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January-February 1979

space-saving “quasi-dynamic storage allocation," and easy setup for construction of large matrices from smaller ones (with the actual construction deferable until and if the need arises).

Cutting the d-cube, J. Lawrence, J. Res. Nat. Bur. Stand.

(U.S.), 84, No. 1, 49-53 (Jan.-Feb. 1979).

Diffusion coefficients of the 455 and 50s states of the large

ribosomal subunit of E. coli by quasielastic light scattering, C. C. Han, I. N. Serdyuk, and H. Yu, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 1, 1-8 (Jan.-Feb. 1979).

Key words: diffusion coefficient; E. coli ribosomal subunit;

quasielastic light scattering: 45S and Sos. The transitional diffusion coefficients of the 455 and 50s states of the large ribosomal subunit of E. coli were determined from the spectral distributions of quasielastically scattered light with a 5 mW He-Ne laser as the source. The spectral analysis was performed by directly Fourier transforming the photocurrent and fitting to double-Lorentzian profile via a non-linear regression routine. A small amount (about 1%) of strongly scattering contaminants required the double-Lorentzian profile in order to extract the diffusion coefficients of the principal components. The results are: Dzoo, w(45S) = (1.79 0.12) 10:? cm/sec, and Dzoo, w(SOS) = (1.91 + 0.06)* 101 cm/sec, the latter being in accord with those reported in the literature. The transition from the SOS state to the 45S state is not attended by a change in its molecular weight if the partial specific volumes are assumed to be the same.

Key words: cube; geometry; hyperplane. Some problems concerned with cutting faces of the cube with affire or linear spaces are considered. It is shown that through any d-3 points of Rd there passes a hyperplane which cuts all the facets of the d-cube. Furthermore, it is shown that if m<d-1 and d' <d-((m + 1)/3), then no m-dimensional affine subspace of Ra cut all the d'-dimensional faces of the cube.

March-April 1979

System for assessing eye injury potential of propelled objects, R.

E. Berger, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 1, 9-19 (Jan-Feb. 1979).

A novel method for analyzing silver sediment with high preci

sion, S. Davis and V. E. Bower, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 2, 157-160 (Mar.-Apr. 1979).

Key words: controlled potential; coulometry; electrochemical equivalent of silver; electrochemistry; Fa day; poten

tiostat; silver; silver analysis. A technique has been devised which is sufficiently accurate to aid in an electrochemical determination of the Faraday constant using the silver coulometer. The technique is used to recover the silver residue which falls from the anode during operation of the silver coulometer. In contrast to previous efforts at recovery, which involved weighing of the silver residue, the method here described is to convert the silver atoms to ions and then to plate the silver onto a cathode held at constant potential with respect to a reference electrode. The current involved in the electrolysis is integrated electronically. An overall standard deviation of 5 mg is achieved for samples' ranging in size from 400 mg to 1.8 mg.

Key words: eye injury; impact; ocular contusion; projec

tiles; propelled objects; test methods; toy safety. A test system is proposed to evaluate the ocular injury potential of propelled objects. The object in question is fired into a thin rubber pad, and the force of impact and the rise time are measured. For a set of test projectiles, the response of the system was shown to correlate with the likelihood of injury, as predicted by a mathematical model. The response was further related to ocular injury tolerance curves which were generated by the math model using data from impact injuries to real eyes. Enhancing Fortran to aid manipulation of large structured

matrices, H. J. Greenberg and J. E. Kalan, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 1, 21-47 (Jan.-Feb. 1979).

Key words: data pooling; data structures; mathematical programming; matrices; name generation; operations

research; programming languages; sparse matrices. This paper presents, for wider discussion by the technical community, suggested means for enhancing (ANS) FORTRAN in order to accommodate the needs of operations research analysts in programming tasks involving large, structured or sparse matrices. Such needs frequently arise in connection with large-scale optimization problems. Most of the text deals with fundamental concepts and descriptions of syntax, but related data structures are also treated. Proposed new capabilities include exploitation of repeated values among matrix entries,

Psychrometric wet elements as a basis for precise physico-chemi

cal measurements, R. G. Wylie, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 2, 161-177 (Mar.-Apr. 1979).

