Showing papers by "California Institute of Technology published in 1968"

Semantics of context-free languages

Abstract: “Meaning” may be assigned to a string in a context-free language by defining “attributes” of the symbols in a derivation tree for that string. The attributes can be defined by functions associated with each production in the grammar. This paper examines the implications of this process when some of the attributes are “synthesized”, i.e., defined solely in terms of attributes of thedescendants of the corresponding nonterminal symbol, while other attributes are “inherited”, i.e., defined in terms of attributes of theancestors of the nonterminal symbol. An algorithm is given which detects when such semantic rules could possibly lead to circular definition of some attributes. An example is given of a simple programming language defined with both inherited and synthesized attributes, and the method of definition is compared to other techniques for formal specification of semantics which have appeared in the literature.

Behavior of Current Divergences under SU 3 × SU 3

Abstract: We investigate the behavior under SU3×SU3 of the hadron energy density and the closely related question of how the divergences of the axial-vector currents and the strangeness-changing vector currents transform under SU3×SU3. We assume that two terms in the energy density break SU3×SU3 symmetry; under SU3 one transforms as a singlet, the other as the member of an octet. The simplest possible behavior of these terms under chiral transformations is proposed: They are assigned to a single (3,3*)+(3*,3) representation of SU3×SU3 and parity together with the current divergences. The commutators of charges and current divergences are derived in terms of a single constant c that describes the strength of the SU3-breaking term relative to the chiral symmetry-breaking term. The constant c is found not to be small, as suggested earlier, but instead close to the value (-sqrt[2]) corresponding to an SU2×SU2 symmetry, realized mainly by massless pions rather than parity doubling. Some applications of the proposed commutation relations are given, mainly to the pseudoscalar mesons, and other applications are indicated.

Minimum-redundancy linear arrays

Abstract: It is shown that there is a class of linear arrays which achieves maximum resolution for a given number of elements by minimizing the number of redundant spacings present in the array. For many-element arrays the degree of redundancy will approach 4/3. Applications of such arrays to aperture synthesis are discussed.

Hemisphere deconnection and unity in conscious awareness.

Abstract: THE following article is a result of studies my colleagues and I have been conducting with some neurosurgical patients of Philip J. Vogel of Los Angeles. These patients were all advanced epileptics in whom an extensive midline section of the cerebral commissures had been carried out in an effort to contain severe epileptic convulsions not controlled by medication. In all these people the surgical sections included division of the corpus callosum in its entirety, plus division also of the smaller anterior and hippocampal commissures, plus in some instances the massa intermedia. So far as I know, this is the most radical disconnection of the cerebral hemispheres attempted thus far in human surgery. The full array of sections was carried out in a single operation. No major collapse of mentality or personality was anticipated as a result of this extreme surgery: earlier clinical observations on surgical section of the corpus callosum in man, as well as the results from dozens of monkeys on which I had carried out this exact same surgery, suggested that the functional deficits might very likely be less damaging than some of the more common forms of cerebral surgery, such as frontal lobotomy, or even some of the unilateral lobotomies performed more routinely for epilepsy. The first patient on whom this surgery was tried had been having seizures for more than 10 years with generalized convulsions that continued to worsen despite treatment that had included a sojourn in Bethesda at the National Institutes of Health. At the time of the surgery, he had been averaging two major attacks per week, each of which left him debilitated for another day or so.

