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At least 1,045 records · Page 58

Lagged average forecasting, some operational considerations

The Lagged Average Forecast (LAF) method differs from the Monte Carlo Forecast (MCF) method in the definition of the ensemble of initial states which are used to generate the ensemble of forecasts. The LAF initial states are the current analysis and the forecasts made from previous analyses verifying the current time. Thus the LAF ensemble is composed of forecasts which are made by a regular operational system of numerical weather prediction and the LAF method is therefore operationally attractive. The application of the authors' previous ideas and results to an operational model requires the resolution of what might be called the degrees of freedom problem, i.e., how to obtain a homogeneous sample large enough to calculate stable statistics. It is suggested that this problem may be solved by carefully modeling the required statistics in terms of a small set of parameters and then estimating only these few parameters from the data. It is noted that there may be considerable information in each initial ensemble relating to the predictability of each particular case, and that this information may be incorporated in the model of the statistics.

Hoffman, R. N.↗

Frequency Reuse, Cell Separation, and Capacity Analysis of VHF Digital Link Mode 3 TDMA

The most recent studies by the Federal Aviation Administration (FAA) and the aviation industry have indicated that it has become increasingly difficult to make new VHF frequency or channel assignments to meet the aviation needs for air-ground communications. FAA has planned for several aggressive improvement measures to the existing systems, but these measures would not meet the projected voice communications needs beyond 2009. FAA found that since 1974 there has been, on the average, a 4 percent annual increase in the number of channel assignments needed to satisfy the air-ground communication traffic (approximately 300 new channel assignments per year). With the planned improvement measures, the channel assignments are expected to reach a maximum number of 16615 channels by about 2010. Hence, the FAA proposed the use of VDL Mode 3 as a new integrated digital voice and data communications systems to meet the future air traffic demand. This paper presents analytical results of frequency reuse; cell separation and capacity estimation of VDL Mode 3 TDMA systems that FAA has planned to implement the future VHF air-ground communications system by the year 2010. For TDMA, it is well understood that the frequency reuse factor is a crucial parameter for capacity estimation. Formulation of this frequency reuse factor is shown, taking into account the limitation imposed by the requirement to have a sufficient Signal to Co-Channel Interference Ratio. Several different values for the Signal to Co-Channel Interference Ratio were utilized corresponding to the current analog VHF DSB-AM systems, and the future digital VDL Mode 3. The required separation of Co-Channel cells is computed for most of the Frequency Protected Service Volumes (FPSV's) currently in use by the FAA. Additionally, the ideal cell capacity for each FPSV is presented. Also, using actual traffic for the Detroit air space, a FPSV traffic distribution model is used to generate a typical cell for channel capacity prediction. Such prediction is useful for evaluating the improvement of future VDL Mode 3 deployment and capacity planning.

Shamma, Mohammed A.↗

Transportation and Systems Analysis Collaborations in Support of a Federal Consolidated Interim Storage Facility

