Showing papers by "Imperial College London published in 1968"

A General Definition of Residuals

Abstract: RESIDUALS are now widely used to assess the adequacy of linear models; see Anscombe (1961) for a systematic discussion of significance tests based on residuals, and for references to earlier work. A second and closely related application of residuals is in time-series analysis, for example in examining the fit of an autoregressive model. In the context of normal-theory linear models, the n x 1 vector of random variables Y is assumed to have the form

The lipid composition of rat brain myelin and subcellular fractions during development.

Abstract: 1. The lipids of whole brain and subcellular fractions of the rat were analysed during development. 2. The deposition of cholesterol occurred in two phases, one related to increasing wet weight of the brain and the second to myelination. Cerebroside accumulation was related only to myelination. 3. The composition of myelin isolated from 12-day-old rat brain was different in some respects from that of the adult. In the former there was an increase of phospholipid in relation to cholesterol and a marked deficiency in cerebroside. 4. It is suggested that early myelin is extruded glial plasma membrane, which only later becomes mature myelin.

On the instability of Taylor vortices

Abstract: It is known experimentally that laminar circular Couette flow between two concentric circular cylinders, the outer of which is fixed, becomes unstable when the speed of the inner cylinder is high enough. The flow is then replaced by a new circumferential flow with superimposed toroidal (or Taylor) vortices spaced periodically along the axis. At a higher speed still the new flow develops another instability, and is replaced by a flow in which the axially periodic vortices are simultaneously periodic travelling waves in the azimuth.In the present paper an attack is made on the problem of instability of the Taylor-vortex flow against perturbations which are periodic both in the axial and azimuthal co-ordinates and, moreover, travel with some phase velocity in the latter. Subject to a number of assumptions and approximations, which are detailed in the paper, it is found that the Taylor-vortex flow is stable against perturbations with the same axial wavelength and phase, but unstable against perturbations differing in phase by ½π. After instability the new flow no longer has planes separating neighbouring vortices, but has wavy surfaces travelling in the azimuth. This feature is in accord with much (though not all) of the experimental evidence.The critical Taylor number (proportional to the square of the speed) at which the Taylor vortices become unstable is found theoretically to be about 8% above the value for which Taylor vortices first appear. This must be compared with a value in the range 5-20% for the experiments which our work models most closely. The azimuthal wave-number given a slight preference by theory is 1, in agreement with those experiments.

TEM wave properties of microstrip transmission lines

Abstract: Wave-propagation properties of microstrip transmission lines can be determined accurately if an exact electrostatic-field solution can be found for a pair of charged conductors separated by a dielectric sheet. The latter problem is framed as an integral equation for whose solution simple numerical methods are available. To determine the kernel function of this integral equation, the classical method of images is generalised to include, multiple partial images; the kernel function is then given by well convergent infinite series. Wave impedances calculated using this theory yield very good agreement with experiment. Detailed results are given for the propagation velocity in microstrip lines with very thin strip conductors, and the method used to solve thick-strip problems is described.

Magnetic Isotherms in the Band Model of Ferromagnetism

Abstract: Calculations are given for the dependence on temperature and magnetic field strength H of the magnetization M of ferromagnetic metals treated on the basis of the itinerant electron model. The spin wave contribution to the low temperature magnetization is considered in the limits of strong and very weak ferromagnetism. For the first limit, problems related to the well-known divergence of the zero field differential susceptibility are briefly discussed. The main part of the paper is concerned with the single particle contributions to the magnetization and associated differential susceptibility for very weak ferromagnetism. A simple equation for the magnetic isotherms is obtained in this limit and shown to be valid over a wide temperature range including 0 °K and the Curie temperature. This equation implies that plots of M 2 against H / M at various temperatures in this range give a series of parallel straight lines. Recently measured isotherms for the material ZrZn 2 are analysed on the basis of the theory, and several characteristic properties of this material are obtained from the analysis.

Piecewise Cubic Interpolation and Two-Point Boundary Problems

Abstract: Cubic splines are employed, experimentally, to approximate to the solution of a simple two-point boundary value problem for a linear ordinary differential equation. Checked by comparison with the analytical solution, the results are encouraging. Comparison is also made with the application of Hermite interpolation, which gives results of the same order of accuracy—but, generally, involves the solution of many more linear equations for the same number of nodes.

