Practicum Abstracts

The theoretical definition of strong stability preservation for a multi-stage time-stepping scheme holds that the total variation of a field must monotonically decrease between each stage. A more practically motivated definition would only require that the total variation decrease between timesteps without regard for the variation at an intermediate stage. We employ a 1D advection model and 1D model of Burger's Equation using any array of spatial interpolators and 3-stage Runge-Kutta timestepping. We demonstrate an increase in the maximum stable timestep under this new definition of strong stability preservation.

In the past decade, the field of deep learning has become incredibly successful in training large neural networks. Yet there remain many open questions about how and what these models are learning, and how that learning may change on a quantum computer. There are several open questions pertaining to the structure of solutions: where minima (corresponding to well-trained models that generalize to new data) sit, how they are shaped, and their connectivity. If minima are connected, understanding the mathematical reason for their connection could allow for easy detection of low loss paths between minima, leading to efficient implementations of geometric ensembles of quantum circuit models. Better understanding the interconnectivity in the lower dimensional landscapes can also assist in discovering new circuit ansatz families that are amenable to QML tasks, and perhaps more robust against barren plateaus. In this study we focus on graph states and how the relationship between two graphs can influence the connectivity between their respective minima. Specifically we investigate whether Local Compliment (LC) equivalence of graph states corresponds to connected minima in the loss landscape.

During this project I performed quantum-mechanics simulations of a thousands of scent-related molecules and then trained a machine learning model to predict their odor. This involved extensive work with programming, machine learning, and literature review.

In the past decade, the field of deep learning has become incredibly successful in training large neural networks. Yet there remain many open questions about how and what these models are learning, and how that learning may change on a quantum computer. There are several open questions pertaining to the structure of solutions: where minima (corresponding to well-trained models that generalize to new data) sit, how they are shaped, and their connectivity. If minima are connected, understanding the mathematical reason for their connection could allow for easy detection of low loss paths between minima, leading to efficient implementations of geometric ensembles of quantum circuit models. Better understanding the interconnectivity in the lower dimensional landscapes can also assist in discovering new circuit ansatz families that are amenable to QML tasks, and perhaps more robust against barren plateaus. In this study we focus on graph states and how the relationship between two graphs can influence the connectivity between their respective minima. Specifically we investigate whether Local Compliment (LC) equivalence of graph states corresponds to connected minima in the loss landscape. We analyze the variational landscape associated with training quantum generative models. One approach taken to accomplish this goal is treating parameterized quantum circuits as Morse functions. However, we find that the loss landscape of our training workflows are dominated by degenerate minima (critical points with zero curvature). As a result, we reframe our analysis by considering parameterized ansate constructed by graph state primitives.

One of the questions often raised in discussions of the potential impacts of climate change is how it may change the severity and frequency of extreme weather events. These events often have substantial impacts on the societies and ecosystems subject to them, particularly when multiple ones coincide in space and/or time, amplifying some of their effects. This can take the form of multiple events which share a set of causes or location, or the form of a chain of unrelated events with the secondary effects of each event intensifying those of the next. In either case, these situations can represent worst case scenarios for the affected regions. Studying the characteristics of such compound and cascading events is a relatively new area of research and so there is likely room for improvements in the state of the art. There has been some success to date in employing deep learning to characterize extreme events. One particular area of interest is attributing compound or cascading events to their proximate causes in the land-ocean-atmosphere continuum. Prior work has shown that atmospheric wave patterns in the Earth System can be important factors in the formation of these groups of events, but the complex nature of these systems and their physical drivers makes recognizing them and connecting them directly to specific natural and/or anthropogenic forcing challenging. Data science and visualization tools could serve as a useful tool for recognizing, categorizing, and even predicting these patterns and - by proxy - the compound and cascading events which are caused by them.