Key words: convective heat transfer; convective mass transfer; emissivity of water; evaporation coefficient; humidity measurement; monomolecular film; ychrometer; psychrometry; radiative heat transfer; temperature depression; water vapor measurement; wet bulb; wet element.

Under appropriate conditions, psychrometric wet elements of simple design can be highly reproducible in behavior. A temperature depression of 10 K can be reproducible from element to element within 2 mK. The properties of a wet element can be determined very accurately by direct comparisons with other wet elements in a common airstream. Comparisons with one specially developed type show the effects of practical waterretaining coverings. Comparisons with another type, which simulates the fully calculable flat-plate system, then give the behavior in absolute terms.

A cotton-yarn covering increases the psychrometer coefficient A by only 0.2 percent. The departure of the flow around a cylinder from laminar boundary-layer flow increases it by 0.7 percent.

'The various NBS publications series are grouped under subheadings within this section. If a particular publications series is sought, consult the table of contents or the edge index on the back cover.

characteristic impedance of striplines as a function of frequency and dielectric thickness. Simulations of pulse transmission are used to evaluate the utility of the example striplines for high-speed digital applications.

The background and theory are outlined. The detailed behavior of a cotton-yarn covered cylinders is deduced from element comparisons; and their absolute value of A obtained as a function of diameter, airspeed, and the temperature, pressure and water content of the airstream. The dependence of A on these parameters is essentially simple. The work leads to a large increase in the accuracy of water vapor measurements and to new methods of measuring some other physico-chemical quantities.

July-August 1979

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Enthalples of solution of KBr, KI, KIO3, and KIO, in H,O, M.

E. Efimov, G. N. Klevaichuk, V. A. Medvedev, and M. V. Kilday, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 4, 273-286 (July-Aug. 1979).

Key words: endothermic solution reactions; enthalpy of solution; KBr, KI, KIO,, KIO,; solution calorimetiy; ther

mochemistry; tris(hydroxymethyl)aminomethane. Enthalpy of solution measurements of four potassium salts in H2O were made in either an adiabatic or an isoperibol calorimeter or both (see p. 273 for table summarizing the measured and recommended values).

The value for KIO, has been corrected for the hydrolysis of the periodate ion. The AC, = -(82.5 = 4.3)J.mol-.K-' for the unhydrolysed reaction. For the reaction of KBr in H,O, AC, was measured as -(166.6 1 7.2)J.mol-'.K-in the temperature range 298 K to 319 K.

Measurements with the isoperibol calorimeter are also reported for

the endothermic reaction of tris(hydroxymethyl)aminomethane, SRM 724a, in aqueous NaOH(0.05 mol/L).

Comparisons, of measurements by different calorimeters on the same samples reveal unidentified calorimetric errors for endothermic reactions which are greater than the imprecision of the measurements.

Enthalpies of solution of the nucleic acid bases. 5. Adenine in

aqueous hydrochloric acid, aqueous sodium hydroxide, methanol, and ethanol, M. V. Kilday, J. Res. Nar. Bur. Stand. (U.S.), 84, No. 3, 231-240 (May-June 1979).

Key words: adenine; enthalpy of dissociation; enthalpy of protonation; enthalpy of reaction; enthalpy of solution;

nucleic acid bases; solution calorimetry; thermochemistry. The two preceding papers in this series described the results of measurements of the enthalpies of solution in water for some of the bases of the nucleic acids. In this work the enthalpies of solution or reaction of adenine (Ade), C,H,N, or 6-amino purine, in other solvents are reported. Sample preparation in lon-chromatography, W. F. Koch, J. Res.

Nat. Bur. Stand. (U.S.), 84, No. 3, 241-246 (May-June 1979).

A preliminary study of the fluid mechanics of liquid penetrant

testing, S. Deutsch, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 4, 287-292 (July-Aug. 1979).

Key words: defect geometry; fluid elasticity; liquid penetrant testing; Rideal-Washbum equation; surface tension.

