Solid State Physics Laboratory

Abstract: We present Raman spectroscopy measurements on single- and few-layer graphene flakes. By using a scanning confocal approach, we collect spectral data with spatial resolution, which allows us to directly compare Raman images with scanning force micrographs. Single-layer graphene can be distinguished from double- and few-layer by the width of the D' line: the single peak for single-layer graphene splits into different peaks for the double-layer. These findings are explained using the double-resonant Raman model based on ab initio calculations of the electronic structure and of the phonon dispersion. We investigate the D line intensity and find no defects within the flake. A finite D line response originating from the edges can be attributed either to defects or to the breakdown of translational symmetry.

Abstract: The electronic structure of the perovskite ${\mathrm{LaCoO}}_{3}$ for different spin states of Co ions was calculated in the local-density approximation LDA+U approach The ground state is found to be a nonmagnetic insulator with Co ions in a low-spin state Somewhat higher in energy, we find two intermediate-spin states followed by a high-spin state at significantly higher energy The calculations show that Co 3d states of ${\mathit{t}}_{2\mathit{g}}$ symmetry form narrow bands which could easily localize, while ${\mathit{e}}_{\mathit{g}}$ orbitals, due to their strong hybridization with the oxygen 2p states, form a broad \ensuremath{\sigma}* band With temperature variation which is simulated by a corresponding change of the lattice parameters, a transition from the low- to intermediate-spin state occurs This intermediate-spin (occupation ${\mathit{t}}_{2\mathit{g}}^{5}$${\mathit{e}}_{\mathit{g}}^{1}$) can develop an orbital ordering which can account for the nonmetallic nature of ${\mathrm{LaCoO}}_{3}$ at 90 KT500 K Possible explanations of the magnetic behavior and gradual insulator-metal transition are suggested \textcopyright{} 1996 The American Physical Society

Abstract: The motion of fluid particles as they are pushed along erratic trajectories by fluctuating pressure gradients is fundamental to transport and mixing in turbulence. It is essential in cloud formation and atmospheric transport, processes in stirred chemical reactors and combustion systems, and in the industrial production of nanoparticles. The concept of particle trajectories has been used successfully to describe mixing and transport in turbulence, but issues of fundamental importance remain unresolved. One such issue is the Heisenberg-Yaglom prediction of fluid particle accelerations, based on the 1941 scaling theory of Kolmogorov. Here we report acceleration measurements using a detector adapted from high-energy physics to track particles in a laboratory water flow at Reynolds numbers up to 63,000. We find that, within experimental errors, Kolmogorov scaling of the acceleration variance is attained at high Reynolds numbers. Our data indicate that the acceleration is an extremely intermittent variable--particles are observed with accelerations of up to 1,500 times the acceleration of gravity (equivalent to 40 times the root mean square acceleration). We find that the acceleration data reflect the anisotropy of the large-scale flow at all Reynolds numbers studied.

Abstract: Performance of iterative clustering algorithms which converges to numerous local minima depend highly on initial cluster centers. Generally initial cluster centers are selected randomly. In this paper we propose an algorithm to compute initial cluster centers for K-means clustering. This algorithm is based on two observations that some of the patterns are very similar to each other and that is why they have same cluster membership irrespective to the choice of initial cluster centers. Also, an individual attribute may provide some information about initial cluster center. The initial cluster centers computed using this methodology are found to be very close to the desired cluster centers, for iterative clustering algorithms. This procedure is applicable to clustering algorithms for continuous data. We demonstrate the application of proposed algorithm to K-means clustering algorithm. The experimental results show improved and consistent solutions using the proposed algorithm.

Abstract: Use of traditional k-mean type algorithm is limited to numeric data. This paper presents a clustering algorithm based on k-mean paradigm that works well for data with mixed numeric and categorical features. We propose new cost function and distance measure based on co-occurrence of values. The measures also take into account the significance of an attribute towards the clustering process. We present a modified description of cluster center to overcome the numeric data only limitation of k-mean algorithm and provide a better characterization of clusters. The performance of this algorithm has been studied on real world data sets. Comparisons with other clustering algorithms illustrate the effectiveness of this approach.