Heterochromatic paths in edge colored graphs without small cycles and heterochromatic-triangle-free graphs

Conditions for the existence of heterochromatic Hamiltonian paths and cycles in edge colored graphs are well investigated in literature. A related problem in this domain is to obtain good lower bounds for the length of a maximum heterochromatic path in an edge colored graph G. This problem is also well explored by now and the lower bounds are often specified as functions of the minimum color degree of G - the minimum number of distinct colors occurring at edges incident to any vertex of G - denoted by v(G). Initially, it was conjectured that the lower bound for the length of a maximum heterochromatic path for an edge colored graph G would be 2v(G)/3]. Chen and Li (2005) showed that the length of a maximum heterochromatic path in an edge colored graph G is at least v(G) - 1, if 1 <= v(G) <= 7, and at least 3v(G)/5] + 1 if v(G) >= 8. They conjectured that the tight lower bound would be v(G) - 1 and demonstrated some examples which achieve this bound. An unpublished manuscript from the same authors (Chen, Li) reported to show that if v(G) >= 8, then G contains a heterochromatic path of length at least 120 + 1. In this paper, we give lower bounds for the length of a maximum heterochromatic path in edge colored graphs without small cycles. We show that if G has no four cycles, then it contains a heterochromatic path of length at least v(G) - o(v(G)) and if the girth of G is at least 4 log(2)(v(G)) + 2, then it contains a heterochromatic path of length at least v(G) - 2, which is only one less than the bound conjectured by Chen and Li (2005). Other special cases considered include lower bounds for the length of a maximum heterochromatic path in edge colored bipartite graphs and triangle-free graphs: for triangle-free graphs we obtain a lower bound of 5v(G)/6] and for bipartite graphs we obtain a lower bound of 6v(G)-3/7]. In this paper, it is also shown that if the coloring is such that G has no heterochromatic triangles, then G contains a heterochromatic path of length at least 13v(G)/17)]. This improves the previously known 3v(G)/4] bound obtained by Chen and Li (2011). We also give a relatively shorter and simpler proof showing that any edge colored graph G contains a heterochromatic path of length at least (C) 2015 Elsevier Ltd. All rights reserved.

Chemical-free graphene by unzipping carbon nanotubes using cryo-milling

Current paper reports synthesis of chemical free graphene by unzipping of the carbon nanotubes (CNTs) using high strain rate deformation at 150K. A specially designed cryomill operating at 150 K was used for the experiments. The mechanism of unzipping was further explored using molecular dynamics (MD) simulations. Both experimental and simulation results reveal two modes of unzipping through radial and shear loading. (C) 2015 Elsevier Ltd. All rights reserved.

Structural crossover from nonmodulated to long-period modulated tetragonal phase and anomalous change in ferroelectric properties in the lead-free piezoelectric Na1/2Bi1/2TiO3-BaTiO3

The highly complex structure-property interrelationship in the lead-free piezoelectric (x) Na1/2Bi1/2TiO3 - (1 - x) BaTiO3 is a subject of considerable contemporary debate. Using comprehensive x-ray, neutron diffraction, dielectric, and ferroelectric studies, we have shown the existence of a new criticality in this system at x = 0.80, i.e., well within the conventional tetragonal phase field. This criticality manifests as a nonmonotonic variation of the tetragonality and coercivity and is shown to be associated with a crossover from a nonmodulated tetragonal phase (for x < 0.8) to a long-period modulated tetragonal phase (for x > 0.80). It is shown that the stabilization of long-period modulation introduces a characteristic depolarization temperature in the system. While differing qualitatively from the two-phase model often suggested for the critical compositions of this system, our results support the view with regard to the tendency in perovskites to stabilize long-period modulated structures as a result of complex interplay of antiferrodistortive modes Bellaiche and Iniguez, Phys. Rev. B 88, 014104 ( 2013); Prosandeev, Wang, Ren, Iniguez, ands Bellaiche, Adv. Funct. Mater. 23, 234 (2013)].

Effect of a mesh on boundary layer transitions induced by free-stream turbulence and an isolated roughness element

Streamwise streaks, their lift-up and streak instability are integral to the bypass transition process. An experimental study has been carried out to find the effect of a mesh placed normal to the flow and at different wall-normal locations in the late stages of two transitional flows induced by free-stream turbulence (FST) and an isolated roughness element. The mesh causes an approximately 30% reduction in the free-stream velocity, and mild acceleration, irrespective of its wall-normal location. Interestingly, when located near the wall, the mesh suppresses several transitional events leading to transition delay over a large downstream distance. The transition delay is found to be mainly caused by suppression of the lift-up of the high-shear layer and its distortion, along with modification of the spanwise streaky structure to an orderly one. However, with the mesh well away from the wall, the lifted-up shear layer remains largely unaffected, and the downstream boundary layer velocity profile develops an overshoot which is found to follow a plane mixing layer type profile up to the free stream. Reynolds stresses, and the size and strength of vortices increase in this mixing layer region. This high-intensity disturbance can possibly enhance transition of the accelerated flow far downstream, although a reduction in streamwise turbulence intensity occurs over a short distance downstream of the mesh. However, the shape of the large-scale streamwise structure in the wall-normal plane is found to be more or less the same as that without the mesh.

