The Gaussian process density sampler

We present the Gaussian Process Density Sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a fixed density function that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We can also infer the hyperparameters of the Gaussian process. We compare this density modeling technique to several existing techniques on a toy problem and a skullreconstruction task.

Imaging the femoral cortex: Thickness, density and mass from clinical CT

There is growing evidence that focal thinning of cortical bone in the proximal femur may predispose a hip to fracture. Detecting such defects in clinical CT is challenging, since cortices may be significantly thinner than the imaging system's point spread function. We recently proposed a model-fitting technique to measure sub-millimetre cortices, an ill-posed problem which was regularized by assuming a specific, fixed value for the cortical density. In this paper, we develop the work further by proposing and evaluating a more rigorous method for estimating the constant cortical density, and extend the paradigm to encompass the mapping of cortical mass (mineral mg/cm 2) in addition to thickness. Density, thickness and mass estimates are evaluated on sixteen cadaveric femurs, with high resolution measurements from a micro-CT scanner providing the gold standard. The results demonstrate robust, accurate measurement of peak cortical density and cortical mass. Cortical thickness errors are confined to regions of thin cortex and are bounded by the extent to which the local density deviates from the peak, averaging 20% for 0.5mm cortex. © 2012 Elsevier B.V.

Electronic and magnetic properties of Ti(2)O(3), Cr(2)O(3), and Fe(2)O(3) calculated by the screened exchange hybrid density functional.

The electronic and magnetic properties of the transition metal sesqui-oxides Cr(2)O(3), Ti(2)O(3), and Fe(2)O(3) have been calculated using the screened exchange (sX) hybrid density functional. This functional is found to give a band structure, bandgap, and magnetic moment in better agreement with experiment than the local density approximation (LDA) or the LDA+U methods. Ti(2)O(3) is found to be a spin-paired insulator with a bandgap of 0.22 eV in the Ti d orbitals. Cr(2)O(3) in its anti-ferromagnetic phase is an intermediate charge transfer Mott-Hubbard insulator with an indirect bandgap of 3.31 eV. Fe(2)O(3), with anti-ferromagnetic order, is found to be a wide bandgap charge transfer semiconductor with a 2.41 eV gap. Interestingly sX outperforms the HSE functional for the bandgaps of these oxides.

Density of photon states in dye-doped chiral nematic liquid crystal cells in the presence of losses and gain

We calculate the density of photon states (DOS) of the normal modes in dye-doped chiral nematic liquid crystal (LC) cells in the presence of various loss mechanisms. Losses and gain are incorporated into the transmission characteristics through the introduction of a small imaginary part in the dielectric constant perpendicular and along the director, for which we assume no frequency dispersion. Theoretical results are presented on the DOS in the region of the photonic band gap for a range of values of the loss coefficient and different values of the optical anisotropy. The obtained values of the DOS at the photonic band gap edges predict a reversal of the dominant modes in the structure. Our results are found to be in good agreement with the experimentally obtained excitation thresholds in chiral nematic LC lasers. The behavior of the DOS is also discussed for amplifying LC cells providing additional insight to the lasing mechanism of these structures. © 2012 American Physical Society.

Density of photon states in dye-doped chiral nematic liquid crystal cells in the presence of losses and gain.

We calculate the density of photon states (DOS) of the normal modes in dye-doped chiral nematic liquid crystal (LC) cells in the presence of various loss mechanisms. Losses and gain are incorporated into the transmission characteristics through the introduction of a small imaginary part in the dielectric constant perpendicular and along the director, for which we assume no frequency dispersion. Theoretical results are presented on the DOS in the region of the photonic band gap for a range of values of the loss coefficient and different values of the optical anisotropy. The obtained values of the DOS at the photonic band gap edges predict a reversal of the dominant modes in the structure. Our results are found to be in good agreement with the experimentally obtained excitation thresholds in chiral nematic LC lasers. The behavior of the DOS is also discussed for amplifying LC cells providing additional insight to the lasing mechanism of these structures.

