Showing papers by "University of Cambridge published in 1975"

Particle Creation by Black Holes

Abstract: In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.

Freeze-etching nomenclature.

Abstract: C3H/He mice chronically infected with murine cYtomegalo virus were given skin allografis fromti histoincompatible BALB/c donors. A significant inicrease in cvtomegalovirus titers occurred within 3 days after placement oJ'the graft in the spleens and kidneYs oJ' the allograft recipients as compared with control aninmals. No significant changes in virus titers were detected in the salivary gland, lung, liver, or blood ofallograJi recipients. These results indicate that the host-versus-graft reaction alone can enihance murine cvtomtiegalovirus in a chronicallY injected host atid maY help explaini the high incidence ofcvvtomegalovirus infection seen after renal and other allograft transplantation

Turbulent wind flow over a low hill

Abstract: An analytical solution is presented for the flow of an adiabatic turbulent boundary layer on a uniformly rough surface over a two-dimensional hump with small curvature, e.g. a low hill. The theory is valid in the limit L/y0 → ∞ when h/L 2k2/ln(δ/y0) where L and h are the characteristic length and height of the hump, y0 the roughness length of the surface and δ the thickness of the boundary layer. For rural terrain, taking δ ∼ 600m these conditions imply that 102 < L < 104m and h/L < 0·05. Considerations of the turbulent energy balance suggest that the eddy viscosity distribution for equilibrium flow near a wall may still be used to a good approximation to determine the changes in Reynolds stress. This result is only required in a thin layer adjacent to the surface - in the main part of the boundary layer the perturbation stresses are shown to be negligible and the disturbance to be almost irrotational. The theory shows that for a log-profile upwind the increase in wind speed near the surface of the hill is O((h/L)u0(L)) where u0(L) is the velocity of the incident wind at a height L. Thus the increase in surface winds can be considerably greater than is predicted by potential flow theory based on an upwind velocity u0(h). It is also found that, at the point above the top of a low hill at which the increase in velocity is a maximum, the velocity is approximately equal to the velocity at the same elevation above level ground upwind of the hill. The surface stress is highly sensitive to changes in the surface elevation, being doubled by a slope as small as one in five. The turning of the wind in the Ekman layer may induce a change in direction of the wind above the hill. The main object of this analysis is to show how the changes in wind speed and shear stress are related to the size and shape of the hill and to the roughness of the surface. Some comparisons are made with measurements of the natural wind and wind tunnel flows. These suggest that the theory may be useful in giving rough estimates of the effect of hills on the wind. The theory and the quoted measurements suggest that the present design recommendation for the increase in wind speeds over hills to be used in wind loading calculations may be an underestimate. It is to be hoped that this analysis will encourage more detailed measurements to be made of the wind over hills.

Superdense Matter: Neutrons Or Asymptotically Free Quarks?

Abstract: We note the following: The quark model implies that superdense matter (found in neutron-star cores, exploding black holes, and the early big-bang universe) consists of quarks rather than of hadrons. Bjorken scaling implies that the quarks interact weakly. An asymptotically free gauge theory allows realistic calculations taking full account of strong interactions.

Metal-insulator transition in vanadium dioxide

Abstract: The basic physical parameters which govern the metal-insulator transition in vanadium dioxide are determined through a review of the properties of this material. The major importance of the Hubbard intra-atomic correlation energy in determining the insulating phase, which was already evidenced by studies of the magnetic properties of ${\mathrm{V}}_{1\ensuremath{-}x}{\mathrm{Cr}}_{x}{\mathrm{O}}_{2}$ alloys, is further demonstrated from an analysis of their electrical properties. An analysis of the magnetic susceptibility of niobium-doped V${\mathrm{O}}_{2}$ yields a picture for the current carrier in the low-temperature phase in which it is accompanied by a spin cloud (owing to Hund's-rule coupling), and has therefore an enhanced mass ($m\ensuremath{\simeq}60{m}_{0}$). Semiconducting vanadium dioxide turns out to be a borderline case for a classical band-transport description; in the alloys at high doping levels, Anderson localization with hopping transport can take place. Whereas it is shown that the insulating phase cannot be described correctly without taking into account the Hubbard correlation energy, we find that the properties of the metallic phase are mainly determined by the band structure. Metallic V${\mathrm{O}}_{2}$ is, in our view, similar to transition metals like Pt or Pd: electrons in a comparatively wide band screening out the interaction between the electrons in a narrow overlapping band. The magnetic susceptibility is described as exchange enhanced. The large density of states at the Fermi level yields a substantial contribution of the entropy of the metallic electrons to the latent heat. The crystalline distortion removes the band degeneracy so that the correlation energy becomes comparable with the band width and a metal-insulator transition takes place.

