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At least 1,531 records · Page 85

Singlet fission for quantum information and quantum computing: the parallel JDE model

Abstract Singlet fission is a photoconversion process that generates a doubly excited, maximally spin entangled pair state. This state has applications to quantum information and computing that are only beginning to be realized. In this article, we construct and analyze a spin-exciton hamiltonian to describe the dynamics of the two-triplet state. We find the selection rules that connect the doubly excited, spin-singlet state to the manifold of quintet states and comment on the mechanism and conditions for the transition into formally independent triplets. For adjacent dimers that are oriented and immobilized in an inert host, singlet fission can be strongly state-selective. We make predictions for electron paramagnetic resonance experiments and analyze experimental data from recent literature. Our results give conditions for which magnetic resonance pulses can drive transitions between optically polarized magnetic sublevels of the two-exciton states, making it possible to realize quantum gates at room temperature in these systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Application of powder densification models to the consolidation processing of composites

Unidirectional fiber reinforced metal matrix composite tapes (containing a single layer of parallel fibers) can now be produced by plasma deposition. These tapes can be stacked and subjected to a thermomechanical treatment that results in a fully dense near net shape component. The mechanisms by which this consolidation step occurs are explored, and models to predict the effect of different thermomechanical conditions (during consolidation) upon the kinetics of densification are developed. The approach is based upon a methodology developed by Ashby and others for the simpler problem of HIP of spherical powders. The complex problem is devided into six, much simpler, subproblems, and then their predicted contributions are added to densification. The initial problem decomposition is to treat the two extreme geometries encountered (contact deformation occurring between foils and shrinkage of isolated, internal pores). Deformation of these two geometries is modelled for plastic, power law creep and diffusional flow. The results are reported in the form of a densification map.

Wadley, H. N. G.↗

HBMax: Optimizing Memory Efficiency for Parallel Influence Maximization on Multicore Architectures

The goal of influence maximization is to select k most-influential vertices or seeds in a network, where influence is defined by a given diffusion process. The problem has a number of important applications such as viral marketing, information spread, and epidemic control. Although computing optimal seed set is NP-Hard, due to the submodular nature of the problem efficient approximation algorithms exist. However, even state-of-the-art parallel implementations are limited by a sampling step that incurs large memory footprints. This in turn limits the problem size reach and approximation quality. In this work, we study the memory footprint of the sampling process collecting reverse reachability information in the IMM algorithm over large real-world social networks. We present an adaptive and memory-efficient optimization approach for a state-of-the-art multi-threaded parallel influence maximization algorithm. Our approach,HuffMax, uses a portion of the reverse reachable (RR) sets collected by the algorithm to learn the characteristics of the graph. Then, it compresses the intermediate reverse reachability information with Huffman coding, and queries directly on the compressed data to preserve the memory savings obtained through compression. We also propose an efficient sampling strategy based on the distribution of RR sets, which can further reduce the computation time for typical social networks with long-tail distributions. Considering a NUMA architecture, we scale up our solution on 128-core CPUs and reduce the memory footprint by up to 45.7% with negligible time overhead (or even faster) and without perceivable loss of accuracy.