Key words: conductivity; ion-chromatography; ion

exchange; liquid chromatography; oil; oyster. lon-chromatography, a relatively new technique in analytical chemistry, has already shown great promise toward solving complex trace analysis problems, in particular the speciation and quantitation of anions. It is especially attractive to the field of microanalysis. The method of sample preparation, however, is crucial in order to realize this capacity. Existing microanalytical methods nearly always must be modified to be compatible with ion-chromatography, and often, more extensive sample cleanup is required than is needed for "single species" methods. These considerations have been applied to the determination of chloride and bromide in waste oil, and to the analysis of oyster tissue. Pretreatment with polystyrene resin and ion-exchange resin is discussed.

Some aspects of the fluid mechanics of liquid penetrant testing are considered. Penetration is represented by surface tension driven flow into defects of small defect width to depth ratio. Defect width is chosen so that both gravitational and non-continuum effects may be ignored. Penetration time is found to follow a Rideal-Washburn relation, in which:

- (Pu)/(YR cos 6) where 1 is time, I defect depth, u the dynamic viscosity, y the surface tension, R the defect width and the contact angle. The proportionality constant, however, is shown to be strongly dependent on defect geometry and penetrant application procedure. The effect of slight fluid elasticity is shown to be negligible.

Miniaturization of normal-state and superconducting striplines,

R. L. Kautz, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 3, 247259 (May-June 1979).

Key words: copper; niobium; stripline; superconductivity;

surface impedance. The properties of normal-state and superconducting striplines are calculated as a function of miniaturization. For normal conductors the Reuter-Sondheimer theory is applied in order to account for the effects of finite film thickness and mean free path. For superconductors the Mattis-Bardeen theory is used in order to include effects due to the energy gap. Calculations for three example conductors, copper at 295 K and 4.2 K and niobium at 4.2 K, examine the attenuation, dispersion, and

Exact coefficients of the limit cycle in Van der Pol's equation,

A. Deprit and D. S. Schmidt, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 4, 293-297 (July-Aug. 1979).

Key words: algebra by computer; differential equations;

mathematical software; non-linear oscillations, A program generator to manipulate automatically Poisson series over the field of rational numbers is applied to develop the limit cycle of Van der Pol's equation in the powers of the small parameter. The results indicate that the recurrence relations in what Melvin calls the algorithm of the shifted phase are stable.

Tensile behavior of some mathematical models of paper net

works, J. C. Smith, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 4, 299-318 (July-Aug. 1979).

Key words: mathematical modeling, network; network, tensile properties; paper, interfiber bonding; paper, low-density handsheets; paper, pulp characterization; paper,' tensile

testing. The tensile behavior of a thin web-like paper network was simulated by two simple mathematical models. The mesh distortion, drop in tensile force and energy loss resulting from breakage of a network junction were calculated. These results were used to formulate two parameters for characterizing interfiber adhesion: a parameter averaging the network energy losses incurred in a series of bond breaks when the network is elongated and a parameter averaging the force drops. The effect of mesh size, local bond adhesive force, and size and shape of the specimen network were calculated. These results based on model studies were used to interpret behavior observed in an actual paper network.

C, and C, are the Mooney-Rivlin constants. Measurements of equilibrium swelling at a given degree of cross-linking are in reasonable agreement with each other. However the entropy components of the modulus and the sub-chain density calculated from swelling measurements are appreciably greater than those calculated from cross-linking or from direct mechanical measurements. They increase linearly with cross-linking. It is concluded that the number of sub-chains effective in limiting swelling is greater than that effective in direct mechanical mea


A class of double integrals involving Gaussian and trigonometric

factors, D. M. Fradkin, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 4, 319-326 (July-Aug. 1979).

Key words: definite integrals; double integrals; error func

tions; Fourier transforms; radiation reaction. The five parameter double integral Soo dy exp(-péya) sin(By +0) times sou dx exp(-x) cos(eßx + $ ) is evaluated in terms of Fourier transforms of exp(-x*)erfc(ar). Some new expressions for these transforms are obtained.

September-October 1979

Theory of flow-induced fibril formation in polymer solutions, J.

