UNIQUENESS OF SOLUTIONS TO SCHRODINGER EQUATIONS ON H-TYPE GROUPS

This paper deals with the Schrodinger equation i partial derivative(s)u(z, t; s) - Lu(z, t; s) = 0; where L is the sub-Laplacian on the Heisenberg group. Assume that the initial data f satisfies vertical bar f(z, t)vertical bar less than or similar to q(alpha)(z, t), where q(s) is the heat kernel associated to L. If in addition vertical bar u(z, t; s(0))vertical bar less than or similar to q(beta)(z, t), for some s(0) is an element of R \textbackslash {0}, then we prove that u(z, t; s) = 0 for all s is an element of R whenever alpha beta < s(0)(2). This result holds true in the more general context of H-type groups. We also prove an analogous result for the Grushin operator on Rn+1.

Hydrophobic hydration driven self-assembly of curcumin in water: Similarities to nucleation and growth under large metastability, and an analysis of water dynamics at heterogeneous surfaces

As the beneficial effects of curcumin have often been reported to be limited to its small concentrations, we have undertaken a study to find the aggregation properties of curcumin in water by varying the number of monomers. Our molecular dynamics simulation results show that the equilibrated structure is always an aggregated state with remarkable structural rearrangements as we vary the number of curcumin monomers from 4 to 16 monomers. We find that the curcumin monomers form clusters in a very definite pattern where they tend to aggregate both in parallel and anti-parallel orientation of the phenyl rings, often seen in the formation of beta-sheet in proteins. A considerable enhancement in the population of parallel alignments is observed with increasing the system size from 12 to 16 curcumin monomers. Due to the prevalence of such parallel alignment for large system size, a more closely packed cluster is formed with maximum number of hydrophobic contacts. We also follow the pathway of cluster growth, in particular the transition from the initial segregated to the final aggregated state. We find the existence of a metastable structural intermediate involving a number of intermediate-sized clusters dispersed in the solution. We have constructed a free energy landscape of aggregation where the metatsable state has been identified. The course of aggregation bears similarity to nucleation and growth in highly metastable state. The final aggregated form remains stable with the total exclusion of water from its sequestered hydrophobic core. We also investigate water structure near the cluster surface along with their orientation. We find that water molecules form a distorted tetrahedral geometry in the 1st solvation layer of the cluster, interacting rather strongly with the hydrophilic groups at the surface of the curcumin. The dynamics of such quasi-bound water molecules near the surface of curcumin cluster is considerably slower than the bulk signifying a restricted motion as often found in protein hydration layer. (C) 2014 AIP Publishing LLC.

Effect of functional groups on separating carbon dioxide from CO2/N-2 gas mixtures using edge functionalized graphene nanoribbons

Development of microporous adsorbents for separation and sequestration of carbon dioxide from flue gas streams is an area of active research. In this study, we assess the influence of specific functional groups on the adsorption selectivity of CO2/N-2 mixtures through Grand Canonical Monte Carlo (GCMC) simulations. Our model system consists of a bilayer graphene nanoribbon that has been edge functionalized with OH, NH2, NO2, CH3 and COOH. Ab initio Moller-Plesset (MP2) calculations with functionalized benzenes are used to obtain binding energies and optimized geometries for CO2 and N-2. This information is used to validate the choice classical forcefields in GCMC simulations. In addition to simulations of adsorption from binary mixtures of CO2 and N-2, the ideal adsorbed solution theory (IAST) is used to predict mixture isotherms. Our study reveals that functionalization always leads to an increase in the adsorption of both CO2 and N-2 with the highest for COOH. However, significant enhancement in the selectivity for CO2 is only seen with COOH functionalized nanoribbons. The COOH functionalization gives a 28% increase in selectivity compared to H terminated nanoribbons, whereas the improvement in the selectivity for other functional groups are much Enure modest. Our study suggests that specific functionalization with COOH groups can provide a material's design strategy to improve CO2 selectivity in microporous adsorbents. Synthesis of graphene nanoplatelets with edge functionalized COOH, which has the potential for large scale production, has recently been reported (Jeon el, al., 2012). (C) 2014 Elsevier Ltd. All rights reserved,

Solution processable diketopyrrolopyrrole (DPP) cored small molecules with BODIPY end groups as novel donors for organic solar cells

Two novel triads based on a diketopyrrolopyrrole (DPP) central core and two 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) units attached by thiophene rings have been synthesised having high molar extinction coefficients. These triads were characterised and used as donor materials in small molecule, solution processable organic solar cells. Both triads were blended with PC71BM as an acceptor in different ratios by wt% and their photovoltaic properties were studied. For both the triads a modest photovoltaic performance was observed, having an efficiency of 0.65%. Moreover, in order to understand the ground and excited state properties and vertical absorption profile of DPP and BODIPY units within the triads, theoretical DFT and TDDFT calculations were performed.