The oxygen isotope geochemistry of igneous rocks

Abstract: Oxygen isotope analyses have been obtained for 443 igneous rock and mineral samples from various localities throughout the world. Detailed studies were made on the Medicine Lake, Newberry, Lassen, Clear Lake, S. E. Guatemala, Hawaii and Easter I. volcanic complexes and on the Bushveld, Muskox, Kiglapait, Guadalupe, Duluth, Nain, Egersund, Lac St. Jean, Laramie, Skaergaard, Mull, Skye, Ardnamurchan and Alta, Utah plutonic complexes, as well as upon several of the zoned ultramafic intrusions of S. E. Alaska. Basalts, gabbros, syenites and andesites are very uniform in O18/O16, commonly with δ-values of 5.5 to 7.0 per mil. Many rhyolite obsidians, particularly those from oceanic areas and the Pacific Coast of the United States, also lie in this range; this indicates that such obsidians are differentiates of basaltic or andesitic magma at high temperatures (about 1,000° C). They cannot represent melted sialic crust. The only plutonic granites with such low δ-values are some of the hypersolvus variety, suggesting that these also might form by fractional crystallization. Obsidians from the continental interior, east of the quartz-diorite line, have higher δ-values. This is compatible with their having assimilated O18-rich sialic crust. A correlation generally exists between the O18/O16 ratios of SiO2-rich differentiates and the chemical trends in volcanic complexes. High O18/O16 ratios accompany those trends having the lower Fe/Mg ratios, while ferrogabbro trends are associated with depletion in O18. Variations in oxygen fugacity may be responsible for these effects, as abundant early precipitation of magnetite should lead to both O18-enrichment and Fe-depletion in later differentiates. Plutonic granites have higher O18/O16 ratios than their volcanic equivalents, because (a) their differentiation occurred at much lower temperatures, or (b) they are in large part derived from O18-rich sialic crust by partial melting or assimilation. Also, the oxygen isotope fractionations among coexisting minerals are distinctly larger in plutonic rocks than in volcanic rocks. This is in keeping with their lower crystallization temperatures and their longer cooling history, which promotes post-crystallization oxygen isotope exchange. Hydrated obsidians and perlites have δO18-values that are much different from their primary, magmatic values. A correlation exists between D/H and O18/O16 ratios in hydrated volcanic glass from the western U.S.A., proving that the isotopic compositions are a result of exchange with meteoric waters. The O18 contents of the glasses appear to be about 25 per mil higher than their associated waters; hence, these hydrated glasses have not simply absorbed H2O, but they have exchanged with large quantities of it. The igneous rocks from Mull, Skye, Ardnamurchan and the Skaergaard intrusion are all abnormally depleted in O18 relative to “normal” igneous rocks. This is a result of their having exchanged at high temperatures with meteoric water that was apparently abundant in the highly jointed plateau lavas into which these igneous rocks were intruded. In part, this exchange occurred with liquid magma and in part with the crystalline rock; in the latter case the feldspar was more easily exchanged and has become much more depleted in O18 than has coexisting quartz or pyroxene. The later differentiates of the Muskox intrusion are markedly O18-rich, but this is not a result of fractional crystallization. It is in large part a result of deuteric exchange between feldspars and an oxygen-bearing fluid (H2O ?) that was either O18-rich or had a relatively low temperature. This phenomenon was also observed in a number of granophyres from other localities, particularly those containing brick-red alkali feldspar. The exchanged feldspars in all these examples are turbid or cloudy, and may be filled with hematite dust. It is concluded that most such feldspar in nature is the result of deuteric exchange and is probably drastically out of oxygen isotopic equilibrium with its coexisting quartz.

Variational Principles in Continuum Mechanics

Abstract: Variational principles for problems in fluid dynamics, plasma dynamics and elasticity are discussed in the context of the general problem of finding a variational principle for a given system of equations. In continuum mechanics, the difficulties arise when the Eulerian description is used; the extension of Hamilton’s principle is straightforward in the Lagrangian description. It is found that the solution to these difficulties is to represent the Eulerian velocity v by expressions of the type v = ∇ X + λ∇ μ introduced by Clebsch (1859) for the case of isentropic fluid flow. The relation with Hamilton’s principle is elucidated following work by Lin (1963). It is also shown that the potential representation of electromagnetic fields and the variational principle for Maxwell’s equations can be fitted into the same overall scheme. The equations for water waves, waves in rotating and stratified fluids, Rossby waves, and plasma waves are given particular attention since the need for variational formulations of these equations has arisen in recent work on wave propagation (Whitham 1967). The idea of solving some of the equations by ‘potential representations’ (such as the Clebsch representation in continuum mechanics and the scalar and vector potentials in electromagnetism), and then finding a variational principle for the remaining equations, seems to be the crucial one for the general problem. An analogy with Pfaff’s problem in differential forms is given to support this idea.

Finite-Energy Sum Rules and Their Application to π N Charge Exchange

Abstract: We derive and discuss the finite-energy sum rules, which form consistency conditions imposed by analyticity on the Regge analysis of a scattering amplitude Their finite form makes them particularly useful in practical applications We discuss the various applications, emphasizing a new kind of bootstrap predicting the Regge parameters from low-energy data alone We apply our methods to $\ensuremath{\pi}N$ charge exchange and are able to derive many interesting features of the high-energy amplitudes at various $t$ In particular, we establish the existence of zeros of the amplitudes and of additional $\ensuremath{\rho}$ poles On the basis of the finiteenergy sum rules and the analysis of the $\ensuremath{\pi}N$ amplitudes, we present theoretical and experimental evidence that double counting is involved in the interference model, which adds direct-channel resonances to the exchanged Regge terms

The Biology of Isolated Chromatin

Abstract: The isolated chromatin of higher organisms possesses several properties characteristic of the same chromatin in life. These include the presence of histone bound to DNA, the state of repression of the genetic material, and the ability to serve as template for the readout of the derepressed portion of the genome by RNA polymerase. The important respect in which isolated chromatin differs from the material in vivo, fragmentation of DNA into pieces shorter (5 x 10^6 to 20 x 10^6 molecular weight) than the original, does not appear to importantly alter such transcription. The study of isolated chromatin has already revealed the material basis of the restriction of template activity; it is the formation of a complex between histone and DNA. Chromatin isolated by the methods now available, together with the basis provided by our present knowledge of chromatin biochemistry and biophysics, should make possible and indeed assure rapid increase in our knowledge of chromosomal structure and of all aspects of the control of gene activity and hence of developmental processes.

