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.

Anomalous helicon wave absorption and parametric excitation of electrostatic fluctuations in a helicon-produced plasma

The nonlinear nature of the rf absorption in a helicon-produced plasma was recently evidenced by the observation that the helicon wave damping as well as the level of short-scale electrostatic fluctuations excited in the helicon plasma increases with rf power. Correlation methods using electrostatic probes as well as microwave back-scattering at the upper-hybrid resonance allow identifying the fluctuations as ion-sound and Trivelpiece– Gould waves satisfying the frequency and wavenumber matching conditions for the parametric decay instability of the helicon pump wave. Furthermore, the growth rates and thresholds deduced from their temporal growth are in good agreement with theoretical predictions for the parametric decay instability that takes into account realistic damping rates for the decay waves as well as a non-vanishing parallel wavenumber of the helicon pump. The close relationship between the rf absorption and the excitation of the fluctuations was investigated in more detail by performing time- and space-resolved measurements of the helicon wave field and the electrostatic fluctuations.

Anomalous fluorinations of 3-aryl-2-hydroxypropanoic esters by diethylaminosulfur trifluoride (DAST).

Anomalous fluorinations of 3-aryl-2-hydroxypropanoic esters by diethylaminosulfur trifluoride (DAST). Haigh, David; Jefcott, Lee J.; Magee, Katherkine; McNab, Hamish. Dep. Med. chem., SmithKline Beecham Pharmaceuticals, Epsom, UK. Journal of the Chemical Society, Perkin Transactions 1: Organic and Bio-Organic Chemistry (1996), (24), 2895-2900. Publisher: Royal Society of Chemistry, CODEN: JCPRB4 ISSN: 0300-922X. Journal written in English. CAN 126:143928 AN 1997:56534 CAPLUS (Copyright (C) 2009 ACS on SciFinder (R)) Abstract Treatment of 3-aryl-2-hydroxypropanoic esters with diethylaminosulfur trifluoride (DAST) gives considerable amts. of rearranged 2-aryl-3-fluoropropanoic esters, together with the expected products. The extent of rearrangement is dependent on solvent and on the substitution pattern of the aryl ring; the mechanism of rearrangement probably involves anchimeric assistance by the aryl group in the SN1 component of the reaction pathway. Reaction of the isomeric 3-hydroxy-2-phenylpropanoic ester shows much less rearrangement under similar conditions, and an elimination product is also obtained.

Anomalous extinction behaviour towards the type Ia SN 2003cg

We present optical and near-infrared photometry and spectroscopy of the Type Ia SN 2003cg, which exploded in the nearby galaxy NGC 3169. The observations cover a period between -8.5 and +414 d post-maximum. SN 2003cg is a normal but highly reddened Type Ia event. Its B magnitude at maximum B-max = 15.94 +/- 0.04 and Delta m(15)(B)(obs) = 1.12 +/- 0.04 [Delta m(15)(B)(intrinsic) = 1.25 +/- 0.05]. Allowing R-V to become a free parameter within the Cardelli et al. extinction law, simultaneous matches to a range of colour curves of normal SNe Ia yielded E(B - V) = 1.33 +/- 0.11, and RV = 1.80 +/- 0.19. While the value obtained for R-V is small, such values have been invoked in the past, and may imply a grain size which is small compared with the average value for the local interstellar medium.

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

We consider the non-equilibrium dynamics of a simple system consisting of interacting spin-1/2 particles subjected to a collective damping. The model is close to situations that can be engineered in hybrid electro/opto-mechanical settings. Making use of large-deviation theory, we find a Gallavotti-Cohen symmetry in the dynamics of the system as well as evidence for the coexistence of two dynamical phases with different activity levels. We show that additional damping processes smooth out this behavior. Our analytical results are backed up by Monte Carlo simulations that reveal the nature of the trajectories contributing to the different dynamical phases.