A priori assessment of algebraic flame surface density models in the context of large eddy simulation for nonunity lewis number flames in the thin reaction zones regime

The performance of algebraic flame surface density (FSD) models has been assessed for flames with nonunity Lewis number (Le) in the thin reaction zones regime, using a direct numerical simulation (DNS) database of freely propagating turbulent premixed flames with Le ranging from 0.34 to 1.2. The focus is on algebraic FSD models based on a power-law approach, and the effects of Lewis number on the fractal dimension D and inner cut-off scale η i have been studied in detail. It has been found that D is strongly affected by Lewis number and increases significantly with decreasing Le. By contrast, η i remains close to the laminar flame thermal thickness for all values of Le considered here. A parameterisation of D is proposed such that the effects of Lewis number are explicitly accounted for. The new parameterisation is used to propose a new algebraic model for FSD. The performance of the new model is assessed with respect to results for the generalised FSD obtained from explicitly LES-filtered DNS data. It has been found that the performance of the most existing models deteriorates with decreasing Lewis number, while the newly proposed model is found to perform as well or better than the most existing algebraic models for FSD. © 2012 Mohit Katragadda et al.

Effects of turbulent reynolds number on the performance of algebraic flame surface density models for large eddy simulation in the thin reaction zones regime: A direct numerical simulation analysis

A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different turbulent Reynolds numbers has been used to assess the performance of algebraic flame surface density (FSD) models based on a fractal representation of the flame wrinkling factor. The turbulent Reynolds number Ret has been varied by modifying the Karlovitz number Ka and the Damköhler number Da independently of each other in such a way that the flames remain within the thin reaction zones regime. It has been found that the turbulent Reynolds number and the Karlovitz number both have a significant influence on the fractal dimension, which is found to increase with increasing Ret and Ka before reaching an asymptotic value for large values of Ret and Ka. A parameterisation of the fractal dimension is presented in which the effects of the Reynolds and the Karlovitz numbers are explicitly taken into account. By contrast, the inner cut-off scale normalised by the Zel'dovich flame thickness ηi/δz does not exhibit any significant dependence on Ret for the cases considered here. The performance of several algebraic FSD models has been assessed based on various criteria. Most of the algebraic models show a deterioration in performance with increasing the LES filter width. © 2012 Mohit Katragadda et al.

Direct simulation of turbulent entrainment due to a plume impinging on a density interface

The law for turbulent entrainment due to plumes and jets impinging on a density interface is subject to significant uncertainty, with reported differences in entrainment rates up to a factor of 10. We report preliminary results obtained by Direct Numerical Simulation which are part of a PRACE project on turbulent entrainment carried out on JUGENE at Jülich, Germany. Various interface tracking methods are discussed and the entrainment coefficient is determined.

Density stratified environments: The double-tank method

We present an alternative method of producing density stratifications in the laboratory based on the 'double-tank' method proposed by Oster (Sci Am 213:70-76, 1965). We refer to Oster's method as the 'forced-drain' approach, as the volume flow rates between connecting tanks are controlled by mechanical pumps. We first determine the range of density profiles that may be established with the forced-drain approach other than the linear stratification predicted by Oster. The dimensionless density stratification is expressed analytically as a function of three ratios: the volume flow rate ratio n, the ratio of the initial liquid volumes λ and the ratio of the initial densities ψ. We then propose a method which does not require pumps to control the volume flow rates but instead allows the connecting tanks to drain freely under gravity. This is referred to as the 'free-drain' approach. We derive an expression for the density stratification produced and compare our predictions with saline stratifications established in the laboratory using the 'free-drain' extension of Oster's method. To assist in the practical application of our results we plot the region of parameter space that yield concave/convex or linear density profiles for both forced-drain and free-drain approaches. The free-drain approach allows the experimentalist to produce a broad range of density profiles by varying the initial liquid depths, cross-sectional and drain opening areas of the tanks. One advantage over the original Oster approach is that density profiles with an inflexion point can now be established. © 2008 Springer-Verlag.