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All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Time Resolved Stereo Particle Image Velocimetry Measurements of the Instabilities Downstream of a Backward-Facing Step in a Swept-Wing Boundary Layer

Time-resolved particle image velocimetry (TRPIV) measurements are performed down-stream of a swept backward-facing step, with a height of 49% of the boundary-layer thickness. The results agree well qualitatively with previously reported hotwire measurements, though the amplitudes of the fluctuating components measured using TRPIV are higher. Nonetheless, the low-amplitude instabilities in the flow are fairly well resolved using TR- PIV. Proper orthogonal decomposition is used to study the development of the traveling cross flow and Tollmien-Schlichting (TS) instabilities downstream of the step and to study how they interact to form the large velocity spikes that ultimately lead to transition. A secondary mode within the traveling cross flow frequency band develops with a wavelength close to that of the stationary cross flow instability, so that at a certain point in the phase, it causes an increase in the spanwise modulation initially caused by the stationary cross flow mode. This increased modulation leads to an increase in the amplitude of the TS mode, which, itself, is highly modulated through interactions with the stationary cross flow. When the traveling cross flow and TS modes align in time and space, the large velocity spikes occur. Thus, these three instabilities, which are individually of low amplitude when the spikes start to occur (U'rms/Ue <0.03), interact and combine to cause a large flow disturbance that eventually leads to transition.

Eppink, Jenna L.↗
DOE OSTI2023

Numerical Circuit Synthesis and Compilation for Multi-State Preparation

Near-term quantum computers have significant error rates and short coherence times, so compilation of circuits to be as short as possible is essential. Two types of compilation problems are typically considered: circuits to prepare a given state from a fixed input state, called 'state preparation'; and circuits to implement a given unitary operation, for example by 'unitary synthesis'. In this paper we solve a more general problem: the transformation of a set of m states to another set of m states, which we call 'multi-state preparation'. State preparation and unitary synthesis are special cases; for state preparation, m=1, while for unitary synthesis, m is the dimension of the full Hilbert space. We generate and optimize circuits for multi-state preparation numerically. In cases where a top-down approach based on matrix decompositions is also possible, our method finds circuits with substantially (up to 40 %) fewer two-qubit gates. We discuss possible applications, including efficient preparation of macroscopic superposition ('cat') states and synthesis of quantum channels.

Szasz, Aaron↗
NASA NTRS2019

Investigation of Transitional Shock-Wave/Boundary Layer Interactions Using Direct Numerical Simulations

Interaction of a transitional boundary layer with a normal-shock is investigated using unstructured tetrahedral meshes under the numerical framework of the space-time conservation element, solution element (CESE) method. The computations mimic recent experimental efforts at the University of Tennessee Space Institute, where a Mach 2.0 flow interacts with a tall cylinder attached to a flat plate. The location of the cylinder with respect to the flat plate leading edge determines if the incoming boundary layer is laminar, transitional or fully turbulent. Four representative flow conditions exemplifying laminar and transitional boundary layers are analyzed by direct numerical simulations. Similar to what was observed in the experiments for the case of transitional interaction, the computations reveal an intermittent upstream influence (UI) shock that repeatedly travels upstream from the lambda-foot toward the leading edge before vanishing. Through detailed unsteady flow analysis obtained using Fourier analysis and dynamic mode decomposition techniques, the presence of disturbances with similar frequencies as those measured in experiments were identified in the flow along with locations that appear to influence the dynamics of the flow.

Venkatachari, Balaji Shankar↗
NASA NTRS2016

Magnesium Sulfate as a Key Mineral for the Detection of Organic Molecules on Mars Using Pyrolysis

