A Self-Consistent First-Principles Technique Having Linear Scaling

An algorithm for first-principles electronic structure calculations having a computational cost which scales linearly with the system size is presented. Our method exploits the real-space localization of the density matrix, and in this respect it is related to the technique of Li, Nunes and Vanderbilt. The density matrix is expressed in terms of localized support functions, and a matrix of variational parameters, L, having a finite spatial range. The total energy is minimized with respect to both the support functions and the elements of the L matrix. The method is variational, and becomes exact as the ranges of the support functions and the L matrix are increased. We have tested the method on crystalline silicon systems containing up to 216 atoms, and we discuss some of these results.Comment: 12 pages, REVTeX, 2 figure

Towards a Linear-Scaling DFT Technique: The Density Matrix Approach

A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by minimization with respect to the density matrix, subject to the condition that the eigenvalues of the latter lie in the range [0,1]. Linear-scaling behavior is achieved by requiring that the density matrix should vanish when the separation of its arguments exceeds a chosen cutoff. The limitation on the eigenvalue range is imposed by the method of Li, Nunes and Vanderbilt. The scheme is implemented by calculating all terms in the energy on a uniform real-space grid, and minimization is performed using the conjugate-gradient method. Tests on a 512-atom Si system show that the total energy converges rapidly as the range of the density matrix is increased. A discussion of the relation between the present method and other linear-scaling methods is given, and some problems that still require solution are indicated.Comment: REVTeX file, 27 pages with 4 uuencoded postscript figure

Efficient Recursion Method for Inverting Overlap Matrix

A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations with the the non-orthogonal localized basis set. This efficient inverting method can be incorporated in several O(N) methods for diagonalization of a generalized secular equation. By studying convergence properties of the 1-norm of an error matrix for diamond and fcc Al, this method is compared to three other O(N) methods (the divide method, Taylor expansion method, and Hotelling's method) with regard to computational accuracy and efficiency within the density functional theory. The test calculations show that the new method is about one-hundred times faster than the divide method in computational time to achieve the same convergence for both diamond and fcc Al, while the Taylor expansion method and Hotelling's method suffer from numerical instabilities in most cases.Comment: 17 pages and 4 figure

An analysis of the FIR/RADIO Continuum Correlation in the Small Magellanic Cloud

The local correlation between far-infrared (FIR) emission and radio-continuum (RC) emission for the Small Magellanic Cloud (SMC) is investigated over scales from 3 kpc to 0.01 kpc. Here, we report good FIR/RC correlation down to ~15 pc. The reciprocal slope of the FIR/RC emission correlation (RC/FIR) in the SMC is shown to be greatest in the most active star forming regions with a power law slope of ~1.14 indicating that the RC emission increases faster than the FIR emission. The slope of the other regions and the SMC are much flatter and in the range of 0.63-0.85. The slopes tend to follow the thermal fractions of the regions which range from 0.5 to 0.95. The thermal fraction of the RC emission alone can provide the expected FIR/RC correlation. The results are consistent with a common source for ultraviolet (UV) photons heating dust and Cosmic Ray electrons (CRe-s) diffusing away from the star forming regions. Since the CRe-s appear to escape the SMC so readily, the results here may not provide support for coupling between the local gas density and the magnetic field intensity.Comment: 19 pages, 7 Figure

Basis Functions for Linear-Scaling First-Principles Calculations

In the framework of a recently reported linear-scaling method for density-functional-pseudopotential calculations, we investigate the use of localized basis functions for such work. We propose a basis set in which each local orbital is represented in terms of an array of `blip functions'' on the points of a grid. We analyze the relation between blip-function basis sets and the plane-wave basis used in standard pseudopotential methods, derive criteria for the approximate equivalence of the two, and describe practical tests of these criteria. Techniques are presented for using blip-function basis sets in linear-scaling calculations, and numerical tests of these techniques are reported for Si crystal using both local and non-local pseudopotentials. We find rapid convergence of the total energy to the values given by standard plane-wave calculations as the radius of the linear-scaling localized orbitals is increased.Comment: revtex file, with two encapsulated postscript figures, uses epsf.sty, submitted to Phys. Rev.

Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

The $B^0$-$\bar B^0$ oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)}$ ps$^{-1}$.Comment: 7 pages, 1 figure, submitted to Physical Review Letter

A hierarchy of heuristic-based models of crowd dynamics

International audienceWe derive a hierarchy of kinetic and macroscopic models from a noisy variant of the heuristic behavioral Individual-Based Model of Moussaid et al, PNAS 2011, where the pedestrians are supposed to have constant speeds. This IBM supposes that the pedestrians seek the best compromise between navigation towards their target and collisions avoidance. We first propose a kinetic model for the probability distribution function of the pedestrians. Then, we derive fluid models and propose three different closure relations. The first two closures assume that the velocity distribution functions are either a Dirac delta or a von Mises-Fisher distribution respectively. The third closure results from a hydrodynamic limit associated to a Local Thermodynamical Equilibrium. We develop an analogy between this equilibrium and Nash equilibia in a game theoretic framework. In each case, we discuss the features of the models and their suitability for practical use

Looking forward through the past: identification of 50 priority research questions in palaeoecology

1. Priority question exercises are becoming an increasingly common tool to frame future agendas in conservation and ecological science. They are an effective way to identify research foci that advance the field and that also have high policy and conservation relevance. 2. To date, there has been no coherent synthesis of key questions and priority research areas for palaeoecology, which combines biological, geochemical and molecular techniques in order to reconstruct past ecological and environmental systems on time-scales from decades to millions of years. 3. We adapted a well-established methodology to identify 50 priority research questions in palaeoecology. Using a set of criteria designed to identify realistic and achievable research goals, we selected questions from a pool submitted by the international palaeoecology research community and relevant policy practitioners. 4. The integration of online participation, both before and during the workshop, increased international engagement in question selection. 5. The questions selected are structured around six themes: human–environment interactions in the Anthropocene; biodiversity, conservation and novel ecosystems; biodiversity over long time-scales; ecosystem processes and biogeochemical cycling; comparing, combining and synthesizing information from multiple records; and new developments in palaeoecology. 6. Future opportunities in palaeoecology are related to improved incorporation of uncertainty into reconstructions, an enhanced understanding of ecological and evolutionary dynamics and processes and the continued application of long-term data for better-informed landscape management

Multi-system neurological disease is common in patients with OPA1 mutations

Additional neurological features have recently been described in seven families transmitting pathogenic mutations in OPA1, the most common cause of autosomal dominant optic atrophy. However, the frequency of these syndromal ‘dominant optic atrophy plus’ variants and the extent of neurological involvement have not been established. In this large multi-centre study of 104 patients from 45 independent families, including 60 new cases, we show that extra-ocular neurological complications are common in OPA1 disease, and affect up to 20% of all mutational carriers. Bilateral sensorineural deafness beginning in late childhood and early adulthood was a prominent manifestation, followed by a combination of ataxia, myopathy, peripheral neuropathy and progressive external ophthalmoplegia from the third decade of life onwards. We also identified novel clinical presentations with spastic paraparesis mimicking hereditary spastic paraplegia, and a multiple sclerosis-like illness. In contrast to initial reports, multi-system neurological disease was associated with all mutational subtypes, although there was an increased risk with missense mutations [odds ratio = 3.06, 95% confidence interval = 1.44–6.49; P = 0.0027], and mutations located within the guanosine triphosphate-ase region (odds ratio = 2.29, 95% confidence interval = 1.08–4.82; P = 0.0271). Histochemical and molecular characterization of skeletal muscle biopsies revealed the presence of cytochrome c oxidase-deficient fibres and multiple mitochondrial DNA deletions in the majority of patients harbouring OPA1 mutations, even in those with isolated optic nerve involvement. However, the cytochrome c oxidase-deficient load was over four times higher in the dominant optic atrophy + group compared to the pure optic neuropathy group, implicating a causal role for these secondary mitochondrial DNA defects in disease pathophysiology. Individuals with dominant optic atrophy plus phenotypes also had significantly worse visual outcomes, and careful surveillance is therefore mandatory to optimize the detection and management of neurological disability in a group of patients who already have significant visual impairment