Pressure-forcing of tightly fitting pellets along fluid-filled elastic tubes

Abstract: Some insight into the behaviour of tightly fitting solid pellets, which may be deformable, and are being forced by a pressure difference to move slowly along a distensible tube filled with viscous fluid, is sought by theoretical study of a simple axisymmetric model (§2). In this, the pellet's clearance in the tube is taken to be a small fraction of the tube radius; the fraction may, at a pressure characteristic of that ahead of the pellet, be either positive or negative. Even if it is positive, the tube may still be distended (or the pellet compressed, or both) as the pellet passes, because the thickness of lubricating film generated may exceed the clearance. Naturally, still greater elastic deformation can occur in the case of negative clearance.Highly simplified elastic properties are assumed; with an eye on tubes occurring in physiological systems (with Poisson's ratio close to 0.5), the local distension of the tube is taken to vary linearly with the local excess pressure; as a still cruder approximation, a similar relation for local reduction of pellet radius is assumed. A parabolic approximation to the pellet's undistorted meridian section, in the region where the lubricating film is thin, is also assumed, leading to a simple relation between pressure and local film thickness which is used, together with Reynolds's lubrication equation, to evaluate both. An arbitrary constant, the rate of leakback of fluid past the pellet, is determined by the condition that the pressure difference forcing the pellet must just balance the skin-frictional resistance to its motion.The problem is non-dimensionalized (§3) and reduced to that of finding a particular solution of a differential equation containing a certain parameter L. In addition to numerical solutions for particular values of L (§6), perturbation solutions for both small and large L are obtained (§§4 and 5), to give mathematical and physical insight; the perturbation for large L (corresponding to negative clearance) is highly singular, requiring the matching of approximate solutions different in each of six different layers.A striking feature of the solutions is a necking of the gap between pellet and tube behind the pellet. This is so pronounced in the case of negative clearance (figure 2) that it might give the false impression that the pellet was being propelled by peristaltic contraction of the tube instead of by fluid pressure gradient. The physical reason for this is elucidated (§6).In the case of positive clearance, rather small pressure differences suffice, on this theory, to propel the pellet, because different parts of the lubricating layer act on it with frictional resistances of different signs, which almost cancel out. By contrast, for negative clearance, the resistance becomes a large multiple of that found in a purely fluid-filled tube of length and mean velocity equal to that of the pellet. This multiple increases, and the film thickness correspondingly decreases (figure 7), as the pellet velocity decreases.One physiological system on which the model may throw some light is the narrow capillary with red blood cells being squeezed through it in single file, lubricated by plasma (§1 and 8). At the higher flow speeds, around 0.1 mm/s, the lubricating film, predicted to be about 0·2μm thick, appears likely to play a significant role in mass transfer to and from the tissue spaces. At much lower speeds, predicted film thicknesses are so small that any of a number of mechanisms, including loss of fluid through the porous capillary wall due to the local excess pressure in the layer, might cause movement to ‘seize up’ altogether.

A laboratory study of the ice nucleating properties of some mineral particulates

Abstract: Laboratory studies using a microscope cold stage with controlled humidity environment have been carried out on the ice nucleation and preactivation properties of several naturally occurring particulate substances. For initial nucleation water saturation was necessary, but below a critical temperature a constant ice supersaturation (water subsaturation), was sufficient. The values of both temperature and supersaturation depended on the substance. In preactivation the behaviour was similar but with a higher initial and critical temperature. Typical values are : for kaolinite, initial nucleation − 10·5, − 19°C, 20 per cent; preactivation − 6, − 11·5°C, 12 per cent: montmorillonite, − 25, below − 27°C; preactivation − 4, − 13·5°C, 14 per cent. The first temperature gives one ice crystal in 104 particles; the second is critical for nucleation at water subsaturation. The low values of supersaturation required for nucleation suggest that preactivation is caused by the freezing of a supercooled, adsorbed, liquid-like layer, rather than by the retention of ice embryos in cavities. A necessary condition for the measurement of the ice nucleating ability of particles from an air sample is that they must not be heated to a temperature above at least − 5°C or subjected to a relative humidity over ice of less than about 35 per cent before the measurement is made.

Electrical Properties of Wet Collagen

Abstract: THE electrical properties of dried collagen and bone have been studied by Fukada and Yasuda1,2. Both were shown to be piezoelectric, producing a measurable potential between opposite faces when stressed and also deforming on application of a voltage. The piezoelectric coefficients d14 belonging to the polycrystalline point group ∞ were found for collagen, and the values reported for d14 were about the same as d11 in quartz. Because both tendon and bone are bathed in ionic fluid of high conductivity when in vivo, it was decided that the electrical activity of wet collagen should be examined.

Motion of a Fluid in a Curved Tube

Abstract: Dean's work on the steady motion of an incompressible fluid through a curved tube of circular cross-section is extended. A method using a Fourier-series development with respect to the polar angle in the plane of cross-section is formulated and the resulting coupled non-linear equations solved numerically. The results are presented in terms of a single variable D = 4R$\surd$(2a/L), where R is the Reynolds number, a the radius of cross-section of the tube, and L the radius of the curve. The results cover the range of D from 96 (the upper limit of Dean's work) to over 600. From these it is found that the secondary flow becomes very appreciable for D = 600, moving the position of maximum axial velocity to a distance less than 0.38 a from the outer boundary, and decreasing the flux by 28% of its value for the straight tube. These calculations fill a large part of the gap in existing knowledge of secondary flow patterns, which lies in the upper range of Reynolds number for which flow is laminar. This range is of particular interest in the investigation of the cardiovascular system.

Equivalence of Localized Spin Fluctuations and the Kondo-Nagaoka Spin-Compensated State

Abstract: The physical equivalence between the Kondo-Nagaoka spin-compensated state and localized spin fluctuations in a dilute "nonmagnetic" alloy is demonstrated. The Kondo temperature is shown to be equal to $\ensuremath{\tau}_{0}^{}{}_{}{}^{\ensuremath{-}1}$, the width of the spin fluctuations, and determines the boundary between magnetic and nonmagnetic behavior of dilute alloys.

