A substantial amount of infrasonic waves was produced by the great Alaskan earthquake in March 1964. It was found that the waves from the earthquake traveling across the United States produced sound waves which traveled almost vertically upward to the ionosphere. The waves amplified enough during the vertical propagation to cause large motions of the ionosphere, with oscillation speeds of more than 100 meters per second.

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Groups of very long-period infrasonic waves sometimes occur in the Washington area. The time periods of such waves are approximately between 250 and 900 seconds. The speeds are in the range between 15 and 70 m/s. These waves seem to be connected with the jet stream in the upper atmosphere about Washington. It is believed that waves can form on the lower boundary surface of the jet stream when the atmosphere verges on having an unstable temperature gradient.

Radio Plasma

Basic research in plasma physics was pursued with emphasis on the study of plasma mechanisms and the development of necessary plasma diagnostics and plasma technology. During this year it was discovered that the negative glow in a d-c helium discharge constitutes a well behaved, noiseless and stable plasma ideally suited for precision measurements. This plasma has been built into experiments for the study of rate and transport mechanisms and wave mechanism.

This source was also used to intercompare different diagnostic tools and methods with sufficiently good agreement to indicate that it may in the future serve as a standard. As a preliminary for wave propagation measurements in a magnetized plasma, tubes have been developed for operation in magnetic fields. Measurements of electromagnetic noise emitted from the tubes indicates that they will serve well for precision measurements of wave propagation.

Plasma Boundaries.-A technique utilizing slow electromagnetic waves for the study of plasma boundary mechanisms has also been developed and put into use. Nonlinear diffusion in the presence and absence of a uniform steady state magnetic field has been solved theoretically and will serve as the basis for future experiments. Also the propagation of electromagnetic waves in an overdense, collision free and bounded magnetoplasma has been treated exhaustively and is expected to be helpful in the measurements of electromagnetic wave propagation in uniform plasmas.

Brush Cathode Plasma.-A brush cathode type of plasma was used to study a variety of effects, particularly pertaining to the diagnosis of plasmas. It was found that measurements with pulse probes gave very good agreement with spectroscopic measurements.

APPLIED MATHEMATICS

Mathematics lies at the foundation of measurement, offering guidance in the development of new measurement techniques and providing the central techniques for evaluation of the results of measurement. The Institute for Basic Standards conducts a program in applied mathematics and statistics to assure effective and productive performance in the measurement of physical quantities associated with the development and maintenance of standards and in the provision of calibration services. The mathematical needs of IBS require the employment of varied and advanced mathematical techniques, and in many cases existing techniques must be modified or new ones developed for the solution of particular problems. Therefore, in order to utilize mathematics effectively, the Institute must conduct fundamental mathematical research on a fairly broad scale.

Plasma Dynamics.-The research project in plasma dynamics was initiated in 1960 as a Bureau-wide program to investigate the dynamic behavior and transport properties of plasmas, and to provide theoretical cooperation in the various plasma activities.

The present research program consists of a selection of problems relevant to the fundamental behavior and properties of plasmas. It attempts to clarify the measurements and diagnostic techniques of primary physical quantities and properties, e.g., density, velocity, temperature, pressure, stresses, field intensity, viscosity, thermal and electrical conductivity in ionized gases under non-equilibrium dynamical conditions.

Statistical Mechanics of Nonequilibrium Ionized Gases.-Plasma turbulence has been observed in fusion experiments, stellar atmosphere, solar wind and in the transition region bounded by the solar wind shock wave and the terrestial magnetosphere. A magnetohydrodynamic theory has been developed and a kinetic theory has been proposed for a rarefied plasma. It is now possible to extend these theories to non-uniform conditions. Furthermore, the knowledge gained will facilitate the derivation of a kinetic equation for a turbulent plasma.

Magnetohydrodynamics.-The expansion of a plasma into a vacuum in the presence of a magnetic field was investigated. The numerical work was performed in cooperation with NASA with the use of the NBS computer and program.

Matroids. During the past year, theoretical interest focused on the study of matroids. Efficient algorithms were found for several basic problems, e.g., for the case of a network to find as many connected subnetworks as possible, no two with an edge in common, and each meeting all the nodes. The first conference ever held on matroid theory was conducted; it gave a marked impetus to research in the field.

Graph Theory-Significant progress in graph theory continued. Past work was extended to provide efficient algorithms for the "Chinese post

man's problem" (to find a tour of minimum total length which traverses every link at least once), the "optimal interconnection problem" (to find a cost-minimizing set of interconnections, given the cost of each and the minimum number of other facilities to which each facility must be joined) and the “circuit packing problem" (to find, in a graph with values attached to its edges, a set of disjoint circuits whose edges have maximum sum of values).

Supersonic Transport.-Substantial assistance was rendered to the Commerce Department's Supersonic Transport Economic Analysis. Simulation and analytic models of air transport competition were developed. Models also were devised for cost-benefit comparisons and for balance-of-paymentseffects analysis. The models were implemented as digital computer programs, and applied to a wide range of future possibilities and parametric values.

Postal Mechanization.-Investigations pertinent to postal mechanization continued to be performed for the Post Office Department. Some studies involved cost-benefit analyses of proposed mail-sorting subsystems and address-coding methods, while others dealt with stochastic aspects of certain mailhandling operations.

