The role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

An exactly solvable four transition point model

Heavy particle collisions, in particular low-energy ion-atom collisions, are amenable to semiclassical JWKB phase integral analysis in the complex plane of the internuclear separation. Analytic continuation in this plane requires due attention to the Stokes phenomenon which parametrizes the physical mechanisms of curve crossing, non-crossing, the hybrid Nikitin model, rotational coupling and predissociation. Complex transition points represent adiabatic degeneracies. In the case of two or more such points, the Stokes constants may only be completely determined by resort to the so-called comparison- equation method involving, in particular, parabolic cylinder functions or Whittaker functions and their strong-coupling asymptotics. In particular, the Nikitin model is a two transition-point one-double-pole problem in each half-plane corresponding to either ingoing or outgoing waves. When the four transition points are closely clustered, new techniques are required to determine Stokes constants. However, such investigations remain incomplete, A model problem is therefore solved exactly for scattering along a one-dimensional z-axis. The energy eigenvalue is b(2)-a(2) and the potential comprises -z(2)/2 (parabolic) and -a(2) + b(2)/2z(2) (centrifugal/centripetal) components. The square of the wavenumber has in the complex z-plane, four zeros each a transition point at z = +/-a +/- ib and has a double pole at z = 0. In cases (a) and (b), a and b are real and unitarity obtains. In case (a) the reflection and transition coefficients are parametrized by exponentials when a(2) + b(2) > 1/2. In case (b) they are parametrized by trigonometrics when a(2) + b(2) <1/2 and total reflection is achievable. In case (c) a and b are complex and in general unitarity is not achieved due to loss of flux to a continuum (O'Rourke and Crothers, 1992 Proc. R. Sec. 438 1). Nevertheless, case (c) coefficients reduce to (a) or (b) under appropriate limiting conditions. Setting z = ht, with h a real constant, an attempt is made to model a two-state collision problem modelled by a pair of coupled first-order impact parameter equations and an appropriate (T) over tilde-tau relation, where (T) over tilde is the Stueckelberg variable and tau is the reduced or scaled time. The attempt fails because (T) over tilde is an odd function of tau, which is unphysical in a real collision problem. However, it is pointed out that by applying the Kummer exponential model to each half-plane (O'Rourke and Crothers 1994 J. Phys. B: At. Mel. Opt. Phys. 27 2497) the current model is in effect extended to a collision problem with four transition points and a double pole in each half-plane. Moreover, the attempt in itself is not a complete failure since it is shown that the result is a perfect diabatic inelastic collision for a traceless Hamiltonian matrix, or at least when both diagonal elements are odd and the off-diagonal elements equal and even.

Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping, occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.

Microscopic models for dielectric relaxation in disordered systems

It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric relaxation from a microscopic model based on a kinetic equation just as in the Debye model. This kinetic equation is obtained by means of a generalization of the noninertial Fokker-Planck equation of conventional Brownian motion (generally known as the Smoluchowski equation) to fractional kinetics governed by the HN relaxation mechanism. For the simple case of noninteracting dipoles it may be solved by Fourier transform techniques to yield the Green function and the complex dielectric susceptibility corresponding to the HN anomalous relaxation mechanism.

More nitrogen rich B-type stars in the SMC cluster, NGC 330

High resolution spectra of seven early B-type giant/supergiant stars in the SMC cluster NGC330 are analysed to obtain their chemical compositions relative to SMC field and Galactic B-type stars. It is found that all seven stars are nitrogen rich with an abundance approximately 1.3 dex higher than an SMC main- sequence field B-type star, AV304. They also display evidence for deficiencies in carbon, but other metals have abundances typical of the SMC. Given the number of B-type stars with low projected rotational velocities in NGC330 (all our targets have v sin i <50 km s(-1)), we suggest that it is unlikely that the stars in our sample are seen almost pole-on, but rather that they are intrinsically slow rotators. Furthermore, none of our objects displays any evidence of significant Balmer emission excluding the possibility that these are Be stars observed pole-on. Comparing these results with the predictions of stellar evolution models including the effects of rotationally induced mixing, we conclude that while the abundance patterns may indeed be reproduced by these models, serious discrepancies exist. Most importantly, models including the effects of initially large rotational velocities do not reproduce the observed range of effective temperatures of our sample, nor the currently observed rotational velocities. Binary models may be able to produce stars in the observed temperature range but again may be incapable of producing suitable analogues with low rotational velocities. We also discuss the clear need for stellar evolution calculations employing the correct chemical mix of carbon, nitrogen and oxygen for the SMC.