Cloud modeling is a critical area of concern for Department of Energy Grand Challenge questions in climate. While clouds must be resolved, they must be simulated at an incredibly fast rate of about 2,000x realtime in order to achieve meaningful lengths of simulation. Algorithmic advances in cloud modeling that maintain accuracy while increasing throughput are critical. My project revolved around the development of novel infinite sound speed mathematical approximations to the stratified Euler equations that govern atmospheric fluid dynamics. In cloud models, sound waves can travel up to 50-100x faster than the speed of wind. They serve to balance thermal changes with density, but beyond this role, the details of their behavior are physically insignificant. Acoustic waves are supported in the full, unapproximated equation set and any solver must respect their limitation on the time steps in order to remain numerically stable. Infinite sound speed approximations treat the equilibration performed by the acoustic modes as instantaneous to circumvent this limitation. To numerically treat this approximation, we followed a projection approach which splits the time step operator into the evolution of the slow (advective and buoyancy) equations and the projection of the resulting momenta into a divergence-free state which would result from an infinitely fast equilibration. For an A-grid (co-locating points at the center of the finite volumes), traditional approaches using a Poisson solver for the second projection step cannot be expected to be stable. Instead, we derived a method that leverages hyperbolic PDE theory to perform this step in a stable fashion. It was crucial that the method be computationally efficient and ideally port well to GPU architectures and our work resolved around development of the method under these constraints. We eventually were able to boil down and implement an incredibly efficient direct linear solve algorithm at 1st, 3rd, and 5th order spatial accuracy (of the divergence derivative) which increasingly improved the fidelity of fine structures in a thermal bubble test case against a fully compressible comparison.

Gene networks are graphs whose nodes are genes and whose edges represent relationships between genes. For example, a co-expression network indicates whether two genes have sufficiently high correlation in their expression. Other kinds of gene networks include protein-protein interaction, metabolic pathways, regulation, and more—each captures a particular kind of relationship between genes. Our project combines multiple types of gene networks into a multiplex network in order to discover functions of uncharacterized genes. We analyze the multiplex network using computational methods such as random walk with restart, graph convolutional neural networks, and other dimensionality reduction techniques.

Using a combination of density functional theory (DFT) and quantum Monte Carlo (QMC), in particular, diffusion quantum Monte Carlo calculations, we studied the magnetic structure, conducting phase, and volume collapse in MnS2.

Our project involved designing krylov methods that act directly on tensor networks, where tensor networks are low-rank factorizations of many-body tensors. One of the key challenges in this project proved to be in redesigning the basic krylov method so as to avoid intermediate states that implicitly project onto smaller-dimensional subspaces. The significance of this project is in accelerating electronic structure calculations that have previously used variational optimization or Davidsons method to calculate the ground state.

Throughout the summer, I worked on various projects under the umbrella of polymer physics. The first project I worked on involved modeling the capacitance of thin films of charged polymers, which were studied experimentally by collaborators on campus. This involved numerical simulation of a previous model that had been developed by my mentor, Rajeev, and others. The second project I worked on was a collaboration with an experimental group that has synthesized bottlebrush polymers and involved field-theoretic simulations in order to understand microphase segregation. It was especially interesting to compare the resulting morphologies to those of block copolymers, which exhibit similar behavior. Finally, I did mathematical work to model the dynamical behavior of charged polymers and understand how scattering data and dielectric spectroscopy measurements are influenced by the presence of charges.

​Understanding how ecosystems are changing in response to anthropogenic pressure is essential for appropriately managing and conserving ecological systems into the future. Loss of species diversity is widely cited as the greatest threat to the stability, resilience, and functioning of ecosystems. Underpinning this assertion is the assumption that species diversity is an appropriate surrogate for the aspects of species identity and interactions that confer those properties, broadly referred to as functional diversity. However, empirical studies document a wide array of relationships between functional and species diversity, and responses of both aspects of diversity to different environmental perturbations are poorly documented. Establishing the relationship between functional and species diversity is further impeded by methodological concerns about the ability of functional diversity metrics to capture change independent of species richness (number of species). Using large-scale biodiversity data for breeding birds of North America, we take a first look at the ability of functional diversity metrics to detect change through a null model approach, assessing i) metric behavior, and ii) variation in the form of the functional diversity-species diversity relationship across biomes.