Textiles. Collaboration in the industrial modeling efforts of the Bureau's textile technology continued.

Northeast Corridor Transportation.-Collaborative efforts were initiated under the Commerce Department's Northeast Corridor Transportation Project. The demand for consulting and advisory services in operations research and related mathematical fields continued to rise, especially from transportation-connected Federal activities.

Statistical Engineering.-NBS conducts a continuing program of research in mathematical statistics and probability. Continuing investigation of mathematical problems in the theory of experiment design led to new results on the classical tournament problem of combinatorial analysis, with applications to the construction of calibration designs for comparing groups of objects. These designs are useful in weighing and any other measurements where the objects to be measured can be combined into groups without loss of precision or accuracy in the comparisons.

Special attention has been given to the application of modern methods of mathematical statistics to the evaluation and clarification of statistical techniques used by physical scientists. Among those examined recently are Chauvenet's criterion for rejection of outlying observations, and propagation-of-error formula. It has been demonstrated that Chanvenet's criterion should usually be discarded in favor of more precise modern techniques. The correct method for constructing and applying propagationof-error formulas has been explained in detail, with particular emphasis on the types of situations that arise in complex experimental programs

were several related measurements and the associated correction factors must be combined into a final result.

Phase Integral.-A successful investigation has been made of phaseintegral methods used for problems of wave propagation and quantum mechanics. Asymptotic theory of differential equations developed earlier at the Bureau has been applied to put phase-integral methods on a firm mathematical foundation with a comprehensive error analysis.

Multiple Integrals.-The evaluation of multiple integrals by a combination of methods, such as the Monte Carlo method and the numbertheoretic methods associated with uniformly distributed sequences, was studied and significant advances in error improvement were made. In certain instances integrals were evaluated by these methods which could not be previously efficiently evaluated.

Laboratory Data Reduction.-The reduction of laboratory data always represents a considerable chore and is often a serious bottleneck in the research process. It is, at first, surprising to note how much of this work is still being performed on desk calculators, even in organizations having large digital computers. One reason for this is that each application is seemingly so specialized that a programming effort is not justified—and, indeed, it often is not justified when the scientist is required to build his program from the ground up in the conventional manner.

At NBS this problem has been solved to a considerable degree by the development of OMNITAB-a general purpose computer program which gives the laboratory scientist the full power of the digital computer without requiring him to learn to program it. OMNITAB can be used for the calculation of tables of functions, for solutions of nonlinear equations, for curve fitting, and for statistical and numerical analysis of tabular data.

PERFORMANCE CHARACTERISTICS

The properties of well-defined simple substances can easily be measured, and results expressed in relation to basic physical quantities. But NBS is also concerned with the performance characteristics of devices-the lens and shutter assembly of a camera, a transistor, or an electric motor. The behavior of such devices is dependent on the properties of its components, and sometimes an exact and reliable connection between the two can be defined. More often, however, the most important question about the device is not its construction, but its performance as a whole, and the answer to the question must be based on testing related to the end use.

Lens and Lens Systems.-The successful use of many devices in metrological work depends upon precise knowledge of the performance characteristics of lenses or other optical elements used in the construction of the device. It is therefore necessary to develop methods of measurement that yield values of optical constants sufficiently accurate to meet current needs.

In addition, methods of analysis must be developed for use in pointing the way toward achieving still higher performance.

New Lens Measurement System.-A Moise fringe system of measurement has been adapted for use in the determination of lens constants. With this device, focal distances can now be measured to the nearest micron as contrasted to the precision of ±20 microns achieved previously. This device is also used in the accurate determination of zone heights, resulting in increased accuracy of longitudinal spherical aberration values of lenses. Also, analytic methods have been developed for predicting the resolving power of a lens when measured or when design values of the longitudinal, spherical and chromatic aberration of the lens are known.

Photographic Information Concentration.-Photographic emulsions can store more information per unit of area than any other device. A microphotograph of a printed page reduced 1,440,000 times in area was made recently, and the copy was legible through a high-powered microscope. Publishable reproductions were obtained by enlarging the copy nearly 4000 diameters. The information concentration on the copy was computed to be over 2 million bits per square millimeter, which more than doubles previous estimates of the emulsion capacity.

Cyclic Bending of Grounding Conductors.-At the request of the Rural Electrification Administration a machine with a reciprocating head, counter circuits and controls was constructed, and bending (fatigue) tests were made of conductors used in the grounding loop of pole-mounted power distribution transformers. Ungrounded transformers have led to substantial property loss and are hazardous to operating personnel. Test results of three widely used soft copper conductors showed 7 wire and 19 wire strands have about equal endurance times and that both types were about 5 times better than the solid wire when tested under similar laboratory conditions.

TECHNICAL ASSISTANCE TO OTHERS

The National Bureau of Standards is a national source of technical assistance and consultation in certain problem areas, and it inevitably assumes a leading role in cooperative efforts and scientific conferences directed at the solution of the problems.

All of the scientific specializations in the Institute for Basic Standards take some part in technical assistance, but the contribution in applied mathematics is especially significant. This emphasis is due primarily to the capability of the NBS staff to combine mathematical competence with thorough familiarity with the scientific fields to which mathematical analysis is applied.

The following are specific examples of technical assistance provided by IBS in the past year.