General Griffiths' Inequalities on Correlations in Ising Ferromagnets

Abstract: Let N = (1, 2, ⋯, n). For each subset A of N, let JA ≥ 0. For eachi∈N, let σi ± 1. For each subset A of N, define σA=∏i∈A σi. Let the Hamiltonian be − ΣACN JA σA. Then for each A, B⊂N, 〈σA〉≥0 and 〈σAσB〉−〈σA〉〈σB〉≥0. This weakens the hypothesis and widens the conclusion of a result due to Griffiths.

A Study of the Interaction of Gaseous Jets from Transverse Slots with Supersonic External Flows

Abstract: The paper describes a study concerning the sonic injection of a gaseous jet through a transverse slot nozzle in a wall into an external flow which is uniform outside of a turbulent boundary layer. An analytic model of the flowfield has been constructed in which conservation of momentum is applied to a control volume at the jet nozzle exit. A series of flat-plate experiments was conducted with normal, sonic jets at external flow Mach numbers of 2.61, 3.50, and 4.54. Pressure data near separation and the plateau were in agreement with existing correlations. Comparisons of the trends predicted by the analysis with two-dimensional force data from these experiments and from other sources showed good agreement. Values of amplification factor, the upstream interaction force plus the jet thrust divided by the vacuum thrust of a sonic jet, of 2.9 to 3.2 were measured. The amplification factor is relatively insensitive to variations in external flow Mach number and variations in injectant gas properties. A correlation of data obtained from experiments with finite-span slots demonstrates that the effective jet penetration height and the slot span are the important characteristic dimensions of such flowfields.

An accurate numerical steady-state one-dimensional solution of the P-N junction

Abstract: A numerical method of solution of the fundamental semiconductor steady-state one-dimensional transport equations, already available in the literature, is improved and extended, and is applied to a single-junction device. A reduced set of ‘exact’ relations is derived directly from the fundamental set with none of the conventional assumptions or approximations, and is solved numerically by a simple iterative procedure. Freedom is available in the choice of the doping profile, recombination law, mobility dependencies, injection level, and boundary conditions applied solely at the external contacts. In spite of the generality of the original method, its analytical formulation is shown to be unsuitable for generating a sound numerical algorithm sufficiently acccurate and valid for high reverse-bias conditions. Difficulties and limitations are exposed, and overcomeby an improved formulation extended to any bias condition. Emphasis is on the selection of a numerical algorithm sufficiently sound and efficient to cope with the several fundamental difficulties present in the numerical analysis, and on achieving a high degree of accuracy in the final results (the most delicate problem). As a simple application of the improved formulation, ‘exact’ and first-order theory results for an idealized structure are presented and compared. The poorness of some of the basic assumptions of the conventional first-order theory is exposed, in spite of a satisfactory agreement between the exact and first-order results of the terminal properties for particular bias conditions. The computation time for the achievement of one set of very accurate solutions for a specified applied voltage amounts to approx 1 min on an IBM 7094/7040 shared-file system.

A review of calculations for unsteady burning of a solid propellant.

Abstract: A = E(l T^ admittance function, Eq. (1) sensitivity of gas phase to pressure changes specific heats of solid and gas activation energy for surface reaction E = ES/RTS enthalpy latent heat for surface reaction; Hp > 0 for exothermic s_urface reaction H = Hp/cT average mass flux fluctuation of mass flux at the surface index in the linear burning rate law, r = ap index in the surface pyrolysis law, Eq. (25) average heat release (per unit volume) in solid heat release in gas phase fluctuations of heat transfer at the average position of the surface, x = 0 fluctuations of heat release at the burning surface linear burning rate universal gas constant initial temperature of propellant, x -*• — co temperature of burning surface flame temperature average chamber temperature, x -*+ °° surface displacement, velocity functions defined in Eqs. (22) and (27) functions defined in Eqs. (22) and (27) stands for p'/p Eqs. (17-20) thermal conductivities of solid and gas stands for (ms'/m)r density of solid propellant and gas phase average density in chamber normalized temperature or a time lag dimensionless frequency parameters for the solid and gas phases; Eqs. (18) and following Eq. (34) real angular frequency mean value fluctuating value evaluated at the solid-gas interface evaluated on the gas (+) or solid ( — ) side evaluated on the gas or solid side of the mean position of the burning surface evaluated at the flame, or just downstream of the flame real part imaginary part

Determination of the Temperature Profile in an Atmosphere from its Outgoing Radiance

Abstract: A highly convergent relaxation method has been developed for the inversion of the full radiative-transfer equation. The results of the iterative solution indicate that convergence can be achieved over a wide range of initial guesses, enabling the temperature profile of a relatively unknown atmosphere to be unambiguously determined. The method is illustrated by examples for the outgoing radiance in the earth’s atmosphere for the region of the 4.3-μ CO2 band, but can be similarly applied in other frequency ranges.