Pyrolysis of soil or rock samples is the preferred preparation technique used on Mars to search for organic molecules up today. During pyrolysis, oxichlorines present in the soil of Mars release oxidant species that alter the organic molecules potentially contained in the samples collected by the space probes.This process can explain the difficulty experienced by in situ exploration probes to detect organic materials in Mars soil samples until recently. Within a few months, the Curiosity rover should reach and analyze for the first time soils rich in sulfates which could induce a different behavior of the organics during the pyrolysis compared with the types of soils analyzed up today. For this reason, we systematically studied the pyrolysis of organic molecules trapped in magnesium sulfate, in the presence or absence of calcium perchlorate. Our results show that organics trapped in magnesium sulfate can undergo some oxidation and sulfuration during the pyrolysis. But these sulfates are also shown to protect organics trapped inside the crystal lattice and/or present in fluid inclusions from the oxidation induced by the decomposition of calcium perchlorate and probably other oxychlorine phases currently detected on Mars. Trapped organics may also be protected from degradation processes induced by other minerals present in the sample, at least until these organics are released from the pyrolyzed sulfate mineral (700C in our experiment). Hence, we suggest magnesium sulfate as one of the minerals to target in priority for the search of organic molecules by the Curiosity and ExoMars 2018 rovers.

Francois, P.↗
DOE OSTI2021

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Forward variable selection enables fast and accurate dynamic system identification with Karhunen-Loève decomposed Gaussian processes

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Loève (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection thus becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. Theoretical computational complexities are O ( N P 2 ) in training and O ( P ) per point in inference, where N is the number of instances and P the number of expansion terms. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a ‘Susceptible, Infected, Recovered’ (SIR) toy problem, along with the experimental ‘Cascaded Tanks’ benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with the SINDy package.

Hayes, Kyle↗
DOE OSTI2022

Bundle Networks: Fiber Bundles, Local Trivializations, and a Generative Approach to Exploring Many-to-one Maps

Many-to-one maps are ubiquitous in machine learning, from the image recognition model that assigns a multitude of distinct images to the concept of ``cat'' to the time series forecasting model which assigns a range of distinct time-series to a single scalar regression value. While the primary use of such models is naturally to associate correct output to each input, in many problems it is also useful to be able to explore, understand, and sample from a model's fibers, which are the set of input values x such that f(x) = y, for fixed y in the output space. In this paper we show that popular generative architectures are ill-suited to such tasks. Motivated by this we introduce a novel generative architecture, a Bundle Network, based on the concept of a fiber bundle from (differential) topology. BundleNets exploit the idea of a local trivialization wherein a space can be locally decomposed into a product space that cleanly encodes the many-to-one nature of the map. By enforcing this decomposition in BundleNets and by utilizing state-of-the-art invertible components, investigating a network's fibers becomes natural.

Courts, Nicolas C.↗
NASA NTRS1994

Hierarchical modeling for reliability analysis using Markov models

Markov models represent an extremely attractive tool for the reliability analysis of many systems. However, Markov model state space grows exponentially with the number of components in a given system. Thus, for very large systems Markov modeling techniques alone become intractable in both memory and CPU time. Often a particular subsystem can be found within some larger system where the dependence of the larger system on the subsystem is of a particularly simple form. This simple dependence can be used to decompose such a system into one or more subsystems. A hierarchical technique is presented which can be used to evaluate these subsystems in such a way that their reliabilities can be combined to obtain the reliability for the full system. This hierarchical approach is unique in that it allows the subsystem model to pass multiple aggregate state information to the higher level model, allowing more general systems to be evaluated. Guidelines are developed to assist in the system decomposition. An appropriate method for determining subsystem reliability is also developed. This method gives rise to some interesting numerical issues. Numerical error due to roundoff and integration are discussed at length. Once a decomposition is chosen, the remaining analysis is straightforward but tedious. However, an approach is developed for simplifying the recombination of subsystem reliabilities. Finally, a real world system is used to illustrate the use of this technique in a more practical context.

Fagundo, Arturo↗
NASA NTRSDate not supplied

Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements for the NASA Unitary Plan Wind Tunnel Tests