Electric field induced short range to long range structural ordering and its influence on the Eu+3 photoluminescence in the lead-free ferroelectric Na1/2Bi1/2TiO3

Eu+3 was incorporated into the lattice of a lead-free ferroelectric Na1/2Bi1/2TiO3 (NBT) as per the nominal formula Na0.5Bi0.5-xEuxTiO3. This system was investigated with regard to the Eu+3 photoluminescence (PL) and structural behaviour as a function of composition and electric field. Electric field was found to irreversibly change the features in the PL spectra and also in the x-ray diffraction patterns below the critical composition x = 0.025. Detailed analysis revealed that below the critical composition, electric field irreversibly suppresses the structural heterogeneity inherent of the host matrix NBT and brings about a long range ferroelectric state with rhombohedral (R3c) distortion. It is shown that the structural disorder on the nano-scale opens a new channel for radiative transition which manifests as a new emission line branching off from the main D-5(0)-> F-7(0) line along with a concomitant change in the relative intensity of the other crystal field induced Stark lines with different J values. The study suggests that Eu+3 luminescence can be used to probe the relative degree of field induced structural ordering in relaxor ferroelectrics and also in high performance piezoelectric alloys where electric field couples very strongly with the lattice and structural degrees of freedom. (C) 2015 AIP Publishing LLC.

A Few Case Studies on the Correlation of Particle Network and Its Stability on the Ionic Conductivity of Solid-Liquid Composite Electrolytes

We discuss here the crucial role of the particle network and its stability on the long-range ion transport in solid liquid composite electrolytes. The solid liquid composite electrolytes chosen for the study here comprise nanometer sized silica (SiO2) particles having various surface chemical functionalities dispersed in nonaqueous lithium salt solutions, viz, lithium perchlorate (LiClO4) in two different polyethylene glycol based solvents. These systems constitute representative examples of an independent class of soft matter electrolytes known as ``soggy sand'' electrolytes, which have tremendous potential in diverse electrochemical devices. The oxide additive acts as a heterogeneous dopant creating free charge carriers and enhancing the local ion transport. For long-range transport, however, a stable spanning particle network is needed. Systematic experimental investigations here reveal that the spatial and time dependent characteristics of the particle network in the liquid solution are nontrivial. The network characteristics are predominantly determined by the chemical makeup of the electrolyte components and the chemical interactions between them. It is noteworthy that in this study the steady state macroscopic ionic conductivity and viscosity of the solid liquid composite electrolyte are observed to be greatly determined by the additive oxide surface chemical functionality, solvent chemical composition, and solvent dielectric constant.

Graphene scavenges free radicals to synergistically enhance structural properties in a gamma-irradiated polyethylene composite through enhanced interfacial interactions

A unique strategy for scavenging free radicals in situ on exposure to gamma irradiation in polyethylene (PE) nanocomposites is presented. Blends of ultra-high molecular weight PE and linear low-density PE (PEB) and their nanocomposites with graphene (GPEB) were prepared by melt mixing to develop materials for biomedical implants. The effect of gamma irradiation on the microstructure and mechanical properties was systematically investigated. The neat blend and the nanocomposite were subjected to gamma-ray irradiation in order to improve the interfacial adhesion between PE and graphene sheets. Structural and thermal characterization revealed that irradiation induced crosslinking and increased the crystallinity of the polymer blend. The presence of graphene further enhanced the crystallinity via crosslinks between the polymer matrix and the filler on irradiation. Graphene was found to scavenge free radicals as confirmed by electron paramagnetic resonance spectroscopy. Irradiation of graphene-containing polymer composites resulted in the largest increase in modulus and hardness compared to either irradiation or addition of graphene to PEB alone. This study provides new insight into the role of graphene in polymer matrices during irradiation and suggests that irradiated graphene-polymer composites could emerge as promising materials for use as articulating surfaces in biomedical implants.

