Quantum manifestations of scattering orbits in the scaled spectrum of a non-hydrogenic atom in crossed fields

Evidence for scattering closed orbits for the Rydberg electron of the singly excited helium atom in crossed electric and magnetic fields at constant scaled energy and constant scaled electric field strength has been found through a quantum calculation of the photo-excitation spectrum. A particular 3D scattering orbit in a mixed regular and chaotic region has been investigated and the hydrogenic 3D closed orbits composing it identified. To the best of our knowledge, this letter reports the first quantum calculation of the scaled spectrum of a non- hydrogenic atom in crossed fields.

Quantum manifestations of closed orbits in the photoexcitation scaled spectrum of the hydrogen atom in crossed fields

The scaled photoexcitation spectrum of the hydrogen atom in crossed electric and magnetic fields has been obtained by means of accurate quantum mechanical calculation using a new algorithm. Closed orbits in the corresponding classical system have also been obtained, using a new, efficient and practical searching procedure. Two new classes of closed orbit have been identified. Fourier transforming each photoexcitation quantum spectrum to yield a plot against scaled action has allowed direct comparison between peaks in such plots and the scaled action values of closed orbits, Excellent agreement has been found with all peaks assigned.

The closed orbits and the photo-excitation scaled spectrum of the hydrogen atom in crossed fields

In a recent Letter to the Editor (J Rao, D Delande and K T Taylor 2001 J. Phys. B: At. Mol. Opt. Phys. 34 L391-9) we made a brief first report of our quantal and classical calculations for the hydrogen atom in crossed electric and magnetic fields at constant scaled energy and constant scaled electric field strength. A principal point of that communication was our statement that each and every peak in the Fourier transform of the scaled quantum photo-excitation spectrum for scaled energy value epsilon = -0.586 538 871028 43 and scaled electric value (f) over tilde = 0.068 537 846 207 618 71 could be identified with a scaled action value of a found and mapped-out closed orbit up to a scaled action of 20. In this follow-up paper, besides presenting full details of our quantum and classical methods, we set out the scaled action values of all 317 closed orbits involved, together with the geometries of many.

Orbits of operators commuting with the Volterra operator

Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on L-P[0,1], with 1 0, but also to operators of the form phi (V), where phi is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann-Liouville operator as well as the Volterra operator can be related to the Levin-Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy-Carleman theorem, are needed to analyze the behavior of the orbits of I - cV, where c > 0. The results are applied to the study of cyclic properties of phi (V), where phi is a holomorphic function at 0.

Inline Interdigital Pseudo-Elliptic Helical Resonator Filters

A new inline coupling topology for narrowband helical resonator filters is proposed that allows to introduce selectively located transmission zeros (TZs) in the stopband. We show that a pair of helical resonators arranged in an interdigital configuration can realize a large range of in-band coupling coefficient values and also selectively position a TZ in the stopband. The proposed technique dispenses the need for auxiliary elements, so that the size, complexity, power handling and insertion loss of the filter are not compromised. A second order prototype filter with dimensions of the order of 0.05 lambda, power handling capability up to 90 W, measured insertion loss of 0.18 dB and improved selectivity is presented.

Hardware elliptic curve cryptographic processor over GF(p)

A novel hardware architecture for elliptic curve cryptography (ECC) over GF(p) is introduced. This can perform the main prime field arithmetic functions needed in these cryptosystems including modular inversion and multiplication. This is based on a new unified modular inversion algorithm that offers considerable improvement over previous ECC techniques that use Fermat's Little Theorem for this operation. The processor described uses a full-word multiplier which requires much fewer clock cycles than previous methods, while still maintaining a competitive critical path delay. The benefits of the approach have been demonstrated by utilizing these techniques to create a field-programmable gate array (FPGA) design. This can perform a 256-bit prime field scalar point multiplication in 3.86 ms, the fastest FPGA time reported to date. The ECC architecture described can also perform four different types of modular inversion, making it suitable for use in many different ECC applications. © 2006 IEEE.

Orbits of semigroups of truncated convolution operators

We prove that a semigroup generated by finitely many truncated convolution operators on $L_p[0, 1]$ with 1 ≤ p < ∞ is non-supercyclic. On the other hand, there is a truncated convolution operator, which possesses irregular vectors.

Positronium-atom collisions

New results are presented for Ps(1s) scattering by H(1s), He(1(1)S) and Li(2s). Calculations have been performed in a coupled state framework, usually employing pseudostates, and allowing for excitation of both the Ps and the atom. In the Ps(1s)-H(1s) calculations the H- formation channel has also been included using a highly accurate H- wave function. Resonances resulting from unstable states in which the positron orbits H- have been calculated and analysed. The new Ps(1s)-He(1(1)S) calculations still fail to resolve existing discrepancies between theory and experiment at very low energies. The possible importance of the Ps(-) formation channel in all three collision systems is discussed. (C) 2004 Elsevier B.V. All rights reserved.