Uniqueness of the Kerr black hole

Abstract: The family of Kerr solutions, with $|a|lm$, is shown to be the unique pseudostationary family of black-hole solutions of the Einstein vacuum field equations when the event horizon is assumed to be nondegenerate.

Theory of the extended x-ray absorption fine structure

Abstract: The extended x-ray absorption fine structure is a consequence of the modification of the photoelectron final state due to scattering by the surrounding atoms. We present a theory of the absorption fine structure starting from theoretically obtained electron-atom scattering phase shifts. The electron scattering is treated using a spherical wave expansion which takes into account the finite size of the atoms. Multiple-scattering effects are included by classifying multiple-scattering paths by their total path lengths. Their effects are quite large but appear to make quantitative but not qualitative changes on the single-scattering contribution. The exceptional case is the fourth shell in fcc or bcc structure, where it is shadowed by the first-shell atom and is profoundly affected by forward scattering due to the first shell. This may account for the anomaly observed experimentally at the fourth-shell radius in metals. A detailed numerical calculation is carried out for copper and is shown to agree quite well with experiment.

Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute

Abstract: This paper describes a reformulation of the Lighthill (1952) theory of aerodynamic sound. A revised approach to the subject is necessary in order to unify the various ad hoc procedures which have been developed for dealing with aerodynamic noise problems since the original appearance of Lighthill's work. First, Powell's (1961 a) concept of vortex sound is difficult to justify convincingly on the basis of Lighthill's acoustic analogy, although it is consistent with model problems which have been treated by the method of matched asymptotic expansions. Second, Candel (1972), Marble (1973) and Morfey (1973) have demonstrated the importance of entropy inhomogeneities, which generate sound when accelerated in a mean flow pressure gradient. This is arguably a more significant source of acoustic radiation in hot subsonic jets than pure jet noise. Third, the analysis of Ffowcs Williams & Howe (1975) of model problems involving the convection of an entropy ‘slug’ in an engine nozzle indicates that the whole question of excess jet noise may be intimately related to the convection of flow inhomogeneities through mean flow pressure gradients. Such problems are difficult to formulate precisely in terms of Lighthill's theory because of the presence of an extensive, non-acoustic, non-uniform mean flow. The convected-entropy source mechanism is actually absent from the alternative Phillips (1960) formulation of the aerodynamic sound problem.In this paper the form of the acoustic propagation operator is established for a non-uniform mean flow in the absence of vortical or entropy-gradient source terms. The natural thermodynamic variable for dealing with such problems is the stagnation enthalpy. This provides a basis for a new acoustic analogy, and it is deduced that the corresponding acoustic source terms are associated solely with regions of the flow where the vorticity vector and entropy-gradient vector are non-vanishing. The theory is illustrated by detailed applications to problems which, in the appropriate limit, justify Powell's theory of vortex sound, and to the important question of noise generation during the unsteady convection of flow inhomogeneities in ducts and past rigid bodies in free space. At low Mach numbers wave propagation is described by a convected wave equation, for which powerful analytical techniques, discussed in the appendix, are available and are exploited.Fluctuating heat sources are examined: a model problem is considered and provides a positive comparison with an alternative analysis undertaken elsewhere. The difficult question of the scattering of a plane sound wave by a cylindrical vortex filament is also discussed, the effect of dissipation at the vortex core being taken into account.Finally an approximate aerodynamic theory of the operation of musical instruments characterized by the flute is described. This involves an investigation of the properties of a vortex shedding mechanism which is coupled in a nonlinear manner to the acoustic oscillations within the instrument. The theory furnishes results which are consistent with the playing technique of the flautist and with simple acoustic measurements undertaken by the author.

