Showing papers by "Durham University published in 1971"

Spectra of some self-exciting and mutually exciting point processes

Abstract: SUMMARY In recent years methods of data analysis for point processes have received some attention, for example, by Cox & Lewis (1966) and Lewis (1964). In particular Bartlett (1963a,b) has introduced methods of analysis based on the point spectrum. Theoretical models are relatively sparse. In this paper the theoretical properties of a class of processes with particular reference to the point spectrum or corresponding covariance density functions are discussed. A particular result is a self-exciting process with the same second-order properties as a certain doubly stochastic process. These are not distinguishable by methods of data analysis based on these properties.

Point Spectra of Some Mutually Exciting Point Processes

Abstract: IN contagious processes (e.g. measles, hijacking, etc.) the occurrence of events increases the probability of further events occurring in the near future. Also several series of events may interact with each other, for example one might consider notifications of some disease in a number of adjacent regions which would interact through infectives or carriers moving between the regions. In this paper we postulate a model for such processes and derive a general expression for the point spectral matrices. These theoretical spectra are useful for comparison with spectra estimated from data and thus provide a means of evaluating the fit of such a model in the manner of Bartlett (1963). The model studied was put forward in an earlier paper (Hawkes, 1971) but the solution was obtained only in special cases. In this paper an elegant solution is obtained for the. general case. Consider a stationary k-variate point process N(t), where Ni(t) represents the cumulative number of events in the ith process up to time t, with intensity vector X = of{dN(t)}/dt and covariance density matrix

Temperature Field and Geophysical Effects of a Downgoing Slab

Abstract: The factors affecting the thermal behavior of a lithospheric slab descending into the mantle are so numerous and complicated that only numerical methods can accurately account for them. A series of finite-difference calculations of the temperature field, including the effects of viscous dissipation, adiabatic compression, phase changes and radioactive heat generation are carried out, and the relative effects of different parameters are investigated. An analysis of the stability and convergence of the numerical method indicates that the errors are small and can be reduced to any desired level by varying the grid size and the time steps. At a crustal spreading rate of 8 cm/yr, with all heat sources, the slab reaches thermal equilibrium with the surrounding mantle at a depth of about 650 km. Among observable geophysical quantities, seismic travel times and amplitudes provide the most information about the slab. Surface heat flow is sensitive to subsurface conditions that are at relatively shallow depths, and gravity anomalies are broad and are masked by crustal effects. Three dimensional calculations predict strong bending of seismic rays near slabs, which causes strong focusing and produces shadow zones. Analysis of travel-time data for the Tonga-Fiji region indicates that waves propagating down the slab from shallow events are advanced by about 4 sec. Observations and theoretical travel-time anomalies based on calculated temperature fields are in general agreement.

Intermetallic rare-earth compounds.

Abstract: The physical properties of many of the rare-earth intermetallic compounds have been collected together. They are discussed in terms of the role that the magnetic exchange and crystal field interactions play in determining these properties. It is pointed out that in this vast number of materials there is an ideal chance of establishing which of several second-order terms are effective in determining structural stability.

Field-aligned particle currents near an auroral arc

Abstract: A Nike-Tomahawk rocket equipped to measure electric and magnetic fields and charged particles from a few eV to several hundred keV energy was flown into an auroral band on April 11, 1970 The purpose of this flight was to obtain evidence of the low-energy electrons and protons that constitute a field-aligned sheet current, and also to obtain the magnetic signature of such a current and the electric field in and near the auroral-arc electric current system Particular attention was given to a sudden increase in the field-aligned current associated with a prior sudden increase in the electric field and a sudden change in the magnetic field, all occurring near the edge of a visual auroral arc Data obtained are discussed and analyzed; they present an important contribution to the problem of mapping of atmospheric auroral phenomena to the magnetospheric equatorial plane

Thermal degradation of nylon 66

Abstract: The rate of gel formation and color formation in poly(hexamethylene adipamide), nylon 66, is found to be dependent upon the rate of removal of the volatile products of degradation. If a sample of nylon is heated above its melting point in a sealed tube, the material will remain soluble for extended periods of time as the intrinsic viscosity first passes through a maximum, then a minimum, followed by the abrupt formation of insoluble material. The color remains reasonably white. On the other hand, if the volatile material is permitted to escape, rapid gelation and color formation will occur, even in the complete absence of oxygen. Intermediate rates of gelation and color formation can be obtained by control of the rate of volatile material distillation. The decrease in molecular weight evidenced in the sealed tubes is probably due to hydrolysis and ammonolysis of the amide groups which occur simultaneously with the formation of multifunctional crosslinking agents. The volatile material contains an intense absorption in the 290 mμ region. Analysis of the volatile material shows that it contains inter alia, water, carbon dioxide, ammonia, cyclic monomer, hexylamine, hexamethyl-eneimine, hexamethylenediamine, cyclopentanone, 2-cyclopentylcyclopentanone, 2-cyclopentylidinecyclopentanone, and 1,2,3,5,6,7-hexahydrodicyclopenta[b,e]pyridine, which has an intense absorption at 287 mμ, e = 8.87 × 104l./mole-cm, (methanol).

