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At least 829 records · Page 46

Implementation and Assessment of Advanced Analog Vector-Matrix Processor

This paper discusses the design and implementation of an analog optical vecto-rmatrix coprocessor with a throughput of 128 Mops for a personal computer. Vector matrix calculations are inherently parallel, providing a promising domain for the use of optical calculators. However, to date, digital optical systems have proven too cumbersome to replace electronics, and analog processors have not demonstrated sufficient accuracy in large scale systems. The goal of the work described in this paper is to demonstrate a viable optical coprocessor for linear operations. The analog optical processor presented has been integrated with a personal computer to provide full functionality and is the first demonstration of an optical linear algebra processor with a throughput greater than 100 Mops. The optical vector matrix processor consists of a laser diode source, an acoustooptical modulator array to input the vector information, a liquid crystal spatial light modulator to input the matrix information, an avalanche photodiode array to read out the result vector of the vector matrix multiplication, as well as transport optics and the electronics necessary to drive the optical modulators and interface to the computer. The intent of this research is to provide a low cost, highly energy efficient coprocessor for linear operations. Measurements of the analog accuracy of the processor performing 128 Mops are presented along with an assessment of the implications for future systems. A range of noise sources, including cross-talk, source amplitude fluctuations, shot noise at the detector, and non-linearities of the optoelectronic components are measured and compared to determine the most significant source of error. The possibilities for reducing these sources of error are discussed. Also, the total error is compared with that expected from a statistical analysis of the individual components and their relation to the vector-matrix operation. The sufficiency of the measured accuracy of the processor is compared with that required for a range of typical problems. Calculations resolving alloy concentrations from spectral plume data of rocket engines are implemented on the optical processor, demonstrating its sufficiency for this problem. We also show how this technology can be easily extended to a 100 x 100 10 MHz (200 Cops) processor.

Gary, Charles K.↗

Global Optimization via Quadratic Disjunctive Programming for Water Networks Design with Energy Recovery

Generalized disjunctive programming (GDP) models with bilinear and concave constraints, often seen in water network design, are challenging optimization problems. This work proposes quadratic and piecewise linear approximations for nonlinear terms to reformulate GDP models into quadratic GDP (QGDP) models that suitable solvers may solve more efficiently. We illustrate the benefits of the quadratic reformulation with a water treatment network design problem in which nonconvexities arise from bilinear terms in the mixers’ mass balances and concave investment cost functions of treatment units. Given the similarities with water network design problems, we suggest quadratic approximation for the GDP model for the optimal design of a large-scale reverse electrodialysis (RED) process. This power technology can recover energy from salinity differences between by-product streams of the water sector, such as desalination brine mixed with regenerated wastewater effluents. The solver Gurobi excels in handling QGDP problems, but weighing the problem’s precision and tractability balance is crucial. The piecewise linear approximation yields more accurate, yet larger QGDP models that may require longer optimization times in large-scale process synthesis problems.

Water Networks↗

The incremental unknowns-a multilevel scheme for the simulation of turbulent channel flows

In numerical simulation of complex flows, it is important to identify different length scales of the flow and treat them differently. In this report, we introduce a new multilevel scheme for simulating turbulent channel flows. Two different versions of the scheme, namely the spectral and finite difference versions, are presented. The spectral version of the scheme is based on a spectral-Galerkin formulation which provides a natural decomposition of the flow into small and large wavelength parts, and which leads to linear systems that can be solved with quasi-optimal computational complexity. In the finite difference version, the Incremental Unknown (IU) is used to separate the length scales. Preliminary numerical results indicate that the scheme is well suited for turbulence computations and provides results which are comparable to that by Direct Numerical Simulation (DNS) but with significantly less CPU time.

