Investigation of the Jahn-Teller Transition in TiF3 using Density Functional Theory

We use first principles density functional theory to calculate electronic and magnetic properties of TiF3 using the full potential linearized augmented plane wave method. The LDA approximation predicts a fully saturated ferromagnetic metal and finds degenerate energy minima for high and low symmetry structures. The experimentally observed Jahn-Teller phase transition at Tc=370K can not be driven by the electron-phonon interaction alone, which is usually described accurately by LDA. Electron correlations beyond LDA are essential to lift the degeneracy of the singly occupied Ti t2g orbital. Although the on-site Coulomb correlations are important, the direction of the t2g-level splitting is determined by the dipole-dipole interactions. The LDA+U functional predicts an aniferromagnetic insulator with an orbitally ordered ground state. The input parameters U=8.1 eV and J=0.9 eV for the Ti 3d orbital were found by varying the total charge on the TiF$_6^{2-}$ ion using the molecular NRLMOL code. We estimate the Heisenberg exchange constant for spin-1/2 on a cubic lattice to be approximately 24 K. The symmetry lowering energy in LDA+U is about 900 K per TiF3 formula unit.Comment: 7 pages, 9 figures, to appear in Phys. Rev.

A Hybrid Artificial Bee Colony Algorithm for Graph 3-Coloring

The Artificial Bee Colony (ABC) is the name of an optimization algorithm that was inspired by the intelligent behavior of a honey bee swarm. It is widely recognized as a quick, reliable, and efficient methods for solving optimization problems. This paper proposes a hybrid ABC (HABC) algorithm for graph 3-coloring, which is a well-known discrete optimization problem. The results of HABC are compared with results of the well-known graph coloring algorithms of today, i.e. the Tabucol and Hybrid Evolutionary algorithm (HEA) and results of the traditional evolutionary algorithm with SAW method (EA-SAW). Extensive experimentations has shown that the HABC matched the competitive results of the best graph coloring algorithms, and did better than the traditional heuristics EA-SAW when solving equi-partite, flat, and random generated medium-sized graphs

Franck-Condon Effect in Central Spin System

We study the quantum transitions of a central spin surrounded by a collective-spin environment. It is found that the influence of the environmental spins on the absorption spectrum of the central spin can be explained with the analog of the Franck-Condon (FC) effect in conventional electron-phonon interaction system. Here, the collective spins of the environment behave as the vibrational mode, which makes the electron to be transitioned mainly with the so-called "vertical transitions" in the conventional FC effect. The "vertical transition" for the central spin in the spin environment manifests as, the certain collective spin states of the environment is favored, which corresponds to the minimal change in the average of the total spin angular momentum.Comment: 8 pages, 8 figure

Heavy Quarks on Anisotropic Lattices: The Charmonium Spectrum

We present results for the mass spectrum of $c{\bar c}$ mesons simulated on anisotropic lattices where the temporal spacing $a_t$ is only half of the spatial spacing $a_s$. The lattice QCD action is the Wilson gauge action plus the clover-improved Wilson fermion action. The two clover coefficients on an anisotropic lattice are estimated using mean links in Landau gauge. The bare velocity of light $\nu_t$ has been tuned to keep the anisotropic, heavy-quark Wilson action relativistic. Local meson operators and three box sources are used in obtaining clear statistics for the lowest lying and first excited charmonium states of $^1S_0$, $^3S_1$, $^1P_1$, $^3P_0$ and $^3P_1$. The continuum limit is discussed by extrapolating from quenched simulations at four lattice spacings in the range 0.1 - 0.3 fm. Results are compared with the observed values in nature and other lattice approaches. Finite volume effects and dispersion relations are checked.Comment: 36 pages, 6 figur

Dirac-Born-Infeld Action on the Tachyon Kink and Vortex

The tachyon effective field theory describing the dynamics of a non-BPS D-brane in superstring theory has an infinitely thin but finite tension kink solution describing a codimension one BPS D-brane. We study the world-volume theory of massless modes on the kink, and show that the world volume action has precisely the Dirac-Born-Infeld (DBI) form without any higher derivative corrections. We generalize this to a vortex solution in the effective field theory on a brane-antibrane pair. As in the case of the kink, the vortex is infinitely thin, has finite energy density, and the world-volume action on the vortex is again given exactly by the DBI action on a BPS D-brane. We also discuss the coupling of fermions and restoration of supersymmetry and $\kappa$-symmetry on the world-volume of the kink. Absence of higher derivative corrections to the DBI action on the soliton implies that all such corrections are related to higher derivative corrections to the original effective action on the world-volume of a non-BPS D-brane or brane-antibrane pair.Comment: LaTeX file, 34 pages; references and other minor comments adde

