First Principles Calculations of Ionic Vibrational Frequencies in PbMg1/3Nb2/3O3

Lattice dynamics for several ordered supercells with composition PbMg1/3Nb2/3O (PMN) were calculated with first-principles frozen phonon methods. Nominal symmetries of the supercells studied are reduced by lattice instabilities. Lattice modes corresponding to these instabilities, equilibrium ionic positions, and infrared (IR) reflectivity spectra are reported.Comment: 6 pages; Fundamental physics of Ferroelectrics 200

Diffusion of Point Defects in Two-Dimensional Colloidal Crystals

We report the first study of the dynamics of point defects, mono and di-vacancies, in a confined 2-D colloidal crystal in real space and time using digital video microscopy. The defects are introduced by manipulating individual particles with optical tweezers. The diffusion rates are measured to be $D_{mono}/a^{2}\cong3.27\pm0.03$Hz for mono-vacancies and $D_{di}/a^{2}\cong3.71\pm0.03$Hz for di-vacancies. The elementary diffusion processes are identified and it is found that the diffusion of di-vacancies is enhanced by a \textit{dislocation dissociation-recombination} mechanism. Furthermore, the defects do not follow a simple random walk but their hopping exhibits memory effects, due to the reduced symmetry (compared to the triangular lattice) of their stable configurations, and the slow relaxation rates of the lattice modes.Comment: 6 pages (REVTEX), 5 figures (PS

Building effective models from sparse but precise data

A common approach in computational science is to use a set of of highly precise but expensive calculations to parameterize a model that allows less precise, but more rapid calculations on larger scale systems. Least-squares fitting on a model that underfits the data is generally used for this purpose. For arbitrarily precise data free from statistic noise, e.g. ab initio calculations, we argue that it is more appropriate to begin with a ensemble of models that overfit the data. Within a Bayesian framework, a most likely model can be defined that incorporates physical knowledge, provides error estimates for systems not included in the fit, and reproduces the original data exactly. We apply this approach to obtain a cluster expansion model for the Ca[Zr,Ti]O3 solid solution.Comment: 10 pages, 3 figures, submitted to Physical Review Letter

Exact Solution of an Octagonal Random Tiling Model

We consider the two-dimensional random tiling model introduced by Cockayne, i.e. the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons. At the appropriate relative densities the correlations have eight-fold rotational symmetry. We reformulate the model in terms of a random tiling ensemble with identical rectangles and isosceles triangles. The partition function of this model can be calculated by diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations can be solved providing {\em exact} values of the entropy and elastic constants.Comment: 4 pages,3 Postscript figures, uses revte

Enhancement of piezoelectricity in a mixed ferroelectric

We use first-principles density-functional total energy and polarization calculations to calculate the piezoelectric tensor at zero temperature for both cubic and simple tetragonal ordered supercells of Pb_3GeTe_4. The largest piezoelectric coefficient for the tetragonal configuration is enhanced by a factor of about three with respect to that of the cubic configuration. This can be attributed to both the larger strain-induced motion of cations relative to anions and higher Born effective charges in the tetragonal case. A normal mode decomposition shows that both cation ordering and local relaxation weaken the ferroelectric instability, enhancing piezoelectricity.Comment: 5 pages, revtex, 2 eps figure

Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment

The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of state-estimation for the liquid suspension can be posed as a time-evolving inverse problem and solved with Bayesian statistical methods. In this article, we extend Bayesian methods to incorporate statistical models for the error that is incurred in the numerical solution of the physical governing equations. This enables full uncertainty quantification within a principled computation-precision trade-off, in contrast to the over-confident inferences that are obtained when all sources of numerical error are ignored. The method is cast within a sequential Monte Carlo framework and an optimized implementation is provided in Python

Vegetation and peat characteristics of restiad bogs on Chatham Island (Rekohu), New Zealand

Restiad bogs dominated by Sporadanthus traversii on Chatham Island, New Zealand, were sampled to correlate vegetation patterns and peat properties, and to compare with restiad systems dominated by Sporadanthus ferrugineus and Empodisma minus in the Waikato region, North Island, New Zealand. Classification and ordination resulted in five groups that reflected a disturbance gradient. The largest S. traversii group, which comprised plots from central, relatively intact bogs, had the lowest levels of total nitrogen (mean 1.20 mg cm-3), total phosphorus (mean 0.057 mg cm-3), total potassium (mean 0.083 mg cm-3), and available phosphorus (mean 18.6 μg cm-3). Modification by drainage, stock, and fires resulted in a decline of S. traversii and an increase of Gleichenia dicarpa fern cover, together with elevated peat nutrient levels and higher bulk density. Compared with peat dominated by Sporadanthus ferrugineus or Empodisma minus in relatively unmodified Waikato restiad bogs, Chatham Island peat under S. traversii has significantly higher total potassium, total nitrogen, available phosphorus, bulk density, and von Post decomposition indices, and significantly lower pH. Sporadanthus traversii and Empodisma minus have similar ecological roles in restiad bog development, occupying a relatively wide nutrient range, and regenerating readily from seed after fire. Despite differences in root morphology, S. traversii and E. minus are the major peat formers in raised restiad bogs on Chatham Island and in Waikato, respectively, and could be regarded as ecological equivalents