FLASH is a high performance multiphysics code currently used for a wide range of astrophysical simulations. In particular, it is a commonly-used tool for the simulation of Type Ia supernovae, in which runaway fusion ignites in a white dwarf and causes it to explode. The heavy element yields of these events remain uncertain. Current simulations track about a dozen isotopes, as opposed to the thousands required to completely capture the nuclear physics of the event. With the next generations of supercomputers, we will have the computational power to greatly extend the nuclear physics in these simulations. There is an Exascale Computing Project underway at several national labs to combine the capabilities of FLASH and other codes, and to prepare these codes for the next generation of supercomputers. The result will be a multiphysics toolkit suitable for exascale simulations of astrophysical explosions. Simulating self-gravity accurately and efficiently is critical for modeling a Type Ia supernova, since fundamentally supernovae are competitions between energy-releasing nuclear reactions and gravity. Currently, the multipole self-gravity solver requires extensive inter-node communication, which is expensive, since the gravitational potential at any point depends on the density at every other point. As such, the default implementation requires that all nodes communicate with each other multiple times. This is expensive, so we overlap computation with communication where possible. In order to test the new self-gravity routine, we simulate an edge-lit sub-Chandrasekhar mass Type Ia supernova. This allows us to verify that we haven't impacted the accuracy of the simulations, and to evaluate the performance of the new multipole solver.

Lithium Lanthanum Titanate (LLTO) is a promising candidate as a solid-electrolyte material for Li-ion batteries due to its high Li-ion conductivity. However, the presence of grain boundaries (GBs) in polycrystalline samples of LLTO reduce the Li-ion conductivity to orders of magnitude below usable levels. GBs in LLTO have a variety of chemical composition and structure. While at ORNL, the purpose of my project was to study the relative stability of different kinds of GBs in LLTO as well as the possible mechanisms of Li-ion diffusion along and across these GBs so as to provide further insight into how we can overcome the GB resistance in this material.

I began the practicum planning to apply existing dynamic distributed task parallelism tools problems in numerical linear algebra and n-body problems. With the guidance of Dr. D'Azevedo, I investigated several options including HPX, Legion, and the Open Community Runtime. These projects are designed to support applications wishing to run on upcoming Exascale systems. As a result, they have innumerable features and options wish are unnecessary at the smaller scales at which I would like to work -- tens of thousands of extra lines of code. Furthermore, these projects are supported by a fickle research community which begins and ends projects like these on a short time frame. Depending on such a library is dangerous once support dissipates. I wasn't convinced that the problem was inherently complex enough to require the complexity present in existing libraries, so I set out to write a new distributed task-parallelism, Taskloaf. The primary goal with Taskloaf was to produce a very small code base while maintaining generality. I use the futures monad where tasks and task dependencies are described with a small vocabulary of verbs like "then" (schedule one task after another) and "ready". I use a data-driven work-stealing scheduling system to balance memory transfer with load balancing. Taskloaf is not complete, but it's getting close. The practicum kick-started the project and I continue to develop it. The codebase is <1500 lines of code so that a skilled C++ programmer can learn the inner workings of the entire library in a couple days. That can be compared to 100,000 for HPX, the most similar existing project. And, since the vocabulary of Taskloaf can describe arbitrary task graphs (nodes are tasks, edges are dependencies), I have succeeded in maintain broad applicability. Finally, tasks can be quite fine-grained. The scheduling system is able to run hundreds of thousands of tasks per second per core. Someday, perhaps, distributed task-parallelism will be as easy as a "#pragma omp parallel for" is for shared memory OpenMP. We're not there yet, but that's my goal.

We were looking for different ways of analyzing a petascale (24M atoms) molecular dynamics trajectory of lignin, cellulose, and cellulases to understand how lignin interferes with cellulase activity.We were looking to analyze