Chen, Xinyu↗

CEED-MS8:Initial Integration of CEED Software in ECP Applications

Key components of CEED software development involve fast finite element operator storage and evaluation, architecture optimizations, performant algorithms for all orders, global kernels for finite element operators, efficient use of the memory sub-system, optimal data locality and motion, enhanced scalability and parallelism, and fast tensor contractions. As ultimate goals of the project, CEED is exploring and identifying the best algorithms for the full range of discretizations and applying algorithmic and software development to support ECP applications’ needs. In this milestone we report on the initial integration of CEED software in the selected first-wave ECP/CEED apps and the continued exploration of other ECP applications as second-wave (milestone CEED-MS23) and third-wave (milestone CEED-MS35) ECP/CEED application candidates. An extensive evaluation of various approaches for GPU acceleration of the CEED computational motives is also a major focus of the report, both in the settings of CEED’s Nekbone and Laghos miniapps, as well as versions of CEED’s bake-off problems (introduced in milestone CEED-MS6). The first-wave ECP applications targeted for coupling with CEED software include the ExaSMR and MARBL applications. We also report on near-term collaboration with the seed-funded Urban Systems project, as well as engagements with ACME, ExaAM, GEOS and the Application Assessment and Proxy App projects. The ExaSMR project involves coupled thermal-hydraulics/neutronics, with the latter based on Monte Carlo methods and the former based on high-order discretizations of the Navier-Stokes and energy equations for accurate simulation of turbulent transport. The project requires fast and efficient turbulence simulation capabilities that will scale to exascale platforms. Work within CEED will ensure that all aspects of the Nek5000 workflow scale to the target problem space, which involves > 10 10 degrees of freedom in typical production runs. CEED’s goal is to provide implementations that perform with maximum attainable efficiency and deliver low turn-around times. A deliverable for this milestone is beta-release of the GPU-based variant of Nek5000. MARBL is targeting high-energy-density physics problems, including single fluid multi-material hydrodynamics and radiation/magnetic diffusion simulation, with applications in inertial confined fusion, pulsed power experiments, and equation of state/material strength analysis. The code uses high-order methods based arbitrary Lagrangian-Eulerian, direct Eulerian, and unstructured adaptive mesh refinement. A deliverable for this milestone is collaboration with MARBL for improved performance based on partially-assembled operators. The Urban exascale project is planning to couple real-time data with high performance simulations to study particulate transport in cities. Nek5000 will be used for large eddy and RANS (Reynolds-averaged Navier-Stokes) simulations of turbulent transport in these domains. Areas where the CEED team is aiding the Urban Canyon group include creating high-order meshes for urban geometries and developing boundary conditions appropriate for simulations close to real-life urban conditions. The software artifacts delivered as part of this milestone include GPU-enabled versions of the Nekbone and Laghos miniapps, which are provided through the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q4 of FY17, including: the CEED first annual meeting and participation of CEED researchers in a variety of outreach activities.

97 MATHEMATICS AND COMPUTING↗

Debugging tasked Ada programs

The applications for which Ada was developed require distributed implementations of the language and extensive use of tasking facilities. Debugging and testing technology as it applies to parallel features of languages currently falls short of needs. Thus, the development of embedded systems using Ada pose special challenges to the software engineer. Techniques for distributing Ada programs, support for simulating distributed target machines, testing facilities for tasked programs, and debugging support applicable to simulated and to real targets all need to be addressed. A technique is presented for debugging Ada programs that use tasking and it describes a debugger, called AdaTAD, to support the technique. The debugging technique is presented together with the use interface to AdaTAD. The component of AdaTAD that monitors and controls communication among tasks was designed in Ada and is presented through an example with a simple tasked program.

Fainter, R. G.↗

Towards fast, accurate predictions of RF simulations via data-driven modeling: Forward and lateral models

Three machine learning techniques (multilayer perceptron, random forest, and Gaussian process) provide fast surrogate models for lower hybrid current drive (LHCD) simulations. A single GENRAY/CQL3D simulation without radial diffusion of fast electrons requires several minutes of wall-clock time to complete, which is acceptable for many purposes, but too slow for integrated modeling and real-time control applications. More accurate simulations with fast electron diffusion are even slower, requiring multiple hours of run time with parallel processing. The machine learning models use a database of 16,000+ GEN-RAY/CQL3D simulations for training, validation, and testing. Latin hypercube sampling methods implemented in πScope ensure that the database covers the range of 9 input parameters (n e0 , T e0 , I p , B t , R 0 , n ∥︀ , Z e f f , V loop , P LHCD ) with sufficient density in all regions of parameter space. The surrogate models reduce the computation time from minutes-hours to ms with high accuracy across the input parameter space. Data-driven surrogate models also allow for solving inverse and “lateral” problems. A surrogate model for the inverse problem maps from a desired current drive or power deposition profile to a set of input parameters that would result in such a profile, while a surrogate model for the lateral problem maps from a measured experimental quantity such as hard x-ray emission to a current drive or power deposition profile. In conclusion, the πScope database creation workflow is flexible and applicable to other RF simulation codes such as TORIC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Parallel Performance Characterization of Columbia