The U.S. Department of Energy’s Integrated Waste Management (IWM) program under the Office of Nuclear Energy is planning for the future transportation, storage, and eventual disposal of spent nuclear fuel (SNF) and high-level radioactive waste (HLW) from nuclear power plant sites across the United States. To better enable informed decision-making regarding the back end of the nuclear fuel cycle, the IWM program has been sponsoring the development and application of system analysis tools capable of analyzing various options for managing SNF and HLW. With these tools, integrated waste management system (IWMS) architecture analyses are being conducted to support the future deployment of a comprehensive nuclear waste management system that considers all major back-end aspects of the nuclear fuel cycle (i.e., transportation, storage, and disposal). System analyses and assessments typically use these modeling and simulation tools to investigate implications of changes in various assumptions and parameters such as acceptance rates, receipt logic, facility capacities and capabilities, use of standardized canisters, start and stop dates of facilities, etc. The Next Generation System Analysis Model (NGSAM) is an agent-based simulation toolkit that is used for a system-level simulation and analysis focused on SNF management in the United States. An analyst using NGSAM has the ability to define several factors like the number of storage facilities, capacity at each facility, transportation schedules, shipment rates, and other conditions. NGSAM’s primary purpose is to provide a system analyst with capabilities to model the IWMS and gain insights into SNF and HLW management alternatives including the impact of system choices, associated cost estimates, and development of integrated yet flexible approaches. IWM is also developing the Stakeholder Tool for Assessing Radioactive Transportation (START). START is a web-based geospatial tool developed to provide visualization and initial evaluation of transportation options associated with future SNF and HLW shipment planning and operations. This includes characterizing safety, economic, and environmental conditions on and in proximity to shipment origins as well as along prospective transportation routes. Information from the START tool can be presented/shared as maps, graphics, geospatial files, and tabular form to enable easy data representation and export functionality. The system analysis, NGSAM, and START teams had been working closely for several years before formalizing this collaboration. START provides the SNF routing information for use in NGSAM. System analysts use the NGSAM tool to generate results (schedule, costs, infrastructure acquisitions, shipment rates, etc.). Subject-matter experts and system analysts work together to inform how NGSAM should model the waste management system. Specifically, this paper discusses the collaborations between the system analysis, NGSAM, and START teams and their accomplishments over the past year. Some examples of these efforts include calibrating and adding data to the START output files to meet NGSAM needs, gaining a better understanding of START data used in NGSAM, as well as how updates in START data could result in an improved NGSAM analysis. Detailed examples of various tasks that have been performed by the team will be discussed in the full paper. Continued efforts in this direction are expected in the coming years.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Convenient analytical formula for cluster mean diameter and diameter dispersion after nucleation burst

Here, we propose an alternative method of estimating the mean diameter and dispersion of clusters of particles, formed in a cooling gas, right after the nucleation stage. Using a moment model developed by Friedlander [S. K. Friedlander, Ann. N. Y. Acad. Sci. 404, 354 (1983)], we derive an analytic relationship for both cluster mean diameter and diameter dispersion as a function of two of the characteristic times of the system: the cooling time and the primary constituents collision time. These formulas can be used to predict diameter and dispersion variation with process parameters, such as the initial primary constituents' concentration or cooling rate. It is also possible to use them as an input to the coagulation stage, without the need to compute complex cluster generation during the nucleation burst. We compared our results with a nodal code (NGDE) and got excellent agreement.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Evaluating Charge Equilibration Methods To Generate Electrostatic Fields in Nanoporous Materials

Charge equilibration (Qeq) methods can estimate the electrostatic potential of molecules and periodic frameworks by assigning point charges to each atom, using only a small fraction of the resources needed to compute density functional (DFT)-derived charges. This makes possible, for example, the computational screening of thousands of microporous structures to assess their performance for the adsorption of polar molecules. Recently, different variants of the original Qeq scheme were proposed to improve the quality of the computed point charges. One focus of this research was to improve the gas adsorption predictions in metal-organic frameworks (MOFs), for which many different structures are available. In this work, we review the evolution of the method from the original Qeq scheme, understanding the role of the different modifications on the final output. We evaluated the result of combining different protocols and set of parameters, by comparing the Qeq charges with high quality DFT-derived DDEC charges for 2338 MOF structures. We focused on the systematic errors that are attributable to specific atom types to quantify the final precision that one can expect from Qeq methods in the context of gas adsorption where the electrostatic potential plays a significant role, namely, CO 2 and H 2 S adsorption. In conclusion, both the type of algorithm and the input parameters have a large impact on the resulting charges, and we draw some guidelines to help the user to choose the proper combination of the two for obtaining a meaningful set of charges. We show that, considering this set of MOFs, the accuracy of the original Qeq scheme is often still comparable with the most recent variants, even if it clearly fails in the presence of certain atom types, such as alkali metals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A neural-network-enhanced parameter-varying framework for multi-objective model predictive control applied to buildings

Management of the electrical grid is becoming more complex due to the increased penetration of alternative energy generation technologies and a broadening diversity of electric loads. This complexity creates challenges in balancing demand and generation that can increase the potential for grid instabilities. One effective way to address this issue is to leverage previously unexploited demand flexibility through advanced control strategies. In this work, we propose an advanced control method, called adaptive neural parameter-varying model predictive control (ANPV-MPC), to control the temperature and energy consumption of a building via its Heating, Ventilation, and Air Conditioning system. ANPV-MPC combines key ideas in parameter-varying control, adaptive control, and online learning strategies to bridge the gap between computationally efficient linear model predictive control and more accurate nonlinear model predictive control. The novelty in ANPV-MPC is the use of a physics-inspired Bayesian neural network to estimate the coefficients of the parameter-varying linear control model. The Bayesian neural network additionally provides uncertainty estimates, triggering online training to capture evolving building system conditions. We show that ANPV-MPC can approximate the building system dynamics with a 28.39% higher accuracy than traditional linear model predictive control, resulting in 36.23% better control performance without increasing complexity of the optimal control problem. ANPV-MPC also adapts in real time to previously unseen conditions using online learning, further improving its performance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Pulsed anodic arc discharge for the synthesis of carbon nanomaterials