An island called India: phylogenetic patterns across multiple taxonomic groups reveal endemic radiations

Island systems from around the world have provided fascinating opportunities for studies pertaining to various evolutionary processes. One recurring feature of isolated islands is the presence of endemic radiations. In this regard, the Indian subcontinent is an interesting entity given it has been an island during much of its history following separation from Madagascar and currently is isolated from much of Eurasia by the Himalayas in the north and the Indian Ocean in the south. Not surprisingly, recent molecular studies on a number of endemic taxa from India have reported endemic radiations. These studies suggest that the uniqueness of Indian biota is not just due to its diverse origin, but also due to evolution in isolation. The isolation of India has generated some peculiarities typically seen on oceanic islands. However, these patterns might be confined to, groups with low dispersal ability.

The X-C---Y (X = O/F, Y = O, S, F, Cl, Br, N, P,) Carbon bond and hydrophobic interactions

While the tetrahedral face of methane has an electron rich centre and can act as a hydrogen bond acceptor, substitution of one of its hydrogens with some electron withdrawing group (such as -F/OH) can make the opposite face electron deficient. Electrostatic potential calculations confirm this and high level quantum calculations show interactions between the positive face of methanol/methyl fluoride and electron rich centers of other molecules such as H2O. Analysis of the wave functions of atoms in molecules shows the presence of an unusual C···Y interaction, which could be called 'carbon bonding'. NBO analysis and vibrational frequency shifts confirm the presence of this interaction. Given the properties of alkyl groups bonded to electronegative elements in biological molecules, such interactions could play a significant role, which is yet to be recognized. This and similar interactions could give an enthalpic contribution to what is called the 'hydrophobic interactions'.

Groups constrain the use of risky habitat by individuals: a new cost to sociality?

Predation risk can strongly constrain how individuals use time and space. Grouping is known to reduce an individual's time investment in costly antipredator behaviours. Whether grouping might similarly provide a spatial release from antipredator behaviour and allow individuals to use risky habitat more and, thus, improve their access to resources is poorly known. We used mosquito larvae, Aedes aegypti, to test the hypothesis that grouping facilitates the use of high-risk habitat. We provided two habitats, one darker, low-risk and one lighter, high-risk, and measured the relative time spent in the latter by solitary larvae versus larvae in small groups. We tested larvae reared under different resource levels, and thus presumed to vary in body condition, because condition is known to influence risk taking. We also varied the degree of contrast in habitat structure. We predicted that individuals in groups should use high-risk habitat more than solitary individuals allowing for influences of body condition and contrast in habitat structure. Grouping strongly influenced the time spent in the high-risk habitat, but, contrary to our expectation, individuals in groups spent less time in the high-risk habitat than solitary individuals. Furthermore, solitary individuals considerably increased the proportion of time spent in the high-risk habitat over time, whereas individuals in groups did not. Both solitary individuals and those in groups showed a small increase over time in their use of riskier locations within each habitat. The differences between solitary individuals and those in groups held across all resource and contrast conditions. Grouping may, thus, carry a poorly understood cost of constraining habitat use. This cost may arise because movement traits important for maintaining group cohesion (a result of strong selection on grouping) can act to exaggerate an individual preference for low-risk habitat. Further research is needed to examine the interplay between grouping, individual movement and habitat use traits in environments heterogeneous in risk and resources. (C) 2015 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Social optimum in social groups with give-and-take criterion

We consider a Social Group' of networked nodes, seeking a universe' of segments. Each node has a subset of the universe and access to an expensive resource for downloading data. Nodes can also acquire the universe by exchanging copies of segments among themselves, at low cost, using inter-node links. While exchanges over inter-node links ensure minimum cost, some nodes in the group try to exploit the system. We term such nodes as non-reciprocating nodes' and prohibit such behavior by proposing the give-and-take' criterion, where exchange is allowed if each node has segments unavailable with the other. Under this criterion, we consider the problem of maximizing the number of nodes with the universe at the end of local exchanges. First, we present a randomized algorithm that is shown to be optimal in the asymptotic regime. Then, we present greedy links algorithm, which performs well for most of the scenarios and yields an optimal result when the number of nodes is four. The polygon algorithm is proposed, which yields an optimal result when each of the nodes has a unique segment. After presenting some intuitive algorithms (e.g., greedy incremental algorithm and rarest first algorithm), we compare the performances of all proposed algorithms with the optimal. Copyright (c) 2015 John Wiley & Sons, Ltd.

