Nodal domains of the equilateral triangle billiard

We characterize the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns of the eigenfunctions follow a group-theoretic connection in a way that makes them predictable as one goes from one state to another. Extensive numerical investigations bring out the distribution functions of the mode number and signed areas. The statistics of the boundary intersections is also treated analytically. Finally, the distribution functions of the nodal loop count and the nodal counting function are shown to contain information about the classical periodic orbits using the semiclassical trace formula. We believe that the results belong generically to non-separable systems, thus extending the previous works which are concentrated on separable and chaotic systems.

Ferroelectric and optical properties of Ba5Li2Ti2Nb8O30 ceramics potential for memory applications

Giant grained (42 mu m) translucent Ba5Li2Ti2Nb8O30 ceramic was fabricated by conventional sintering technique using the powders obtained via solid state reaction route. These samples were confirmed to possess tetragonal tungsten bronze structure (P4bm) at room temperature. The scanning electron microscopy established the average grain size to be close to 20 mu m. The photoluminescence studies carried out on these ceramics indicated sharp emission bands around 433 and 578 nm at an excitation wavelength of 350 nm which were attributed to band-edge emission as the band gap was 2.76 eV determined by Kubelka-Munk function. The dielectric properties of these ceramics were studied over wide frequency range (100-1 MHz) at room temperature. The decrease in dielectric constant with frequency could be explained on the basis of Koops theory. The dielectric constant and the loss were found to decrease with increasing frequency. The Curie temperature was confirmed to be similar to 370 A degrees C based on the dielectric anomaly observed when these measurements were carried out over a temperature range of 30-500 A degrees C. This shows a deviation from Curie-Weiss behaviour and hence an indicator of the occurrence of disordering in the system, the gamma = 1.23 which confirms the diffuse ferroelectric transition. These ceramics at room temperature exhibited P-E hysteresis loops, though not well saturated akin to that of their single crystalline counterparts. These are the suitable properties for ferroelectric random access memory applications.

Model domains in C-3 with abelian automorphism group

It is shown that every hyperbolic rigid polynomial domain in C-3 of finite-type, with abelian automorphism group is equivalent to a domain that is balanced with respect to some weight.

Phase transformation, improved ferroelectric and magnetic properties of (1-x) BiFeO3-xPb(Zr0.52Ti0.48)O-3 solid solutions

The authors prepared (1 - x) BiFeO3 - (x)Pb(Zr0.52Ti0.48)O-3 for x <= 0.30 by sol-gel method and investigated the material's structures, magnetic and electrical properties. Detailed Rietveld analysis of X-ray diffraction data revealed that the system retains distorted rhombohedral R3c structure for x <= 0.10 but transforms to monoclinic (Cc) structure for x > 0.10. Disappearance of some Raman modes corresponding to A1 modes and the decrease in the intensities of the remaining A1 modes with increasing x in the Raman spectra, which is a clear indication of structural modification and symmetry changes brought about by PZT doping. Enhanced magnetization with PZT doping content may be attributed to the gradual change and destruction in the spin cycloid structure of BiFeO3. The leakage current density at 3.5 kV/cm was reduced by approximately three orders of magnitude by doping PZT (x = 0.30), compared with BFO ceramics. (C) 2014 AIP Publishing LLC.

Process induced electroactive beta-polymorph in PVDF: effect on dielectric and ferroelectric properties

The effects of various processing conditions, like annealing, poling, mechanical rolling and their combinations, on the dielectric and ferroelectric properties of PVDF poly(vinylidene fluoride)] were systematically studied in this work. Further, the effect of processing sequence on the structure and properties was investigated. While all the processing conditions adopted here resulted in phase transformation of the alpha- to electroactive beta-polymorph in PVDF, the fraction of beta-phase developed was observed to be strongly contingent on the adopted process. The transformation of alpha- to electroactive beta-polymorph was determined by X-ray diffraction and FTIR. The neat PVDF showed only beta-phase, whereas mechanically rolled samples exhibited the highest ca. 85% beta-phase in PVDF. Both the permittivity and the loss tangent decreased in the samples which had undergone different processing conditions. The polarization-electric field (P-E) loops for all the samples were evaluated. Interestingly, the energy density, estimated from the electrical displacement-electric field (D-E) loops, was observed to be highest for the poled samples which were initially rolled. The results indicate that various processing conditions can influence the dielectric and the ferroelectric properties differently.

