Computations reporting

B. GarciarArchilla, J. M. Sanz-Serna, and R. Skeel. Long-time-step methods for oscillatory differential equations. Applied Mathematics and Computation Reports 1996/7, Universidad de Valladolid, 1996. 

When a mass spectrum has been acquired by the spectrometer/computer system, it is already in digital form as m/z values versus peak heights (ion abundances), and it is a simple matter for the computer to compare each spectrum in the library with that of the unknown until it finds a match. The shortened search is carried out first, and the computer reports the best fits or matches between the unknown and spectra in the library. A search of even 60,000 to 70,000 spectra takes only a few seconds, particularly if transputers are used, thus saving the operator a great deal of time. Even a partial match can be valuable because, although the required structure may not have been found in the library, it is more than likely that some of the library compounds will have stractural pieces that can be recognized from a partial fit and so provide information on at least part of the structure of the unknown. 

To do the computations, we again use the random number generator of MATLAB to produce Normally-distributed random numbers with unity variance to represent the noise values of Er will then directly represent the S/N ratio of the data being evaluated. For the computations reported here, we use 100,000 synthetic values of the expression on the RHS of equation 44-76a to calculate the variance of, for each combination of conditions we investigate. 

As well as being of great interest in their own right, the computations reported here are important for a second reason. 

Comparing Equations 21 and 23 it is apparent that the main difference computationally lies in the appearance of y + in Equation 23. The TLM has been modified accordingly to eliminate activity corrections like y + in Equation 23 for the modeling computations reported here. A detSiled discussion of the thermodynamic basis for making this change can be found in Hayes (8) and Hayes and Leckie (19). 

TABLE I. Computer Report of the Quantitative Analysis of the Spectrum of Fig. 6... 

In speaking of the protein as being in a state of highest statistical weight, it must be emphasized that the statement is made about the total system, protein plus solvent. At one temperature (or solvent, pH, etc.), the statistical weight of the system may be maximized if the protein is in its native state, while, at another temperature (or solvent, pH, etc.), the statistical weight may be maximized if the protein is in a denatured state. The computations reported here pertain to conditions under which, hopefully, the protein will be in its native state. 

Resonantly enhanced two-photon dissociation of Na2 from a bound state of the. ground electronic state occurs [202] by initial excitation to an excited intermediate bound state Em,Jm, Mm). The latter is a superposition of states of the A1 1+ and b3Il electronic curves, a consequence of spin-orbit coupling. The continuum states reached in the two-photon excitation can have either a singlet or a triplet character, but, despite the multitude of electronic states involved in the computation reported J below, the predominant contributions to the products Na(3s) + Na(3p) and Na(3s) + Na(4s) are found to come from the 1 flg and 3 + electronic states, respectively. The resonant character of the two-photon excitation allows tire selection of a Single initial state from a thermal ensemble here results for vt = Ji — 0, where vt,./, denote the vibrational and rotational quantum numbers of the initial state, are stJjseussed. 

A. P. acknowledges the Italian Ministry of the University and the Scientific and Technological Research, and in part the National Research Council through its Centro Studi sugli Stati Molecolari supporting his stay at Cornell University. The computations reported here were performed at the Cornell National Supercomputer Facility. 

Different calculators or computers report different numbers of decimal places in their answers. For example, perhaps a computer reports the answer to 4.9800 divided by 453.6 as 0.01097883597884. If we were to report this result as the mass of our nickel, we would be suggesting that we were certain of the mass to a precision of +0.00000000000001, which is not the case. Instead, we report 0.01098 lb (or 1.098 X 10 lb), which is a better reflection of the uncertainty in the numbers we used to calculate our answer. 

Equations (10.4) and (10.5) is the fact that the more remote positions (4 and 2 ) change less than the substituted positions. Local softness parameters have also been calculated by a bond electronegativity equalization approach.All the computations reported to date refer to diene (HOMO)-dienophile (LUMO) combination pairs, so it is not possible to see if this approach successfully predicts the case in which both the diene and the dienophile carry EWG substiments. 

Microcirculation Using Monte Carlo Techniques on the Hybrid Computer, Report, Chemical Engineering Department, Clemson University, Clemson, S. C. 

Based on the experiments in Ref. 54 with CF3I H2 Ar= 1 1 50 torr. In the computations reported in the text the Ar pressure which measures the R-T rate was taken as a variable. 

In this section we report on the results of computations which appear in [6, 7]. Unless otherwise stated for all of the computations reported here we fixed N = 2b and cr = 0.6 so that Z = b. Eor these parameters, the uiuformly propagating planar solution is unstable. The stability boundary is approximately Z = 4.2 and is very close to the analytically predicted value which is calculated for function kinetics rather than the distributed kinetics that we employ. The control parameter is R which is varied over approximately the interval 0 < i < 20. 

Chapman Adkinson waited for fifteen seconds after he d datavised the visual file. The crippled flight computer reported the communications channel was being maintained. Nothing happened, there was no update from the ISA officer. 

The contented babble coming from the spaceplane s cabin was quieting considerably. Acceleration had now declined to a twentieth of a gee as the orbital injection bum was finalized. Both rocket engines cut out. The flight computer reported four kilos of reaction mass were left in the tanks. 

In applications, the reduced system is embedded in a 1 + ID computational scheme for the overall fuel cell. This includes a model of the membrane s water content and temperature, the anode GDL, and the variation of the oxygen and water vapor contents in the flow field channels in the along-the-channel direction, providing the channel conditions and fluxes which were taken as prescribed in the analysis. To present numerical results from the reduced system, we simulate this coupling by providing along-the-channel data for the oxygen and water vapor concentrations, temperature, current density, and catalyst layer production of heat and total water from a previous 1 + ID computation reported in [3]. These values vary in the y direction but are constant in time and do not couple back to the reduced simulations. 

The numerical details of the CC calculations are published elsewhere [23], where some preliminary comparisons of the methods were made. The present comparison is more complete as we include CSA, BCRLM and RBCRLM results. Furthermore, all the lOSA and ESA-CSA computations reported in this Section used the initial rotational parameter 7=0. 

The photochemistry of the azo functional group continues to be investigated. A recent computational report has been devoted to the simplest term of the series, trow -azomethane in the gas phase as well as in hexane and water solution. It has been found the non adiabatic decay of the njt state... 

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