widely used as working fluid for the vapor-compression refrigeration systems in large marine device. Due to the potential energy efficiency and the favorable environmental properties of CO2 as a working fluid, CO2 heat pump water heater (HPWH) systems are regarded a promising technology for centralized domestic hot water (DHW) heating in residential and commercial buildings. However, there is still at the early stage of appropriately optimizing and improving the energy performance of CO2 HPWH. This requires CO2 HPWH simulation tools capable of capturing the accurate impact of the emerging compressor, throttle device, and heat exchanger technology on CO2 heat transfer and energy efficiency. In this study, high efficiency components (compressors, pumps, fans, heat exchangers) were identified and applied to the state-of-art CO2 HPWH designs and analyzed their performance by using numerical simulation. This was done by simulating the performance of CO2 HPWH using ACMODEL design model combined with the component models developed at Oak Ridge National Laboratory (ORNL) for orifice tube, map-based compressor, and tube-in-tube gas cooler. ACMODEL is an equipment design model for CO2-based air conditioners and heat pumps developed by Purdue University to account for the details of each component. The simulated CO2 HPWH performance was then compared with the heat pump water heater using conventional refrigerants.

Gao, Zhiming↗

Application of a Null-Space Monte Carlo Flow Model Set to the Composite Analysis Base Case Fate and Transport Modeling

The Plateau to River Groundwater Model (P2R Model) is a groundwater flow and contaminant fate and transport (F&T) simulation model used to support remedial activities conducted by CH2M HILL Plateau Remediation Company at the Hanford Site in Washington State. Figure 1-1 illustrates the P2R Model extents, discretization, and boundary conditions. The P2R Model is utilized in the Composite Analysis (CA) for the Hanford Site as the computational engine for computing F&T predictions as described in CP-60406, Hanford Site Composite Analysis Technical Approach Description: Groundwater. The model simulates contaminants of concern within the saturated zone of the uppermost aquifer beneath the Central Plateau and downgradient to the Columbia River. CP-57037, Model Package Report for the Plateau to River Model Version 8.3, documents the current version of the P2R Model including a description of the conceptual site model, model development and calibration, and limitations to the model application. The overall objective of the saturated zone modeling effort is to provide a basis for making informed remedial action decisions based on descriptions of current and expected future contaminant concentrations in groundwater at decision points within and downgradient of the Central Plateau of the Hanford Site. Specifically, the purpose of this environmental calculation is to describe the application of the hydraulic property fields and recharge parameters documented in ECF-HANFORD-20-0027, Null Space Monte Carlo Evaluation of the Plateau to River Model, to the CA flow and fate and transport simulation results to quantify the uncertainty in the simulated results due to input parameter selection. Use of numerical groundwater models is always accompanied with uncertainty in the results produced by a model because models are approximations of reality. Thus, by definition, models lack the detail to fully represent observed behavior. Use of numerical techniques, such as a NSMC analysis, can help in identifying and quantifying the potential uncertainties associated with a numerical model such as the P2R Model. The result of NSCM analysis is a set of F&T simulations that provide an estimate of the range of possible outcomes that are used to quantify the uncertainty in simulated concentrations produced using the base case simulations. The simulated concentrations from all simulations will support calculation of the uncertainty of the total dose calculated in a separate calculation.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Modeling and Simulation of Fuel Dispersal During the Loss-of-Coolant Accident

This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Discrete Element Model for Simulations of Early-Life Thermal Fracturing Behaviors in Ceramic Nuclear Fuel Pellets

A discrete element Model (DEM) representation of coupled solid mechanics/fracturing and heat conduction processes has been developed and applied to explicitly simulate the random initiations and subsequent propagations of interacting thermal cracks in a ceramic nuclear fuel pellet during initial rise to power and during power cycles. The DEM model clearly predicts realistic early-life crack patterns including both radial cracks and circumferential cracks. Simulation results clearly demonstrate the formation of radial cracks during the initial power rise, and formation of circumferential cracks as the power is ramped down. In these simulations, additional early-life power cycles do not lead to the formation of new thermal cracks. They do, however clearly indicate changes in the apertures of thermal cracks during later power cycles due to thermal expansion and shrinkage. The number of radial cracks increases with increasing power, which is consistent with the experimental observations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

System Modeling and Simulation of In-Stream Hydrokinetic Turbines for Power Management and Control

Electricity generation from moving currents without using dams (i.e., in-stream hydrokinetic electricity) has the potential to introduce multiple GW of renewable power to U.S. grids. Here this study evaluates a control system designed to regulate the generator rotor rate (rpm) to improve power production from in-stream hydrokinetic turbines. The control algorithm is evaluated using numerical models of both a rigidly mounted tidal turbine (TT) and a moored ocean current turbine (OCT) coupled to an induction electric machine model. The moored simulation utilizes an innovative approach for coupling a multiple degrees-of-freedom (DOF) nonlinear hydrodynamic/mechanical turbine model with a nonlinear electromechanical generator model. Based on the turbine torque-speed characteristic, as well as the asynchronous machine features, a proportional–integral (PI) controller is used to generate a correction term for the frequency of the three-phase sinusoidal voltages that are supplied to the asynchronous generator. The speed control of the induction generator through the supply frequency is accomplished by a simplified voltage source inverter (VSI). The simplified VSI consists of control voltage sources (CVSs), while the comparison with a real VSI using diodes and transistors, which are controlled by pulse width modulation (PWM) technique, is also presented. Simulations are used to evaluate the developed algorithms showing that rpm fluctuations are around 0.02 for a tidal turbine operating in a wave field with a 6 m significant wave height and around 0.005 for a moored ocean current turbine operating in a wave field with a 2 m significant wave height.

16 TIDAL AND WAVE POWER↗

Modeling and simulation of high dimensional stochastic multiscale PDE systems at the exascale

Predictive Modeling of multiscale and Multiphysics systems requires accurate data driven characterization of the input uncertainties, and understanding of how they propagate across scales and alter the final solution. This project develops a rigorous mathematical framework and scalable uncertainty quantification algorithms to efficiently construct realistic low dimensional input models, and surrogate low complexity systems for the analysis, design, and control of physical systems represented by multiscale stochastic PDEs. The work can be applied to many areas including physical and biological processes, from climate modeling to systems biology.

97 MATHEMATICS AND COMPUTING↗