Operator splitting for the Benjamin-Ono equation

In this paper we analyze operator splitting for the Benjamin-Ono equation, u_t = uu_x + Hu_xx, where H denotes the Hilbert transform. If the initial data are sufficiently regular, we show the convergence of both Godunov and Strang splitting.Comment: 18 Page

Work function engineering of graphene

Graphene is a two dimensional one atom thick allotrope of carbon that displays unusual crystal structure, electronic characteristics, charge transport behavior, optical clarity, physical & mechanical properties, thermal conductivity and much more that is yet to be discovered. Consequently, it has generated unprecedented excitement in the scientific community; and is of great interest to wide ranging industries including semiconductor, optoelectronics and printed electronics. Graphene is considered to be a next-generation conducting material with a remarkable band-gap structure, and has the potential to replace traditional electrode materials in optoelectronic devices. It has also been identified as one of the most promising materials for post-silicon electronics. For many such applications, modulation of the electrical and optical properties, together with tuning the band gap and the resulting work function of zero band gap graphene are critical in achieving the desired properties and outcome. In understanding the importance, a number of strategies including various functionalization, doping and hybridization have recently been identified and explored to successfully alter the work function of graphene. In this review we primarily highlight the different ways of surface modification, which have been used to specifically modify the band gap of graphene and its work function. This article focuses on the most recent perspectives, current trends and gives some indication of future challenges and possibilities.Rajni Garg, Naba K. Dutta and Namita Roy Choudhur

Neutrino Mixing Predictions of a Minimal SO(10) Model with Suppressed Proton Decay

During the past year, a minimal renormalizable supersymmetric SO(10) model has been proposed with the following properties: it predicts a naturally stable dark matter and neutrino mixing angles theta_atm and theta_13 while at the same time accommodating CKM CP violation among quarks with no SUSY CP problem. Suppression of proton decay for all allowed values of tan beta strongly restricts the flavor structure of the model making it predictive for other processes as well. We discuss the following predictions of the model in this paper, e.g. down-type quark masses, and neutrino oscillation parameters, U_e3, delta_MNSP, which will be tested by long baseline experiments such as T2K and subsequent experiments using the neutrino beam from JPARC. We also calculate lepton flavor violation and the lepton asymmetry of the Universe in this model.Comment: 22 pages, 11 figure

Incidence of HI 21-cm absorption in strong FeII systems at 0.5<z<1.50.5<z<1.5

We present the results from our search for HI 21-cm absorption in a sample of 16 strong FeII systems ($W_{\rm r}$(MgII $\lambda2796$) $\ge1.0$ \AA\ and $W_{\rm r}$(FeII $\lambda2600$) or $W_{\rm FeII}$ $\ge1$ \AA) at $0.5<z<1.5$ using the Giant Metrewave Radio Telescope and the Green Bank Telescope. We report six new HI 21-cm absorption detections from our sample, which have increased the known number of detections in strong MgII systems at this redshift range by $\sim50$%. Combining our measurements with those in the literature, we find that the detection rate of HI 21-cm absorption increases with $W_{\rm FeII}$, being four times higher in systems with $W_{\rm FeII}$ $\ge1$ \AA\ compared to systems with $W_{\rm FeII}$ $<1$ \AA. The $N$(HI) associated with the HI 21-cm absorbers would be $\ge 2 \times 10^{20}$ cm$^{-2}$, assuming a spin temperature of $\sim500$ K (based on HI 21-cm absorption measurements of damped Lyman-$\alpha$ systems at this redshift range) and unit covering factor. We find that HI 21-cm absorption arises on an average in systems with stronger metal absorption. We also find that quasars with HI 21-cm absorption detected towards them have systematically higher $E(B-V)$ values than those which do not. Further, by comparing the velocity widths of HI 21-cm absorption lines detected in absorption- and galaxy-selected samples, we find that they show an increasing trend (significant at $3.8\sigma$) with redshift at $z<3.5$, which could imply that the absorption originates from more massive galaxy haloes at high-$z$. Increasing the number of HI 21-cm absorption detections at these redshifts is important to confirm various trends noted here with higher statistical significance.Comment: 17 pages, 10 figures, 8 tables, accepted for publication in MNRA