CCD photometry of distant comets. III - Ensemble properties of Jupiter-family comets

We describe the results of a ground-based observational "snapshot" study of Jupiter-family comets in the heliocentric range 2.29 AU less than or equal to R-h less than or equal to 5.72 AU. Results are presented based on observations from the 1m JKT on the island of La Palma. A total of 25 comets were targeted with 15 being positively detected. Broad-band VRI photometry was performed to determine dimensions, colour indices, and dust production rates in terms of the "A frho" formalism. The results for selected comets are compared with previous investigations. Ensemble properties of the Jupiter- family population have been investigated by combining the results presented here with those of Lowry et al. (1999), and Lowry & Fitzsimmons (2001). We find that the cumulative size distribution of the Jupiter-family comets can be described by a power law of the form; Sigma(> r) proportional to r(-1.6+/- 0.1). This size distribution is considerably shallower than that found for the observed Edgeworth-Kuiper belt objects, which may reflect either an intrinsic difference at small km- sizes in the belt, or the various processes affecting the nuclei of comets as their orbits evolve from the Edgeworth- Kuiper belt to the inner Solar system. Also, there would appear to be no correlation between nuclear absolute magnitude and perihelion distance. Finally, for the sample of active comets, there is a distinct correlation between absolute R band magnitude and perihelion distance, which can be explained by either a discovery bias towards brighter comets or in terms of "rubble" mantle formation.

Optical colors of 56 near-Earth objects: trends with size and orbit

We present the results of BVRIZ photometry of 56 near-Earth objects (NEOs) obtained with the 1-m Jacobus Kapteyn telescope on La Palma during 2000 and 2001. Our sample includes many NEOs with particularly deep 1 - mum pyroxene/olivine absorption bands, similar to Q-type asteroids. We also classify three NEOs with particularly blue colors. No D-type asteroids were found, placing an upper limit of similar to2% on the fraction of the NEO population originating in the outer main belt or the Trojan clouds. The ratio of dark to bright objects in our sample was found to be 0.40, significantly higher than current theoretical predictions. As well as classifying the NEOs, we have investigated color trends with size and orbit. We see a general trend for larger silicate objects to have shallower absorption bands but find no significant difference in the distribution of taxonomic classes at small and large sizes. Our data clearly show that different taxonomic classes tend to occupy different regions of (a, e) space. By comparing our data with current model predictions for NEO dynamical evolution we see that Q- R-, and V-type NEOs tend to have orbits associated with "fast track" delivery from the main belt, whereas S-type NEOs tend to have orbits associated with "slow track" delivery. This outcome would be expected if space weathering occurs on time scales of >10(6) years. (C) 2003 Elsevier Science (USA). All rights reserved.

WASP-1b and WASP-2b: Two new transiting exoplanets detected with SuperWASP and SOPHIE

We have detected low-amplitude radial-velocity variations in two stars, USNO-B1.0 1219-0005465 (GSC 02265-00107 = WASP-1) and USNO-B1.0 0964-0543604 (GSC 00522-01199 = WASP-2). Both stars were identified as being likely host stars of transiting exoplanets in the 2004 SuperWASP wide-field transit survey. Using the newly commissioned radial-velocity spectrograph SOPHIE at the Observatoire de Haute-Provence, we found that both objects exhibit reflex orbital radial-velocity variations with amplitudes characteristic of planetary-mass companions and in-phase with the photometric orbits. Line-bisector studies rule out faint blended binaries as the cause of either the radial-velocity variations or the transits. We perform preliminary spectral analyses of the host stars, which together with their radial-velocity variations and fits to the transit light curves yield estimates of the planetary masses and radii. WASP-1b and WASP-2b have orbital periods of 2.52 and 2.15 d, respectively. Given mass estimates for their F7V and K1V primaries, we derive planet masses 0.80-0.98 and 0.81-0.95 times that of Jupiter, respectively. WASP-1b appears to have an inflated radius of at least 1.33 RJup, whereas WASP-2b has a radius in the range 0.65-1.26 RJup.

An adaptable and scalable asymmetric cryptographic processor

In this paper a novel scalable public-key processor architecture is presented that supports modular exponentiation and Elliptic Curve Cryptography over both prime GF(p) and binary GF(2) extension fields. This is achieved by a high performance instruction set that provides a comprehensive range of integer and polynomial basis field arithmetic. The instruction set and associated hardware are generic in nature and do not specifically support any cryptographic algorithms or protocols. Firmware within the device is used to efficiently implement complex and data intensive arithmetic. A firmware library has been developed in order to demonstrate support for numerous exponentiation and ECC approaches, such as different coordinate systems and integer recoding methods. The processor has been developed as a high-performance asymmetric cryptography platform in the form of a scalable Verilog RTL core. Various features of the processor may be scaled, such as the pipeline width and local memory subsystem, in order to suit area, speed and power requirements. The processor is evaluated and compares favourably with previous work in terms of performance while offering an unparalleled degree of flexibility. © 2006 IEEE.

WASP-14b: 7.3 M-J transiting planet in an eccentric orbit

We report the discovery of a 7.3 M-J exoplanet WASP-14b, one of the most massive transiting exoplanets observed to date. The planet orbits the 10th-magnitude F5V star USNO-B1 11118-0262485 with a period of 2.243 752 d and orbital eccentricity e = 0.09. A simultaneous fit of the transit light curve and radial velocity measurements yields a planetary mass of 7.3 +/- 0.5 M-J and a radius of 1.28 +/- 0.08 R-J. This leads to a mean density of about 4.6 g cm(-3) making it the densest transiting exoplanets yet found at an orbital period less than 3 d. We estimate this system to be at a distance of 160 +/- 20 pc. Spectral analysis of the host star reveals a temperature of 6475 +/- 100 K, log g = 4.07 cm s(-2) and v sin i = 4.9 +/- 1.0 km s(-1), and also a high lithium abundance, log N(Li) = 2.84 +/- 0.05. The stellar density, effective temperature and rotation rate suggest an age for the system of about 0.5-1.0 Gyr.