Profile driven interfaces in 1 + 1 dimensions : periodic steady states, dynamical melting and detachment

We study the steady state structure and dynamics of a 2-d Ising interface placed in an inhomogeneous external field with a sigmoidal profile which moves with velocity $v_{e}$. In the strong coupling limit the problem maps onto an assymmetric exclusion process involving motion of particles in 1-d with position dependent right and left jump probabilities. For small $v_{e}$, the interface is stuck to the field profile. As $v_{e}$ increases the profile detaches from the interface. At the transition point(and beyond), the interfacial structure and dynamics is characterized by KPZ exponents. For small $v_{e}$, on the other hand, the interface is macroscopically smooth with a vanishing roughness exponent $\alpha$. The interfacial structure is periodic with a periodicity which depends on the orientation of the interface. For a fixed orientation this periodic structure ``melts'' as $v_e$ is increased. We determine the dynamical ``phase - diagram'' of this system in the $v_e$ - orientation plane.Comment: 11 pages, 6 figures, To appear in Physica A as conference proceedings of Statphys - Kolkata I

Mechanical Failure of a Small and Confined Solid

Starting from a commensurate triangular thin solid strip, confined within two hard structureless walls, a stretch along its length introduces a rectangular distortion. Beyond a critical strain the solid fails through nucleation of "smectic"-like bands. We show using computer simulations and simple density functional based arguments, how a solid-smectic transition mediates the failure. Further, we show that the critical strain introducing failure is {\em inversely} proportional to the channel width i.e. thinner strips are stronger!Comment: 6 pages, 7 figures, to be published in Indian Journal of Physics (in press) as a Conference proceeding of CMDAYS-0

REVENUE-EXPENDITURE NEXUS FOR SOUTHERN STATES : SOME POLICY ORIENTED ECONOMETRIC OBSERVATIONS

The paper examines the temporal relationship between revenues and expenditures for the four southern states during 1980 to 2005. Using an error-correction model and Granger causality test, it finds that the taxspend hypothesis is supported by the analsysis. The spend-tax hypothesis is valid for Karnataka; fiscal synchronization hypothesis is supported for Andhra Pradesh and Kerala, while the data for Tamil Nadu failed to show any causality.Revenue Expenditure, Indian States, Cointegration

Stress relaxation in a perfect nanocrystal by coherent ejection of lattice layers

We show that a small crystal trapped within a potential well and in contact with its own fluid, responds to large compressive stresses by a novel mechanism -- the transfer of complete lattice layers across the solid-fluid interface. Further, when the solid is impacted by a momentum impulse set up in the fluid, a coherently ejected lattice layer carries away a definite quantity of energy and momentum, resulting in a sharp peak in the calculated phonon absorption spectrum. Apart from its relevance to studies of stability and failure of small sized solids, such coherent nanospallation may be used to make atomic wires or monolayer films.Comment: 4 pages, 4 figures, published version, changed conten

Anomalous structural and mechanical properties of solids confined in quasi one dimensional strips

We show using computer simulations and mean field theory that a system of particles in two dimensions, when confined laterally by a pair of parallel hard walls within a quasi one dimensional channel, possesses several anomalous structural and mechanical properties not observed in the bulk. Depending on the density $\rho$ and the distance between the walls $L_y$, the system shows structural characteristics analogous to a weakly modulated liquid, a strongly modulated smectic, a triangular solid or a buckled phase. At fixed $\rho$, a change in $L_y$ leads to many reentrant discontinuous transitions involving changes in the number of layers parallel to the confining walls depending crucially on the commensurability of inter-layer spacing with $L_y$. The solid shows resistance to elongation but not to shear. When strained beyond the elastic limit it fails undergoing plastic deformation but surprisingly, as the strain is reversed, the material recovers completely and returns to its original undeformed state. We obtain the phase diagram from mean field theory and finite size simulations and discuss the effect of fluctuations.Comment: 14 pages, 13 figures; revised version, accepted in J. Chem. Phy

Fluctuations at a constrained liquid-solid interface

Open Access. This material is posted here with the permission of the publisher.We study the interface between a solid trapped within a bath of liquid by a suitably shaped nonuniform external potential. Such a potential may be constructed using lasers, external electric or magnetic fields, or a surface template. We study a two-dimensional case where a thin strip of solid, created in this way, is surrounded on either side by a bath of liquid with which it can easily exchange particles. Since height fluctuations of the interface cost energy, this interface is constrained to remain flat at all length scales. However, when such a solid is stressed by altering the depth of the potential beyond a certain limit, it responds by relieving stress by novel interfacial fluctuations, which involve addition or deletion of entire lattice layers of the crystal. This “layering” transition is a generic feature of the system regardless of the details of the interaction potential. We show how such interfacial fluctuations influence mass, momentum, and energy transport across the interface. Tiny momentum impulses produce weak shock waves, which travel through the interface and cause the spallation of crystal layers into the liquid. Kinetic and energetic constraints prevent spallation of partial layers from the crystal, a fact which may be of some practical use. We also study heat transport through the liquid-solid interface and obtain the resistances in liquid, solid, and interfacial regions (Kapitza resistance) as the solid undergoes such layering transitions. Heat conduction, which shows strong signatures of the structural transformations, can be understood using a free volume calculation

Simply having a social media profile does not make teens more likely to be bullied online. Demographics and online behavior play a larger role

For many, the internet and social media is a double edged sword. On one hand it can bring people together to socialize, discuss, and collaborate in ways unthinkable mere decades ago. On the other, it can expose us to abuse and harassment from complete and often anonymous strangers, with teenagers especially at risk. But does having a social media profile make it more likely that teenagers will be harassed online? Using national survey data of teenagers and their parents, Anirban Sengupta and Anoshua Chaudhuri find that demographic and behavioral characteristics of teenagers are stronger predictors of online abuse than simply having an online profile. They find that girls and those who post large amounts of personal information online are more prone to online harassment

Multi-scale Kernel discrminant analysis

The bandwidth that minimizes the mean integrated square error of a kernel density estimator may not always be good when the density estimate is used for classification purpose. On the other hand cross-validation based techniques for choosing bandwidths may not be computationally feasible when there are many competing classes. Instead of concentrating on a single optimum bandwidth for each population density estimate, it would be more useful in practice to look at the results for different scales of smoothing. This paper presents such a multi-scale approach for classification using kernel density estimates along with a graphical device that leads to a more informative discriminant analysis. Usefulness of this proposed methodology has been illustrated using some benchmark data sets