This paper discusses the Dynamic Mode Decomposition (DMD) of the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected with four Phantom high-speed cameras at a constant sample frequency in the Ascent Transient Aerodynamics Test (ATAT) of the Space Launch System (SLS) Block 1 cargo vehicle with the Unitary Plan Wind Tunnel (UPWT) 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD). For the data with zero mean, the DMD is equivalent to the Discrete Fourier Transform (DFT). Since the uPSP is mainly used to determine the unsteady property of the aerodynamic flow, the DMD of the uPSP measurements is implemented in two steps: (1) subtract the mean value from the uPSP measurement; (2) apply the Fast Fourier Transform (FFT) on the resulting data with zero mean. The DMD of the uPSP measurements with FFT has two advantages: (1) the FFT algorithm is well known for its computational efficiency, therefore, compared to the SVD-based DMD algorithm, the DMD with FFT reduces the computation time; (2) the DMD with FFT can be easily implemented in parallel processing. The DMD outputs were generated with the execution in parallel of a code in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, on the NASA Pleiades supercomputer. In this paper, the results of DMD of the uPSP measurements in the tests of Mach sweep runs of the SLS ATAT are presented, and the effectiveness of the DMD of the uPSP measurements in the diagnosis of the unsteady, aerodynamic phenomena is demonstrated. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding for this research was provided by the NASA Aeroscience Evaluation and Test Capabilities Project.

Pressure-Sensitive Paint↗
DOE OSTI2020

Data-driven modeling and control of dynamical systems using Koopman and Perron-Frobenius operators

This dissertation studies the data-driven modeling and control problem of nonlinear systems by exploiting the linear operator theoretic framework involving Koopman and Perro-Frobenius operator. A systematic linear-operator based controller design procedure has been established, which can be used to solve a variety of nonlinear control problems, including feedback stabilization using control Lyapunov functions, optimal quadratic regulation using Koopman eigenfunctions and convex optimization formulation of optimal control problem using P-F and Koopman operator approximation. As the core of data-driven modeling, we first propose a new algorithm for the finite-dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time-series data. We argue that the existing approach for the finite-dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose preserves these two properties. We call the proposed algorithm as naturally structured DMD (NSDMD) since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite-dimensional approximation play an important role for controller and estimator design of nonlinear systems. To solve the feedback stabilization problem for nonlinear control systems, we tried to take advantage of the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this dissertation is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Next, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite-dimensional bilinear system. The optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite-dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. We applied a variety of examples and compared the simulation results between our framework and conventional LQR control using linearized model. For more general optimal control problems, we provide a density-function based convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the stability theory of a dynamical system involving density function and Perron-Frobenius operator. The optimal control problem is formulated as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the data-driven computation of the Koopman operator, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.

Huang, Bowen↗
NASA NTRS1995

Monitoring Composite Material Pressure Vessels with a Fiber-Optic/Microelectronic Sensor System

We discuss the concept of an integrated, fiber-optic/microelectronic distributed sensor system that can monitor composite material pressure vessels for Air Force space systems to provide assessments of the overall health and integrity of the vessel throughout its entire operating history from birth to end of life. The fiber optic component would include either a semiconductor light emitting diode or diode laser and a multiplexed fiber optic sensing network incorporating Bragg grating sensors capable of detecting internal temperature and strain. The microelectronic components include a power source, a pulsed laser driver, time domain data acquisition hardware, a microprocessor, a data storage device, and a communication interface. The sensing system would be incorporated within the composite during its manufacture. The microelectronic data acquisition and logging system would record the environmental conditions to which the vessel has been subjected to during its storage and transit, e.g., the history of thermal excursions, pressure loading data, the occurrence of mechanical impacts, the presence of changing internal strain due to aging, delamination, material decomposition, etc. Data would be maintained din non-volatile memory for subsequent readout through a microcomputer interface.

Klimcak, C.↗
NASA NTRS2000

Interannual Atmospheric Oscillations and Their Gravitational Effects

Past studies have examined the effects of the interannual atmospheric oscillations (IAO), or often called teleconnection patterns, on the Earth's rotation, such as El Nino/Southern Oscillation (ENSO), the quasi-biennial oscillation, and to a lesser extent the North Atlantic Oscillation (NAO). The present study focuses on IAO's effects on the gravitational field and geocenter; the purpose is to be able to identify and isolate the contributions of each prominent IAO in relation to the total contribution of the atmosphere, in terms of their magnitudes, their geographical patterns, and their interannual time history. We use the 40-year NCEP reanalysis of the monthly, global atmospheric surface pressure field as our basic data set. The method we apply to isolate the IAOs is the empirical orthogonal function (EOF) decomposition which is widely used in meteorological investigations. We do the EOF analysis first on IAOs' seasonal signals (by "collapsing" the 40-year series into 12 mean-months for each grid point) and obtain estimates for their respective contributions. Then we remove these seasonal signals from the data to focus on the (broad-band) interannual EOFs. We examine ENSO, NAO, North Pacific Oscillation, and other less prominent IAOs that can be identified from our data set, and compute their respective contributions to the variation of global gravitational field and geocenter motion. Finally, we compare the results with the available observational data, and discuss the implications w.r.t. the upcoming space missions such as GRACE.

