Newman-Penrose approach to twisting degenerate metrics

The well known method ofNewman andPenrose is used to find solutions of the Einstein empty space field equations, which are algebraically special and where the degenerate principal null vectors are not hypersurface orthogonal. As is to be expected the method systematically yields the results obtained byKerr. An explanation is given of the complex coordinate transformation technique of generating new metrics from Schwarzschild's; also a generalisation of Kerr and Schild type metrics is investigated.This work was completed as part of a proposed Ph. D. Thesis, while the author was receiving a Research Studentship Grant from the University of Bradford.     

Some observations on cochlear mechanics.

A set of experiments was conducted using the M?ssbauer effect to determine the vibratory characteristics of the basilar membrane, Reissner's membrane, the malleus, incus, and oval window in squirrel monkey. A few measurements were also made in guinea pig in the basal cochlear region. The nonlinear vibration properties of the basilar membrane are described in detail for the midfrequency region in the squirrel monkey. Only in this region have nonlinear effects been observed. A comparison of mechanical and neural data indicates good qualitative agreement.     

Some observations on models of absorption spectra

The question of models of absorption spectra as applied to the problems which arise in investigations of the propagation of infrared radiation in the atmosphere is discussed. The general and asymptotic formulas for the absorption function of individual lines, models of equidistant lines of equal intensity and statistical models are considered successively. Certain new formulas are introduced without mathematical derivation. Inaccuracies and errors in the literature are corrected, and the square-toot law is considered critically. The general conclusions resulting from the investigations into spectral models are analyzed.     

Some observations on the development of anticipatory coarticulation

The influence of vocalic context on various temporal and spectral properties of preceding acoustic segments was investigated in utterances containing [schwa No. CV] sequences produced by two girls aged 4;8 and 9;5 years and by their father. The younger (but not the older) child's speech showed a systematic lowering of [s] noise and [th] release burst spectra before [u] as compared to [i] and [ae]. The older child's speech, on the other hand, showed an orderly relationship of the second-formant frequency in [] to the transconsonantal vowel. Both children tended to produce longer [s] noises and voice onset times as well as higher second-formant peaks at constriction noise offset before [i] than before [u] and [ae]. All effects except the first were shown by the adult who, in addition, produced first-formant frequencies in [] that anticipated the transconsonantal vowel. These observations suggest that different forms of anticipatory coarticulation may have different causes and may follow different developmental patterns. A strategy for future research is suggested.     

Some observations on uncertainty propagation through a simple nonlinear system

This paper discusses a number of issues relating to the analysis of uncertain systems or data in the context of (low-frequency) structural dynamics. In order to illustrate potential problems in applying ‘classical’ uncertainty analysis methods to nonlinear systems, a simple nonlinear system is simulated and the breakdown of two standard approaches is demonstrated on data from the system. By relaxing the requirements of the analysis, it is shown that an alternative uncertainty theory gives useful qualitative information about the system. This motivates a discussion of how uncertainty frameworks should be chosen to suit the problem in hand and leads to a clustering of uncertainty problems in structural dynamics into three types: quantification, fusion and propagation.     

PHOBOS at RHIC: Some global observations

Particle production in Au+Au collisions has been measured in the PHOBOS experiment at RHIC for a range of collision energies for a large span of pseudorapidities, |η| < 5.4. Three empirical observations have emerged from this data set which require theoretical examination. First, there is clear evidence of limiting fragmentation. Namely, particle production in central Au + Au collisions, when expressed as dN/dη′ ( η′ ≡ – y_beam), becomes energy independent at high energy for a broad region of η′ around η′ = 0. This energy-independent region grows with energy, allowing only a limited region (if any) of longitudinal boost-invariance. Second, there is a striking similarity between particle production in e⁺e⁻and Au + Au collisions (scaled by the number of participating nucleon pairs). Both the total number of produced particles and the longitudinal distribution of produced particles are approximately the same in e⁺e⁻and in scaled Au + Au. This observation This presentation is based in large part on the PHOBOS summary talk by M Baker at the16th Int. Conf. on Ultrarelativistic Nucleus- Nucleus Collisions, Quark Matter 2002, Nantes, France was not predicted and has not been explained. Finally, particle production has been found to scale approximately with the number of participating nucleon pairs for (N _part ) > 65. This scaling occurs both for the total multiplicity and for highp _T particles (3 <p _T < 4.5 GeV/c). This presentation is based in large part on the PHOBOS summary talk by M Baker at the16th Int. Conf. on Ultrarelativistic Nucleus-Nucleus Collisions, Quark Matter 2002, Nantes, France     

Canonical connections of Finsler metrics and Finslerian connections on Riemannian metrics

A concept of canonical connection of a Finsler metric is developed. Connections that are compatible with Finsler metrics are compared with the canonical connection itself. They are also compared with the corresponding Cartan connection. A necessary and sufficient condition on metric Finsler connections is given for the metric to be Riemannian. This study unearths different ways in which Finsler geometry could be used to generalize the theory of general relativity.     