Pulsed arc discharges can improve arc control and tailor the ablation process in the production of 1D and 2D nanostructures from carbon anodes. In this work, low-dimensional carbon nanoparticles have been generated by means of anodic arc discharge in helium atmosphere excited with a square-wave modulated signal (1–5 Hz, 10% duty cycle). The discharges were performed between two graphite electrodes with maximal peak current of 250 A and maximal voltage of 65 V. The erosion rates and conversion efficiency of the ablated anode are compared to reference samples grown in DC steady arc mode. Ablation rates in pulsed arcs are typically of the order of 1 mg/s. Combination of fast Langmuir probe diagnostics and optical emission spectroscopy provided plasma parameters of the discharges at the arc column. Ranges of 10 16 –10 17 m -3 for electron density and 0.5–2.0 eV for electron temperature are estimated. The obtained samples were characterized with Raman spectroscopy and scanning electron microscopy. The deposit on the cathode after pulsed arc consisted of carbon nanostructures such as graphene nano-platelets and carbon nanotubes. Erosion dynamics of pulsed arc discharge has been described in terms of a global model and compared to steady arc discharge. A correlation is identified among discharge regimes, optical emission patterns and ablation modes. In conclusion, pulsed anodic arc discharge is a very efficient source of carbon nanomaterials. The large control of the discharge characteristics will permit to tailor accurately the production and the properties of carbon nanotubes and graphene. Here, this deposition method is promising for the fabrication of semiconducting nanomaterials with tuneable electrical and optical properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Roadmap for a Lightning Modeling Grand Challenge

This document is a roadmap for building an interconnected model of the physical processes that produce a lightning discharge, and its observable optical and radio signals. We call this a Lightning Modeling Grand Challenge, recognizing that significant effort and coordination of human and financial resources is required to realize the capability. The roadmap serves to outline the coordination of resources necessary to enable stitching together existing knowledge and model components to make a lightning prediction, and to test these predictions with observations. Such a capability does not currently exist. The roadmap is motivated not only by a spirit of scientific inquiry, but by practical challenges faced by US Federal and societal stakeholders. Advancements in lightning observations have outpaced our tests of integrated understanding, leaving many stakeholders unsure how to design their missions to properly detect and discriminate lightning, and unsure how to apply the sometimes-disagreeing lightning signals from diverse instruments. The time is right to connect existing theories and models to support stakeholders in understanding the signals they observe, for needs as diverse as climate monitoring, national security, weather forecasting, public safety, and protection of natural and built environments. The roadmap’s two main technical sections describe the components of a linked physical model, followed by a description of models of lightning signals and sensors that are driven by outputs from the physical model. The goal is to predict the time-varying physical properties of lightning that are self-consistent with the thunderstorm’s structure and dynamics. These lightning signals then propagate through the storm, with realistic dispersion and attenuation, to receivers on the ground or in space. At a high level, the model begins with weather (cloud) model output, including explicit prediction of the electrification of cloud particles. The cloud’s electrical structure drives a model of lightning physics, from initiation, through channel development, and discharges along those channels. Key lightning parameters, such as the temperature and currents in the channel, and their space and time distribution, are then used to produce optical and electromagnetic signal sources that propagate to modeled receivers. This architecture therefore generates a dataset suitable for comparison to existing and envisioned observing systems. The need for additional measurements and field campaigns to support model development is described. In each model sub-component, inputs, outputs, uncertainties, evaluation methods, and next steps are summarized, interleaved with references to the scientific literature. Identifying boundaries between the model sub-components aids in segmenting an integrated, complex model into practical work packages and system sub-components, allowing a diverse team to contribute and maintain the system. We estimate that at least five years of effort and a $\$$10M initial investment is necessary to make a significant step forward. Mechanisms to facilitate community coordination, including annual workshops and open-source code repositories, are described.

