Showing papers by "California Institute of Technology published in 1976"

Breakdown of Predictability in Gravitational Collapse

Abstract: The principle of equivalence, which says that gravity couples to the energy-momentum tensor of matter, and the quantum-mechanical requirement that energy should be positive imply that gravity is always attractive. This leads to singularities in any reasonable theory of gravitation. A singularity is a place where the classical concepts of space and time break down as do all the known laws of physics because they are all formulated on a classical space-time background. In this paper it is claimed that this breakdown is not merely a result of our ignorance of the correct theory but that it represents a fundamental limitation to our ability to predict the future, a limitation that is analogous but additional to the limitation imposed by the normal quantum-mechanical uncertainty principle. The new limitation arises because general relativity allows the causal structure of space-time to be very different from that of Minkowski space. The interaction region can be bounded not only by an initial surface on which data are given and a final surface on which measurements are made but also a "hidden surface" about which the observer has only limited information such as the mass, angular momentum, and charge. Concerning this hidden surface one has a "principle of ignorance": The surface emits with equal probability all configurations of particles compatible with the observers limited knowledge. It is shown that the ignorance principle holds for the quantum-mechanical evaporation of black holes: The black hole creates particles in pairs, with one particle always falling into the hole and the other possibly escaping to infinity. Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state. This means there is no $S$ matrix for the process of black-hole formation and evaporation. Instead one has to introduce a new operator, called the superscattering operator, which maps density matrices describing the initial situation to density matrices describing the final situation.

A general unified approach to modelling switching-converter power stages

Abstract: A method for modelling switching-converter power stages is developed, whose starting point is the unified state-space representation of the switched networks and whose end result is either a complete state-space description or its equivalent small-signal low<-f requency linear circuit model. A new canonical circuit model is proposed, whose fixed topology contains all the essential inputr-output and control properties of any dc-todc switching converter, regardless of its detailed configuration, and by which different converters can be characterized in the form of a table conveniently stored in a computer data bank to provide a useful tool for computer aided design and optimization. The new canonical circuit model predicts that, in general;switching action introduces both zeros and poles into the duty ratio to output transfer function in addition to those from the effective filter network.

Black Holes and Thermodynamics

Abstract: A black hole of given mass, angular momentum, and charge can have a large number of different unobservable internal configurations which reflect the possible different initial configurations of the matter which collapsed to produce the hole. The logarithm of this number can be regarded as the entropy of the black hole and is a measure of the amount of information about the initial state which was lost in the formation of the black hole. If one makes the hypothesis that the entropy is finite, one can deduce that the black holes must emit thermal radiation at some nonzero temperature. Conversely, the recently derived quantum-mechanical result that black holes do emit thermal radiation at temperature $\frac{\ensuremath{\kappa}\ensuremath{\hbar}}{2\ensuremath{\pi}kc}$, where $\ensuremath{\kappa}$ is the surface gravity, enables one to prove that the entropy is finite and is equal to $\frac{{c}^{3}A}{4G\ensuremath{\hbar}}$, where $A$ is the surface area of the event horizon or boundary of the black hole. Because black holes have negative specific heat, they cannot be in stable thermal equilibrium except when the additional energy available is less than 1/4 the mass of the black hole. This means that the standard statistical-mechanical canonical ensemble cannot be applied when gravitational interactions are important. Black holes behave in a completely random and time-symmetric way and are indistinguishable, for an external observer, from white holes. The irreversibility that appears in the classical limit is merely a statistical effect.