Chao, Benjamin F.↗
NASA NTRS2000

A Domain-Decomposed Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

Preliminary verification and validation of an efficient Euler solver for adaptively refined Cartesian meshes with embedded boundaries is presented. The parallel, multilevel method makes use of a new on-the-fly parallel domain decomposition strategy based upon the use of space-filling curves, and automatically generates a sequence of coarse meshes for processing by the multigrid smoother. The coarse mesh generation algorithm produces grids which completely cover the computational domain at every level in the mesh hierarchy. A series of examples on realistically complex three-dimensional configurations demonstrate that this new coarsening algorithm reliably achieves mesh coarsening ratios in excess of 7 on adaptively refined meshes. Numerical investigations of the scheme's local truncation error demonstrate an achieved order of accuracy between 1.82 and 1.88. Convergence results for the multigrid scheme are presented for both subsonic and transonic test cases and demonstrate W-cycle multigrid convergence rates between 0.84 and 0.94. Preliminary parallel scalability tests on both simple wing and complex complete aircraft geometries shows a computational speedup of 52 on 64 processors using the run-time mesh partitioner.

Aftosmis, M. J.↗
NASA NTRS1999

Parallelization of the Physical-Space Statistical Analysis System (PSAS)

Atmospheric data assimilation is a method of combining observations with model forecasts to produce a more accurate description of the atmosphere than the observations or forecast alone can provide. Data assimilation plays an increasingly important role in the study of climate and atmospheric chemistry. The NASA Data Assimilation Office (DAO) has developed the Goddard Earth Observing System Data Assimilation System (GEOS DAS) to create assimilated datasets. The core computational components of the GEOS DAS include the GEOS General Circulation Model (GCM) and the Physical-space Statistical Analysis System (PSAS). The need for timely validation of scientific enhancements to the data assimilation system poses computational demands that are best met by distributed parallel software. PSAS is implemented in Fortran 90 using object-based design principles. The analysis portions of the code solve two equations. The first of these is the "innovation" equation, which is solved on the unstructured observation grid using a preconditioned conjugate gradient (CG) method. The "analysis" equation is a transformation from the observation grid back to a structured grid, and is solved by a direct matrix-vector multiplication. Use of a factored-operator formulation reduces the computational complexity of both the CG solver and the matrix-vector multiplication, rendering the matrix-vector multiplications as a successive product of operators on a vector. Sparsity is introduced to these operators by partitioning the observations using an icosahedral decomposition scheme. PSAS builds a large (approx. 128MB) run-time database of parameters used in the calculation of these operators. Implementing a message passing parallel computing paradigm into an existing yet developing computational system as complex as PSAS is nontrivial. One of the technical challenges is balancing the requirements for computational reproducibility with the need for high performance. The problem of computational reproducibility is well known in the parallel computing community. It is a requirement that the parallel code perform calculations in a fashion that will yield identical results on different configurations of processing elements on the same platform. In some cases this problem can be solved by sacrificing performance. Meeting this requirement and still achieving high performance is very difficult. Topics to be discussed include: current PSAS design and parallelization strategy; reproducibility issues; load balance vs. database memory demands, possible solutions to these problems.