Stabilization of a Tetrahedral (Mn5+O4) Chromophore in Ternary Barium Oxides as a Strategy toward Development of New Turquoise/Green-Colored Pigments

An experimental investigation of the stabilization of the turquoise-colored chrornophore (Mn5+O4) in various oxide hosts, viz., A(3)(VO4)(2) (A = Ba, Sr, Ca), YVO4, and Ba2MO4 (M = Ti, Si), has been carried out. The results reveal that substitution of Mn5+O4 occurs in Ba-3(VO4)(2) forming the entire solid solution series Ba-3(V1-x MnxO4)(2) (0 < x <= 1.0), while with the corresponding strontium derivative, only up to about 10% of Mn5+O4 substitution is possible. Ca-3(VO4)(2) and YVO4 do not stabilize Mn5+O4 at all. With Ba2MO4 (M = Ti, Si), we could prepare only partially substituted materials, Ba2M1-xMn5+O4+x/2 for x up to 0.15, that are turquoise-colored. We rationalize the results that a large stabilization of the O 2p-valence band states occurs in the presence of the electropositive barium that renders the Mn5+ oxidation state accessible in oxoanion compounds containing PO43-, VO43-, etc. By way of proof-of-concept, we synthesized new turquoise-colored Mn5+O4 materials, Ba-5(BO3)(MnO4)(2)Cl and Ba-5(BO3)(PO4)(MnO4)Cl, based on the apatite-Ba-5(PO4)(3)Cl-structure.

The effects of introducing ester linking groups on the flexoelectro-optic properties of symmetric bimesogens

In the chiral nematic phase, flexoelectricity can give rise to an interesting electrooptic switching effect, known as flexoelectro-optic switching. Flexoelectro-optic switching gives a fast v-shaped switching regime. Previous studies show that symmetric bimesogens are particularly suited for flexoelectro-optic switching. By introducing two ester linking groups into the molecular structure of a symmetric bimesogen, it was hypothesised that the flexoelectric properties will be enhanced significantly because of the resulting increase in the dipole moment of the molecules. This was found to be the correct; however, the inclusion of ester linking groups reduced the liquid crystallinity of the material.

Models and algorithms for detection and tracking of coordinated groups

In this paper, we describe models and algorithms for detection and tracking of group and individual targets. We develop two novel group dynamical models, within a continuous time setting, that aim to mimic behavioural properties of groups. We also describe two possible ways of modeling interactions between closely using Markov Random Field (MRF) and repulsive forces. These can be combined together with a group structure transition model to create realistic evolving group models. We use a Markov Chain Monte Carlo (MCMC)-Particles Algorithm to perform sequential inference. Computer simulations demonstrate the ability of the algorithm to detect and track targets within groups, as well as infer the correct group structure over time. ©2008 IEEE.

Influence of ion energy and substrate temperature on the optical and electronic properties of tetrahedral amorphous carbon (ta-C) films

The properties of amorphous carbon (a-C) deposited using a filtered cathodic vacuum arc as a function of the ion energy and substrate temperature are reported. The sp3 fraction was found to strongly depend on the ion energy, giving a highly sp3 bonded a-C denoted as tetrahedral amorphous carbon (ta-C) at ion energies around 100 eV. The optical band gap was found to follow similar trends to other diamondlike carbon films, varying almost linearly with sp2 fraction. The dependence of the electronic properties are discussed in terms of models of the electronic structure of a-C. The structure of ta-C was also strongly dependent on the deposition temperature, changing sharply to sp2 above a transition temperature, T1, of ≈200°C. Furthermore, T1 was found to decrease with increasing ion energy. Most film properties, such as compressive stress and plasmon energy, were correlated to the sp3 fraction. However, the optical and electrical properties were found to undergo a more gradual transition with the deposition temperature which we attribute to the medium range order of sp2 sites. We attribute the variation in film properties with the deposition temperature to diffusion of interstitials to the surface above T1 due to thermal activation, leading to the relaxation of density in context of a growth model. © 1997 American Institute of Physics.

Doping mechanism in tetrahedral amorphous carbon

Doping in hydrogenated amorphous silicon occurs by a process of an ionised donor atom partially compensated by a charged dangling bond. The total energies of various dopant and dopant/bonding combinations are calculated for tetrahedral amorphous carbon. It is found that charged dangling bonds are less favoured because of the stronger Coulombic repulsion in ta-C. Instead the dopants can be compensated by weak bond states in the lower gap associated with odd-membered π-rings or odd-numbered π-chains. The effect is that the doping efficiency is low but there are not charged midgap recombination centres, to reduce photoconductivity or photoluminescence with doping, as occurs in a-Si:H.