Using a collection of benchmark problems of increasing levels of realism and computational effort, we will characterize the strengths and limitations of the 10,240 processor Columbia system to deliver supercomputing value to application scientists. Scientists need to be able to determine if and how they can utilize Columbia to carry extreme workloads, either in terms of ultra-large applications that cannot be run otherwise (capability), or in terms of very large ensembles of medium-scale applications to populate response matrices (capacity). We select existing application benchmarks that scale from a small number of processors to the entire machine, and that highlight different issues in running supercomputing-calss applicaions, such as the various types of memory access, file I/O, inter- and intra-node communications and parallelization paradigms. http://www.nas.nasa.gov/Software/NPB/

Biswas, Rupak↗

Particle Interaction Physics Model Formulation for Plume-Surface Interaction Erosion and Cratering

The Predictive Simulation Capability development team of the STMD Game Changing Development sponsored PSI project is implementing computational simulation capability for the efficient and accurate prediction of Plume-Surface Interaction induced surface erosion and cratering in Martian and Lunar environments. The status of the Focus Area 3 of the PSI project in the generation and efficient application of accurate soil particle composition modeling in the Gas-Granular Flow Solver (GGFS) computational framework is presented. The process of constitutive closure model database generation using DEM particle interaction modeling for capturing the effects of irregular particle shape and poly-disperse mixture distribution effects is outlined. This capability has now been ported to NASA supercomputer assets and NASA engineers successfully demonstrated technology and skillset transfer in model generation for spherical and irregularly shaped, mono-disperse and bi-disperse mixture compositions. Assessment of the computational efficiency and practicality of the academic serially executed DEM tools on NASA supercomputers identified the need to migrate to a DEM framework capable of performing parallel simulations in a simultaneous process orchestrated in an automated setup, execution, database extraction, and dataset delivery ready for application simulations. The LIGGGHTS DEM toolset has been selected as the most suitable tool to migrate the DEM simulations. Once the soil model generation process is implemented, models capturing the shape and poly-dispersity effects will be generated to perform much refined validation simulations against the experiments performed under the PSI project. The application readiness of the soil models currently operational in GGFS was presented for the example of a full scale, 3-D simulation of the plume induced erosion and crater formation of the Apollo LM at an elevation of 5m above ground in a low pressure, near vacuum background.

Peter A Liever↗

Particle Interaction Physics Model Formulation for Plume-Surface Interaction Erosion and Cratering

The Predictive Simulation Capability development team of the STMD Game Changing Development sponsored PSI project is implementing computational simulation capability for the efficient and accurate prediction of Plume-Surface Interaction induced surface erosion and cratering in Martian and Lunar environments. The status of the Focus Area 3 of the PSI project in the generation and efficient application of accurate soil particle composition modeling in the Gas-Granular Flow Solver (GGFS) computational framework is presented. The process of constitutive closure model database generation using DEM particle interaction modeling for capturing the effects of irregular particle shape and poly-disperse mixture distribution effects is outlined. This capability has now been ported to NASA supercomputer assets and NASA engineers successfully demonstrated technology and skillset transfer in model generation for spherical and irregularly shaped, mono-disperse and bi-disperse mixture compositions. Assessment of the computational efficiency and practicality of the academic serially executed DEM tools on NASA supercomputers identified the need to migrate to a DEM framework capable of performing parallel simulations in a simultaneous process orchestrated in an automated setup, execution, database extraction, and dataset delivery ready for application simulations. The LIGGGHTS DEM toolset has been selected as the most suitable tool to migrate the DEM simulations. Once the soil model generation process is implemented, models capturing the shape and poly-dispersity effects will be generated to perform much refined validation simulations against the experiments performed under the PSI project. The application readiness of the soil models currently operational in GGFS was presented for the example of a full scale, 3-D simulation of the plume induced erosion and crater formation of the Apollo LM at an elevation of 5m above ground in a low pressure, near vacuum background.