Influence of shear flow on vesicles near a wall: a numerical study

We describe the dynamics of three-dimensional fluid vesicles in steady shear flow in the vicinity of a wall. This is analyzed numerically at low Reynolds numbers using a boundary element method. The area-incompressible vesicle exhibits bending elasticity. Forces due to adhesion or gravity oppose the hydrodynamic lift force driving the vesicle away from a wall. We investigate three cases. First, a neutrally buoyant vesicle is placed in the vicinity of a wall which acts only as a geometrical constraint. We find that the lift velocity is linearly proportional to shear rate and decreases with increasing distance between the vesicle and the wall. Second, with a vesicle filled with a denser fluid, we find a stationary hovering state. We present an estimate of the viscous lift force which seems to agree with recent experiments of Lorz et al. [Europhys. Lett., vol. 51, 468 (2000)]. Third, if the wall exerts an additional adhesive force, we investigate the dynamical unbinding transition which occurs at an adhesion strength linearly proportional to the shear rate.Comment: 17 pages (incl. 10 figures), RevTeX (figures in PostScript

Confinement Effects in Antiferromagnets

Phase equilibrium in confined Ising antiferromagnets was studied as a function of the coupling (v) and a magnetic field (h) at the surfaces, in the presence of an external field H. The ground state properties were calculated exactly for symmetric boundary conditions and nearest-neighbor interactions, and a full zero-temperature phase diagram in the plane v-h was obtained for films with symmetry-preserving surface orientations. The ground-state analysis was extended to the H-T plane using a cluster-variation free energy. The study of the finite-T properties (as a function of v and h) reveals the close interdependence between the surface and finite-size effects and, together with the ground-state phase diagram, provides an integral picture of the confinement in anisotropic antiferromagnets with surfaces that preserve the symmetry of the order parameter.Comment: 10 pages, 8 figures, Accepted in Phys. Rev.

Chemostratigraphy of Neoproterozoic carbonates: implications for 'blind dating'

The delta C-13(carb) and Sr-87/Sr-86 secular variations in Neoproteozoic seawater have been used for the purpose of 'isotope stratigraphy' but there are a number of problems that can preclude its routine use. In particular, it cannot be used with confidence for 'blind dating'. The compilation of isotopic data on carbonate rocks reveals a high level of inconsistency between various carbon isotope age curves constructed for Neoproteozoic seawater, caused by a relatively high frequency of both global and local delta C-13(carb) fluctuations combined with few reliable age determinations. Further complication is caused by the unresolved problem as to whether two or four glaciations, and associated negative delta C-13(carb) excursions, can be reliably documented. Carbon isotope stratigraphy cannot be used alone for geological correlation and 'blind dating'. Strontium isotope stratigraphy is a more reliable and precise tool for stratigraphic correlations and indirect age determinations. Combining strontium and carbon isotope stratigraphy, several discrete ages within the 590-544 Myr interval, and two age-groups at 660-610 and 740-690 Myr can be resolved

Semiparametric theory and empirical processes in causal inference

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory gives a framework for benchmarking efficiency and constructing estimators in such settings. In the second part of the paper we discuss empirical process theory, which provides powerful tools for understanding the asymptotic behavior of semiparametric estimators that depend on flexible nonparametric estimators of nuisance functions. These tools are crucial for incorporating machine learning and other modern methods into causal inference analyses. We conclude by examining related extensions and future directions for work in semiparametric causal inference

Sequential design of computer experiments for the estimation of a probability of failure

This paper deals with the problem of estimating the volume of the excursion set of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold, under a probability measure on $\mathbb{R}^d$ that is assumed to be known. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of $f$ and aim at performing evaluations of $f$ as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.Comment: This is an author-generated postprint version. The published version is available at http://www.springerlink.co