Nd isotopic variations and petrogenetic models

Abstract: ^(147)Sm ɑ-decays to ^(143)Nd so that ^(143)Nd/^(144)Nd reflects the time-integrated Sm/Nd environment of a sample. The increase in 143/144 in a reservoir with chondritic Sm/Nd is 1.2% in 4.5AE. There exists sufficient variation of Sm/Nd to cause sizeable effects in 143/144. Young samples were measured to elucidate the nature of their source regions. An oceanic high Fe, Ti basalt (113152) and alk. basalt (113031), a continental alk. besalt (BCR-l), an apatite (Khibiny massif) and two reagent "normals", NN1 and NN2, were analyzed. Isotopic ratios of NN2 and BCR-1, normalized to 148/144=0.241572 are tabulated. Following the pioneering work of Lugmair, et al. (EPSL 27, 79) our 143/144 data are presented relative to the total rock value for Juvinas (0.51278). the present value of a chondritic reservoir. Data are given as deviations from this value in parts in 10^4 (є) and show a wide range. Nd in the source regions of the rock samples evolved in an environment of approximately chondritic Sm/Nd (±5%) over the history of the earth. Small variations exist, reflecting long time scale differences of Sm/Nd in the source regions. The low Sm/Nd observed in alkali basalts cannot reflect an ancient source region with low Sm/Nd as є is near zero. REE patterns of alkali basalts must thus reflect relatively recent fractionation from a source with essentially chondritic relative abundances. Study of initial ^(143)Nd/^(144)Nd in conjunction with REE patterns promises to contribute important petrogenetic information.

Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole

Abstract: Hawking has predicted that a black hole will emit particles as if it had a temperature proportional to its surface gravity. This paper combines Hawking's quantum formalism with the black-hole perturbation methods of Teukolsky and Press to calculate the emission rate for the known massless particles. Numerical results indicate that a hole of mass $M\ensuremath{\gg}{10}^{17}$ g should emit a total power output of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\ensuremath{\hbar}{c}^{6}{G}^{\ensuremath{-}2}{M}^{\ensuremath{-}2}$, of which 81% is in neutrinos, 17% is in photons, and 2% is in gravitons. These rates plus an estimate for the emission rates of massive particles from smaller holes allow one to infer that a primordial black hole will have decayed away within the present age of the universe if and only if its initial mass was $Ml(5\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{14}$ g.

Path-integral derivation of black-hole radiance

Abstract: The Feynman path-integral method is applied to the quantum mechanics of a scalar particle moving in the background geometry of a Schwarzschild black hole. The amplitude for the black hole to emit a scalar particle in a particular mode is expressed as a sum over paths connecting the future singularity and infinity. By analytic continuation in the complexified Schwarzschild space this amplitude is related to that for a particle to propagate from the past singularity to infinity and hence by time reversal to the amplitude for the black hole to absorb a particle in the same mode. The form of the connection between the emission and absorption probabilities shows that a Schwarzschild black hole will emit scalar particles with a thermal spectrum characterized by a temperature which is related to its mass, $M$, by $T=\frac{\ensuremath{\hbar}{c}^{3}}{8\ensuremath{\pi}}\mathrm{GMk}$. Thereby a conceptually simple derivation of black-hole radiance is obtained. The extension of this result to other spin fields and other black-hole geometries is discussed.

Velocity dispersion due to anelasticity; implications for seismology and mantle composition

Abstract: The concept of a relaxation spectrum is used to compute the absorption and dispersion of a linear anelastic solid. The Boltzmann after-effect equation is solved for a solid having a linear relationship between stress and strain and their first time derivatives, the ‘standard linear solid’, and having a distribution of relaxation times. The distribution function is chosen to give a nearly constant Q over the seismic frequency range. Both discrete and continuous relaxation spectra are considered. The resulting linear solid has a broad absorption band which can be interpreted in terms of a superposition of absorption peaks of individual relaxation mechanisms. The accompanying phase and group velocity dispersion imply that one cannot directly compare body wave, surface wave, and free oscillation data or laboratory and seismic data without correcting for absorption. The necessary formalism for making these corrections is given. In the constant Q regions the correction is the same as that implied in the theories of Futterman, Lomnitz, Strick and Kolsky.

Inferences about magma sources and mantle structure from variations of ^(143)Nd/^(144)Nd

Abstract: Continental flood basalts and mid-ocean ridge (MOR) tholeiitic basalts have distinctly different ^(143)Nd/^(144)Nd which may permit a priori distinction between "continental" and "oceanic" igneous rocks. Initial ^(143)Nd/^(144)Nd of continental igneous rocks through time fall on a Sm/Nd evolution curve with chondritic REE abundance ratio. These observations indicate that many continental igneous rocks are derived from a reservoir with chondritic REE pattern which may represent primary material remaining since the formation of the earth. Oceanic igneous rocks are derived from a different ancient reservoir which has Sm/Nd higher than chondritic. Initial ^(143)Nd/^(144)Nd and ^(87)Sr/^(86)Sr in young basalts from both oceans and continents show a strong correlation suggesting that Sm-Nd and Rb-Sr fractionation events in the mantle may be correlative and caused by the same process. From this correlation Rb/Sr for the earth is inferred to be 0.029.

