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

Violation of Entropic Leggett-Garg Inequality in Nuclear Spins

We report an experimental study of recently formulated entropic Leggett-Garg inequality (ELGI) by Usha Devi et al. (arXiv: 1208.4491v2 (2012)). This inequality places a bound on the statistical measurement outcomes of dynamical observables describing a macrorealistic system. Such a bound is not necessarily obeyed by quantum systems, and therefore provides an important way to distinguish quantumness from classical behavior. Here we study ELGI using a two-qubit nuclear magnetic resonance system. To perform the noninvasive measurements required for the ELGI study, we prepare the system qubit in a maximally mixed state as well as use the `ideal negative result measurement' procedure with the help of an ancilla qubit. The experimental results show a clear violation of ELGI by over four standard deviations. These results agree with the predictions of quantum theory. The violation of ELGI is attributed to the fact that certain joint probabilities are not legitimate in the quantum scenario, in the sense they do not reproduce all the marginal probabilities. Using a three-qubit system, we experimentally demonstrate that three-time joint probabilities do not reproduce certain two-time marginal probabilities.Comment: 5 pages, 5 figures, 1 page supplementar

Statistical Model Checking for Cops and Robbers Game on Random Graph Models

Cops and robbers problem has been studied over the decades with many variants and applications in graph searching problem. In this work, we study a variant of cops and robbers problem on graphs. In this variant, there are di�erent types of cops and a minimum number of each type of cops are required to catch a robber. We studied this model over various random graph models and analyzed the properties using statistical model checking. To the best of our knowledge this variant of the cops and robber problem has not been studied yet. We have used statistical techniques to estimate the probability of robber getting caught in di�erent random graph models. We seek to compare the ease of catching robbers performing random walk on graphs, especially complex networks. In this work, we report the experiments that yields interesting empirical results. Through the experiments we have observed that it is easier to catch a robber in Barab�asi Albert model than in Erd�os-R�enyi graph model. We have also experimented with k-Regular graphs and real street networks. In our work, the model is framed as the multi-agent based system and we have implemented a statistical model checker, SMCA tool which veri�es agents based systems using statistical techniques. SMCA tool can take the model in JAVA programming language and support Probabilistic - Bounded LTL logic for property specification

Plasma flows in the cool loop systems

We study the dynamics of low-lying cool loop systems for three datasets as observed by the Interface Region Imaging Spectrograph (IRIS). Radiances, Doppler shifts and line widths are investigated in and around observed cool loop systems using various spectral lines formed between the photosphere and transition region (TR). Footpoints of the loop threads are either dominated by blueshifts or redshifts. The co-spatial variation of velocity above the blue-shifted footpoints of various loop threads shows a transition from very small upflow velocities ranging from (-1 to +1) km/s in the Mg\,{\sc ii} k line (2796.20~\AA; formation temperature: log (T/K) = 4.0) to the high upflow velocities from (-10 to -20) km/s in Si\,{\sc iv}. Thus, the transition of the plasma flows from red-shift (downflows) to the blue-shift (upflows) is observed above the footpoints of these loop systems in the spectral line C\,{\sc ii} (1334.53~\AA; \log (T/K) = 4.3) lying between Mg\,{\sc ii} k and Si\,{\sc iv} (1402.77~\AA; log (T / K) = 4.8). This flow inversion is consistently observed in all three sets of the observational data. The other footpoint of loop system always remains red-shifted indicating downflowing plasma. The multi-spectral line analysis in the present paper provides a detailed scenario of the plasma flows inversions in cool loop systems leading to the mass transport and their formation. The impulsive energy release due to small-scale reconnection above loop footpoint seems to be the most likely cause for sudden initiation of the plasma flows evident at TR temperatures.Comment: 29 Pages, 14 figures, The Astrophysical Journal (in press

Torus Polynomials: An Algebraic Approach to ACC Lower Bounds

We propose an algebraic approach to proving circuit lower bounds for ACC^0 by defining and studying the notion of torus polynomials. We show how currently known polynomial-based approximation results for AC^0 and ACC^0 can be reformulated in this framework, implying that ACC^0 can be approximated by low-degree torus polynomials. Furthermore, as a step towards proving ACC^0 lower bounds for the majority function via our approach, we show that MAJORITY cannot be approximated by low-degree symmetric torus polynomials. We also pose several open problems related to our framework