54 ENVIRONMENTAL SCIENCES↗

A wall interference assessment/correction system

The Hackett method (a Wall Pressure Signature Method) was selected to be adapted for the 12 ft Wind Tunnel WIAC system. This method uses limited measurements of the static pressure at the wall, in conjunction with the solid wall boundary condition, to determine the strength and distribution of singularities representing the test article. The singularities are used in term for estimating wall interference at the model location. Hackett's method will have to be formulated for application to the unique geometry of the 12 ft tunnel. The WIAC code will be validated by conducting numerically simulated experiments rather than actual wind tunnel experiments. The simulations will be used to generate both free air and confined wind tunnel flow fields for each of the test articles over a range of test configurations. Specifically the pressure signature at the test section wall will be computed for the confined case to provide the simulated 'measured' data. These data will serve as the input for the WIAC method. The performance of the WIAC method then may be evaluated by comparing the corrected parameters with those for the free air simulation.

Lo, C. F.↗

ANALYTIC H i-to-H{sub 2} PHOTODISSOCIATION TRANSITION PROFILES

We present a simple analytic procedure for generating atomic (H i) to molecular (H{sub 2}) density profiles for optically thick hydrogen gas clouds illuminated by far-ultraviolet radiation fields. Our procedure is based on the analytic theory for the structure of one-dimensional H i/H{sub 2} photon-dominated regions, presented by Sternberg et al. Depth-dependent atomic and molecular density fractions may be computed for arbitrary gas density, far-ultraviolet field intensity, and the metallicity-dependent H{sub 2} formation rate coefficient, and dust absorption cross section in the Lyman–Werner photodissociation band. We use our procedure to generate a set of H I-to-H{sub 2} transition profiles for a wide range of conditions, from the weak- to strong-field limits, and from super-solar down to low metallicities. We show that if presented as functions of dust optical depth, the H I and H{sub 2} density profiles depend primarily on the Sternberg “αG parameter” (dimensionless) that determines the dust optical depth associated with the total photodissociated H I column. We derive a universal analytic formula for the H I-to-H{sub 2} transition points as a function of just αG. Our formula will be useful for interpreting emission-line observations of H i/H{sub 2} interfaces, for estimating star formation thresholds, and for sub-grid components in hydrodynamics simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

Magnetostrophic balance in planetary dynamos - Predictions for Neptune's magnetosphere

With the purpose of estimating Neptune's magnetic field and its implications for nonthermal Neptune radio emissions, a new scaling law for planetary magnetic fields was developed in terms of externally observable parameters (the planet's mean density, radius, mass, rotation rate, and internal heat source luminosity). From a comparison of theory and observations by Voyager it was concluded that planetary dynamos are two-state systems with either zero intrinsic magnetic field (for planets with low internal heat source) or (for planets with the internal heat source sufficiently strong to drive convection) a magnetic field near the upper bound determined from magnetostrophic balance. It is noted that mass loading of the Neptune magnetosphere by Triton may play an important role in the generation of nonthermal radio emissions.

Curtis, S. A.↗

On Lidar Sounding of the Atmosphere to Estimate Static and Dynamic Characteristics of Aerosol Inhomogeneities