Structure of Turbulent Shear Flows: A New Look

Abstract: The problem of turbulent now continues to be an outstanding one in technology and in physics. Of the nine Dryden research lectures so far, four have been on some aspect of the turbulence problem. At meetings such as this one the turbulence problem is always the subject of some sessions and lurks in the background of many others; for example, separated now, combustion, jet noise, chemical lasers, atmospheric problems, etc. It is continually the subject of conferences, workshops and reviews. In his time Hugh Dryden wrote several reviews of turbulent now. In reading some of them again, one statement particularly relevant to the present lecture caught my attention: "-it is necessary to separate the random processes from the nonrandom processes. It is not yet fully clear what the random elements are in turbulent now." Neither is it fully clear what the nonrandom, orderly elements are, but some of them are beginning to be recognized and described. Generally the picture one has had of turbulence is of chaos and disorder, implicit in the name. Although it was known that organized motion could exist, superimposed on the background of "turbulence," for example, vortex shedding from a circular cylinder up to Reynolds numbers of 10^7, such examples were regarded as special cases closely tied to their particular geometric origins and not characteristic of "well-developed" turbulence. It was known that large structures are important in the development of turbulent shear flows and that these ought to possess some definable features. But even when the concept of a characteristic "big eddy" was explored, it was usually in the context of a statistical quantity. The earliest and most decisive attempts to define the form of such large eddies were made by Townsend and his students. In recent years it has become increasingly evident that turbulent shear flows do contain structures or eddies whose description is more deterministic than had been thought, possessing identifiable characteristics, existing for significant lifetimes, and producing recognizable and important events. More accurate descriptions of their properties, how they fit into the complete description of a turbulent flow, to what extent are they central to its development, and how they can be reconciled with the apparent chaos and disorder, are problems which are becoming of interest to an increasing number of researchers. It is the purpose of this lecture to describe some of these new developments. The discussion will draw largely on experiences from our own laboratory; it is not intended to be a complete survey. Other discussions of these ideas can be found in various recent publications.

Waves in active and passive periodic structures: A review

Abstract: The theory and recent applications of waves in periodic structures are reviewed. Both the Floquet and coupled waves approach are analyzed in some detail. The theoretical part of the paper includes wave propagation in unbounded and bounded active or passive periodic media, wave scatterring from periodic boundaries, source radiation (dipole, Cerenkov, transition, and Smith-Purcell) in-periodic media, and pulse transmission through a periodic slab. The applications part covers the recent development in a variety of fields: distributed feedback oscillators, filters, mode convertors, couplers, second-harmonic generators, deflectors, modulators and transducers in the fields of integrated optics and integrated surface acoustics. We also review the work on insect compound eyes, mehanical structures ocean waves, pulse compressions, temperature waves, and cholestric liquid crystals. Particles interaction with crystals is briefly reviewed, especially in the case of zeolite crystals and supelattices. Recent advances in fabrication techniques for very fine gratings me also covered. Finally, speculations about future problems and development in the field of waves in periodic structures are given.

Depletion of brain catecholamines: failure of ocular dominance shift after monocular occlusion in kittens

Abstract: Monocularly deprived kittens were compared with littermates that had had their eyelids sutured for the same time but that had, in addition, been treated with 6-hydroxydopamine to deplete their forebrains of catecholamines. The visual cortices of all the catecholamine-depleted kittens showed high proportions of binocular neurons, in contrast to the control group, most of whose visual cortical neurons were driven exclusively by the nondeprived eye. Catecholamines may play an important role in the maintenance of cortical plasticity during the critical period.

