Local-spin-density functional for multideterminant density functional theory

Based on exact limits and quantum Monte Carlo simulations, we obtain, at any density and spin polarization, an accurate estimate for the energy of a modified homogeneous electron gas where electrons repel each other only with a long-range coulombic tail. This allows us to construct an analytic local-spin-density exchange-correlation functional appropriate to new, multideterminantal versions of the density functional theory, where quantum chemistry and approximate exchange-correlation functionals are combined to optimally describe both long- and short-range electron correlations.Comment: revised version, ti appear in PR

A Local Density-Based Approach for Local Outlier Detection

This paper presents a simple but effective density-based outlier detection approach with the local kernel density estimation (KDE). A Relative Density-based Outlier Score (RDOS) is introduced to measure the local outlierness of objects, in which the density distribution at the location of an object is estimated with a local KDE method based on extended nearest neighbors of the object. Instead of using only $k$ nearest neighbors, we further consider reverse nearest neighbors and shared nearest neighbors of an object for density distribution estimation. Some theoretical properties of the proposed RDOS including its expected value and false alarm probability are derived. A comprehensive experimental study on both synthetic and real-life data sets demonstrates that our approach is more effective than state-of-the-art outlier detection methods.Comment: 22 pages, 14 figures, submitted to Pattern Recognition Letter

Local-Density Driven Clustered Star Formation

A positive power-law trend between the local surface densities of molecular gas, $\Sigma_{gas}$, and young stellar objects, $\Sigma_{\star}$, in molecular clouds of the Solar Neighbourhood has been identified by Gutermuth et al. How it relates to the properties of embedded clusters, in particular to the recently established radius-density relation, has so far not been investigated. In this paper, we model the development of the stellar component of molecular clumps as a function of time and initial local volume density so as to provide a coherent framework able to explain both the molecular-cloud and embedded-cluster relations quoted above. To do so, we associate the observed volume density gradient of molecular clumps to a density-dependent free-fall time. The molecular clump star formation history is obtained by applying a constant SFE per free-fall time, \eff. For volume density profiles typical of observed molecular clumps (i.e. power-law slope $\simeq -1.7$), our model gives a star-gas surface-density relation $\Sigma_{\star} \propto \Sigma_{gas}^2$, in very good agreement with the Gutermuth et al relation. Taking the case of a molecular clump of mass $M_0 \simeq 10^4 Msun$ and radius $R \simeq 6 pc$ experiencing star formation during 2 Myr, we derive what SFE per free-fall time matches best the normalizations of the observed and predicted ($\Sigma_{\star}$, $\Sigma_{gas}$) relations. We find \eff \simeq 0.1. We show that the observed growth of embedded clusters, embodied by their radius-density relation, corresponds to a surface density threshold being applied to developing star-forming regions. The consequences of our model in terms of cluster survivability after residual star-forming gas expulsion are that due to the locally high SFE in the inner part of star-forming regions, global SFE as low as 10% can lead to the formation of bound gas-free star clusters.Comment: 16 pages, 15 figures, Astronomy & Astrophysics, in pres

Measuring the local dark matter density

We examine systematic problems in determining the local matter density from the vertical motion of stars, i.e. the 'Oort limit'. Using collisionless simulations and a Monte Carlo Markov Chain technique, we determine the data quality required to detect local dark matter at its expected density. We find that systematic errors are more important than observational errors and apply our technique to Hipparcos data to reassign realistic error bars to the local dark matter density.Comment: 3 pages, 1 figure, to be published in "Hunting for the Dark: The Hidden Side of Galaxy Formation", Malta, 19-23 Oct. 2009, eds. V.P. Debattista & C.C. Popescu, AIP Conf. Se

Time-Dependent Superfluid Local Density Approximation

The time-dependent superfluid local density approximation (TDSLDA) is an extension of the Hohenberg-Kohn density functional theory (DFT) to time-dependent phenomena in superfluid fermionic systems. Unlike linear response theory, which is only valid for weak external fields, the (TDSLDA) approach allows one to study non-linear excitations in fermionic superfluids, including large amplitude collective modes, and the response to strong external probes. Even in the case of weak external fields, the (TDSLDA) approach is technically easier to implement. We will illustrate the implementation of the (TDSLDA) for the unitary Fermi gas, where dimensional arguments and Galilean invariance simplify the form of the functional, and ab initio input from (QMC) simulations fix the coefficients to quite high precision.Comment: 6 pages, 1 figure. Unedited version of chapter to appear in Quantum Gases: Finite Temperature and Non-Equilibrium Dynamics (Vol. 1 Cold Atoms Series). N.P. Proukakis, S.A. Gardiner, M.J. Davis and M.H. Szymanska, eds. Imperial College Press, London, 2013 (in press). See http://www.icpress.co.uk/physics/p817.htm