Chen, M.↗

Multi-Scale Analysis of Effective Mechanical Properties of 3D Woven Composite Materials

This work aims to compute and analyze the mechanical properties of 3D woven composite materials that share the same yarn structure but differ in their matrix porosity and fiber volume fraction. Assuming linear elastic behavior, the software PuMA, developed at NASA, was used to characterize the different composites from their constituents' data averaging their elastic properties in three main directions to obtain their effective orthotropic mechanical properties. This was performed in three steps: firstly, the different phases (yarns/matrix) were analyzed as anisotropic materials separately at the micro-scale; then, the results from these analyses were homogenized and used to obtain the anisotropic elasticity tensor at the meso-scale for the different woven materials; and finally, assuming orthotropic mechanical behavior for the unit cell the mechanical properties were obtained at the macro-scale. The 3D woven composite materials selected for this study are made of phenolic resin with porosity values between 0 and 0.6, and resin infiltrated carbon fiber with volume fractions between 0.5 and 0.9 for the yarns. Results from PuMA were validated with external FEA simulations for the non-porous 3D woven material with a fiber volume fraction of 0.9 in the yarns. Results will be included in the final paper after completing the study detailed in Section II.

Sergio Fraile Izquierdo↗

Multi-Scale Analysis of Effective Mechanical Properties of Porous 3D Woven Composite Materials

This work aims to compute and analyze the mechanical properties of 3D woven composite materials that share the same yarn structure but differ in their matrix porosity and yarn's fiber volume fraction. Assuming linear elastic behavior, NASA's PuMA software was used to characterize the different composites from their constituents' data, averaging their elastic properties in three main directions to obtain their effective orthotropic mechanical properties. This was performed in three steps: firstly, the porous matrix phase was analyzed at the micro-scale; then, these results were used, along with the mechanical properties of the fibers, to model the yarns at the meso-scale; finally, results from the constituents were homogenized and used to model the mechanical behavior of the unit cell at the macro-scale. The 3D woven composite materials selected for this study are made of a mixture of phenolic resin with porosity values between 0 and 0.6, and infiltrated carbon fiber yarns with fiber volume fractions between 0.5 and 0.8. Results from this study show the effect of different matrix porosities and fiber volume fractions on the macro-scale mechanical properties, and were validated through theoretical and semi-empirical expressions found in the literature.

3D woven materials↗

A polymer, random walk model for the size-distribution of large DNA fragments after high linear energy transfer radiation

DNA double-strand breaks (DSBs) produced by densely ionizing radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. Stochastic DSB clustering at large scales, from > 100 Mbp down to < 0.01 Mbp, is modeled using computer simulations and analytic equations. A random-walk, coarse-grained polymer model for chromatin is combined with a simple track structure model in Monte Carlo software called DNAbreak and is applied to data on alpha-particle irradiation of V-79 cells. The chromatin model neglects molecular details but systematically incorporates an increase in average spatial separation between two DNA loci as the number of base-pairs between the loci increases. Fragment-size distributions obtained using DNAbreak match data on large fragments about as well as distributions previously obtained with a less mechanistic approach. Dose-response relations, linear at small doses of high linear energy transfer (LET) radiation, are obtained. They are found to be non-linear when the dose becomes so large that there is a significant probability of overlapping or close juxtaposition, along one chromosome, for different DSB clusters from different tracks. The non-linearity is more evident for large fragments than for small. The DNAbreak results furnish an example of the RLC (randomly located clusters) analytic formalism, which generalizes the broken-stick fragment-size distribution of the random-breakage model that is often applied to low-LET data.

DNA/radiation effects↗

A computer graphics display and data compression technique

The computer program discussed is intended for the graphical presentation of a general dependent variable X that is a function of two independent variables, U and V. The required input to the program is the variation of the dependent variable with one of the independent variables for various fixed values of the other. The computer program is named CRP, and the output is provided by the SD 4060 plotter. Program CRP is an extremely flexible program that offers the user a wide variety of options. The dependent variable may be presented in either a linear or a logarithmic manner. Automatic centering of the plot is provided in the ordinate direction, and the abscissa is scaled automatically for a logarithmic plot. A description of the carpet plot technique is given along with the coordinates system used in the program. Various aspects of the program logic are discussed and detailed documentation of the data card format is presented.

