Alternatives to Kronig-Kramers Transformation and Testing, and Estimation of Distributions

Two alternatives to Kronig-Kramers analysis of small-signal ac immittance data are discussed and illustrated using both synthetic and experimental data. The first, a derivative method of approximating imaginary-part response from real-part data, is found to be too approximate in regions where the imaginary-part varies appreciably with frequency. The second, a distribution of relaxation-times fitting method, is shown to be valuable for testing whether a data set satisfies the Kronig-Kramers relations and so is associated with a system whose properties are time-invariant. It also is valuable for estimating real- or imaginary-part response from the other part, usually with small error. Unlike Kronig-Kramers analysis, the second method usually requires no extrapolation outside the range of the measured data. Finally, this discrete-function method also allows one to estimate the distribution of relaxation times or activation energies associated with a given set of frequency-response data. This application is described and illustrated for both synthetic and experimental data and is shown to yield good but somewhat approximate results for the estimation of continuous distributions. It is particularly valuable for identifying response regions arising from a continuous distribution and distinguishing them from those associated with discrete time-constant response

NLO Leptoquark Production and Decay: The Narrow-Width Approximation and Beyond

We study the leptoquark model of Buchm\"uller, R\"uckl and Wyler, focusing on a particular type of scalar ($R_2$) and vector ($U_1$) leptoquark. The primary aim is to perform the calculations for leptoquark production and decay at next-to-leading order (NLO) to establish the importance of the NLO contributions and, in particular, to determine how effective the narrow-width-approximation (NWA) is at NLO. For both the scalar and vector leptoquarks it is found that the NLO contributions are large, with the larger corrections occurring for the case vector leptoquarks. For the scalar leptoquark it is found that the NWA provides a good approximation for determining the resonant peak, however the NWA is not as effective for the vector leptoquark. For both the scalar and vector leptoquarks there are large contributions away from the resonant peak, which are missing from the NWA results, and these make a significant difference to the total cross-section.Comment: 22 pages, 17 figure

Comment on the Coupling of Zero Sound to the J=1−J=1^- Modes of 3^3He-B

Features in the zero sound attenuation near the pair-breaking edge in superfluid $^3$He-B have been observed in large magnetic fields. Schopohl and Tewordt [{\sl J. Low Temp. Phys.} {\bf 57}, 601 (1984)] claim that the $J=1^-, M=\pm 1$ order-parameter collective modes couple to zero sound as a result of the distortion of the equilibrium order parameter by a magnetic field; they identify the new features with these modes. However, we show that, when the effect of gap distortion on the collective modes is properly taken into account, the collective mode equations of Schopohl and Tewordt yield no direct coupling of zero sound to the $J=1^-$ modes. Thus, the identification of the absorption features reported by Ling, Saunders and Dobbs [{\sl Phys. Rev. Lett.} {\bf 59}, 461 (1987)] near the pair-breaking edge with the $J=1^-$ modes is not clearly established.Comment: 6 pages (Tex with jnl.tex

Preliminary power train design for a state-of-the-art electric vehicle

The state-of-the-art (SOTA) of electric vehicles built since 1965 was reviewed to establish a base for the preliminary design of a power train for a SOTA electric vehicle. The performance of existing electric vehicles were evaluated to establish preliminary specifications for a power train design using state-of-the-art technology and commercially available components. Power train components were evaluated and selected using a computer simulation of the SAE J227a Schedule D driving cycle. Predicted range was determined for a number of motor and controller combinations in conjunction with the mechanical elements of power trains and a battery pack of sixteen lead-acid batteries - 471.7 kg at 0.093 MJ/Kg (1040 lbs. at 11.7 Whr/lb). On the basis of maximum range and overall system efficiency using the Schedule D cycle, an induction motor and 3 phase inverter/controller was selected as the optimum combination when used with a two-speed transaxle and steel belted radial tires. The predicted Schedule D range is 90.4 km (56.2 mi). Four near term improvements to the SOTA were identified, evaluated, and predicted to increase range approximately 7%

Iron line profiles including emission from within the innermost stable orbit of a black hole accretion disc

Reynolds & Begelman (1997) have recently proposed a model in which the broad and extremely redshifted iron line seen during a deep minimum of the light curve of the Seyfert 1 galaxy MCG-6-30-15 originates from matter spiralling into a Schwarzschild black hole, contrary to previous claims that the black hole may be spinning rapidly (Iwasawa et al 1996; Dabrowski et al 1997). Here we calculate in detail the X-ray spectrum produced by their model using the full reflected continuum emission, including absorption features. This calculation takes into account the doppler and relativistic effects. For the range of parameters we consider, we find that the spectrum should show a large photoelectric absorption edge of iron, which is not seen in the data. The absorption edge is a consequence of the line emitting matter within the innermost stable orbit being highly ionized, and is largely independent of the parameters chosen for their model. If we restrict our attention to the 3-10 keV band we may effectively remove this absorption edge by fitting a steeper power law, but this results in a significant underprediction of the 0.4-0.5 keV flux. We conclude that the data on MCG-6-30-15 are more consistent with the Kerr than the Schwarzschild model.Comment: 5 pages with 5 postscript figures. Accepted for publication in MNRA

Objective detection by signal analysis of the auditory evoked cortical E.E.G. potential

Imperial Users onl

Graphical Methods in Device-Independent Quantum Cryptography

We introduce a framework for graphical security proofs in device-independent quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography more accessible, facilitate the discovery of new proofs, and enable automated proof verification. As an example of our framework, we reprove a previous result from device-independent quantum cryptography: any linear randomness expansion protocol can be converted into an unbounded randomness expansion protocol. We give a graphical proof of this result, and implement part of it in the Globular proof assistant.Comment: Publishable version. Diagrams have been polished, minor revisions to the text, and an appendix added with supplementary proof