EFFECT OF AGING ON IMPRESSION CREEP BEHAVIOR OF Pb-FREE SOLDERS

During service and/or storage, Sn-Ag-Cu (SAC) solder alloys are subjected to temperatures ranging from 0.4 to 0.8 Tm (where Tm is the melting temperature of SAC alloys), making them highly prone to significant microstructural coarsening. The microstructures of these low melting point alloys continuously evolve during service. This results in evolution of creep properties of the joint over time, thereby influencing the long-term reliability of microelectronic packages. Here, we study microstructure evolution and creep behavior of two Sn-Ag-Cu (SAC) alloys, namely Sn-3.0Ag-0.5Cu and Sn-1.0Cu-0.5Cu, isothermally aged at 150 degrees C for various lengths of time. Creep behavior of the two SAC solders after different aging durations was systematically studied using impression creep technique. The key microstructural features that evolve during aging are Ag3Sn particle size and inter-particle spacing. Creep results indicate that the creep rate increases considerably with increasing inter-particle spacing although the creep stress exponent and creep activation energy are independent of the aging history.

Interrelationship between Interphase Boundaries and Phase Contents near the Critical Compositions of Lead-Free Ferroelectric (Na0.5Bi0.5)TiO3-BaTiO3

Heterophase structures in lead-free perovskite-type ferroelectric solid solutions of (1 - z)(Na0.5Bi0.5)TiO3 - zBaTiO(3) are analysed for a few critical compositions near the morphotropic phase boundary (z = 0.05-0.07). Examples of the phase coexistence and elastic matching of the phases from different symmetry groups are considered to find optimum volume fractions of specific domain types and coexisting phases at the complete stress relief in two-phase samples. Some interrelations between these volume fractions are described using variants of the domain arrangement at changes in the composition and unit-cell parameters. The evaluated room-temperature volume fractions of the ferroelectric monoclinic (Cm symmetry) and tetragonal (P4mm symmetry) phases near the morphotropic phase boundary are in agreement with experimental data.

Template-free coordination-driven self-assembly of discrete hexanuclear prismatic cages employing half-sandwich octahedral Ru-2(II) acceptors and triimidazole donors

Coordination-driven self-assembly of dinuclear half-sandwich p-cymene ruthenium(II) complexes Ru-2(mu-eta(4)-C2O4)(CH3OH)(2)(eta(6)-p-cymene)(2)](O3SCF3)(2) (1a) and Ru-2(mu-eta(4)-C6H2O4)(CH3OH)(2)(eta(6)-p-cymene)(2)](O3SCF3)(2) (1b) separately with imidazole-based tritopic donors (L-1-L-2) in methanol yielded a series of hexanuclear 3+2] trigonal prismatic cages (2-5), respectively L-1 = 1,3,5-tris(imidazole-1-yl) benzene; L-2 = 4,4',4 `'-tris(imidazole-1-yl) triphenylamine]. All the self-assembled cages 2-5 were characterized by various spectroscopic techniques (multinuclear NMR, Infra-red and ESI-MS) and their sizes, shapes were obtained through geometry optimization using molecular mechanics universal force field (MMUFF) computation. Despite the possibility due to the free rotation of donor sites of imidazole ligands, of two different atropoisomeric prismatic cages (C-3h or C-s) and polymeric product, the self-selection of single (C(3)h) conformational isomeric cages as the only product is a noteworthy observation. (C) 2015 Elsevier B.V. All rights reserved.

Ferromagnetism and the effect of free charge carriers on electric polarization in the double perovskite Y2NiMnO6

The double perovskite Y2NiMnO6 displays ferromagnetic transition at T-c approximate to 81 K. The ferromagnetic order at low temperature is confirmed by the saturation value of magnetization (Ms) and also validated by the refined ordered magnetic moment values extracted from neutron powder diffraction data at 10 K. This way, the dominant Mn4+ and Ni2+ cationic ordering is confirmed. The cation-ordered P2(1)/n nuclear structure is revealed by neutron powder diffraction studies at 300 and 10 K. Analysis of the frequency-dependent dielectric constant and equivalent circuit analysis of impedance data take into account the bulk contribution to the total dielectric constant. This reveals an anomaly which coincides with the ferromagnetic transition temperature (T-c). Pyrocurrent measurements register a current flow with onset near T-c and a peak at 57 K that shifts with temperature ramp rate. The extrinsic nature of the observed pyrocurrent is established by employing a special protocol measurement. It is realized that the origin is due to reorientation of electric dipoles created by the free charge carriers and not by spontaneous electric polarization at variance with recently reported magnetism-driven ferroelectricity in this material.