Modern society is shaped by the ability to transmit, manipulate, and store large amounts of information. Although we tend to think of information as abstract, information is physical, and computing is a physical process. How then should we understand information in a quantum world, in which physical systems may exist in multiple states at once and are altered by the very act of observation? This question has evolved into an exciting new field of research called Quantum Information. The design and analysis of dynamical systems with tightly coupled quantum, analog, and digital elements—called QuAD systems—presents novel challenges and requires corresponding advancements in theories and tools. To that end, Bennink et al. have introduced the notion of a QuAD automaton and established some of its general properties. The QuAD automaton may be seen as a natural extension of systems with analog (continuous) and digital (discrete) components, called hybrid systems. In this practicum, we investigated new logics to provide rigorous and symbolic methods for quantum computing devices. While there exists a logic (called differential dynamic logic [1]) which has had success verifying classical hybrid systems, there is currently no such logic which could be used to verify or even describe how the additional complexities inherent in computing at the quantum level interact with the analog and digital components. Quantum devices are highly probabilistic, and the simple act of taking a measurement affects the state of the system. It is impossible to isolate qubits from their environment, and as a result, quantum computers decay from a given quantum state to an incoherent state. Such properties make quantum devices challenging verification problems and more importantly make their behavior difficult for humans to understand, making correct design nearly impossible without computer-aided design tools. [1] A. Platzer. Differential dynamic logic for hybrid systems.

The goal of this study was to evaluate the sustainability of biofuel crop production in the context of climate change. The specific biofuel crop considered was switchgrass (Panicum virgatum L.), a crop which may provide an economically feasible feedstock for cellulosic biofuel production in the south-central US according to the Billion Ton Update(US Department of Energy, 2011). We assessed the impact of a large-scale shift in agricultural production from winter wheat, a shallow-rooted, annual row crop, to switchgrass, a deep-rooted perennial grass.

The project was in the modeling of sand behavior under impact loading. The work group, consisting of a professor at the University of Tennessee and research staff at ORNL, seeks to build a detailed model of granular material behavior starting from high-quality tomographic imagery to characterize the geometry and arrangements of the particles. The geometry is used to build computational models using the discrete element method and the finite element method, and the models will be validated by comparing against fundamental physical experiments. Then, the models will be applied to the impact problem and fine-tuned by comparing against data from impact experiments.

Simulating problems with multi-scale physics has served as a major obstacle to scientific computing. The standard numerical approaches are complicated by the vast range of length and time scales required. MADNESS(Multiresolution ADaptive Numerical Environment for Scientific Simulation) is a pseudo-spectral code that utilizes multiwavelet bases which allows for a high-degree of accuracy, has built-in adaptivity, and is computationally efficient. It has been used extensively in fields such as chemistry, electronic structure, and nuclear physics. However, this methodology has been limited by the prescribed boundary conditions and geometry, whose proper treatment is essential if one wishes to use this framework for a wider class of problems. My work has involved addressing the inherent theoretical issues and developing high performance massively parallel software to track the evolution of implicitly defined boundaries and solving PDE's within those boundaries inside the MADNESS framework.

The main goal of this project was to construct high performance kernels to be used in stencil computations on graphical processing units (GPUs). Stencil computations are used in many scientific applications including finite difference schemes and multigrid solvers. During this practicum, I developed several stencil computations to be used in a multigrid solver, which is still being developed. We were able to utilize the GPU to reach close to peak bandwidth.

We have made many improvements to the FLASH code to enable it to scale well on current- and next-generation supercomputers. Specifically, we optimized the communication algorithm of the in-line halo finder, an essential tool for analysis in cosmological simulations. The optimizations allowed us to use the halo finder at much larger problem sizes and distributed over many more processors than before. Also, we adapted the FLASH I/O routines to support reading and writing using the ADIOS library. The I/O improvements lead to a ~40x speedup in reading and writing checkpoints.

The project was the implementation of isotopic depletion in a three dimensional deterministic radiation transport code. Tracking the isotopic composition of the simulated materials is important in modeling nuclear reactors.

The shallow moist convective parameterization scheme in the Community Atmosphere Model (a component of the Community Climate System Model) has been documented to show a strong sensitivity to the vertical grid spacing. The sensitivity is so strong that physically unrealistic atmospheric simulations arise from vertical grids finer than 26 levels. We discovered the cause to be the 3-layer model of detection and adjustment in the scheme. If the vertical grid spacing is decreased, the scales of detection and adjustment in the scheme decrease as well and no longer work on physical spatial scales. We decoupled the vertical grid of the parameterization scheme from the model vertical grid via remapping and performed the adjustment on physical spatial scales. Results supported the hypothesized reason for the sensitivity, and the sensitivity was greatly reduced after applying the fix.

