New conditional symmetries and exact solutions of nonlinear reaction-diffusion-convection equations. II

In the first part of this paper math-ph/0612078, a complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It was shown that all the known results for reaction-diffusion equations with power diffusivities follow as particular cases from those obtained in math-ph/0612078 but not vise versa. In the second part the symmetries obtained in are successfully applied for constructing exact solutions of the relevant equations. In the particular case, new exact solutions of nonlinear reaction-diffusion-convection (RDC) equations arising in application and their natural generalizations are found

A multi-layer extension of the stochastic heat equation

Motivated by recent developments on solvable directed polymer models, we define a 'multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions.Comment: v4: substantially extended and revised versio

Operando spectroscopy study of the carbon dioxide electro-reduction by iron species on nitrogen-doped carbon

The carbon–carbon coupling via electrochemical reduction of carbon dioxide represents the biggest challenge for using this route as platform for chemicals synthesis. Here we show that nanostructured iron (III) oxyhydroxide on nitrogen-doped carbon enables high Faraday efficiency (97.4%) and selectivity to acetic acid (61%) at very-low potential (−0.5 V vs silver/silver chloride). Using a combination of electron microscopy, operando X-ray spectroscopy techniques and density functional theory simulations, we correlate the activity to acetic acid at this potential to the formation of nitrogen-coordinated iron (II) sites as single atoms or polyatomic species at the interface between iron oxyhydroxide and the nitrogen-doped carbon. The evolution of hydrogen is correlated to the formation of metallic iron and observed as dominant reaction path over iron oxyhydroxide on oxygen-doped carbon in the overall range of negative potential investigated, whereas over iron oxyhydroxide on nitrogen-doped carbon it becomes important only at more negative potentials

The role of the copper oxidation state in the electrocatalytic reduction of CO2 into valuable hydrocarbons

Redox-active copper catalysts with accurately prepared oxidation states (Cu0, Cu+ and Cu2+) and high selectivity to C2 hydrocarbon formation, from electrocatalytic cathodic reduction of CO2, were fabricated and characterized. The electrochemically prepared copper-redox electro-cathodes yield higher activity for the production of hydrocarbons at lower oxidation state. By combining advanced X-ray spectroscopy and in situ micro-reactors it was possible to unambiguously reveal the variation in the complex electronic structure that the catalysts undergo at different stages (i.e. during fabrication and electrocatalytic reactions). It was found that the surface, sub-surface and bulk properties of the electrochemically prepared catalysts are dominated by the formation of copper carbonates on the surface of cupric-like oxides, which prompts catalyst deactivation by restraining effective charge transport. Furthermore, the formation of reduced or partially-reduced copper catalysts yields the key dissociative proton-consuming reactive adsorption of CO2 to produce CO, allowing the subsequent hydrogenation into C2 and C1 products by dimerization and protonation. These results yield valuable information on the variations in the electronic structure that redox-active copper catalysts undergo in the course of the electrochemical reaction, which, under extreme conditions are mediated by thermodynamics but, critically, kinetics dominate near the oxide/metal phase transitions

Small molecule sensitization to TRAIL is mediated via nuclear localization, phosphorylation and inhibition of chaperone activity of Hsp27

10.1038/cddis.2013.413Cell Death and Disease410

Ab-initio study of model guanine assemblies: The role of pi-pi coupling and band transport

Several assemblies of guanine molecules are investigated by means of first-principle calculations. Such structures include stacked and hydrogen-bonded dimers, as well as vertical columns and planar ribbons, respectively, obtained by periodically replicating the dimers. Our results are in good agreement with experimental data for isolated molecules, isolated dimers, and periodic ribbons. For stacked dimers and columns, the stability is affected by the relative charge distribution of the pi orbitals in adjacent guanine molecules. pi-pi coupling in some stacked columns induces dispersive energy bands, while no dispersion is identified in the planar ribbons along the connections of hydrogen bonds. The implications for different materials comprised of guanine aggregates are discussed. The bandstructure of dispersive configurations may justify a contribution of band transport (Bloch type) in the conduction mechanism of deoxyguanosine fibres, while in DNA-like configurations band transport should be negligible.Comment: 21 pages, 6 figures, 3 tables, to be published in Phys. Rev.

Symmetries of a class of nonlinear fourth order partial differential equations

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \be u_{tt} = \left(\kappa u + \gamma u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2, \ee where $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both ``compacton'' and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are no} obtainable through the classical method

New variable separation approach: application to nonlinear diffusion equations

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig

Satellite sensor requirements for monitoring essential biodiversity variables of coastal ecosystems.

The biodiversity and high productivity of coastal terrestrial and aquatic habitats are the foundation for important benefits to human societies around the world. These globally distributed habitats need frequent and broad systematic assessments, but field surveys only cover a small fraction of these areas. Satellite-based sensors can repeatedly record the visible and near-infrared reflectance spectra that contain the absorption, scattering, and fluorescence signatures of functional phytoplankton groups, colored dissolved matter, and particulate matter near the surface ocean, and of biologically structured habitats (floating and emergent vegetation, benthic habitats like coral, seagrass, and algae). These measures can be incorporated into Essential Biodiversity Variables (EBVs), including the distribution, abundance, and traits of groups of species populations, and used to evaluate habitat fragmentation. However, current and planned satellites are not designed to observe the EBVs that change rapidly with extreme tides, salinity, temperatures, storms, pollution, or physical habitat destruction over scales relevant to human activity. Making these observations requires a new generation of satellite sensors able to sample with these combined characteristics: (1) spatial resolution on the order of 30 to 100-m pixels or smaller; (2) spectral resolution on the order of 5 nm in the visible and 10 nm in the short-wave infrared spectrum (or at least two or more bands at 1,030, 1,240, 1,630, 2,125, and/or 2,260 nm) for atmospheric correction and aquatic and vegetation assessments; (3) radiometric quality with signal to noise ratios (SNR) above 800 (relative to signal levels typical of the open ocean), 14-bit digitization, absolute radiometric calibration <2%, relative calibration of 0.2%, polarization sensitivity <1%, high radiometric stability and linearity, and operations designed to minimize sunglint; and (4) temporal resolution of hours to days. We refer to these combined specifications as H4 imaging. Enabling H4 imaging is vital for the conservation and management of global biodiversity and ecosystem services, including food provisioning and water security. An agile satellite in a 3-d repeat low-Earth orbit could sample 30-km swath images of several hundred coastal habitats daily. Nine H4 satellites would provide weekly coverage of global coastal zones. Such satellite constellations are now feasible and are used in various applications