Phase boundary at x=0.03 and its anomalous influence on the structure and properties in the lead-free piezoelectric (1-x)Na1/2Bi1/2TiO3-(x)BaTiO3

The complexity associated with local structures continues to pose challenges with regard to the understanding of the structure-property relationship in Na1/2Bi1/2TiO3-based lead-free piezoceramics. (1-x)Na1/2Bi1/2TiO3-(x)BaTiO3 is an extensively studied system because of its interesting piezoelectric properties. Recently, a room temperature phase boundary was reported at x = 0.03 in this system Ma et al., Adv. Funct. Mater. 23, 5261 (2013)]. In the present work we have examined this subtle phase boundary using x-ray diffraction, neutron diffraction, dielectric measurements as a function of composition (x < 0.06), temperature, and electric field. Our results show that this boundary separates an R3c + Cc-like structural state for x < 0.03 from an R3c+ cubiclike structural state for 0.03 <= x <= 0.05 in the unpoled specimens. This phase boundary is characterized by an anomalous reduction in the depolarization temperature, and a suppression of the tetragonal distortion of the high temperature P4bm phase. Our results also provide the clue to understand the pathway leading to the cubiclike structure of the critical composition x = 0.06, known for its highest piezoelectric response.

Relaxor ferroelectricity and electric-field-driven structural transformation in the giant lead-free piezoelectric (Ba,Ca)(Ti, Zr)O-3

There is great interest in lead-free (Ba0.85Ca0.15)(Ti0.90Zr0.10)O-3 (15/10BCTZ) because of its exceptionally large piezoelectric response Liu and Ren, Phys. Rev. Lett. 103, 257602 (2009)]. In this paper, we have analyzed the nature of: (i) crystallographic phase coexistence at room temperature, (ii) temperature-and field-induced phase transformation to throw light on the atomistic mechanisms associated with the large piezoelectric response of this system. A detailed temperature-dependent dielectric and lattice thermal expansion study proved that the system exhibits a weak dielectric relaxation, characteristic of a relaxor ferroelectric material on the verge of exhibiting a normal ferroelectric-paraelectric transformation. Careful structural analysis revealed that a ferroelectric state at room temperature is composed of three phase coexistences, tetragonal (P4mm)+ orthorhombic (Amm2) + rhombohedral (R3m). We also demonstrate that the giant piezoresponse is associated with a significant fraction of the tetragonal phase transforming to rhombohedral. It is argued that the polar nanoregions associated with relaxor ferroelectricity amplify the piezoresponse by providing an additional degree of intrinsic structural inhomogeneity to the system.

Efficient coupled polynomial interpolation scheme for out-of-plane free vibration analysis of curved beams

The performance of two curved beam finite element models based on coupled polynomial displacement fields is investigated for out-of-plane vibration of arches. These two-noded beam models employ curvilinear strain definitions and have three degrees of freedom per node namely, out-of-plane translation (v), out-of-plane bending rotation (theta(z)) and torsion rotation (theta(s)). The coupled polynomial interpolation fields are derived independently for Timoshenko and Euler-Bernoulli beam elements using the force-moment equilibrium equations. Numerical performance of these elements for constrained and unconstrained arches is compared with the conventional curved beam models which are based on independent polynomial fields. The formulation is shown to be free from any spurious constraints in the limit of `flexureless torsion' and `torsionless flexure' and hence devoid of flexure and torsion locking. The resulting stiffness and consistent mass matrices generated from the coupled displacement models show excellent convergence of natural frequencies in locking regimes. The accuracy of the shear flexibility added to the elements is also demonstrated. The coupled polynomial models are shown to perform consistently over a wide range of flexure-to-shear (EI/GA) and flexure-to-torsion (EI/GJ) stiffness ratios and are inherently devoid of flexure, torsion and shear locking phenomena. (C) 2015 Elsevier B.V. All rights reserved.

Electric field and temperature dependence of the local structural disorder in the lead-free ferroelectric Na0.5Bi0.5TiO3: An EXAFS study

The complex nature of the structural disorder in the lead-free ferroelectric Na1/2Bi1/2TiO3 has a profound impact on the perceived global structure and polar properties. In this paper, we have investigated the effect of electric field and temperature on the local structure around theBi and Ti atoms using extended x-ray absorption fine structure. Detailed analysis revealed that poling brings about a noticeable change in the bond distances associated with the Bi-coordination sphere, whereas the Ti coordination remains unaffected. We also observed discontinuity in the Bi-O bond lengths across the depolarization temperature of the poled specimen. These results establish that the disappearance of the monoclinic-like (Cc) global distortion, along with the drastic suppression of the short-ranged in-phase octahedral tilt after poling B. N. Rao et al., Phys. Rev. B 88, 224103 (2013)] is a result of the readjustment of theA-O bonds by the electric field, so as to be in conformity with the rhombohedral R3c structure.