Vector and parallel computing for matrix balancing

Estimating the entries of a large matrix to satisfy a set of internal consistency relations is a problem with several applications in economics, urban and regional planning, transportation, statistics and other areas. It is known as theMatrix Balancing Problem. Matrix balancing applications arising from the estimation of telecommunication or transportation traffic and from multi-regional trade flows give rise to huge optimization problems. In this report, we show that the RAS algorithm can be specialized for vector and parallel computing and used for the solution of very large problems. The algorithm is specialized for vector computations on a CRAY X-MP and is parallelized on an Alliant FX/8. A variant of the algorithm — developed here for its potential parallelism — turns out to be more efficient than the original algorithm even when implemented serially. We use the algorithms to estimate disaggregated input/output tables and a multi-regional trade flow table of the U.S. The larger problem solved has approximately 12 000 constraints and over 370 000 nonlinear variables. This is the first of two papers that aim at the solution of very large matrix balancing problems. Zenios [20] is using the same algorithm for the same models on a massively parallel Connection Machine CM-2.Research partially supported by NSF grants ECS-8718971 and CCR-8811135, and AFOSR grant 89-0145. Computing resources were made available through the ACRF at Argonne National Laboratory and CRAY Research, Inc.     

Vectorization and multitasking of nonlinear network programming algorithms

Vector supercomputers are designed with two levels of parallelism in order to achieved computational efficiency: low level parallelism through vector operations and high level parallelism with multiple independent processors. These innovations have a significant impact on the development of algorithms for network optimization.In this paper a framework for the vectorization and multitasking of optimization software is developed. It is then applied on the primal truncated Newton algorithm for nonlinear generalized network problems. The vectorization and multitasking of the algorithm is discussed and illustrated with computational experiments with the software system NLPNETG on the CRAY series of vector multiprocessors.     

Computed current density in the case of slow charge-transfer coupled with a second order chemical reaction,under potentiostatic conditions (SnIV/SnII system)

Current-time curves at constant potential on plane and spherical electrode have been computed by numerical integration of the transport equations in the case of a slow charge-transfer coupled with a chemical reaction leading to a non-reactive product E₃, following the scheme:E₁+e→E₂E₁+E→E₂?E₃Results indicate that this mechanism is characterized by lower current densities than those of simple diffusion-transfer control. The current density is not proportional to depolarizer E₁ concentration. The main characteristic of these systems is that, when polarograms are analysed in terms of log k versus potential E, different straight lines are obtained depending on the concentration of the depolarizer; consequently, the apparent transfer coefficient α varies with concentration. Moreover all lines intersect at a same point lying at a potential near the equilibrium value, where the charge-transfer rate constant k is sufficiently small to be rate determining.     

Nonlinear PDE's for stochastic optimal control with switchings and impulses

We show existence, uniqueness, andW ^2, -regularity of the system of nonlinear partial differential equations, associated with stochastic optimal control problems involving costly switchings and impulses. The impulse obstacle is approximated by a sequence of switching obstacles in the proof of regularity. The semiconcavity of the impulse obstacle is exploited.     

Scalar dispersion by coherent structures in uniformly sheared flow generated in a water tunnel

In order to investigate the role of coherent structures as mechanisms of scalar dispersion, we studied measurements of a passive scalar plume released in a uniformly sheared turbulent flow generated in a water tunnel. The flow had homogeneous turbulence properties in the measurement domain and contained hairpin vortices similar to those in boundary layers, and so was an ideal test bed to study the effects of coherent structures on turbulent dispersion, free from the effects of inhomogeneities or boundaries. Measurements of the velocity and concentration fields were acquired simultaneously using stereo particle image velocimetry and planar laser-induced fluorescence. We found that dye was preferentially located far away from vortices and was less likely to appear in close proximity to vortices, which is attributed to the high dissipation at the periphery of the vortices. However, we also found that dye was not directly correlated with the uniform momentum zones in the flow, suggesting a more complex relationship exists between these zones, the locations of vortices, and dye transport. Considering scalar flux events rather than simply the presence of dye as our condition of interest, a conditional eddy analysis demonstrated that hairpin vortices are responsible for the large scalar flux events as well as the large Reynolds stress events in the flow. The fact that the Reynolds stress was correlated with the scalar flux further confirmed that coherent structures are dominant mechanisms for scalar transport. Furthermore, we found that the scalar flux vector was preferentially inclined by 155° and ?25° with respect to the streamwise direction, and was thus approximately orthogonal to the planes of the legs of the most common upright and inverted hairpin structures in the flow. These findings demonstrate that coherent structures play an important and intricate role in turbulent diffusion.     

The interfacial properties of MgCl(2) thin films grown on Si(111)7 x 7

Photoelectron spectroscopy with synchrotron radiation and low energy electron diffraction (LEED) were used in order to study the MgCl(2)Si(111) system. At submonolayer coverage of MgCl(2), a new LEED pattern was observed corresponding to a (sqr rt 3 x sqr rt 3)R30 degrees overlayer superimposed on the underlying reconstructed Si(111)7 x 7. The surface species at this stage are mainly molecular MgCl(2) and MgCl(x) (x<2) or MgO(x)Cl(y) attached to the Si substrate through Cl bridges coexisting with monodentate SiCl. The interfacial interaction becomes more pronounced when the submonolayer coverage is obtained by annealing thicker MgCl(2) layers, whereby desorption of molecular MgCl(2) is observed leaving on the nonreconstructed silicon surface an approximately 0.2 ML thick MgCl(x) layer which again forms the (sqr rt 3 x sqr rt 3 )R30 degrees superstructure.     

Direct versus indirect H atom elimination from photoexcited phenol molecules

The active role of the optically dark pi sigma* state, following UV absorption, has been implicated in the photochemistry of a number of biomolecules. This work focuses on the role of the pi sigma* state in the photochemistry of phenol upon excitation at 200 nm. By probing the neutral hydrogen following UV excitation, we show that hydrogen elimination along the dissociative pi sigma* potential energy surface occurs within 103 +/- 30 fs, indicating efficient coupling at the S1/S2 and S0/S2 conical intersections, with no identifiable role of statistical unimolecular decay of vibronically excited (S0) phenol in the timeframe of our measurements.     

Resonances of CH2(a 1A1) and their roles in unimolecular and bimolecular reactions

Low-lying resonances of the CH2(a 1A1) system (J=0) in an accurate ab initio potential energy surface are studied using a filter-diagonalization method. The width of these resonances fluctuates by more than two orders of magnitude and on average increases with the energy. Analysis of the resonance states concludes that the unimolecular decay of the excited molecular system near the dissociation threshold is neither mode specific nor statistical state specific. This is apparently due to remnant regularity embedded in the largely chaotic classical phase space, as evidenced by periodic orbit analysis. As a result, the Rice-Ramsperger-Kassel-Marcus and statistical adiabatic channel models overestimate the average unimolecular decay rate. The implications of the resonances for the bimolecular C(1D)+H2 reaction are also discussed.