A chemical analysis of five hot stars towards the Galactic centre

High resolution echelle spectroscopy is presented for thirteen stars lying in the direction of the Galactic centre which, on the basis of photographic photometry and low dispersion spectroscopy, have been classified as early-B-type. Eight of these stars have large rotational velocities which preclude a detailed analysis. The five stars with moderate to low projected rotational velocities have been analysed using model atmosphere techniques to determine atmospheric parameters and chemical compositions. Two of these stars appear to be evolved blue horizontal branch objects on the basis of their chemical compositions and small projected rotational velocity. The evolutionary status of a third is ambiguous but it is probably a post-asymptotic-giant branch star. The remaining two objects are probably young massive stars and show enhanced abundances of N, C, Mg and Si, consistent with their formation in the inner part of the Galactic disk. However their O abundances are normal, confirming results found previously for other early- type stars, which would imply a flat abundance gradient for this element in the inner region of our Galaxy.

Understanding B-type supergiants in the low metallicity environment of the SMC

Spectroscopic analyses of 7 SMC B-type supergiants and 1 giant have been undertaken using high resolution optical data obtained on the VLT with UVES. FASTWIND, a non-LTE, spherical, line-blanketed model atmosphere code was used to derive atmospheric and wind parameters of these stars as well as their absolute abundances. Mass-loss rates, derived from H-alpha profiles, are in poor agreement with metallicity dependent theoretical predictions. Indeed the wind-momenta of the SMC stars appear to be in good agreement with the wind-momentum luminosity relationship (WLR) of Galactic B-type stars, a puzzling result given that line-driven wind theory predicts a metallicity dependence. However the galactic stars were analysed using unblanketed model atmospheres which may mask any dependence on metallicity. A mean nitrogen enhancement of a factor of 14 is observed in the supergiants whilst only an enrichment of a factor of 4 is present in the giant, AV216. Similar excesses in nitrogen are observed in O-type dwarfs and supergiants in the same mass range, suggesting that the additional nitrogen is produced while the stars are still on the main-sequence. These nitrogen enrichments can be reproduced by current stellar evolution models, which include rotationally induced mixing, only if large initial rotational velocities of 300 kin s(-1) are invoked. Such large rotational velocities appear to be inconsistent with observed v sin i distributions for O-type stars and B-type supergiants. Hence it is suggested that the currently available stellar evolution models require more efficient mixing for lower rotational velocities.

The VLT-FLAMES survey of massive stars: mass loss and rotation of early-type stars in the SMC