Microfractures, aftershocks, and seismicity

Abstract: Laboratory investigation of microfracturing in brittle rock has revealed that microfracturing events can be detected after brittle fracture of rock in compression, provided the specimen remains intact. If the sample is isolated after fracture, microfracturing activity decays hyperbolically in a manner similar to typical earthquake aftershock sequences. If reloaded, the sequence is disturbed and a cumulative aftershock pattern develops which is similar to that described by Benioff as strain release due to shear creep. These two types of sequences are discussed with respect to a Markovian model of time dependent fracture in an inhomogeneous brittle medium. This model is then expanded to apply to earthquake aftershock sequences. According to this theory aftershocks are produced by creep rupture due to stress corrosion in the regions of stress concentration following the main shock. The conclusions from laboratory investigations of microfracturing are summarized with respect to the implications regarding the sequence of earthquakes.

On high-frequency oscillatory viscous flows

Abstract: The equations governing high-frequency oscillatory viscous flows are investigated through the separation of the steady and the unsteady parts All Reynolds number ranges are studied and the orders of magnitude of the steady streaming produced by the Reynolds stresses are establishedThe oscillating circular cylinder at low Reynolds numbers is studied through the method of inner and outer expansions Steady recirculating cells exist near the cylinder The results compare very well with experiments Analytic expressions for the streamfunction and the drag coefficient are obtainedThe oscillating flow towards an infinite plate is investigated in detail The steady streaming is caused by the steady component of the Reynolds stress The pressure gradient always causes reverse flow near the solid boundary

Periodic orbits in the restricted three-body problem with earth-moon masses

Abstract: Classification scheme for symmetric periodic orbits in restricted three body problem with two dimensions and earth-moon mass ratio

Denaturation of RNA with dimethyl sulfoxide.

Abstract: The denaturation of single-stranded and double-stranded RNA's in solutions with varying proportions of dimethyl sulfoxide has been followed by changes in absorbancy, optical rotation, and—with a double-stranded form of bacteriophage of MS2 RNA— infectivity for bacterial spheroplasts. By these criteria the RNA's studied, including the synthetic polynucleotide rG:rC, are completely denatured at room temperature in high concentrations of this solvent. In lower concentrations, the T_m of the RNA preparation is decreased only slightly as the dimethyl sulfoxide concentration is raised until a critical concentration is reached. The T_m falls sharply with small further increases in dimethyl sulfoxide concentration. Sedimentation studies can be conducted directly in these media. The determination of sedimentation velocity in 99% dimethyl sulfoxide containing 0.001M EDTA provides a reliable estimate of RNA molecular weights.

Present Status of the Theoretical Predictions for the ^(37)Cl Solar-Neutrino Experiment

Abstract: The theoretical predictions for the ^(37)Cl solar-neutrino experiment are summarized and compared with the experimental results of Davis, Harmer, and Hoffman. Three important conclusions about the sun are shown to follow.

Rheological Comparison of Hemoglobin Solutions and Erythrocyte Suspensions

Abstract: Hemoglobin solutions prepared from hemolyzed human erythrocyte packs have Newtonian flow properties. Diluted solutions are also Newtonian. All solutions have a viscosity lower than the apparent viscosity of erythrocyte suspensions of equal oxygen-carrying capacity. The presence of cell debris in hemoglobin solutions causes non-Newtonian (pseudoplastic or rheopectic) flow behavior.

Experimental investigation of supersonic laminar, two-dimensional boundary-layer separation in a compression corner with and without cooling.

Abstract: An experimental investigation of the boundary layer separation associated with a compression corner was conducted in the GALCIT Mach 6 wind tunnel, and a supplementary study was performed in the JPL supersonic wind tunnel. Special emphasis was placed on the development of a wind tunnel model which approximated true two-dimensional flow, and which could be run in either a highly cooled or an adiabatic configuration. The basic measurements consist of the model surface pressure and temperature, and Pitot surveys of the boundary layer. The surface pressure distributions for the adiabatic wall configurations are compared with the theory of Lees and Reeves (modified by Klineberg and Lees). The surface pressure distribution for the cold wall was compared with the adiabatic configuration for a laminar interaction, and the dependence on Reynolds number for both laminar and transitional interactions are observed. The "free interaction" similarity suggested by Chapman is empirically tested and found to be a good approximation for the adiabatic configuration, but it fails to correlate the cooled with the adiabatic case. The scaling suggested by Curle was tested and found to eliminate this deficiency.