Changes in the Structure of Wet-Spun Acrylic Fibers During Processing

Abstract: The structural changes that occur during processing of a wet-spun 93% polyacrylonitrile -7% polyvinyl acetate co polymer are discussed. Stress-strain, x-ray diffraction, shrinkage, and electron microscopy data are explained in terms of a model in which the molecules are in an irregular helical conformation in the relaxed state and can extend during de formation. The molecules are arranged in fibrils which, in turn, form a three-dimensional network. The fibrillar ele ments remain intact through the coagulation, hot-stretching, and drying, although network junctures break and reform. The model proposed is an extension of that used by Rosenbaum to describe the behavior of acrylic fibers after processing and is in agreement with previous work on the structural characterization of polyacrylonitrile.

The deep structure of the Iceland-Faeroe Ridge

Abstract: Two long seismic refraction lines along the crest of the Iceland-Faeroe Ridge reveal a layered crust resembling the crust beneath Iceland but differing from normal continental or oceanic crust The Moho was recognised at the south-eastern end of the lines at an apparent depth of 16–18 km A refraction line in deeper water west of the ridge and south of Iceland indicates a thin oceanic type crust underlain by a 71 km/s layer which may be anomalous upper mantle

Some studies relating to nonuniqueness in gravity and magnetic inverse problems

Abstract: Polygonal models which are of uniform density or magnetization contrast and which contain no cavities are sufficient to ensure the uniqueness of solutions in gravity and magnetic problems. Nonuniqueness is then attributed to a number of other factors which are discussed in detail. We study the problem of nonuniqueness using mainly a parameter hyperspace in which ambiguity takes the form of a scatter of local minima or a continuous domain bounded by a contour whose value is determined by the amplitude of observational errors. The possible solutions to the problem being examined are contained in a region which would have contained the unique solution under exact conditions and which decreases in extent as the factors causing ambiguity decrease. Thus, under favorable conditions, a large degree of uniqueness may occur. By starting the search from a good initial point based on all available information, we may obtain a satisfactory solution without specifying any of the parameters defining the model. Different solutions produced by different initial points vary in their emphases but are, generally, of the correct order of magnitude. When such favorable conditions are lacking, the extent of ambiguity may be reduced by specifying one or more parameters. With the aid of the parameter hyperspace, we may thus conceive why and how ambiguity is present and determine what means can be found to limit it.

Crustal Structure in the Vicinity of South-west England

Abstract: Summary This paper describes the interpretation of results from a sea-to-land crustal seismic experiment based on south-west England and extending to Ireland and Brittany. Only P, and P,, were observed as first arrivals and these have been subjected to time-term analysis yielding estimates of 5.82 and 8-05 km s-' respectively. A remarkably uniform and consistent structure was observed along line 1 of the project, which overlies the granite batholith of south-west England and its seaward extension to the WSW. Along line 1, the crustal structure was determined using first arrival data supplemented by the well displayed wide angle reflection P,,, P, yielding the following estimates: P, = 5-85 kms-'; P,, = 8.07 km s-'; mean crustal velocity = 6*2Okms-'; crustal thickness = 27 km; dip of Moho insignificant. No discontinuities were detected within the crust, but there is a gradual increase in velocity with depth between the base of the batholith (10 km depth) and the Moho. The upper crustal channel wave F, was observed along this line. Line 2 extends from South Ireland to Land's End, and the time-terms are about 10 per cent larger than along line 1. P, time-terms along the northern part of line 2 reflect the presence of a sedimentary basin known from gravity anomalies, but corrected P,, time-terms suggest that the Moho is not detectably upwarped or downwarped beneath this basin. Line 3 extends from Land's End to Brittany, and displays a similar crustal thickness to that of line 1, except that the Moho shallows slightly beneath the sedimentary trough which crosses this line.

Intraendothelial inclusions in kidneys of patients with systemic lupus erythematosus.