D. Hoffman, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 5, 359384 (Sept.-Oct. 1979).

Key words: core fibril; cumulative stress; flow-induced crystallization; nucleation theory; polyethylene; polymer

fiber; shish; volume strain. A treatment of the formation of a basic core fibril (shish) of the type that is generated by flow-induced crystallization of a polymer from solution is given that features the concept of cumulative strain. Multiple nucleation acts by flow-elongated molecules produce an empbryonic fibril that is a connected set of bundlelike nuclei. Surface stress resulting from repulsion of the quasi-random coil chains in the amorphous zone between the nuclei or crystallites builds up at the bundle ends as the nuclei mature, leading ultimately to a high end surface free energy, and to volume strain in the crystallites comprising the core fibril. The theory leads to a stable (or metastable) fibril diameter a, and mean characteristic length I, with a fixed axial ratio, and predicts why the diameter does not grow further even in a medium that is supersaturated with polymer. The predicted dependence of a,, ,, and the axial ratio, on undercooling is in approximate agreement with experiment. The lattice expansion in the crystal resulting from volume strain is also in fair accord with experiment. The effect of annealing, including the commonly encountered case where the volume strain relaxes to give normal lattice dimensions, but with a high end surface energy still remaining, is noted. The effect of volume strain and the distribution of core fibril lengths about I, on the melting behavior is calculated. The theory can reproduce crystallinity versus temperature data on polyethylene fibrils. This procedure yields an independent value of l,. The overall treatment implies that the core fibril is a set of concatenated and substantially extended-chain crystallites with bundlelike ends and a somewhat expanded lattice when unannealed and under tension, the molecular connections between the crystallites consisting of short amorphous ciliary bridges. It is suggested that prolonged annealing at high temperatures can

a substantial number of the amorphous zones.


A high precision load cell mass comparator, R. M. Schoonover,

J. Res. Nat. Bur. Stand. (U.S.), 84, No. 5, 347-351 (Sept.Oct. 1979).

Key words: constant loading; force; high precision; highprecision weighing; load cell; mass; mass comparator; mass difference; strain-gage; substitution weighing; weighing;

weights. Described here is a simple mechanical method used to fabricate a high precision mass comparator using a bonded strain gage load cell. Results indicate that a standard deviation of less than 0.0003% is readily attainable, and the device works well for objects normally considered too unwieldy for large high-precision balances. Molecular interpretations of modulus and swelling relations in

natural rubber cross-linked by dicumyl peroxide, L. A. Wood, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 5, 353-358 (Sept.Oct. 1979).

Key words: cross-linking of rubber; dicumyl peroxide; elasticity theory of rubber; modulus of rubber; MooneyRivlin constants; rubber elasticity theory; rubber, natural;

swelling of rubber network. A survey of published experimental work on the modulus of natural rubber cross-linked by dicumyl peroxide permits a comparison with the results and molecular interpretations obtained in recent NBS work (J. Res. NBS 76A, No. 1, 51 (1972), 77A, No. 1, 171 (1973) and 80A, No. 3, 451 (1976)). Excellent agreement was found among values of the shear modulus G at the same cross-linking when the cross-linking is calculated from the amount of decomposed dicumyl peroxide. The types of deformation included torsion as well as uniaxial extension and compression. G increases lincarly with cross-linking (except at the lowest degrees) with a slope from 5 to 15 percent greater than that predicted by the simple statistical theory. Data of Mullins demonstrated that at each degree of cross-linking the value of G is intermediate between 2C, and 2(C, + C,) where

Observations of surface changes in platinum crucibles, C. P.

Saylor, E. Wichers, and J. I. Hoffman, J. Res. Nat. Bur. Stand. (U.S.), 84, No. 5, 385-394 (Sept.-Oct. 1979).

Key words: contrast augmentation of reflecting surfaces; double-diaphragm; faces (crystal) on platinum crucibles; hematite forming on platinum; iron as alloy in platinum; platinum ware; surface of platinum influenced by method

heating lon which has been in solid solution in a platinum crucible will cause iron determinations in analyses to become high. Likewise the iron, oxidizing to ferric oxide during ignition, segregates along the boundaries between platinum crystals. It causes embrittlement and eventual crumbling of the crucible.

During these studies it was observed that after heating in an electric muffle furnace the surface of a crucible was covered by tiny crystallographic faces. When, however, heating to the same temperature was carried out in a gas flame the facets almost smoothed out of existence.

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