Peter A Liever↗

A general and computationally fast formulation for radiative transfer with scattering

A general formulation of monocromatic radiative transfer with scattering has been developed for plane-parallel geometry. The inhomogeneous and nonisothermal medium absorbs, emits, and anisotropically scatters radiation. Surfaces can emit and scatter radiation in any specified manner. The solution procedure uses the fact that phase incoherent scattering is linear in radiative sources. Certain basic scattering functions are then defined and calculated by an adding computer code using matrix algebra. These scattering functions are weighted by the temperature field and summed (superimposed) to obtain the solution for any specific problem. Numerical results for exiting intensities and one-sided heat fluxes from general media bound by one arbitrary surface are presented. These parametric studies demonstrate the effects of scattering particles and surfaces on radiative transfer from inhomogeneous and nonisothermal media. Application of the formulation to radiative equilibrium is also discussed. The conclusion is that all problems in plane-parallel radiative transfer with scattering can be solved by a common and computationally fast algorithm based on this formulation.

Cogley, A. C.↗

Parallel solution of finite element equations

The paper examines several parallel processing solution algorithms for finite element equations arising in linear equilibrium problems. Two basic groups of algorithms, direct and iterative, are investigated with respect to a number of parallel computer architectures and associated selection criteria. The direct algorithms include: LR-Gauss, Crout, Cholesky, Cyclic Reduction and WZ-factorization. The iterative methods examined are: Accelerated Gauss-Seidel, Surrogate Stiffness, Jacobi, Series Expansion, and Energy Monte Carlo. For real-time applications, where the object is to minimize the execution time, Cyclic Reduction appears to be best suited. This assumes a computer with an unlimited number of parallel processors. However, for computers with a limited number of parallel processors that must be used efficiently, both Gauss factorization and Jacobi-like iterative methods rank favorably.

Salama, M.↗

Performance of improved magnetostrictive vibrational power generator, simple and high power output for practical applications

Vibration based power generation technology is utilized effectively in various fields. Author has invented novel vibrational power generation device using magnetostrictive material. The device is based on parallel beam structure consisting of a rod of iron-gallium alloy wound with coil and yoke accompanied with permanent magnet. When bending force is applied on the tip of the device, the magnetization inside the rod varies with induced stress due to the inverse magnetostrictive effect. In vibration, the time variation of the magnetization generates voltage on the wound coil. The magnetostrictive type is advantageous over conventional such using piezoelectric or moving magnet types in high efficiency and high robustness, and low electrical impedance. Here, author has established device configuration, simple, rigid, and high power output endurable for practical applications. In addition, the improved device is lower cost using less volume of Fe-Ga and permanent magnet compared to our conventional, and its assembly by soldering is easy and fast suitable for mass production. Average power of 3 mW/cm{sup 3} under resonant vibration of 212 Hz and 1.2 G was obtained in miniature prototype using Fe-Ga rod of 2 × 0.5× 7 mm{sup 3}. Furthermore, the damping effect was observed, which demonstrates high energy conversion of the generator.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Aspen-based performance and energy modeling frameworks

Now with the anticipation of exascale architectures, energy consumption is becoming one of the critical design parameters, especially in light of the energy budget of 20-30 Megawatts set by the U.S. Department of Energy. Understanding an application’s execution pattern and its energy footprint is critical to improving application operation on a diverse heterogeneous architecture. Applying application-specific performance optimization can consequently improve energy consumption. However, this approach is only applicable to current systems. As we enter a new era of exascale architectures that is projected to contain more complex memory hierarchies, increased levels of parallelism, heterogeneity in hardware, and complex programming models and techniques, energy and performance management is getting more cumbersome. We therefore propose techniques that predict the energy consumption beforehand or at runtime to enable proactive tuning. Such energy prediction approaches must be generic and adapt themselves at runtime to changing application and hardware configurations. Most existing energy estimation and prediction approaches are empirical in nature and thus tied to current systems. To overcome this limitation, we propose two energy estimation techniques: ACEE (Algorithmic and Categorical Energy Estimation), which uses a combination of analytical and empirical modeling techniques; and AEEM (Aspen’s Embedded Energy Estimation), a system-level analytical energy estimation technique. Both of these models incorporate the Aspen domain specific language for performance modeling. We present the methodologies of these two models and test their accuracy using five proxy applications. We also describe three use cases.