Larson, J. W.↗
NASA NTRS2017

A Space-Based Observational Strategy for Characterizing the First Stars and Galaxies Using the Redshifted 21cm Global Spectrum

The redshifted 21 cm monopole is expected to be a powerful probe of the epoch of the first stars and galaxies(10 less than z less than 35). The global 21 cm signal is sensitive to the thermal and ionization state of hydrogen gas and thusprovides a tracer of sources of energetic photonsprimarily hot stars and accreting black holeswhich ionize andheat the high redshift intergalactic medium (IGM). This paper presents a strategy for observations of the globalspectrum with a realizable instrument placed in a low-altitude lunar orbit, performing night-time 40120 MHzspectral observations, while on the farside to avoid terrestrial radio frequency interference, ionospheric corruption,and solar radio emissions. The frequency structure, uniformity over large scales, and unpolarized state of theredshifted 21 cm spectrum are distinct from the spectrally featureless, spatially varying, and polarized emissionfrom the bright foregrounds. This allows a clean separation between the primordial signal and foregrounds. Forsignal extraction, we model the foreground, instrument, and 21 cm spectrum with eigenmodes calculated viaSingular Value Decomposition analyses. Using a Markov Chain Monte Carlo algorithm to explore the parameterspace defined by the coefficients associated with these modes, we illustrate how the spectrum can be measured andhow astrophysical parameters (e.g., IGM properties, first star characteristics) can be constrained in the presence offoregrounds using the Dark Ages Radio Explorer (DARE).

Burns, Jack O.↗
NASA NTRS2013

Applying Model Based Systems Engineering to NASA's Space Communications Networks

System engineering practices for complex systems and networks now require that requirement, architecture, and concept of operations product development teams, simultaneously harmonize their activities to provide timely, useful and cost-effective products. When dealing with complex systems of systems, traditional systems engineering methodology quickly falls short of achieving project objectives. This approach is encumbered by the use of a number of disparate hardware and software tools, spreadsheets and documents to grasp the concept of the network design and operation. In case of NASA's space communication networks, since the networks are geographically distributed, and so are its subject matter experts, the team is challenged to create a common language and tools to produce its products. Using Model Based Systems Engineering methods and tools allows for a unified representation of the system in a model that enables a highly related level of detail. To date, Program System Engineering (PSE) team has been able to model each network from their top-level operational activities and system functions down to the atomic level through relational modeling decomposition. These models allow for a better understanding of the relationships between NASA's stakeholders, internal organizations, and impacts to all related entities due to integration and sustainment of existing systems. Understanding the existing systems is essential to accurate and detailed study of integration options being considered. In this paper, we identify the challenges the PSE team faced in its quest to unify complex legacy space communications networks and their operational processes. We describe the initial approaches undertaken and the evolution toward model based system engineering applied to produce Space Communication and Navigation (SCaN) PSE products. We will demonstrate the practice of Model Based System Engineering applied to integrating space communication networks and the summary of its results and impact. We will highlight the insights gained by applying the Model Based System Engineering and provide recommendations for its applications and improvements.

Bhasin, Kul↗
DOE OSTI2021

The role of precursor decomposition in the formation of samarium doped ceria nanoparticles via solid-state microwave synthesis

The impact on the final morphology of ceria (CeO 2 ) nanoparticles made from different precursors (commercial: cerium acetate/nitrate) and in house: cerium tri(methylsilyl)amide (Ce-TMSA)) via a microwave solid state reaction has been determined. In all instances, powder X-ray diffraction indicated that the cubic fluorite CeO 2 phase (PDF# 04–004-9150, with the space group Fm-3 m) had formed. Scanning electron microscopy (SEM) images revealed spherical nanoparticles were produced from the Ce-TMSA precursor. The commercial acetate and nitrate precursors produced particles with irregular morphology. The roles of the precursor decomposition and binding energy in the synthesis of the nanocrystals with various morphologies, as well as a possible growth mechanism, were evaluated based on experimental and computational data. The formation of spherical shaped nanoparticles was determined to be due to the preferential single-step decomposition of the Ce-TMSA as well as the low activation energy to overcome decomposition. Due to the complicated decomposition of the commercial precursors and high activation energy the resulting particles adopted an irregular morphology. Highly uniform samarium doped ceria (Sm x Ce 1-x O 2-δ ) nanospheres were also synthesized from Ce-TMSA and samarium tri(methylsilyl)amide (Sm-TMSA). The effects of reaction time and temperature, on the final morphology were observed through SEM. The rapid single-step decomposition of TMSA-based precursors as observed through thermogravimetric analysis (TGA) and confirmed through the calculation of potential energy surfaces and binding energies from density functional theory (DFT) calculations, indicated that nanoparticle formation follows LaMer’s classical nucleation theory.

36 MATERIALS SCIENCE↗