Quasi-Einstein metrics on hypersurface families

We construct quasi-Einstein metrics on some hypersurface families. The hypersurfaces are circle bundles over the product of Fano, Kähler–Einstein manifolds. The quasi-Einstein metrics are related to various gradient Kähler–Ricci solitons constructed by Dancer and Wang and some Hermitian, non-Kähler, Einstein metrics constructed by Wang and Wang on the same manifolds.     

Some observations on Levy stability and intermittency in nucleus-nucleus interactions at SPS energies

The power law relation between higher order and second order scaled factorial moments is studied in one dimensional pseudo-rapidity phase (η) space in the interactions of ³²S beam with CNO, AgBr and Emulsion at incident energy of 200 AGeV. Observation for such a power law may indicate a self similar cascade mechanism in multiparticle production process. The values of slope, β_q are found to be independent of target size. The value of the scaling exponent υ = 1.412 obtained is higher than the critical value υ = 1.304, indicating that no second order phase transition exists in our data. The ratio of anomalous fractal dimensions, d_q/d₂ is found to increase with increase in the order of moments, q. The dependence of d_q/d₂ on q indicates a multifractal structure and the presence of self-similar cascading mechanism in our data. The d_q/d₂ values are well described by the Levy-stable distribution with Levy index μ = 1.562 which is consistent with and lies within the Levy stable region (0 ≤ μ ≤ 2). The multifractal spectrum is concave downward with a maximum at q = 0. The decrease in D_q with increasing q shows that there is a self affine multifractal behaviour in multiparticle production in our data.     

Dragged metrics

We show that the path of any accelerated body in an arbitrary spacetime geometry $g_{\mu \nu }$ can be described as a geodesic in a dragged metric $\hat{q}_{\mu \nu }$ that depends only on the background metric and on the motion of the body. Such procedure allows the interpretation of all kinds of non-gravitational force as modifications of the spacetime metric. This method of effective elimination of the forces by changing the metric of the substratum can be understood as a generalization of the d’Alembert principle applied to all relativistic processes.     

Some observations on the appearance of instability of a plane charged liquid surface

A dispersion relation is obtained for the capillary oscillations of a hemispherical protrusion (oblate or prolate) on the plane surface of a conducting liquid in a uniform electrostatic field parallel to the symmetry axis of the protrusion. For the fundamental mode of the capillary oscillations realized on the protrusion the critical dependence of the parameter characterizing its stability in an external electrostatic field is obtained as a function of the square of the eccentricity as the protrusion is drawn out from the an oblate to a prolate hemisphere. Such a change in shape lowers the threshold electric field for instability of the protrusion. Zh. Tekh. Fiz. 69, 15–22 (July 1999)     

Some leed and electron spectroscopic observations on disordered EuO(100) surfaces

Three vacuum-cleaved surfaces of EuO have been studied using LEED, Auger electron spectroscopy, electron loss spectrocopy and mass spectroscopy. The (100) surface is stable in the electron beam but is disordered after cleavage at room temperature. The Auger spectrum below 150 eV is assigned to initial state holes in the 4d shell of europium and to autoionisation processes. The consequences of the observation of disorder upon the interpretation of various magnetic and optical experiments are discussed.     

Gravity action on rapidly varying metrics

We consider a four-dimensional simplicial complex and the minisuperspace general relativity system on it. The metric is flat in most parts of the interior of every 4-simplex, with the exception of a thin layer of thickness \({\propto \varepsilon}\) along each three-dimensional face. In this layer the metric undergoes a jump between the two 4-simplices sharing this face. At \({\varepsilon \to 0}\) this jump would become a discontinuity. However, a discontinuity of the metric induced on the face is not allowed in general relativity: terms arise in the Einstein action tending to infinity as \({\varepsilon \to 0}\) . In the path integral approach, these terms lead to the pre-exponent factor with δ-functions requiring that the metric induced on the faces be continuous. That is, the 4-simplices fit on their common faces. The other part of the path integral measure corresponds to the action, which is the sum of independent terms over the 4-simplices. Therefore this part of the path integral measure is the product of independent measures over the 4-simplices. The result obtained is in accordance with our previous one obtained from symmetry considerations.     

X-ray and microscope observations on the texture and stability of polyethylene crystallized under pressure: Some new observations on the triclinic crystal form

It is known that linear polyethylene, which has been crystallized from the melt under hydrostatic pressures above 4000 atm, has properties that are distinctly different from the usual melt crystallized polyethylene [1]. The examination of replicas of fracture surfaces of such material under the electron and optical microscopes reveals a texture on an unusually large scale [2, 2a]. Bands several microns in width were observed that were concluded to be the edge-on views of large lamellae. A fine structure of continuous striations was also observed running perpendicular to the broad faces of the lamellae. It was shown that the molecules lie perpendicular to the band or lamellar surfaces and parallel to the striations. As the band width is comparable with the average chain length, it was concluded that the molecules are in an extended state or, at any rate, that they cannot fold back on themselves any appreciable number of times. Even greater extension of the crystalline order is implied by the lateral dimension of the bands, if the fine structure is ignored. There is strong support for the contention that this fine structure is not intrinsic but merely the expected result of fracturing an intrinsically fibrillating material [3]. In addition, it must be remembered that surface replication does not lend itself to unique interpretations of the texture of a material and is inherently incapable of defining the extension of a uniformly diffracting crystal area.