Ferroelectric phase coexistence by crystallite size reduction in BiFeO3-PbTiO3

Size effect in ferroelectrics has been extensively investigated in the past with the general consensus that the long-range ferroelectric ordering gradually disappears with decreasing crystallite size, eventually leading to the paraelectric state. In this paper, we show that the compositions exhibiting giant tetragonality (c/a similar to 1.18) of the ferroelectric alloy system BiFeO3-PbTiO3 transform from a pure tetragonal phase to a state comprising tetragonal and rhombohedral phases as the average crystallite size is reduced from similar to 10 to similar to 1 mu m. It is argued that the increased surface energy in the smaller sized crystallites creates an equivalent compressive stress that drives the system towards tetragonal-rhombohedral criticality.

Trace Formulae for Curvature of Jet Bundles over Planar Domains

For a domain Omega in C and an operator T in B-n(Omega), Cowen and Douglas construct a Hermitian holomorphic vector bundle E-T over Omega corresponding to T. The Hermitian holomorphic vector bundle E-T is obtained as a pull-back of the tautological bundle S(n, H) defined over by Gr(n, H) a nondegenerate holomorphic map z bar right arrow ker(T - z), z is an element of Omega. To find the answer to the converse, Cowen and Douglas studied the jet bundle in their foundational paper. The computations in this paper for the curvature of the jet bundle are rather intricate. They have given a set of invariants to determine if two rank n Hermitian holomorphic vector bundle are equivalent. These invariants are complicated and not easy to compute. It is natural to expect that the equivalence of Hermitian holomorphic jet bundles should be easier to characterize. In fact, in the case of the Hermitian holomorphic jet bundle J(k)(L-f), we have shown that the curvature of the line bundle L-f completely determines the class of J(k)(L-f). In case of rank Hermitian holomorphic vector bundle E-f, We have calculated the curvature of jet bundle J(k)(E-f) and also obtained a trace formula for jet bundle J(k)(E-f).

Grain and the concomitant ferroelectric domain size dependent physical properties of Ba0.85Ca0.15Zr0.1Ti0.9O3 ceramics fabricated using powders derived from oxalate precursor route

Fine powders comprising nanocrystallites of Ba0.85Ca0.15Zr0.1Ti0.9O3 (BCZT) were synthesized via oxalate precursor method, which facilitated to obtain homogenous and large grain sized ceramics at a lower sintering temperature. The compacted powders were sintered at various temperatures in the range of 1200 degrees C-1500 degrees C for an optimized duration of 10 h. Interestingly the one that was sintered at 1450 degrees C/10 h exhibited well resolved Morphotrophic Phase Boundary. The average grain size associated with this sample was 30 mu m accompanied by higher domain density mostly with 90 degrees twinning. These were believed to have significant contribution towards obtaining large strain of about 0.2% and piezoelectric coefficient as high as 563 pC/N. The maximum force that was generated by BCZT ceramic (having 30 mu m grain size) was found to be 161 MPa, which is much higher than that of known actuator materials such as PZT (40MPa) and NKN-5-LT (7 MPa). (C) 2014 AIP Publishing LLC.

Room temperature ferromagnetic and ferroelectric properties of Bi1-xCaxMnO3 thin films

Bi1-xCaxMnO3 (BCMO) thin films with x = 0, 0.1, 0.2, 0.3 and 0.4 are successfully deposited on the n-type Si (100) substrate at two different temperatures of 400 degrees C and 800 degrees C using RF magnetron sputtering. The stoichiometry of the films and oxidation state of the elements have been described by X-ray photoelectron spectroscopy analysis. Dielectric measurement depicts the insulating property of BCMO films. Magnetic and ferroelectric studies confirm the significant enhancement in spin orientation as well as electric polarization at room temperature due to incorporation of Ca2+ ions into BiMnO3 films. The BCMO (x = 0.2) film grown at 400 degrees C shows better magnetization (M-sat) and polarization (P-s) with the measured values of 869 emu / cc and 6.6 mu(C)/cm(2) respectively than the values of the other prepared films. Thus the realization of room temperature ferromagnetic and ferroelectric ordering in Ca2+ ions substituted BMO films makes potentially interesting for spintronic device applications. (C) 2014 Author(s).

PROPER HOLOMORPHIC MAPS BETWEEN BOUNDED SYMMETRIC DOMAINS REVISITED

We prove that a proper holomorphic map between two nonplanar bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the various special cases in which this result is known. We discuss an application of these methods to domains having noncompact automorphism groups that are not assumed to act transitively.

Ferroelectric instabilities and enhanced piezoelectric response in Ce modified BaTiO3 lead-free ceramics

The crystal structure, ferroelectric, and piezoelectric behaviors of the Ba(Ti1-xCex)O-3 solid solution have been investigated at close composition intervals in the dilute concentration regime. Ce concentration as low as 2 mol. % induces tetragonal-orthorhombic instability and coexistence of the phases, leading to enhanced high-field strain and direct piezoelectric response. Detailed structural analysis revealed tetragonal + orthorhombic phase coexistence for x = 0.02, orthorhombic for 0.03 <= x <= 0.05, and orthorhombic + rhombohedral for 0.06 <= x <= 0.08. The results suggest that Ce-modified BaTiO3 is a potential lead-free piezoelectric material. (C) 2015 AIP Publishing LLC.