Particle creation by black holes.

Abstract: In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.

Bifurcation phenomena in the plane tension test

Abstract: A basic tensile bifurcation problem is studied. Bifurcations from a state of homogeneous inplane tension are investigated for an incompressible rectangular block constrained to undergo plane deformations. The sides of the block are traction-free, and it is elongated by a uniform, shearfree, relative displacement of its ends. For a wide class of incrementally-linear, time-independent materials only two instantaneous moduli enter into the analysis. Symmetric and anti-symmetric bifurcations are examined in each of the characteristic regimes of the governing equations (elliptic, parabolic and hyperbolic). Both diffuse modes and localized shearing modes are considered. Lowest bifurcation stresses are computed for essentially the entire range of possible combinations of material properties and geometry. A number of limiting cases are studied in detail, including those for slender and stubby specimens and for specimens which are rigid in shear. Applications to elastic and elastic/plastic solids are discussed.

Course notes

Abstract: Algebraic manipulation covers branches of software, particularly list processing, mathematics, notably logic and number theory, and applications largely in physics. The lectures will deal with all of these to a varying extent. The mathematical content will be kept to a minimum.

Vacuum polarization and the spontaneous loss of charge by black holes

Abstract: The spontaneous loss of charge by black holes due to particle emission is discussed. For large black holes (more massive than 1017g) the process is shown to be governed by a Schwinger type formula. For smaller black holes the method of calculating the process is described and asymptotic forms for scattering and superradiant coefficients given.

Visual evoked responses in the diagnosis and management of patients suspected of multiple sclerosis.

Abstract: Averaged visual evoked responses to pattern reversal stimuli have been recorded in 54 control subjects, 51 patients with multiple sclerosis, and 55 patients with other neurological diseases which might involve the visual apparatus. The latency to the peak of the major positive potential in normal subjects under the age of 60 was 104 msec or less (mean 90-5 msec+3 SD). The latency of the VER was prolonged above this value in one or both eyes in 67 per cent of the patients with multiple sclerosis (in 84 per cent of those with definite multiple sclerosis, in 83 per cent of those with probable multiple sclerosis, and in 21 per cent of those with possible multiple sclerosis). The latency of the VER was also prolonged in 25 percent of those with an acute spinal cord lesion of unknown cause; in 46 per cent of those with an isolated brain-stem lesion unknown cause; and in 49 per cent of patients presenting with a progressive spastic paraparesis. The extra delay in latency varied from a few msec to as much as a 100 msec. In patients with multiple sclerosis, a delayed VER was found in the affected eye in all with a previous history of optic neuritis, and in 47 per cent of those with no such history....

Preparation of Native Chromatin and Damage Caused by Shearing

Abstract: Chromatin prepared by a method involving limited nuclease digestion contains the same repeating structure as chromatin in the nucleus, whereas chromatin prepared by conventional methods involving shear does not.

Two genes in the major histocompatibility complex control immune response

Abstract: Antibody production in mice is controlled by two functionally distinct gene types in the I region of the major histocompatibility complex. One controls T cell recognition of antigen and T cell mediators of cell cooperation, and the other controls the B cell response to T cell mediators.

Mixing across an interface due to turbulence generated by an oscillating grid

Abstract: Many experimenters have used oscillating grids to produce turbulence for various laboratory purposes, especially in studies of mixing, but there have been few direct measurements of the properties of the turbulence itself. In the present paper we report experiments which attempt to relate the turbulent velocity and length scales to the external parameters, the frequency and amplitude, for three forms of grid oscillated in a tank of water. Turbulent velocities have been measured in the absence of a mean flow by using a hot film moved through the fluid to provide its own mean velocity. The output is stored and analysed in a small computer, which rapidly evaluates velocity and length scale statistics from an ensemble of records. The spatial variation of these quantities with distance from the stirrer is of special interest. It agrees with results suggested by an inertial-decay theory, and with previous measurements made by Bouvard & Dumas (1967) using a different form of stirrer. A particular purpose of the work has been to ‘calibrate’ the entrainment experiments of Turner (1968), by providing absolute scales of velocity and length in the fluid near a mixing interface, for the same grid as was used in the earlier experiments. Evidence is presented which suggests that other forms of grid may not be calibrated simply by extrapolating these results.