Teague, M. J.↗

Elastic wave propagation in a highly scattering medium - A diffusion approach

The propagation of elastic waves in the moon, where the first seismograms were characterized by the presence of a long coda attributed to strongly scattered waves, is modeled with the aid of the time-dependent equation of radiative transfer. The average energy density as a function of time and space is described by the diffusion equation with linear dissipation on the assumption that all the energy present has been scattered many times and the time and distance scales of the problem are long compared to the scales of the scattering process. Ultrasonic experiments in the laboratory confirm the applicability of the formalism.

Dainty, A. M.↗

Large-scale motion in the Venus stratosphere

To examine a postulate that the horizontal momentum exchanges in the Venusian stratosphere are quasi-nondivergent, the properties of two-dimensional turbulence on a slowly rotating sphere in a high-resolution, one-level numerical model are investigated. It is concluded that the forcing which maintains the stratospheric flow is weak and influences the dynamics far less than the inertial effects. Consequently, the behavior resembles that of vorticity-conserving, two-dimensional flows. On a slowly rotating planet like Venus, such flows are dominated by solid-body rotation and by a planetary wave of unit zonal wavenumber - this wave corresponds to the observed Y-shaped UV feature. Although these largest scales of motion stand out, the dynamic balances of the flow are fundamentally nonlinear, in contrast to the quasi-linear Rossby wave regime on rapidly rotating planets.

Rossow, W. B.↗

Nonparallel stability of three-dimensional flows

The linear stability of three-dimensional incompressible, isothermal, nonparallel boundary-layer flows has been investigated. The method of multiple scales is used to derive the partial-differential equations that describe the spatial modulations of the amplitude, phase and wavenumber of a disturbance. Group velocities are used to determine the disturbance growth direction. The envelope method is used to calculate the logarithmic amplitude growth rate N. The theory is applied to the flows over a swept-back tapered wing with boundary-layer suction. Results of such analysis for the X-21 wing are discussed. It is found that the nonparallel effects for this wing is substantial.

Padhye, A. R.↗

Mixing of a passive scalar in isotropic and sheared homogeneous turbulence

In order to calculate the velocity and scalar fields, the three dimensional, time-dependent equations of motion and the diffusion equation were solved numerically. The following cases were treated: isotropic, homogeneous turbulence with decay of a passive scalar; and homogeneous turbulent shear flow with a passive scalar whose mean varies linearly in the spanwise direction. The solutions were obtained at relatively low Reynolds numbers so that all of the turbulent scales could be resolved without modeling. Turbulent statistics such as integral length scales, Taylor microscales, Kolmogorov length scale, one- and two-point correlations of velocity-velocity and velocity-scalar, turbulent Prandtl/Schmidt number, r.m.s. values of velocities, the scalar quantity and pressure, skewness, decay rates, and decay exponents were calculated. The results are compared with the available expermental results, and good agreement is obtained.

Shirani, E.↗

A dynamic measure of controllability and observability for the placement of actuators and sensors on large space structures

The degree of controllability of a large space structure is found by a four step procedure: (1) finding the minimum control energy for driving the system from a given initial state to the origin in the prescribed time; (2) finding the region of initial state which can be driven to the origin with constrained control energy and time using optimal control strategy; (3) scaling the axes so that a unit displacement in every direction is equally important to control; and (4) finding the linear measurement of the weighted "volume" of the ellipsoid in the equicontrol space. For observability, the error covariance must be reduced toward zero using measurements optimally, and the criterion must be standardized by the magnitude of tolerable errors. The results obtained using these methods are applied to the vibration modes of a free-free beam.