We have studied the optical spectra of a sample of 31 O- and early B-type stars in the Small Magellanic Cloud, 21 of which are associated with the young massive cluster NGC 346. Stellar parameters are determined using an automated fitting method (Mokiem et al. 2005, A&A, 441, 711), which combines the stellar atmosphere code FASTWIND (Puls et al. 2005, A&A, 435, 669) with the genetic algorithm based optimisation routine PIKAIA (Charbonneau 1995, ApJS, 101, 309). Comparison with predictions of stellar evolution that account for stellar rotation does not result in a unique age, though most stars are best represented by an age of 1-3 Myr. The automated method allows for a detailed determination of the projected rotational velocities. The present day v(r) sin i distribution of the 21 dwarf stars in our sample is consistent with an underlying rotational velocity (v(r)) distribution that can be characterised by a mean velocity of about 160-190 km s(-1) and an effective half width of 100-150 km s(-1). The vr distribution must include a small percentage of slowly rotating stars. If predictions of the time evolution of the equatorial velocity for massive stars within the environment of the SMC are correct (Maeder & Meynet 2001, A&A, 373, 555), the young age of the cluster implies that this underlying distribution is representative for the initial rotational velocity distribution. The location in the Hertzsprung-Russell diagram of the stars showing helium enrichment is in qualitative agreement with evolutionary tracks accounting for rotation, but not for those ignoring vr. The mass loss rates of the SMC objects having luminosities of log L-star/L-circle dot greater than or similar to 5.4 are in excellent agreement with predictions by Vink et al. (2001, A&A, 369, 574). However, for lower luminosity stars the winds are too weak to determine. M accurately from the optical spectrum. Three targets were classified as Vz stars, two of which are located close to the theoretical zero-age main sequence. Three lower luminosity targets that were not classified as Vz stars are also found to lie near the ZAMS. We argue that this is related to a temperature effect inhibiting cooler from displaying the spectral features required for the Vz luminosity class.

Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Detection of C8H- and Comparison with C8H toward IRC+10216

We report the detection of new transitions of octatetraynyl (C8H) toward the circumstellar envelope IRC +10 216 using data taken with the 100 m Green Bank Telescope (GBT). In addition, we report five features from the Ku, K, and Q bands that have been identified as transitions of the octatetraynyl anion (C8H-). From a rotational temperature diagram and an assumed source size of 30", we find a total C8H column density of 8(3)×10^12 cm-2 and a rotational temperature of ~13 K. From the five detected transitions of C8H-, we find a total C8H- column density of ~2.1×10^12 cm-2 consistent with a rotational temperature of ~34 K for a total C8H/C8H- column density ratio of ~3.8. This observed C8H/C8H- column density ratio is similar to the theoretical prediction of 3.6, while the observed column densities were lower than that predicted by a factor of ~30. This prompted us to reinvestigate the initial conditions of the circumstellar envelope (CSE) model. The new model results are presented, and they more closely match the C8H and C8H- abundances observed with the GBT. Finally, we use the new CSE model results to predict the abundance of decapentaynyl (C10H), and we compare them with the measured upper limit found from the GBT observations.

R-matrix theory of electron molecule scattering

This paper presents an overview of R-matrix theory of electron scattering by diatomic and polyatomic molecules. The paper commences with a detailed discussion of the fixed-nuclei approximation which in recent years has been used as the basis of the most accurate ab initio calculations. This discussion includes an overview of the computer codes which enable electron collisions with both diatomic and polyatomic molecules to be calculated. Nuclear motion including rotational and vibrational excitation and dissociation is then discussed. In non-resonant energy regions, or when the scattered electron energy is not close to thresholds, the adiabatic-nuclei approximation can be successfully used. However, when these conditions are not applicable, non-adiabatic R-matrix theory must be used and a detailed discussion of this theory is given. Finally, recent applications of the theory to treat electron scattering by polyatomic molecules are reviewed and a detailed comparison of R-matrix calculations and experimental measurements for water is presented.

Influence of mix proprtions on rheolgy of cement grouts containing limestone powder

In this paper the parameters of cement grout affecting rheological behaviour and compressive strength are investigated. Factorial experimental design was adopted in this investigation to assess the combined effects of the following factors on fluidity, rheological properties, induced bleeding and compressive strength: water/binder ratio (W/B), dosage of superplasticiser (SP), dosage of viscosity agent (VA), and proportion of limestone powder as replacement of cement (LSP). Mini-slump test, Marsh cone, Lombardi plate cohesion meter, induced bleeding test, coaxial rotating cylinder viscometer were used to evaluate the rheology of the cement grout and the compressive strengths at 7 and 28 days were measured. A two-level fractional factorial statistical model was used to model the influence of key parameters on properties affecting the fluidity, the rheology and compressive strength. The models are valid for mixes with 0.35-0.42 W/B, 0.3-1.2% SP, 0.02-0.7% VA (percentage of binder) and 12-45% LSP as replacement of cement. The influences of W/B, SP, VA and LSP were characterised and analysed using polynomial regression which can identify the primary factors and their interactions on the measured properties. Mathematical polynomials were developed for mini-slump, plate cohesion meter, inducing bleeding, yield value, plastic viscosity and compressive strength as function of W/B, SP, VA and proportion of LSP. The statistical approach used highlighted the limestone powder effect and the dosage of SP and VA on the various rheological characteristics of cement grout

