LAPW vs. LMTO full-potential simulations and anharmonic dynamics of KNbO3

With the aim to get an insight in the origin of differences in the earlier reported calculation results for KNbO3 and to test the recently proposed implementation of the FP-LMTO method by Methfessel and van Schilfgaarde, we perform a comparative study of the ferroelectric instability in KNbO3 by FP-LMTO and LAPW methods. It is shown that a high precision in the description of the charge density variations over the interstitial region in perovskite materials is essential; the technical limitations of the accuracy of charge-density description apparently accounted for previously reported slight disagreement with the LAPW results. With more accurate description of the charge density by sufficiently fine real-space grid, the results obtained by both methods became almost identical. In order to extract additional information (beyond the harmonic approximation) from the total energy fit obtainable in total-energy calculations, a scheme is proposed to solve the multidimensional vibrational Schroedinger equation in the model of non-interacting anharmonic oscillators via the expansion in hyperspherical harmonics.Comment: 11 pages, 2 figures, uses aipproc.sty. Presented at the Fifth Williamsburg Workshop on First-Principles Calculations for Ferroelectric

Primary gamma ray selection in a hybrid timing/imaging Cherenkov array

This work is a methodical study on hybrid reconstruction techniques for hybrid imaging/timing Cherenkov observations. This type of hybrid array is to be realized at the gamma-observatory TAIGA intended for very high energy gamma-ray astronomy (>30 TeV). It aims at combining the cost-effective timing-array technique with imaging telescopes. Hybrid operation of both of these techniques can lead to a relatively cheap way of development of a large area array. The joint approach of gamma event selection was investigated on both types of simulated data: the image parameters from the telescopes, and the shower parameters reconstructed from the timing array. The optimal set of imaging parameters and shower parameters to be combined is revealed. The cosmic ray background suppression factor depending on distance and energy is calculated. The optimal selection technique leads to cosmic ray background suppression of about 2 orders of magnitude on distances up to 450 m for energies greater than 50 TeV.Comment: 4 pages, 5 figures; proceedings of the 19th International Symposium on Very High Energy Cosmic Ray Interactions (ISVHECRI 2016

The Discrete Fundamental Group of the Associahedron, and the Exchange Module

The associahedron is an object that has been well studied and has numerous applications, particularly in the theory of operads, the study of non-crossing partitions, lattice theory and more recently in the study of cluster algebras. We approach the associahedron from the point of view of discrete homotopy theory. We study the abelianization of the discrete fundamental group, and show that it is free abelian of rank $\binom{n+2}{4}$. We also find a combinatorial description for a basis of this rank. We also introduce the exchange module of the type $A_n$ cluster algebra, used to model the relations in the cluster algebra. We use the discrete fundamental group to the study of exchange module, and show that it is also free abelian of rank $\binom{n+2}{3}$.Comment: 16 pages, 4 figure