79 ASTRONOMY AND ASTROPHYSICS↗

Modeling and Prediction of the Noise from Non-Axisymmetric Jets

The new source model was combined with the original sound propagation model developed for rectangular jets to produce a new version of the rectangular jet noise prediction code. This code was validated using a set of rectangular nozzles whose geometries were specified by NASA. Nozzles of aspect ratios two, four and eight were studied at jet exit Mach numbers of 0.5, 0.7 and 0.9, for a total of nine cases. Reynolds-averaged Navier-Stokes solutions for these jets were provided to the contactor for use as input to the code. Quantitative comparisons of the predicted azimuthal and polar directivity of the acoustic spectrum were made with experimental data provided by NASA. The results of these comparisons, along with a documentation of the propagation and source models, were reported in a journal article publication (Ref. 4). The complete set of computer codes and computational modules that make up the prediction scheme, along with a user's guide describing their use and example test cases, was provided to NASA as a deliverable of this task. The use of conformal mapping, along with simplified modeling of the mean flow field, for noise propagation modeling was explored for other nozzle geometries, to support the task milestone of developing methods which are applicable to other geometries and flow conditions of interest to NASA. A model to represent twin round jets using this approach was formulated and implemented. A general approach to solving the equations governing sound propagation in a locally parallel nonaxisymmetric jet was developed and implemented, in aid of the tasks and milestones charged with selecting more exact numerical methods for modeling sound propagation, and developing methods that have application to other nozzle geometries. The method is based on expansion of both the mean-flowdependent coefficients in the governing equation and the Green's function in series of orthogonal functions. The method was coded and tested on two analytically prescribed mean flows which were meant to represent noise reduction concepts being considered by NASA. Testing (Ref. 5) showed that the method was feasible for the types of mean flows of interest in jet noise applications. Subsequently, this method was further developed to allow use of mean flow profiles obtained from a Reynolds-averaged Navier-Stokes (RANS) solution of the flow. Preliminary testing of the generalized code was among the last tasks completed under this contract. The stringent noise-reduction goals of NASA's Fundamental Aeronautics Program suggest that, in addition to potentially complex exhaust nozzle geometries, next generation aircraft will also involve tighter integration of the engine with the airframe. Therefore, noise generated and propagated by jet flows in the vicinity of solid surfaces is expected to be quite significant, and reduced-order noise prediction tools will be needed that can deal with such geometries. One important source of noise is that generated by the interaction of a turbulent jet with the edge of a solid surface (edge noise). Such noise is generated, for example, by the passing of the engine exhaust over a shielding surface, such as a wing. Work under this task supported an effort to develop a RANS-based prediction code for edge noise based on an extension of the classical Rapid Distortion Theory (RDT) to transversely sheared base flows (Refs. 6 and 7). The RDT-based theoretical analysis was applied to the generic problem of a turbulent jet interacting with the trailing edge of a flat plate. A code was written to evaluate the formula derived for the spectrum of the noise produced by this interaction and results were compared with data taken at NASA Glenn for a variety of jet/plate configurations and flow conditions (Ref. 8). A longer-term goal of this task was to work toward the development of a high-fidelity model of sound propagation in spatially developing non-axisymmetric jets using direct numerical methods for solving the relevant equations. Working with NASA Glenn Acoustics Branch personnel, numerical methods and boundary conditions appropriate for use in a high-resolution calculation of the full equations governing sound propagation in a steady base flow were identified. Computer codes were then written (by NASA) and tested (by OAI) for an increasingly complex set of flow conditions to validate the methods. The NASA-supplied codes were ported to the High-End Computing resources of the NASA Advanced Supercomputing facility for testing and validation against analytical (where possible) and independent numerical solutions. The cases which were completed during the course of this contract were solutions of the two-dimensional linearized Euler equations with no mean flow, a uniform mean flow and a nonuniform mean flow representative of a parallel flow jet.