Vandervelde, W. E.↗

Optimal output fast feedback in two-time scale control of flexible arms

Control of lightweight flexible arms moving along predefined paths can be successfully synthesized on the basis of a two-time scale approach. A model following control can be designed for the reduced order slow subsystem. The fast subsystem is a linear system in which the slow variables act as parameters. The flexible fast variables which model the deflections of the arm along the trajectory can be sensed through strain gage measurements. For full state feedback design the derivatives of the deflections need to be estimated. The main contribution of this work is the design of an output feedback controller which includes a fixed order dynamic compensator, based on a recent convergent numerical algorithm for calculating LQ optimal gains. The design procedure is tested by means of simulation results for the one link flexible arm prototype in the laboratory.

Siciliano, B.↗

The structure of red-infrared scattergrams of semivegetated landscapes

A physically based linear stochastic geometric canopy soil reflectance model is presented for characterizing spatial variability of semivegetated landscapes at subpixel and regional scales. Landscapes are conceptualized as stochastic geometric surfaces, incorporating not only the variability in geometric elements, but also the variability in vegetation and soil background reflectance which can be important in some scenes. The model is used to investigate several possible mechanisms which contribute to the often observed characteristic triangular shape of red-infrared scattergrams of semivegetated landscapes. Scattergrams of simulated and semivegetated scenes are analyzed with respect to the scales of the satellite pixel and subpixel components. Analysis of actual aerial radiometric data of a pecan orchard is presented in comparison with ground observations as preliminary confirmation of the theoretical results.

Jasinski, Michael F.↗

Non-WKB evolution of solar wind fluctuations - A turbulence modeling approach

Recent observations indicate systematic changes in the interplanetary inertial range velocity-magnetic field correlation with increasing heliocentric distance. Here, a multiple length scale model for the evolution of the small scale fluctuations due to local nonlinear couplings as well as couplings to large scale gradients is outlined, which is similar to that used in turbulence modeling of inhomogeneous shear flows. A simple special case solution is given, indicating that couplings to large scale flow gradients can cause radial evolution of the type seen in observations. The strongest couplings of this type are linear and do not appear in the usual WKB orderings. The relationship of the present approach to WKB theory is not fully understood at present.

Ye, Zou↗

The structure of red-infrared scattergrams of semivegetated landscapes

A physically based linear stochastic geometric canopy soil reflectance model is presented for characterizing spatial variability of semivegetated landscapes at subpixel and regional scales. Landscapes are conceptualized as stochastic geometric surfaces, incorporating not only the variability in geometric elements, but also the variability in vegetation and soil background reflectance which can be important in some scenes. The model is used to investigate several possible mechanisms which contribute to the often observed characteristic triangular shape of red-infrared scattergrams of semivegetated landscapes. Scattergrams of simulated semivegetated scenes are analyzed with respect to the scales of the satellite pixel and subpixel components. Analysis of actual aerial radiometric data of a pecan orchard is presented in comparison with ground observations as preliminary confirmation of the theoretical results.

Jasinski, Michael F.↗

Boundary layer receptivity to unsteady free-stream pressure gradients

A linear triple-deck theory is applied to an examination of the response of a boundary layer to short-scale variations in an unsteady free-stream disturbance field. Two-dimensional incompressible flows are considered, and a locally-parallel Blasius mean flow is assumed. A simple pulsating pressure source and a traveling pressure field in the free-stream are modeled by introducing appropriate pressure sources in the upper deck of the triple-deck structure. The modification in unsteady thickness is obtained for these cases, the results are related to the Tollmien-Schlichting instability wave, and the generation of unstable Tollmien-Schlichting waves for both experiments modeled is confirmed.

Heinrich, Roland A. E.↗

Efficient Minimum-Polynomial And Reduced-Rank Extrapolation

MPERRE computer program accelerates convergence of sequence of vectors by use of minimum-polynomial extrapolation (MPE) and reduced-rank extrapolation (RRE). Effective in accelerating convergences of such sequences of vectors as those obtained from iterative solution of systems of linear and nonlinear equations. In conjunction with various iterative techniques, successfully employed in finite-difference solution of large-scale elliptic boundary-value problems and problems in computational-fluid-dynamics. Only input required is sequence of vectors, convergence of which is accelerated. Program economical and easy to use. Written in FORTRAN 77.

Sidi, Avram↗