Ck-regularity for the $$\bar \partial $$ -equation with a support condition

Let D be a C ^d q-convex intersection, d ≥ 2, 0 ≤ q ≤ n ? 1, in a complex manifold X of complex dimension n, n ≥ 2, and let E be a holomorphic vector bundle of rank N over X. In this paper, C ^k -estimates, k = 2, 3,...,∞, for solutions to the \(\bar \partial \)-equation with small loss of smoothness are obtained for E-valued (0, s)-forms on D when n ? q ≤ s ≤ n. In addition, we solve the \(\bar \partial \)-equation with a support condition in C ^k -spaces. More precisely, we prove that for a \(\bar \partial \)-closed form f in C _0,q ^k (X D,E), 1 ≤ q ≤ n ? 2, n ≥ 3, with compact support and for ε with 0 < ε < 1 there exists a form u in C _0,q?1 ^k?ε (X D,E) with compact support such that \(\bar \partial u = f\) in \(X\backslash \bar D\). Applications are given for a separation theorem of Andreotti-Vesentini type in C ^k -setting and for the solvability of the \(\bar \partial \)-equation for currents.     

General Energy Decay for a Viscoelastic Equation of Kirchhoff Type with Acoustic Boundary Conditions

This paper is concerned with a viscoelastic equation of Kirchhoff type with acoustic boundary conditions in a bounded domain of \(\mathbb {R}^{n}.\) We show that, under suitable conditions on the initial data, the solution exists globally in time. Then, we prove the general energy decay of global solutions by applying a lemma of Martinez, which allows us to get our decay result for a class of relaxation functions wider than that usually considered.     

The Effect of Conducting Boundaries on Weakly Nonlinear Darcy–Bénard Convection

We consider convection in a uniform fluid-saturated porous layer which is bounded by conducting plates and heated from below. The primary aim is to determine the identity of the postcritical convection planform as a function of the thicknesses and conductivities of the bounding plates relative to that of the porous layer. This work complements and extends an early paper by Riahi (J Fluid Mech 129:153–171, 1983) who considered a situation where the porous layer is bounded by infinitely thick conducting media. We present regions in parameter space wherein convection in the form of rolls is unstable and within which cells with square planform form the preferred pattern.     

The crossover from collective motion to periphery diffusion for two-dimensional adatom-islands on Cu(111)

The diffusion of two-dimensional adatom-islands (up to 100 atoms) on Cu(111) has been studied, using the self-learning kinetic Monte Carlo method (Trushin et?al 2005 Phys. Rev. B 72 115401). A variety of multiple-?and single-atom processes are revealed in the simulations, and the size dependences of the diffusion coefficients and effective diffusion barriers are calculated for each. From the tabulated frequencies of events found in the simulation, we show a crossover from diffusion due to the collective motion of the island to a regime in which the island diffuses through periphery-dominated mass transport. This crossover occurs for island sizes between 13 and 19 atoms. For islands containing 19-100 atoms the scaling exponent is 1.5, which is in good agreement with previous work. The diffusion of islands containing 2-13 atoms can be explained primarily on the basis of a linear increase of the barrier for the collective motion with the size of the island.     

Nanostructured layered double hydroxide aerogels with enhanced adsorption properties

Aerogels of layered double hydroxides were prepared by a simple and eco-friendly method involving a quick coprecipitation followed by supercritical CO(2) drying. Such aerogels display high surface areas and enhanced adsorption behavior.     

Experimental and theoretical study of AC electrical conduction mechanisms of semicrystalline parylene C thin films

The electrical conduction mechanisms of semicrystalline thermoplastic parylene C (-H(2)C-C(6)H(3)Cl-CH(2)-)(n) thin films were studied in large temperature and frequency regions. The alternative current (AC) electrical conduction in parylene C is governed by two processes which can be ascribed to a hopping transport mechanism: correlated barrier hopping (CBH) model at low [77-155 K] and high [473-533 K] temperature and the small polaron tunneling mechanism (SPTM) from 193 to 413 K within the framework of the universal law of dielectric response. The conduction mechanism is explained with the help of Elliot's theory, and the Elliot's parameters are determined. From frequency- and temperature-conductivity characteristics, the activation energy is found to be 1.27 eV for direct current (DC) conduction interpreted in terms of ionic conduction mechanism. The power law dependence of AC conductivity is interpreted in terms of electron hopping with a density N(E(F)) (~10(18) eV cm(-3)) over a 0.023-0.03 eV high barrier across a distance of 1.46-1.54 ?.     

Extended pattern recognition scheme for self-learning kinetic Monte Carlo simulations

We report the development of a pattern recognition scheme that takes into account both fcc and hcp adsorption sites in performing self-learning kinetic Monte Carlo (SLKMC-II) simulations on the fcc(111) surface. In this scheme, the local environment of every under-coordinated atom in an island is uniquely identified by grouping fcc sites, hcp sites and top-layer substrate atoms around it into hexagonal rings. As the simulation progresses, all possible processes, including those such as shearing, reptation and concerted gliding, which may involve fcc-fcc, hcp-hcp and fcc-hcp moves are automatically found, and their energetics calculated on the fly. In this article we present the results of applying this new pattern recognition scheme to the self-diffusion of 9-atom islands (M(9)) on M(111), where M = Cu, Ag or Ni.     

Generation of Pseudocontact Shifts in Proteins with Lanthanides Using Small “Clickable” Nitrilotriacetic Acid and Iminodiacetic Acid Tags

Pseudocontact shifts (PCS) induced by paramagnetic lanthanide ions provide unique long‐range structural information in nuclear magnetic resonance (NMR) spectra, but the site‐specific attachment of lanthanide tags to proteins remains a challenge. Here we incorporated p‐azido‐phenylalanine (AzF) site‐specifically into the proteins ubiquitin and GB1, and ligated the AzF residue with alkyne derivatives of small nitrilotriacetic acid and iminodiacetic acid tags using the Cu^I‐catalysed “click” reaction. These tags form lanthanide complexes with no or only a small net charge and produced sizeable PCSs with paramagnetic lanthanide ions in all mutants tested. The PCSs were readily fitted by single magnetic susceptibility anisotropy tensors. Protein precipitation during the click reaction was greatly alleviated by the presence of 150 mM NaCl.