Fall Chinook salmon typically migrate to the ocean as age-0 subyearlings, but the appearance of a strategy whereby juveniles residualize in freshwater and migrate to the ocean as age-1 yearlings has arisen over the past few decades in Idaho's Snake River population. The yearling life history appears with varying frequency in different river reaches and years, and its recent emergence has conservation implications for this threatened population because of survival and reproductive differences between the two life histories. Temperature differences are thought to play some role in accounting for variation in the numbers of yearlings observed among reaches and years, but understanding of how juveniles make decisions about which life history to pursue is lacking. We advance a hypothesis for the mechanism by which juveniles make this decision, formalize it with a model, and present the results of fitting this model to life-history variation data. The model's simulation output captures patterns of life-history variation among reaches and years and appears robust to uncertainty in a key unknown parameter. The results also shed light on the ways juveniles make decisions about which life history to pursue and suggest directions for future empirical research. Finally, the model offers those interested in the management and conservation of Snake River fall Chinook salmon a useful tool to account for life history variation in population viability analyses and decision making.

Multiresolution methods provide convenient ways to simulate systems with disparate length scales and/or complicated structures. Specifically, non-uniform grids complicate finite difference methods and mesh generation can be both problem-specific and expensive for finite element methods. The multiwavelet basis used in multiresolution methods permits adaptive resolution as needed in the domain, and also efficient algorithms for applying integral operators. My work at Oak Ridge National Laboratory focused on extending the "Multiresolution Adaptive Numerical Environment for Scientific Simulation" package (MADNESS) to solve both the time-independent and time-dependent versions of Maxwell's equations (electrostatics and electrodynamics, respectively). This work also required the implementation of "interior boundary conditions" to specify physical data on known domains inside the computational domain.

We developed a novel load-balancing algorithm for MADNESS (Multiresolution Adaptive Numerical Environment for Scientific Simulation). Computations in MADNESS generate octrees with millions of nodes distributed across tens or hundreds of thousands of processors, making load balancing crucial for performance. This scheme monitors the computational load on each tree node, allowing adaptive balancing of the octree based on actual performance data as the simulation progresses.

Engineering effective materials for future solar cell applications involves optimizing many material properties: a material must capture light in the energy range of the solar spectrum, have a usable interface for extracting the energy and contain a high enough mobility for the excited electrons/holes to reach the interface. Computational science provides an excellent avenue to explore large classes of materials for potential applicability and also to run detailed calculations on optimizing current promising candidates. In my practicum at Oak Ridge, we calculated in detail the photovoltaic properties of a particular polymer system PVK (Poly(N-vinylcarbazole) (C42-H33-N3)) that has shown promise for solid-state lighting and solar cell applications. This system represents a large theoretical and computational challenge due to its extremely large size (over 100 atoms per unit cell) and large spatial distribution of atoms. A lot of effort was placed into improving the current computational techniques for studying these properties of PVK and other future nanosystems and systems that could not have been studied under existing methodology.

In the summer project at ORNL, we extended the AMROC (adaptive mesh refinement in object-orientated C++) software framework, to the simulation of diffusive shocks and detonation waves. AMROC is also used actively for detonation and shock-driven fluid-structure interaction simulation, both at the Department of Energy Advanced Scientific Computing Center at the California Institute of Technology and at ORNL. The software had already contained a number of shock-capturing schemes for reactive supersonic flows and had been applied extensively to simulating detonation waves with the Euler equations. For a more physically correct simulation of shock and detonation waves, we extended the methods from the reactive Euler to the diffusive Navier-Stokes model. We resolved and studied the diffusing effects in the flow, in particular for the shock/detonation wave two-dimensional wedge interaction problem. The main configuration was for Mach 4.5 shock and detonation waves at shock surface angles that produced double Mach reflections. The double Mach reflection is a fundamental structure influencing the propagation of detonation waves. Here, hydrodynamics, viscous shear, combustion, and mass transport interact at scales which create a computationally difficult problem. For this configuration we also investigated shock transition criterion and compared the robustness of the more classical finite volume methods with that of a hybrid WENO-TCD finite difference method.