1. A possible application of intensity fluctuations of a pulse light signal reflected by atmospheric aerosols is analyzed by the correlation method to evaluate static (medium sizes, shape) and dynamic (speed and direction of movement, lifetime) characteristics of aerosol inhomogeneities. The aerosol inhomogeneities are assumed to be expanded, pressed, disintegrated and originated constantly in accordance with random laws, the set of inhomogeneities as a whole traveling together with air masses and having predominant movement in wind direction. It is shown that the characteristics of aerosol inhomogeneities considered can be expressed by the coefficients of the correlation function expansion of the reflected signal fluctuation intensity in Tailor series. 2/ Correlation systems for evaluating static and dynamic characteristics of driving objects can be divided into two types according to the kind and quantity of used information: the systems with coordinates of the information removal "points" to be fixed in space, and the systems with a parallel simultaneous information removal at discrete moments of time. The systems for determination of wind direction considered in are the examples of the first type system. However, the operating information removal for two points is insufficient to estimate completely static and dynamic characteristics of inhomogenities, their quantity ought to be increased up to three of them for two-dimensional problem and up to four of them for three-dimensional problem as it is usually done in the ionospheric studies. The second type systems are used for the investigation of a medium shape and speed of the clouds according to photographs made from satellites. These systems are also used for solution of navigation problems. The use of optical quantum generators with a scanning beam is seen to increase greatly the working information removal in comparison with the first type systems. Nevertheless, scanning rate is not sufficient sometimes in order· to consider a general picture of aerosol inhomogeneities to be stationary. In this connection the use of the systems of second type treatment becomes a matter of essential difficulty. 3. Aerosol inhomogeneities simulation has been carried out on the basis of the digital computer experiments with the aim of estimating static and dynamic characteristics of inhomogeneities by an optical beam in the atmosphere at different scanning procedures. The dependence of determination accuracy of these characteristics on the type of chosen laws of aerosol particle distribution in the atmosphere, the parameters of inhomogeneities geometry, their speed and the law of scanning have been obtained.

Zuev, V. E.↗

1960 Chile - New estimate of polar motion excitation

A recent reanalysis of the International Latitude Serivce (ILS) polar motion data-day has been processed using Kalman filtering techniques to generate the polar motion excitation function over the time-span from 1960 to 1965. The resulting excitation function has been examined for the effects of 1960 Chile in an attempt to determine experimentally how large earthquake affect polar motion. The resulting upper bound of about 75 x 10 to the 22nd N-m for a 10-deg dip (about 36 x 10 to the 22nd N-m for 20-deg dip) is consistent with results obtained from previous seismic studies, including a recent normal mode excitation result. Following future great earthquakes, monitoring of polar motion by space-based techniques such as VLBI should continue at high temporal resolution for several weeks in order to directly measure the rheological parameters of the upper mantle.

Slade, M. A.↗

Next Generation Fiber-Encapsulated Nanoscale Hybrid Materials for Direct Air Capture with Selective Water Rejection

Recently, NOHMs sorbents have been demonstrated to be highly stable and tunable for CO2 capture and have negligible vapor pressure, but their main drawbacks are high viscosity and high gas transfer limitation in their neat bulk phase. This project explored gas-assisted electrospinning processing coupled with promising encapsulation matrices such as Polymers with Intrinsic Microporosity (PIM-1) and polyacrylonitrile (PAN)/organopolysilizane (OPSZ) polymer/ceramic hybrid materials, which were demonstrated to be effective novel carriers for the active NOHMs sorbents. These encapsulation materials were evaluated by their thermal stability, hydrophobicity, permeability, and CO2 selectivity. The manufacturing parameters such as component composition and processing solvent were linked to bulk sorbent properties, e.g., surface area, pore volume, fiber thickness, capture capacity, capture kinetics, etc. These investigations resulted in fundamental knowledge and technical know-how that will be useful for scaling up the nanofiber mat contactor design. The encapsulation materials and design has been shown to not only increase the thermal oxidative stability of the NOHMs, but also yield significantly reduced pressure drop and increased performance of large modular air filters. 70 PAN: 30 OPSZ/NIPEI fibers exhibited the highest capture performance with 1.5 mmol CO2/g∙h kinetics the first hour under 100% CO2 condition, followed by 80 PAN: 20 OPSZ/NIPEI and 90 PAN: 10 OPSZ/NIPEI, while 90 PAN: 10 OPSZ/NIPEI fibers performed the best with 0.25 mmol CO2/g∙h of the initial kinetics under 400 ppm CO2 concentration. All the fabricated fibers demonstrated stable capture performances up to 15 cycles of adsorption and desorption. Using encapsulated NOHMs, the study found that the microwave could help regenerate the capture materials within 20 minutes without chemically degrading the materials. A high-level TEA/LCA study was performed to evaluate the feasibility of this technology at scale. These estimates show that the sorbent cost and environmental impact levels are comparable to other existing technologies. Overall, these findings increase the technological feasibility of using liquid-like, low vapor pressure NOHMs as a next generation sorbent for the direct air capture of CO2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

