Finite temperature behavior of impurity doped Lithium cluster {\em viz} Li6_6Sn

We have carried out extensive isokinetic {\it ab initio} molecular dynamic simulations to investigate the finite temperature properties of the impurity doped cluster Li$_6$Sn along with the host cluster Li$_7$. The data obtained from about 20 temperatures and total simulation time of at least 3 ns is used to extract thermodynamical quantities like canonical specific heat. We observe a substantial charge transfer from all Li atoms to Sn which inturn weakens the Li-Li bonds in Li$_6$Sn compared to the bonds in Li$_7$. This weakening of bonds changes the finite temperature behavior of Li$_6$Sn significantly. Firstly, Li$_6$Sn becomes liquid-like around 250 K, a much lower temperature than that of Li$_7$ ($\approx$~425 K). Secondly, an additional quasirotational motion of lithium atoms appears at lower temperatures giving rise to a shoulder around 50 K in the specific heat curve of Li$_6$Sn. The peak in the specific heat of Li$_7$ is very broad and the specific heat does not show any premelting features.Comment: 16 pages, 10 figures Submitted to J. Chem. Phy

Magic Melters' Have Geometrical Origin

Recent experimental reports bring out extreme size sensitivity in the heat capacities of Gallium and Aluminum clusters. In the present work we report results of our extensive {\it ab initio} molecular dynamical simulations on Ga$_{30}$ and Ga$_{31}$, the pair which has shown rather dramatic size sensitivity. We trace the origin of this size sensitive heat capacities to the relative order in their respective ground state geometries. Such an effect of nature of the ground state on the characteristics of heat capacities is also seen in case of small Gallium and Sodium clusters indicating that the observed size sensitivity is a generic feature of small clusters.Comment: 4 pages, 6 figure

Finite Temperature Behavior of Small Silicon and Tin Clusters: An Ab Initio Molecular Dynamics Study

The finite temperature behavior of small Silicon (Si$_{10}$, Si$_{15}$, and Si$_{20}$) and Tin (Sn$_{10}$ and Sn$_{20}$) clusters is studied using isokinetic Born-Oppenheimer molecular dynamics. The lowest equilibrium structures of all the clusters are built upon a highly stable tricapped trigonal prism unit which is seen to play a crucial role in the finite temperature behavior of these clusters. Thermodynamics of small tin clusters (Sn$_{10}$ and Sn$_{20}$) is revisited in light of the recent experiments on tin clusters of sizes 18-21 [G. A. Breaux et. al. Phys. Rev. B {\bf 71} 073410 (2005)]. We have calculated heat capacities using multiple histogram technique for Si$_{10}$, Sn$_{10}$ and Si$_{15}$ clusters. Our calculated specific heat curves have a main peak around 2300 K and 2200 K for Si$_{10}$ and Sn$_{10}$ clusters respectively. However, various other melting indicators such as root mean square bond length fluctuations, mean square displacements show that diffusive motion of atoms within the cluster begins around 650 K. The finite temperature behavior of Si$_{10}$ and Sn$_{10}$ is dominated by isomerization and it is rather difficult to discern the temperature range for transition region. On the other hand, Si$_{15}$ does show a liquid like behavior over a short temperature range followed by the fragmentation observed around 1800 K. Finite temperature behavior of Si$_{20}$ and Sn$_{20}$ show that these clusters do not melt but fragment around 1200 K and 650 K respectively.Comment: 9 figure

Dopant Induced Stabilization of Silicon Cluster at Finite Temperature

With the advances in miniaturization, understanding and controlling properties of significant technological systems like silicon in nano regime assumes considerable importance. It turns out that small silicon clusters in the size range of 15-20 atoms are unstable upon heating and in fact fragment in the temperature range of 1200 K to 1500 K. In the present work we demonstrate that it is possible to stabilize such clusters by introducing appropriate dopant (in this case Ti). Specifically, by using the first principle density functional simulations we show that Ti doped Si$_{16}$, having the Frank-Kasper geometry, remains stable till 2200 K and fragments only above 2600 K. The observed melting transition is a two step process. The first step is initiated by the surface melting around 600 K. The second step is the destruction of the cage which occurs around 2250 K giving rise to a peak in the heat capacity curve.Comment: 6 pages, 8 Figs. Submitted to PR

