Self-similarity of electrostatic fluctuations in a linear magnetised plasma system

In this Letter the long-range time correlations present in the fluctuation data in presence of electrostatic instability in a magnetised dc discharge plasma is presented. The electrostatic instability is generated due to the effect of crossed electric and magnetic field (E×B flow) and has intermediate frequency ranging from 50 to 100 MHz. Hurst exponent, the self-similarity parameter is calculated with the help of different statistical methods suggested by many researchers to determine the long-range time correlation present in fluctuation dynamics in the plasma column. The fluctuation in the ion saturation current is measured by a Langmuir probe for the study and the measurement is done both radially and axially in the plasma system. Estimated results clearly expose the self-similar character of the fluctuations with self-similarity parameters having values from 0.65 to 0.90 through the presence of long-range time correlation.     

On the Carey–Helton–Howe–Pincus trace formula

In this article, we give a new proof of the Carey–Helton–Howe–Pincus trace formula using Kato's theory of “relatively-smooth” operators and Krein's trace formula.     

Convergence of linear functions of Pfeifer records

The probabilistic behaviour of partial sums of upper and lower records has been studied in the literature. In this article, we take a broader view and study partial sums of record like sequences. We show that such sequences converge in distribution to normal and lognormal distribution. In particular our results apply to Pfeifer records. We also show the strong convergence of partial sums of lower Pfeifer records under suitable assumptions.     

Modulating magnetic anisotropy in Ln(iii) single-ion magnets using an external electric field

Single-molecule magnets have potential uses in several nanotechnology applications, including high-density information storage devices, the realisation of which lies in enhancing the barrier height for magnetisation reversal (U_eff). However, Ln(iii) single-ion magnets (SIMs) that have been reported recently reveal that the maximum value of U_eff values that can be obtained by modulating the ligand fields has already been achieved. Here, we have explored, using a combination of DFT and ab initio CASSCF calculations, a unique way to enhance the magnetisation reversal barrier using an oriented external electric field in three well-known Ln(iii) single-ion magnets: [Dy(Py)₅(O^tBu)₂]⁺ (1), [Er{N(SiMe₃)₂}₃Cl]⁻ (2) and [Dy(Cp^Me3)Cl] (3). Our study reveals that, for apt molecules, if the appropriate direction and values of the electric fields are chosen, the barrier height can be enhanced by twice that of the limit set by the ligand field. The application of an electric field along the equatorial direction was found to be suitable for oblate shaped Dy(iii) complexes and an electric field along the axial direction was found to enhance the barrier height for a prolate Er(iii) complex. For complexes 2 and 3, the external electric field was able to magnify the barrier height to 2–3 times that of the original complexes. However, a moderate enhancement was noticed after application of the external electric field in the case of complex 1. This novel non-chemical fine-tuning approach to modulate magnetic anisotropy is expected to yield a new generation of SIMs.

Using a combination of theoretical tools, we show that the application of an external electric field in a certain direction can boost the axiality beyond that set by the ligands, opening up a new avenue for the generation of novel SIMs.     

Macromolecules at surfaces: Research challenges and opportunities from tribology to biology

A comprehensive review of ongoing and recommended research directions concerning the structure, dynamics, and interfacial activity of synthetic and naturally occurring macromolecules at the solid–liquid interface is presented. Many new developments stem from the ability to target new size regimes of 1–100 nm. These rapid developments are reviewed critically with respect to chemical synthesis, processing, structural characterization, dynamic processes, and theoretical and computational analysis. The common problems shared by flat and particulate surfaces are emphasized. A broad spectrum of material properties are discussed, from the control of interfacial friction between surfaces in moving contact, to the mechanical strength and durability of the interfaces in hybrid materials, to optical and electronic properties. Future research opportunities are identified that involve (1) the emergence of nanoscale material properties, (2) polymer‐assisted nanostructures, and (3) the crossroads between interfacial science and biological and bioinspired applications. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2755–2793, 2003     

A note on random coin tossing

Harris and Keane [Probab. Theory Related Fields 109 (1997) 27-37] studied absolute continuity/singularity of two probabilities on the coin-tossing space, one representing independent tosses of a fair coin, while in the other a biased coin is tossed at renewal times of an independent renewal process and a fair coin is tossed at all other times. We extend their results by allowing possibly different biases at the different renewal times. We also investigate the contiguity and asymptotic separation properties in this kind of set-up and obtain some sufficient conditions.Keywords:renewal process, absolute continuity, singularity, contiguity, asymptotic separation, martingale convergence theorem     

Compensation for temperature dependence of Stokes signal and dynamic self-calibration of a Raman distributed temperature sensor

This article discusses a powerful calibration technique that compensates for the temperature dependence of the Stokes signal in a Raman distributed temperature sensor. The Stokes signal is conventionally used for normalization since its scattering cross-section is a weaker function of temperature than that of the anti-Stokes signal. The potential of this temperature dependence of the Stokes signal to introduce errors in measurements has received only cursory mention in the literature. We show that this effect degrades the temperature accuracy by as much as 90%. Additionally the heavy fiber attenuation at the operating wavelength also makes calibration non-trivial. The technique described implements a corrective mechanism for this temperature dependence, offers the additional benefit of self-referencing of a heated curve rather than referencing to the fiber at room temperature, and demonstrates the viability of such a system despite the heavy fiber attenuation at the operating wavelength. This obviates the impractical and erroneous approach of storing an initial room temperature profile for subsequent temperature calculation. This dynamic self-referencing adds substantial immunity to the tolerances in the actual numerical values of the Raman wavelengths thereby making the system robust.