ENSEMBLE KALMAN FILTERS FOR RELIABILITY ESTIMATION IN PERFUSION INFERENCE

We consider the solution of inverse problems in dynamic contrast–enhanced imaging by means of ensemble Kalman filters. Our quantity of interest is blood perfusion, i.e., blood flow rates in tissue. While existing approaches to compute blood perfusion parameters for given time series of radiological measurements mainly rely on deterministic, deconvolution–based methods, we aim at recovering probabilistic solution information for given noisy measurements. To this end, we model radiological image capturing as a sequential data assimilation process and solve it by an ensemble Kalman filter. Thereby, we recover deterministic results as an ensemble–based mean and are able to compute reliability information such as probabilities for the perfusion to be in a given range. Our target application is the inference of blood perfusion parameters in the human brain. A numerical study shows promising results for artificial measurements generated by a digital perfusion phantom.

Engineering↗

Physics informed neural network can retrieve rate and state friction parameters from acoustic monitoring of laboratory stick-slip experiments

Various machine learning (ML) and deep learning (DL) techniques have been recently applied to the forecasting of laboratory earthquakes from friction experiments. The magnitude and timing of shear failures in stick-slip cycles are predicted using features extracted from the recorded ultrasonic or acoustic emission (AE) signals. In addition, the Rate and State Friction (RSF) constitutive laws are extensively used to model the frictional behavior of faults. In this work, we use data from shear experiments coupled with passive acoustic (variance, kurtosis, and AE rate) interleaved with active source ultrasonic monitoring (transmitted wave amplitude) to develop physics-informed neural network (PINN) models incorporating the RSF law and AE rate generation equation with wave amplitude serving as a proxy for friction state variable. This PINN framework allows learning RSF parameters from stick-slip experiments rather than measuring them through a series of velocity step experiments. We observe that when the stick-slip cycles are irregular, the PINN models outperform the data-driven DL models. Transfer learning (TL) PINN models are also developed by pre-training on data collected at one normal stress level followed by forecasting shear failures and retrieving RSF parameters at other stress levels (i.e., with different recurrence intervals) after retraining on a limited amount of new data. Our findings suggest that TL models perform better compared to standalone models. Both standalone and TL PINN-estimated RSF parameters and their ground truth values show excellent agreements thus demonstrating that RSF parameters can be retrieved from laboratory stick-slip experiments using the corresponding acoustic data and that the transmitted wave amplitude provides a good representation of the evolving frictional state during stick-slips.

58 GEOSCIENCES↗

Error analysis of numerical methods for thick diffusive neutron transport problems on Shishkin mesh

A thin layer will develop at the boundary if the incoming angular flux is anisotropic in thick diffusive neutron transport problems. Solving such singularly perturbed problems, which have non-smooth solutions with singularity near the boundary, is computationally challenging. Standard finite difference schemes on a uniform mesh cannot yield ε-uniform convergence, where ε is a small parameter, while it can be achieved on a suitable piecewise-uniform Shishkin mesh. We present a formal error analysis of the diamond difference (DD) method and step difference (SD) method for solving the S{sub N} neutron transport equation. The analysis can be extended to other finite difference methods. Numerical results are presented to confirm the error estimates and the advantages of the Shishkin mesh. (author)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Simulating Dopant Diffusion in a Detalied Porous Structure

The National Ignition Facility (NIF) at Lawrence Livermore National Laboratory (LLNL) uses highpowered lasers to explore cutting edge fusion technology. Specialized optics, known as fiber lasers, generate and amplify the NIF’s high-powered lasers that facilitate fusion experiments. Fiber lasers are glass fibers that are doped with heavy elements to stimulate light emission. The fiber laser doping processing uses a predeposited layer of porous silica nanoparticles on the surface of the glass to absorb a dopant rich salt solution. Our project simulated the diffusion of dopants into porous silica with prescribed colloidal stacking geometries using COMSOL Multiphysics. With these simulations we identified the porosity and tortuosity of the porous nanoparticle structures as the primary parameters that will dictate how the dopants will diffusive into the porous surface of the glass. Porosity and Tortuosity are geometric parameters that can easily be input into more detailed simulations to estimate an effective diffusivity within the porous layer. Future work should account for surface reactions to accurately simulate the full-scale diffusion of the solution doping process.

36 MATERIALS SCIENCE↗