I participated in an ongoing research program at the Oak Ridge National Lab and the University of Tennessee that integrates modeling, analysis, simulation and experimental techniques to investigate the relationship between patterns of gene expression noise and the architecture and parameters of the underlying gene circuit. Gene expression noise is defined as the stochastic deviations from mean protein expression level and originates from the discrete nature and random timing of the regulation, transcription, translation and decay events that control a gene's expression level. To fully characterize the noise, one must consider the relationships between noise magnitude (how large are the deviations from mean behavior?), noise autocorrelation (how long do the deviations last?), and the mean protein expression level of the gene. A 3-dimensional "noise map" emerges when these three measurements (mean expression level, noise magnitude, and noise autocorrelation) are considered together. An environmental or physiological perturbation resulting in a change in a gene's mean expression level also results in a change in the gene's position on the noise map. The vector describing this change in position on the noise map depends on the architecture of the circuit controlling its expression level. The theoretical dependence of these vectors on the gene circuit architecture and parameters can be analyzed using a "frequency domain analysis" technique developed by the ORNL research group that I joined. In the case of more complex circuits, the vectors can be predicted by simulation. Experimentally, the three map coordinates can be measured by analysis of the intensity of a fluorescent reporter protein (such as GFP) in cell images obtained from time-lapse microscopy. During my practicum, I learned about the experimental and theoretical techniques used by this research group and applied them to experimentally validate some of the theoretical predictions of the noise maps.

This project aims to study the dynamics of the antiporter behavior of the bacterial chloride channel homolog ClC-ec1. The impact of the recently identified tyrosine switch on the central chloride binding site was investigated using umbrella sampling and integrated into a larger view of the channel as a whole by kinetic modeling. The combination of these two methods has provided insight into the unique mechanism of this antiporter.

Type II supernovae are explosions of stars several to dozens of times more massive than the Sun which occur following the collapse of the core of the star due to lack of pressure support. Nearly twenty years of simulations have attempted to discern the exact physical mechanism for driving the supernova explosion with limited success. Specifically, the energy gained from the "bounce" of the core has proven to be not enough, as well as the energy from neutrino transport. Adam Burrows et al. (Burrows et al. 2006, A New Mechanism for Core-Collapse Supernovae Explosions) have proposed an alternative mechanism for driving the explosion relying on acoustic power in the form of gravity waves that are driven by oscillations in the inner core. My project was to artificially generate such waves in such an model in 3D to see if such an explosion could be produced.

In order to simulate nuclear reactors, a neutron transport equation must be solved. This transport equation is dependant on time, energy, angle, and space, with each variable being discretized separately. At ORNL a reactor analysis software package called SCALE has been developed to simulate various neutronic parameters within a nuclear reactor. CENTRM is a piece of SCALE which focuses on developing a energy dependent flux to use as a weighting function to average important physic parameters such as cross sections. CENTRM generates a piecewise continuous flux spectrum by accumulating the source of neutron into each energy point of interest and distributing the source to its correct energy. CENTRM develops a highly accurate flux spectrum for complex systems with multiple materials, multiple material regions, and detailed energy data. Because the CENTRM calculations are so complex, they require a lot of computation time relative to other parts of the SCALE package.

The LandScan Project is designed to build maps of global population distributions by fusing census data with ancillary data, including: land cover, topography, high resolution satellite imagery, and transportation networks.

I analyzed soil moisture dynamics in a coupled atmosphere-ocean global climate model, the Community Climate Simulation Model v. 2 (CCSM2). A control run of the model was perturbed with a negative soil moisture anomaly (dry soils), and run for 10 years of simulation time. Comparison of the control and anomaly runs gave indications that the soil moisture evolution algorithms were not satisfactory, prompting an investigation into causes and remedies for this problem.

During the practicum I spent roughly a third of my time studying the underestimate, by theory, of the resistivity in permalloy using first principles electronic structure methods. The rest of the time, I spent implementing a method to solve a generalized eigenvalue problem and comparing it to other methods. The specific problem I'm interested in solving comes from using a finite-element basis set in a density functional theory calculation, which would allow one to study much larger systems from first principles.

