Magnetic and orbital order in overdoped bilayer manganites

The magnetic and orbital orders for the bilayer manganites in the doping region $0.5 < x <1.0$ have been investigated from a model that incorporates the two $e_g$ orbitals at each Mn site, the inter-orbital Coulomb interaction and lattice distortions. The usual double exchange operates via the $e_g$ orbitals. It is shown that such a model reproduces much of the phase diagram recently obtained for the bilayer systems in this range of doping. The C-type phase with ($\pi,0,\pi$) spin order seen by Ling et al. appears as a natural consequence of the layered geometry and is stabilised by the static distortions of the system. The orbital order is shown to drive the magnetic order while the anisotropic hopping across the $e_g$ orbitals, layered nature of the underlying structure and associated static distortions largely determine the orbital arrangements.Comment: 8 pages, 5 figure

Adaptive Seeding for Gaussian Mixture Models

We present new initialization methods for the expectation-maximization algorithm for multivariate Gaussian mixture models. Our methods are adaptions of the well-known $K$-means++ initialization and the Gonzalez algorithm. Thereby we aim to close the gap between simple random, e.g. uniform, and complex methods, that crucially depend on the right choice of hyperparameters. Our extensive experiments indicate the usefulness of our methods compared to common techniques and methods, which e.g. apply the original $K$-means++ and Gonzalez directly, with respect to artificial as well as real-world data sets.Comment: This is a preprint of a paper that has been accepted for publication in the Proceedings of the 20th Pacific Asia Conference on Knowledge Discovery and Data Mining (PAKDD) 2016. The final publication is available at link.springer.com (http://link.springer.com/chapter/10.1007/978-3-319-31750-2 24

Density functional theory in one-dimension for contact-interacting fermions

A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for short-ranged interactions. The exact-exchange contribution to the total energy is a local functional of the density. A local density approximation for correlation is obtained using perturbation theory and Bethe-Ansatz results for the one-dimensional contact-interacting uniform Fermi gas. The ground-state energies are calculated for two finite systems, the analogs of Helium and of Hooke's atom. The local approximation is shown to be excellent, as expected.Comment: 10 pages, 7 Figure

Applications of Image Reconstruction in NDE

The nondestructive evaluation (NDE) of materials often involves the solution of an inverse problem. It is shown that image reconstruction techniques lead to the direct solution of the 3-D inverse problem when radiographic measurements are made. In particular, it is suggested that the convolve-and-backproject solution to the 3-D divergent ray geometry problem should be useful for NDE. There is also a discussion of the accept-reject criteria appropriate for various classes of defects

Semiclassical Electron Correlation in Density-Matrix Time-Propagation

Lack of memory (locality in time) is a major limitation of almost all present time-dependent density functional approximations. By using semiclassical dynamics to compute correlation effects within a density-matrix functional approach, we incorporate memory, including initial-state dependence, as well as changing occupation numbers, and predict more observables in strong-field applications.Comment: 4.5 pages, 1 figur

Predator-prey ecosystem with group defence in prey against generalist predator

In this paper, we proposed a population model depicting the dynamics of a prey showing group defence against a generalist predator. The group defence characteristic is represented by Hassell-Varley functional response. We studied the local and global stability and behaviour of the model around the co-existent equilibrium solution. Analysis on Hopf bifurcation and power spectra has also been done. Numerical simulations have been done to confirm the obtained analytical results as well as to validate the proposed model