Quadrature Domains in C-n

We prove two density theorems for quadrature domains in , . It is shown that quadrature domains are dense in the class of all product domains of the form , where is a smoothly bounded domain satisfying Bell's Condition R and is a smoothly bounded domain and also in the class of all smoothly bounded complete Hartogs domains in C-2.

Metastable monoclinic and orthorhombic phases and electric field induced irreversible phase transformation at room temperature in the lead-free classical ferroelectric BaTiO3

For decades it has been a well-known fact that among the few ferroelectric compounds in the perovskite family, namely, BaTiO3, KNbO3, PbTiO3, and Na1/2Bi1/2TiO3, the dielectric and piezoelectric properties of BaTiO3 are considerably higher than the others in polycrystalline form at room temperature. Further, similar to ferroelectric alloys exhibiting morphotropic phase boundary, single crystals of BaTiO3 exhibit anomalously large piezoelectric response when poled away from the direction of spontaneous polarization at room temperature. These anomalous features in BaTiO3 remained unexplained so far from the structural standpoint. In this work, we have used high-resolution synchrotron x-ray powder diffraction, atomic resolution aberration-corrected transmission electron microscopy, in conjunction with a powder poling technique, to reveal that at 300 K (i) the equilibrium state of BaTiO3 is characterized by coexistence of metastable monoclinic Pm and orthorhombic (Amm2) phases along with the tetragonal phase, and (ii) strong electric field switches the polarization direction from the 001] direction towards the 101] direction. These results suggest that BaTiO3 at room temperature is within an instability regime, and that this instability is the fundamental factor responsible for the anomalous dielectric and piezoelectric properties of BaTiO3 as compared to the other homologous ferroelectric perovskite compounds at room temperature. Pure BaTiO3 at room temperature is therefore more akin to lead-based ferroelectric alloys close to the morphotropic phase boundary where polarization rotation and field induced ferroelectric-ferroelectric phase transformations play a fundamental role in influencing the dielectric and piezoelectric behavior.

Preferential polarization and its reversal in polycrystalline BiFeO3/La0.5Sr0.5CoO3 heterostructures

Polycrystalline BiFeO3 thin films were grown on La0.5Sr0.5CoO3 buffered Pt (200)/TiO2/SiO2/Si substrates under different oxygen partial pressures (10, 25, 50 and 100 mTorr) by puked laser ablation. Piezo-response Force Microscopy and Piezo-Force Spectroscopy have shown that all the films are ferroelectric in nature with locally switchable domains. It has also revealed a preferential downward domain orientation in as-grown films grown under lower oxygen partial pressure (10 and 25 mTorr) with a reversal of preferential domain orientation as the oxygen partial pressure is increased to 100 mTorr during laser ablation. Such phenomena are atypical of multi-grained polycrystalline ferroelectric films and have been discussed On the basis of detect formation with changing growth conditions. For the 50 mTorr grown film, asymmetric domain stability and retention during write-read studies has been observed which is attributed to grain-size-related defect concentration, affecting pinning centres that inhibit domain wall motion. (C) 2015 Elsevier Ltd. All rights reserved.

The beta hairpin structure within ribosomal protein S5 mediates interplay between domains II and IV and regulates HCV IRES function

Translation initiation in Hepatitis C Virus (HCV) is mediated by Internal Ribosome Entry Site (IRES), which is independent of cap-structure and uses a limited number of canonical initiation factors. During translation initiation IRES-40S complex formation depends on high affinity interaction of IRES with ribosomal proteins. Earlier, it has been shown that ribosomal protein S5 (RPS5) interacts with HCV IRES. Here, we have extensively characterized the HCV IRES-RPS5 interaction and demonstrated its role in IRES function. Computational modelling and RNA-protein interaction studies demonstrated that the beta hairpin structure within RPS5 is critically required for the binding with domains II and IV. Mutations disrupting IRES-RPS5 interaction drastically reduced the 80S complex formation and the corresponding IRES activity. Computational analysis and UV cross-linking experiments using various IRES-mutants revealed interplay between domains II and IV mediated by RPS5. In addition, present study demonstrated that RPS5 interaction is unique to HCV IRES and is not involved in 40S-3 ` UTR interaction. Further, partial silencing of RPS5 resulted in preferential inhibition of HCV RNA translation. However, global translation was marginally affected by partial silencing of RPS5. Taken together, results provide novel molecular insights into IRES-RPS5 interaction and unravel its functional significance in mediating internal initiation of translation.