Scaling of the Thue-Morse diffraction measure

We revisit the well-known and much studied Riesz product representation of the Thue-Morse diffraction measure, which is also the maximal spectral measure for the corresponding dynamical spectrum in the complement of the pure point part. The known scaling relations are summarised, and some new findings are explained

The measurement of very low conductivity and dielectric loss in XLPE cables: A possible method to detect degradation due to thermal aging

The dielectric response of crosslinked polyethylene (XLPE) insulated, miniature power cables, extruded with inner and outer semicons, was measured over the frequency range 10-4 to 104 Hz at temperatures from 20 to 100 °C. A dielectric spectrometer was used for the frequency range 10-4 to 10-2 Hz. A bespoke noise-free power supply was constructed and used to measure the dc conductivity and, using a Fourier transform technique, it was also used to measure the very low dielectric tanδ losses encountered at frequencies of 1 to 100 Hz. Tanδ measurements of <;10-5 were found in this frequency range and attributed to a β-mode dielectric relaxation lying above 100 Hz due to motion of chain segments in the amorphous region and an β-mode relaxation lying below 1 Hz window due to twists of chains in the crystal lamellae. The dc conductivity measurements were consistent with those of the dielectric spectrometer and indicate lower dc conductivities in vacuum degassed cables than have been previously reported for XLPE (less than 10-17 S.m-1). The conduction process is thermally activated with an activation energy of approximately 1.1 eV. Higher conductivities were found for non-degassed cables. A transformer ratio bridge was used for measurements in the range 1 to 10 kHz; loss in this region was shown to be due to the series resistance of the semicon layers. Thermal ageing of the cables at 135 °C for 60 days caused significant increases in the conductivity and tanδ and it is considered that such measurements may be a sensitive way of measuring electrical degradation due to thermal aging

Timelike self-similar spherically symmetric perfect-fluid models

Einstein's field equations for timelike self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively using the theory of dynamical systems.Comment: 23 pages, 6 eps-figure

Influence of semicon shields on the dielectric loss of XLPE cables

Dielectric response measurement techniques in both time and frequency domains are studied in order to measure the dielectric loss of XLPE cables, which have very low losses. A high sensitivity transformer ratio bridge system, which can measure loss tangents as low as 10-5, has been developed with the ability to measure these cables. A tuned amplifier was designed to help to extend the frequency range from 200Hz to 20kHz. Different model cables from Borealis AB with different semiconducting materials have been measured in the temperature range 15⁰C to 120⁰C. It is found that the semiconducting layers dominate the dielectric loss in the insulation system of the XLPE cables, when the outer semicon is treated as measuring electrode. In this case, steadily increasing dielectric loss has been measured at higher frequencies. The resistivity of the semiconducting materials was measured, which confirmed that the increasing slope is due to the semiconducting layers. After using conductive tapes to wrap the cable samples, monotonically decreasing losses were measured, corresponding to the actual dielectric frequency response of the XLPE cables. It is concluded that the axial resistance of semiconducting shields have a substantial influence on the dielectric loss of XLPE cables, especially for dielectric response in high frequency range. A device on measuring the loss of such cables is presented

Mass-metallicity relation from z=5 to the present: Evidence for a transition in the mode of galaxy growth at z=2.6 due to the end of sustained primordial gas infall

We analyze the redshift evolution of the mass-metallicity relation in a sample of 110 Damped Ly$\alpha$ absorbers spanning the redshift range $z=0.11-5.06$ and find that the zero-point of the correlation changes significantly with redshift. The evolution is such that the zero-point is constant at the early phases of galaxy growth (i.e. no evolution) but then features a sharp break at $z=2.6\pm 0.2$ with a rapid incline towards lower redshifts such that damped absorbers of identical masses are more metal rich at later times than earlier. The slope of this mass metallicity correlation evolution is $0.35 \pm 0.07$ dex per unit redshift. We compare this result to similar studies of the redshift evolution of emission selected galaxy samples and find a remarkable agreement with the slope of the evolution of galaxies of stellar mass log$(M_{*}/M_\odot) \approx 8.5$. This allows us to form an observational tie between damped absorbers and galaxies seen in emission. We use results from simulations to infer the virial mass of the dark matter halo of a typical DLA galaxy and find a ratio $(M_{vir}/M_{*}) \approx 30$. We compare our results to those of several other studies that have reported strong transition-like events at redshifts around $z=2.5-2.6$ and argue that all those observations can be understood as the consequence of a transition from a situation where galaxies were fed more unprocessed infalling gas than they could easily consume to one where they suddenly become infall starved and turn to mainly processing, or re-processing, of previously acquired gas.Comment: 8 pages, 5 figures, accepted for publication in MNRA

Spinorial cohomology and maximally supersymmetric theories

Fields in supersymmetric gauge theories may be seen as elements in a spinorial cohomology. We elaborate on this subject, specialising to maximally supersymmetric theories, where the superspace Bianchi identities, after suitable conventional constraints are imposed, put the theories on shell. In these cases, the spinorial cohomologies describe in a unified manner gauge transformations, fields and possible deformations of the models, e.g. string-related corrections in an alpha' expansion. Explicit cohomologies are calculated for super-Yang-Mills theory in D=10, for the N=(2,0) tensor multiplet in D=6 and for supergravity in D=11, in the latter case from the point of view of both the super-vielbein and the super-3-form potential. The techniques may shed light on some questions concerning the alpha'-corrected effective theories, and result in better understanding of the role of the 3-form in D=11 supergravity.Comment: 23 pp, plain tex. v2: Minor changes, references adde