Particle emission rates from a black hole. II. Massless particles from a rotating hole

Abstract: The calculations of the first paper of this series (for nonrotating black holes) are extended to the emission rates of massless or nearly massless particles from a rotating hole and the consequent evolution of the hole. The power emitted increases as a function of the angular momentum of the hole, for a given mass, by factors of up to 13.35 for neutrinos, 107.5 for photons, and 26 380 for gravitons. Angular momentum is emitted several times faster than energy, so a rapidly rotating black hole spins down to a nearly nonrotating state before most of its mass has been given up. The third law of black-hole mechanics is proved for small perturbations of an uncharged hole, showing that it is impossible to spin up a hole to the extreme Kerr configuration. If a hole is rotating fast enough, its area and entropy initially increase with time (at an infinite rate for the extreme Kerr configuration) as heat flows into the hole from particle pairs created in the ergosphere. As the rotation decreases, the thermal emission becomes dominant, drawing heat out of the hole and decreasing its area. The lifetime of a black hole of a given mass varies with the initial rotation by a factor of only 2.0 to 2.7 (depending upon which particle species are emitted). If a nonrotating primordial black hole with initial mass 5 \ifmmode\times\else\texttimes\fi{} ${10}^{14}$ g would have just decayed away within the present age of the universe, a hole created maximally rotating would have just died if its initial mass were about 7 \ifmmode\times\else\texttimes\fi{} ${10}^{14}$ g. Primordial black holes created with larger masses would still exist today, but they would have a maximum rotation rate determined uniquely by the present mass. If they are small enough today to be emitting many hadrons, they are predicted to be very nearly nonrotating.

Observations of interaction regions and corotating shocks between one and five AU: Pioneers 10 and 11

Abstract: Interaction regions between adjacent solar-wind streams have been identified between 1 and 5 AU by Pioneer 10 and 11 magnetic-field and plasma measurements. Beyond 1 AU, a relatively large fraction of the interaction regions have been found to be accompanied by either forward shocks, reverse shocks, or shock pairs. The observations are consistent with previous theoretical proposals that the interaction between adjacent streams leads to the development of corotating interplanetary shocks.

The mixing layer at high Reynolds number - Large-structure dynamics and entrainment

Abstract: A turbulent mixing layer in a water channel was observed at Reynolds numbers up to 3 × 10^6. Flow visualization with dyes revealed (once more) large coherent structures and showed their role in the entrainment process; observation of the reaction of a base and an acid indicator injected on the two sides of the layer, respectively, gave some indication of where molecular mixing occurs. Autocorrelations of streamwise velocity fluctuations, using a laser-Doppler velocimeter (LDV) revealed a fundamental periodicity associated with the large structures. The surprisingly long correlation times suggest time scales much longer than had been supposed; it is argued that the mixing-layer dynamics at any point are coupled to the large structure further downstream, and some possible consequences regarding the effects of initial conditions and of the influence of apparatus geometry are discussed.

Genetic dissection of the photoreceptor system in the compound eye of Drosophila melanogaster

Abstract: 1. Three mutations which eliminate specific types of photoreceptors in Drosophila were characterized. 2. Of the eight photoreceptors in each facet, two mutations delete the outer six (R 1-6). The third eliminates R 7, one of the two central photoreceptors. Double mutants can be constructed in which only photoreceptor R 8 is present. 3. The spectral sensitivities, photopigments, and behavioural properties of these mutants were investigated. 4. R 1-6 have two sensitivity peaks, near 350 and 470 nm. These receptors contain a rhodopsin with these absorption peaks. It interconverts with a metarhodopsin that absorbs around 570 nm. 5. R 7 is a U.V.-receptor, containing rhodopsin that absorbs around 370 nm and interconverts with a metarhodopsin which absorbs around 470 nm. 6. R 8 is a non-adapting blue-receptor with a third type of rhodopsin. 7. The properties of these photopigments explain the different sensitivities and spectral adaptation phenomena of the various photoreceptors. 8. All the photoreceptors have input into phototaxis. Spectral analysis of this behaviour provides evidence for integration of the input from the different photoreceptors.

Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations

Abstract: Approximate constitutive equations are derived for a dilute suspension of rigid spheroidal particles with Brownian rotations, and the behaviour of the approximations is explored in various flows. Following the suggestion made in the general formulation in part 1, the approximations take the form of Hand's (1962) fluid model, in which the anisotropic microstructure is described by a single second-order tensor. Limiting forms of the exact constitutive equations are derived for weak flows and for a class of strong flows. In both limits the microstructure is shown to be entirely described by a second-order tensor. The proposed approximations are simple interpolations between the limiting forms of the exact equations. Predictions from the exact and approximate constitutive equations are compared for a variety of flows, including some which are not in the class of strong flows analysed.