The Size and Growth of Firms

Abstract: This paper is a sequel to the analysis of the growth process of firms presented in Chapters 4 and 5 of our book Growth, Profitability and Valuation [17]. The relationship between size and growth of firms is explored using a more comprehensive set of data than was used in the book. In particular, the book was based on data relating to individual quoted companies in the UK in only three large industries, whereas, in this paper, we extend the analysis to cover all major industrial groups in manufacturing, construction and distribution. The relationship between size and growth of firms, and particularly stochastic models based on the Law of Proportionate Effect or Gibrat's Law, have previously been studied by a number of economists other than ourselves (see among other [5, 6, 7, 8, 12, 15 and 18]). Relatively few of these studies have used individual industry data. Industry is, however, an important variable, because the characteristics of the average firm vary significantly and systematically between industries (see [16]). Furthermore, none of the previous studies is based on as comprehensive a set of data as is the analysis presented below. The availability of data on such an extensive scale, showing the growth experience over the period 1948-60 of nearly 2000 individual firms, divided into 21 industrial groups, yields some interesting insights which have not been possible in earlier studies. It also leads to the revision of some important conclusions of our own previous study and of other similar studies.

Chronic Antiepileptic Toxicity: A Review

Abstract: Introduction .............................................................. Definition ................................................................. Predisposing Factors .......................................................... Classification .............................................................. TheNervousSystem ........................................................ Thecerebellum ......................................................... PeripheralNeuropathy .................................................... Subacute or Chronic Encephalopathy ........................................ Other Mental Symptoms .................................................... ....... ........................................... Folic Acid Deficiency ..................................................... MegaloblasticAnemia ..................................................... Folic Acid and Vitamin B1 Metabolism in Nonanemic Epileptic Patients ................................................ ClinicalImplicatio ns ...................................................... Neonatal Coagulation Defects .............................................. TheSkeletalSystem ........................................................ Metabolic Bone Disease and Vitamin D Deficiency ConnectiveTissue ........................................................... GumHypertrophy ....................................................... Facial Skin Changes .............. : .......................................

Scattering of surface waves by a conical island

Abstract: A model equation is derived which approximately describes the propagation of periodic surface waves in water of slowly varying depth. Numerical solutions to the model equation are obtained for the scattering of an incident plane wave by a conical island.

The estimation of pairwise relationships.

Abstract: Relationships between the individuals of a population have been previously studied from the point of view of prediction. Edwards (1967) suggested that the problem of detailed population structure could also be studied from the point of view of inference. Even where inferences of practical applicability cannot be made, such an approach can increase understanding of the relation between genealogical and genetic structure. In this paper we consider a specific problem which provides an introduction to the ideas and methods of genealogical inference. This is the problem of estimating the pairwise relationship between two individuals on the basis of their phenotypes at several loci. There is no theoretical problem in the extension from pairwise to joint relationship.

Carbon Catabolite Repression in Aspergillus nidulans

Abstract: Mutations leading to relief of carbon catabolite repression of the syntheses of a number of enzymes in Aspergillus nidulans can be selected in several different ways. They map at the cre A locus in linkage group I and are recessive. Their phenotype is not due to defective carbon source uptake.

The Anderson transition

Abstract: An outline is given of the electrical properties expected in a disordered solid or fluid which shows a metal-insulator transition of Anderson type. This is one in which the Fermi energy of the electrons passes through a mobility edge separating extended states from states localized by disorder, as the composition or some other parameter is changed. Some of the experimental evidence for this kind of transition is described. In particular, a relatively detailed account is given of the two dimensional inversion layer system in which the relevant parameters may be varied in a single device by direct electrical means.