Australia Telescope Compact Array 1.2cm Observations of the Massive Star Forming Region G305.2+0.2

We report on Australia Telescope Compact Array observations of the massive star-forming region G305.2+0.2 at 1.2 cm. We detected emission in five molecules towards G305A, confirming its hot core nature. We determined a rotational temperature of 26 K for methanol. A non-local thermodynamic equilibrium excitation calculation suggests a kinematic temperature of the order of 200 K. A time-dependent chemical model is also used to model the gas-phase chemistry of the hot core associated with G305A. A comparison with the observations suggest an age of between 2 × 104 and 1.5 × 105 yr. We also report on a feature to the south-east of G305A which may show weak Class I methanol maser emission in the line at 24.933 GHz. The more evolved source G305B does not show emission in any of the line tracers, but strong Class I methanol maser emission at 24.933 GHz is found 3 arcsec to the east. Radio continuum emission at 18.496 GHz is detected towards two H ii regions. The implications of the non-detection of radio continuum emission towards G305A and G305B are also discussed.

High-resolution optical spectroscopy of the sharp-lined B-type star HD83206

Very-high-resolution (R~160000) spectroscopic observations are presented for the early B-type star, HD83206. Because it has very sharp metal lines, this star affords an opportunity to test theories of model atmospheres and line formation. Non-LTE model atmosphere calculations have been used to estimate the atmospheric parameters and absolute metal abundances (C, N, O, Mg and Si); an LTE analysis was also undertaken to investigate the validity of this simpler approach and to estimate an iron abundance. For the non-LTE calculations, there is excellent agreement with observations of the Balmer lines Ha and Hd and the lines of Siii and Siiii for atmospheric parameters of Teff~=21700+/-600K and logg~=4.00+/-0.15dex. The agreement is less convincing for the LTE calculations, and a higher gravity is deduced. Careful comparison of the metal line profiles with non-LTE calculations implies that the projected rotational and microturbulent velocities have maximum values of ~=5 and ~=2kms-1, respectively. The latter value is smaller than has often been adopted in LTE model atmosphere analyses of main-sequence stars. Non-LTE absolute metal abundances are estimated, and a comparison with those for normal B-type stars (deduced using similar non-LTE techniques) shows no significant differences. A comparison of the abundances deduced using non-LTE and LTE calculations implies systematic differences of 0.1-0.2dex, showing the importance of using a non-LTE approach when accurate absolute abundances are required. Its location in the Hertzsprung-Russell diagram and normal metal abundance lead us to conclude that HD83206 is probably a main-sequence B-type star. As such, it is among the sharpest-lined young B-type star discovered to date.

Isolated vibrational wavepackets in D-2(+): Defining superposition conditions and wavepacket distinguishability

Tunnel ionization of room-temperature D-2 in an ultrashort (12 femtosecond) near infrared (800 nm) pump laser pulse excites a vibrational wavepacket in the D-2(+) ions; a rotational wavepacket is also excited in residual D-2 molecules. Both wavepacket types are collapsed a variable time later by an ultrashort probe pulse. We isolate the vibrational wavepacket and quantify its evolution dynamics through theoretical comparison. Requirements for quantum computation (initial coherence and quantum state retrieval) are studied using this well-defined (small number of initial states at room temperature, initial wavepacket spatially localized) single-electron molecular prototype by temporally stretching the pump and probe pulses.