Involutions in Chevalley groups over fields of even order

Abstract: Let G = G(q) be a Chevalley group defined over a field Fq of characteristic 2. In this paper we determine the conjugacy classes of involutions in Aut(G) and the centralizers of these involutions. This study was begun in the context of a different problem.

Brownian motion in thin sheets of viscous fluid

Abstract: The drag on a cylindrical particle moving in a thin sheet of viscous fluid is calculated. It is supposed that the sheet is embedded in fluid of much lower viscosity. A finite steady drag is obtained, which depends logarithmically on the ratio of the viscosities. The Einstein relation is used to determine the diffusion coefficient for Brownian motion of the particle, with application to the movement of molecules in biological membranes. In addition, the Brownian motion is calculated using the Langevin equation, and a logarithmically time-dependent diffusivity is obtained for the case when the embedding fluid has zero viscosity.

Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. II. Accurate cross sections for H+H2

Abstract: Accurate three‐dimensional reactive and nonreactive quantum mechanical cross sections for the H+H_2 exchange reaction on the Porter–Karplus potential energy surface are presented. Tests of convergence in the calculations indicate an accuracy of better than 5% for most of the results in the energy range considered (0.3 to 0.7 eV total energy). The reactive differential cross sections are exclusively backward peaked, with peak widths increasing monotonically from about 32° at 0.4 eV to 51° at 0.7 eV. Nonreactive inelastic differential cross sections show backwards to sidewards peaking, while elastic ones are strongly forward peaked with a nearly monotonic decrease with increasing scattering angle. Some oscillations due to interferences between the direct and exchange amplitudes are obtained in the para‐to‐para and ortho‐to‐ortho antisymmetrized cross sections above the effective threshold for reaction. Nonreactive collisions do not show a tendency to satisfy a "j_z‐conserving" selection rule. The reactive cross sections show significant rotational angular momentum polarization with the m_j=m′_j=0 transition dominating for low reagent rotational quantum number j. In constrast, the degeneracy averaged rotational distributions can be fitted to statistical temperaturelike expressions to a high degree of accuracy. The integral cross sections have an effective threshold total energy of about 0.55 eV, and differences between this quantity and the corresponding 1D and 2D results can largely be interpreted as resulting from bending motions in the transition state. In comparing these results with those of previous approximate dynamical calculations, we find best overall agreement between our reactive integral and differential cross sections and the quasiclassical ones of Karplus, Porter, and Sharma [J. Chem. Phys. 43, 3259 (1965)], at energies above the quasiclassical effective thresholds. This results in the near equality of the quantum and quasiclassical thermal rate constants at 600 K. At lower temperatures, however, the effects of tunneling become very important with the quantum rate constant achieving a value larger than the quasiclassical one by a factor of 3.2 at 300 K and 18 at 200 K.

Neurons selective for orientation and binocular disparity in the visual Wulst of the barn owl (Tyto alba)

Abstract: The visual response properties of single neurons in the owl's visual Wulst suggest that this forebrain structure is an analog of the mammalian visual cortex. Features in common with the cat and the monkey visual cortex include a precise topographic organization, a high degree of binocular interaction, and selectivity for orientation, direction of movement, and binocular disparity of straight-line contours.

Experimental investigation of oscillations in flows over shallow cavities

Abstract: Wind tunnel experiments were carried out with three axisymmetric models to study laminar axisymmetric flows over shallow cavities at low subsonic speeds. The first model had a hemispherical nose, the second an ogive-shape nose, and the third an elliptic nose. Constant-temperature hot-wire anemometry was used in measuring both mean and fluctuating quantities. Flow around the cavity was visualized by heating the first model. To study the effect of mass injection on cavity oscillations, air was injected circumferentially all along the base of the cavity. Major results are that the cavity depth has little effect on oscillations in shallow cavities except when the depth is of the order of the thickness of the cavity shear flow, that downstream corner is the key factor in inducing self-sustained oscillations in the cavity shear layer, and that the presence of a back face results in an integral relation between wave length of the propagating disturbances and the cavity width in each mode of cavity operation.