Deformation Modes of the Intermediate Phase NiAl

Abstract: The deformation modes of single crystal NiAl deformed in compression in the range 77 to 1000 °K were found to be dependent on orientation and temperature. The preferred slip direction was confirmed as 〈001〉, but this may be constrained geometrically to allow kinking, or slip in 〈111〉 or 〈011〉 directions, depending on temperature. When 〈001〉 slip occurred, the slip plane was invariably {110} at 77 °K but was dependent on orientation at higher temperatures. The slip planes were also sensitive to temperature when slip occurred in other directions. The von Mises criterion for polycrystalline ductility can be satisfied by combinations of the observed slip systems.

Conditions for the occurrence of severe local storms

Abstract: The technique of relative-flow analysis on isentropic surfaces is used to examine the large- (“synoptic”-) scale situations associated with selected severe local storms near southern England and over the mid-western USA (including the Horsham, Wokingham, and Geary storms whose behaviour has been described in several previous publications) The storms occur ahead of major troughs, in the vicinity of confluence-lines (usually recognised as cold fronts over western Europe but as “dry-lines” over the USA), where an increase of wind with height favours the organisation and intensification of cumulonimbus convection Extreme instability arises where small-scale convection is confined to a lowermost 1 or 2 km (leading to an abnormally high wetbulb potential temperature) beneath a plume of very warm air lying downwind of an extensive arid plateau (Spain or Mexico) The instability is released where the (backed) low-level flow eventually reaches the edge of the restraining plume aloft It appears that the occurrence of severe local storms demands a peculiarly favourable combination of geographical features and atmospheric flow-pattern DOI: 101111/j2153-34901968tb00364x

Viruses in fungi and interferon stimulation.

Abstract: The active component of statolon—an anti-viral agent—is RNA of viral origin and not a polyanionic polysaccharide as previously thought. This article describes the isolation and some properties of the P. stoloniferum virus which is active in stimulating interferon production. An interferon inducing virus has also been found in a strain of Penicillium funiculosum.

Electron-Electron Scattering in Transition Metals

Abstract: Recent measurements of electronic transport properties showing the dominance of electron-electron scattering in transition metals at low temperatures are suggested to have an interpretation in terms of Baber's model.

Analytic and clustering properties of thermodynamic functions and distribution functions for classical lattice and continuum systems

Abstract: Our most complete results concern the Ising spin system with purely ferromagnetic interactions in a magnetic fieldH (or the corresponding lattice gas model with fugacityz=const. exp(−2mHβ) wherem is the magnetic moment of each spin). We show that, in the limit of an infinite lattice, (i) the free energy per site and the distribution functionsn s (x 1, ...,x s ; β,z) are analytic in the two variables β andH if the reciprocal temperature β>0 and the complex numberH is not a limit point of zeros of the grand partition function ξ, and (ii) the Ursell functionsu s (x 1, ...,x s ; β,z) tend to 0 as Δ s ≡Max i, j |x i −x j | → ∞ if β>0 and ReH≠0; in particular, if the interaction potential vanishes for separations exceeding some fixed cutoff value λ, then |u s |0 and the complex fugacityz is less than the radius of convergence of the Mayerz expansion; for the continuum gas, however,n s andu s must be replaced by their values integrated over small volumes surrounding each of the pointsx 2, ...,x s . It is shown that the pressurep is analytic in both β andz, if it is analytic inz at fixed β over a suitable range of values of β andz, and further that, except for continuum systems without hard cores,p,n s andu s have convergent Maclaurin expansions in β for small enoughz.

The fluorescence of indoles and aniline derivatives.

Abstract: 1. The variations in the excitation and fluorescence wavelengths and fluorescence intensities of a number of indole and aniline derivatives over a wide range of acidity and alkalinity (36n-sulphuric acid to 10n-potassium hydroxide) have been studied. 2. The changes in fluorescence with pH of the indoles and anilines had many characteristics in common, and the most fluorescent species were found to be the non-ionized or neutral forms showing fluorescence maxima at about λ 350mμ. 3. In 10n-potassium hydroxide most of the compounds examined, except those containing a tertiary nitrogen atom, showed a bathochromic shift in fluorescence wavelength attributable to an anion due to a negatively charged nitrogen, but in strong acid (3n-sulphuric acid) these compounds were non-fluorescent, except the anisidines and the 5-hydroxyindoles. 4. p-Anisidine but not the o- and m-isomers showed excited-state ionization in acid solution. 5. Of the hydroxyindoles only the 5-hydroxy derivatives showed a fluorescence (λmax. 520–540mμ) in acid solution. It is suggested that this fluorescence is due to a proton-transfer reaction in the excited state, and various arguments for this suggestion are given. 6. Stokes shifts for the various ionic and neutral species of the indoles and anilines have been calculated, and the large shifts found with indole and p-anisidine may be due to solvent–solute interaction.