The key to studying the long-time dynamics of molecular systems is to overcome the severe limitations posed by current methods for treating Newton's equations of motion, Our goal in this project was to explore several new methods for determining the appropriate spatial and temporal scales for the coarse-graining of various molecular systems, including lattice models and linear polymer models. The primary methods were developed from the principle that pair-distribution and site-site correlation functions can be used to determine upper bounds on the length scale of coarse-grained objects, while time-correlation functions can determine 'natural' frequencies for various types of motion in molecules. Incorporating these measurements into existing molecular simulations can lead to improvements of several orders of magnitude in the size of systems which can be simulated, and more importantly, in the length of time that can be studied within constraints of CPU time.

Forward and adjoint transport methods may both be used to determine the dosimetric relationship between source parameters and individual tissue elements (e.g. voxels within a patient). Forward transport methods consider one specific tuple of source parameters and calculate the response in all voxels of interest. One such calculation must be performed for each combination of source parameters. Adjoint transport methods, conversely, consider one particular voxel and calculate the response of that voxel as a function of all possible source parameters. In this regard, adjoint methods provide a source parameter sensitivity analysis in addition to a dose computation. This information can be used as the basis for an inverse treatment planning process which seeks the best combination of source parameters to deliver a prescribed dose distribution. This project examined the practicality of using adjoint Monte Carlo transport, as compared to conventional forward transport, for determining in a general manner the relationship between source variations and dose in a patient. Comparisons were made in terms of consistency of results, ease of use, and the level of computational effort required to achieve various types of results. The possibility of developing variance reduction techniques was discussed for both methods.

Computational Science at the Terascale was the name of the project in which I participated in. The project involved developing and using potential models for classical simulations of molecules on a gold surface, and the evaluation of the molecules' conductance between two gold surfaces. The purpose for these calculations were to eventually be able to predict the ability of many molecules to be used in molecular electronics.

The project was designed to examine alternatives for parallelizing existing fish population simulation code. A major thrust of this effort was to minimize the alteration of the original code to determine the efficacy of developing parallel code from existing models. We examined three alternatives, automatic parallelization, the use of data parallel languages and the use of MPI.

Used wavelet decomposition based techniques to try to extract important features from a signal created by turbulence of the Fusion Process in a reactor.

In a published paper, Len Gray and a colleague of his proved that the near-tip displacement field along the edge of the crack had no linear component. The goal of the project was to see whether a modified crack-tip element that had no linear component would improve the accuracy of the K1 and K2 calculations.

I performed nonlinear calculations using a reduced version of the magnetohydrodynamic (MHD) code FAR to investigate the bifurcation of coherent peaks in the frequency spectrum of the density fluctuations observed during weak, negative central shear discharges in D-III-D.

The purpose of the project was to provide me an opportunity to work with and on microfabricated devices as well as all aspects of laser detection. I learned a lot about working in a chemistry laboratory. I think that it really enhances my understanding of the problems faced and what is worth simulating.

The idea was to reformulate the control synthesis methodology of Levin and Norendra so as to make the analysis less conservative and to improve performance by switching from an n-step definition of performance to i-step.

The code resulting from this analysis enables faster, higher order solution for the engineering design of the Advanced Neutron Source (ANS) being conducted at ORNL and other national laboratories. This product greatly aids neutronic simulation capability (much reduced computing time) for the group.

As part of an ongoing effort to develop an adaptive mesh refinement strategy for use in a state-of-the-art nodal nuclear reactor kinetics code, we developed a prior error bounds for the quartic nodal expansion method (NEM) in one-dimensional cartesian geometry. This serves as both encouragement that our goal of fully adaptive mesh refinement can be reached and as a launching pad for similar progress in multiple spatial dimensions. Pleasingly, the error bounds derived approximate the true value of the error for the test problem we chose.

The purpose of this project is to implement a correlation processor for single bit data streams that can operate at a frequency of a GHz. The implementation used is about 3 orders of magnitude faster than previous schemes for calculating the correlation function. THe design consists of a high speed sampling system, an array of and gates and counters and a host computer.

We have calculated the band narrowing and the effective mass of electrons in a three-dimensional electron gas.