Abstract: Recent renal biopsy material was reviewed to determine the relationship between intraendothelial virus-like structures and a diagnosis of lupus erythematosus, to establish the specificity ...

Ecological studies on macroinvertebrate populations associated with polluted kelp forests in the North Sea

Abstract: 1 The English Counties of Midlothian and Durham are situated on the North Western Edge of the North Sea Both counties have a high population density and a variety of industries located in them 2 The coastal seas adjacent to these areas are heavily polluted 3 In one of these industrial areas, County Durham, the coastal waters have been polluted for 150 years — from the beginning of the Industrial Revolution 4 Two gradients of pollution, one estuarine and one off the open coast, are described The intervening sea coast has little or no pollution 5 A comparative method of pollution surveying is presented which makes use of the epifauna in the holdfast or hapteron of the large brown algaLaminaria hyperborea (Gunn)Fosl 6 The size of the habitat is measured in cubic millilitres and called ecospace 7 The rate of invertebrate colonisation is measured in ecoperiods 8 Statistical investigation reveals similar habitats in clean and polluted water 9 The ‘normal’ sequence of habitat colonisation by invertebrates is described for clean waters It contains species groups commonly found on rocky sublittoral kelp forests elsewhere in the North Atlantic 10 Ecological comparison is made of the community development described for clean and polluted stations 11 Results indicate that in polluted water, invertebrate ‘succession’ is retarded; the species composition of the community is simplified, 43 % of the species are lost, rates of habitat colonisation by individuals of pollution tolerant species are speeded up; the polluted community undergoes neotenous development ie retaining juvenile characteristics throughout development to community maturity 12 Functional aspects of ‘new’ (pollution present) and ‘old’ (pollution absent) communities are discussed 13 The marginal presence of some species in polluted water is also discussed 15 Two ecological barriers to normal community development in the polluted environment are postulated

Mean Curvature of Riemannian Immersions

Abstract: 1. Let M and M' denote complete riemannian manifolds of dimension n and m respectively, and suppose that M is compact and oriented. For simplicity we assume that both manifolds and their metrics are smooth (i.e. of class C). In terms of local co-ordinates (x, x, ...,x") on M and local co-ordinates (y,y, •••,/") on M', the riemannian metrics are written ds = gtJ dx l dx, ds' = g'aP dy* dy * where Roman suffixes take values 1,2, ..., n and Greek suffixes take values 1,2,..., m. Let/: M ->• M' be a smooth map. Following Eells and Sampson [1], we associate with / a real number called its energy. We define an inner product on the space of 2-covariant tensors at P £ M in terms of local co-ordinates by

Maximum and actual field feeding-rates in larvae of the damselfly Pyrrhosoma nymphula (Sulzer) (Odonata: Zygoptera)

Abstract: Summary The paper presents information on factors influencing maximum feeding-rates (measured in the laboratory) in larvae of the damselfly Pyrrhosoma nymphula, and compares estimates of feeding rates in the field with maximum feeding-rates for larvae of the same size at the same temperature. Maximum feeding-rates in Pyrrhosoma larvae of different sizes were measured at 4, 5, 10 and 15°C. At low temperatures (4–5°C) maximum feeding-rate was depressed more than predicted either from the effects of temperature on the gut-clearance time of larvae or their respiratory rate. Maximum feeding-rate declined steadily throughout metamorphosis in the final instar and stopped completely prior to emergence of the adult. Feeding-rates in the field were calculated from ‘balanced’ energy equations, i.e. from the sum of larval growth, respiration and the production of faeces and exuviae. Feeding rates in the field were always much less than maximum feeding-rates for the same size of larva at the same temperature, and at the most were never more than 70% of the latter; they were closer to the maximum in summer than in winter, when they fell as low as 20% of the maximum. The relevance of these findings to studies on the efficiency with which carnivores utilize energy in the field, and the importance of Odonata larvae as predators in aquatic ecosystems is discussed.

The Kolar Gold Fields neutrino experiment I. The interactions of cosmic ray neutrinos

Abstract: Final results are presented of an experiment to study the interactions of cosmic ray neutrinos deep underground, at a depth of 7.6 x 10 5 g cm -2 (standard rock). Clear examples have been recorded of neutrino-induced muons, including cases of upward moving particles and neutrino interactions within the detector assembly itself. The observed rate of events is compared with expectation and conclusions are made about the variation of the inelastic cross-section with energy and the lower limit to the mass of the intermediate boson. An examination has also been made of the celestial coordinates of the detected neutrinos and details are presented.