A complete radio study of SNR G15.4+0.1 from new GMRT observations

The supernova remnant G15.4+0.1 is considered to be the possible counterpart of the gamma-ray source HESSJ1818-154. With the goal of getting a complete view of this remnant and understanding the nature of the gamma-ray flux, we conducted a detailed radio study that includes the search for pulsations and a model of the broadband emission for the G15.4+0.1/HESSJ1818-154 system. Low-frequency imaging at 624 MHz and pulsar observations at 624 and 1404 MHz towards G15.4+0.1 were carried out with the Giant Metrewave Radio Telescope (GMRT). We correlated the new radio data with observations of the source at X-ray and infrared wavelengths from XMM-Newton and Herschel observatories, respectively. To characterize the neutral hydrogen medium (HI) towards G15.4+0.1, we used data from the Southern Galactic Plane Survey. We modelled the spectral energy distribution using both hadronic and leptonic scenarios. From the combination of the new GMRT observations with existing data, we derived a continuum spectral index alpha=-0.62+-0.03 for the whole remnant. The local synchrotron spectra of G15.4+0.1, calculated from the combination of the GMRT data with 330 MHz observations from the VLA, tends to be flatter in the central part of the remnant, accompanying the region where the blast wave is impinging molecular gas. No spectral index trace was found indicating the radio counterpart to the pulsar wind nebula proposed from X-ray observations. In addition, the search for radio pulsations yielded negative results. Emission at far-infrared wavelengths is observed in the region where the SNR shock is interacting with dense molecular clumps. We also identified HI features forming a shell that wraps most of the outer border of G15.4+0.1. Characteristic parameters were estimated for the shocked HI gas. We found that either a purely hadronic or leptonic model is compatible with the broadband emission known so far.Comment: 11 pages, 9 figures, accepted for publication in Astronomy & Astrophysic

Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations

The truncation method is a collective name for techniques that arise from truncating a Laurent series expansion (with leading term) of generic solutions of nonlinear partial differential equations (PDEs). Despite its utility in finding Backlund transformations and other remarkable properties of integrable PDEs, it has not been generally extended to ordinary differential equations (ODEs). Here we give a new general method that provides such an extension and show how to apply it to the classical nonlinear ODEs called the Painleve equations. Our main new idea is to consider mappings that preserve the locations of a natural subset of the movable poles admitted by the equation. In this way we are able to recover all known fundamental Backlund transformations for the equations considered. We are also able to derive Backlund transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages

Why do gallium clusters have a higher melting point than the bulk?

Density functional molecular dynamical simulations have been performed on Ga$_{17}$ and Ga$_{13}$ clusters to understand the recently observed higher-than-bulk melting temperatures in small gallium clusters [Breaux {\em et al.}, Phys. Rev. Lett. {\bf 91}, 215508 (2003)]. The specific-heat curve, calculated with the multiple-histogram technique, shows the melting temperature to be well above the bulk melting point of 303 K, viz. around 650 K and 1400 K for Ga$_{17}$ and Ga$_{13}$, respectively. The higher-than-bulk melting temperatures are attributed mainly to the covalent bonding in these clusters, in contrast with the covalent-metallic bonding in the bulk.Comment: 4 pages, including 6 figures. accepted for publication in Phys. Rev. Let

Gravitational collapse of an isentropic perfect fluid with a linear equation of state

We investigate here the gravitational collapse end states for a spherically symmetric perfect fluid with an equation of state $p=k\rho$. It is shown that given a regular initial data in terms of the density and pressure profiles at the initial epoch from which the collapse develops, the black hole or naked singularity outcomes depend on the choice of rest of the free functions available, such as the velocities of the collapsing shells, and the dynamical evolutions as allowed by Einstein equations. This clarifies the role that equation of state and initial data play towards determining the final fate of gravitational collapse.Comment: 7 Pages, Revtex4, To appear in Classical and Quantum Gravit

Instability of black hole formation under small pressure perturbations

We investigate here the spectrum of gravitational collapse endstates when arbitrarily small perfect fluid pressures are introduced in the classic black hole formation scenario as described by Oppenheimer, Snyder and Datt (OSD) [1]. This extends a previous result on tangential pressures [2] to the more physically realistic scenario of perfect fluid collapse. The existence of classes of pressure perturbations is shown explicitly, which has the property that injecting any smallest pressure changes the final fate of the dynamical collapse from a black hole to a naked singularity. It is therefore seen that any smallest neighborhood of the OSD model, in the space of initial data, contains collapse evolutions that go to a naked singularity outcome. This gives an intriguing insight on the nature of naked singularity formation in gravitational collapse.Comment: 7 pages, 1 figure, several modifications to match published version on GR