Leib, Stewart J.↗

Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes

In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used to project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.

97 MATHEMATICS AND COMPUTING↗

Efficient Parallel Sparse Symmetric Tucker Decomposition for High-Order Tensors

Tensor based methods are receiving renewed attention in recent years due to their prevalence in diverse real-world applications. There is considerable literature on tensor representations and algorithms for tensor decompositions, both for dense and sparse tensors. Many applications in hypergraph analytics, machine learning, psychometry, and signal processing result in tensors that are both sparse and symmetric, making it an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTMc) in general sparse tensors, the Sparse Symmetric Tensor Times Same Matrix chain (S3TTMc) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. In this work, we present a novel compressed storage format CSS for sparse symmetric tensors, along with an efficient parallel algorithm for the S3TTMc operation. We theoretically establish that S3TTMc on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations. We demonstrate experimental findings that confirm these results and achieve up to 2.9× speedup on synthetic and real datasets.

Shivakumar, Shruti↗

Parallel processing for scientific computations

The scope of this project dealt with the investigation of the requirements to support distributed computing of scientific computations over a cluster of cooperative workstations. Various experiments on computations for the solution of simultaneous linear equations were performed in the early phase of the project to gain experience in the general nature and requirements of scientific applications. A specification of a distributed integrated computing environment, DICE, based on a distributed shared memory communication paradigm has been developed and evaluated. The distributed shared memory model facilitates porting existing parallel algorithms that have been designed for shared memory multiprocessor systems to the new environment. The potential of this new environment is to provide supercomputing capability through the utilization of the aggregate power of workstations cooperating in a cluster interconnected via a local area network. Workstations, generally, do not have the computing power to tackle complex scientific applications, making them primarily useful for visualization, data reduction, and filtering as far as complex scientific applications are concerned. There is a tremendous amount of computing power that is left unused in a network of workstations. Very often a workstation is simply sitting idle on a desk. A set of tools can be developed to take advantage of this potential computing power to create a platform suitable for large scientific computations. The integration of several workstations into a logical cluster of distributed, cooperative, computing stations presents an alternative to shared memory multiprocessor systems. In this project we designed and evaluated such a system.

Alkhatib, Hasan S.↗

Microgravity Processing and Photonic Applications of Organic and Polymeric Materials

Some of the primary purposes of this work are to study important technologies, particularly involving thin films, relevant to organic and polymeric materials for improving applicability to optical circuitry and devices and to assess the contribution of convection on film quality in unit and microgravity environments. Among the most important materials processing techniques of interest in this work are solution-based and by physical vapor transport, both having proven gravitational and acceleration dependence. In particular, PolyDiAcetylenes (PDA's) and PhthaloCyanines (Pc's) are excellent NonLinear Optical (NLO) materials with the promise of significantly improved NLO properties through order and film quality enhancements possible through microgravity processing. Our approach is to focus research on integrated optical circuits and optoelectronic devices relevant to solution-based and vapor processes of interest in the Space Sciences Laboratory at the Marshall Space Flight Center (MSFC). Modification of organic materials is an important aspect of achieving more highly ordered structures in conjunction with microgravity processing. Parallel activities include characterization of materials for particular NLO properties and determination of appropriation device designs consistent with selected applications. One result of this work is the determination, theoretically, that buoyancy-driven convection occurs at low pressures in an ideal gas in a thermalgradient from source to sink. Subsequent experiment supports the theory. We have also determined theoretically that buoyancy-driven convection occurs during photodeposition of PDA, an MSFC-patented process for fabricating complex circuits, which is also supported by experiment. Finally, the discovery of intrinsic optical bistability in metal-free Pc films enables the possibility of the development of logic gate technology on the basis of these materials.

Frazier, Donald O.↗