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

Release kinetics of oleyl alcohol from a self-lubricating silicone biomaterial

The development of self-lubricating silicone elastomeric biomaterials, prepared using the novel crosslinking agent tetra( oleyloxy) silane and having very low coefficients of friction, has recently been reported. In this study, the in vitro release characteristics of lubricious oleyl alcohol produced during the silicone curing reaction have been quantitatively evaluated for a range of tetra( propoxy) silane/tetra(oleyloxy) silane crosslinker compositions using a novel evaporative light scattering detection method in combination with high performance liquid chromatography. The mechanism of oleyl alcohol release was seen to deviate from a simple, matrix-controlled diffusion process and instead obeyed an anomalous transport mechanism. An explanation for the observed release behaviour has been proposed based on competitive reaction kinetics between the tetra( oleyloxy) silane and tetra( propoxy) silane substituents of the silicone crosslinking agents.

Environmental Isotopes as Indicators for Ground Water Recharge to Fractured Granite

To assess the contribution of accumulated winter precipitation and glacial meltwater to the recharge of deep ground water flow systems in fracture crystalline rocks, measurements of environmental isotope ratios, hydrochemical composition, and in situ parameters of ground water were performed in a deep tunnel. The measurements demonstrate the significance of these ground water recharge components for deep ground water flow systems in fractured granites of a high alpine catchment in the Central Alps, Switzerland. Hydrochemical and in situ parameters, as well as d18O in ground water samples collected in the tunnel, show only small temporal variations. The precipitation record of d18O shows seasonal variations of ~14‰ and a decrease of 0.23‰ ± 0.03‰ per 100 m elevation gain. d2H and d18O in precipitation are well correlated and plot close to the meteoric water line, as well as d2H and d18O in ground water samples, reflecting the meteoric origin of the latter. The depletion of 18O in ground water compared to 18O content in precipitation during the ground water recharge period indicates significant contributions from accumulated depleted winter precipitation to ground water recharge. The hydrochemical composition of the encountered ground water, Na-Ca-HCO3-SO4(-F), reflects an evolution of the ground water along the flowpath through the granite body. Observed tritium concentrations in ground water range from 2.6 to 16.6 TU, with the lowest values associated with a local negative temperature anomaly and anomalous depleted 18O in ground water. This demonstrates the effect of local ground water recharge from meltwater of submodern glacial ice. Such localized recharge from glaciated areas occurs along preferential flowpaths within the granite body that are mainly controlled by observed hydraulic active shear fractures and cataclastic faults.

An analytic geometry-variant approach to line ratio enhancement above the optically thin limit

We describe a simple theoretical model to investigate the anomalous effects of opacity on spectral line ratios, as previously studied in elements such as Fe XV and Fe XVII. The model developed is general: it is not specific to a particular atomic system, thus giving applicability to a number of coronal and chromospheric plasmas; furthermore, it may be applied to a variety of astrophysically relevant geometries. The analysis is underpinned by geometrical arguments, and we outline a technique for it to be used as a tool for the explicit diagnosis of plasma geometry in distant astrophysical objects.

d-outcome measurement for a nonlocality test

For the purpose of a nonlocality test, we propose a general correlation observable of two parties by utilizing local d- outcome measurements with SU(d) transformations and classical communications. Generic symmetries of the SU(d) transformations and correlation observables are found for the test of nonlocality. It is shown that these symmetries dramatically reduce the number of numerical variables, which is important for numerical analysis of nonlocality. A linear combination of the correlation observables, which is reduced to the Clauser- Home-Shimony-Holt (CHSH) Bell's inequality for two outcome measurements, leads to the Collins-Gisin-Linden-Massar-Popescu (CGLMP) nonlocality test for d-outcome measurement. As a system to be tested for its nonlocality, we investigate a continuous- variable (CV) entangled state with d measurement outcomes. It allows the comparison of nonlocality based on different numbers of measurement outcomes on one physical system. In our example of the CV state, we find that a pure entangled state of any degree violates Bell's inequality for d(greater than or equal to2) measurement outcomes when the observables are of SU(d) transformations.