Shape Optimization and Electron Bubbles

We present an analytical treatment of the shape optimization problem that arises in the study of electron bubbles. The problem is to minimize a weighted sum of a Laplace eigenvalue, volume, and surface area with respect to the shape of the domain. The analysis employs the calculus of moving surfaces and yields surprising conclusions regarding the stability of equilibrium spherical configurations. Namely, all but the lowest eigenvalue result in unstable configurations and certain combinations of parameters, near-spherical equilibrium stable configurations exist. Two-dimensional and three-dimensional problems are considered and numerical results are presented for the two-dimensional case.     

The kaolinite (0 0 1) polar basal plane

Kaolinite is thought to be an efficient ice nucleating agent because kaolinite crystals expose perfect unreconstructed (0 0 1) basal surfaces which provide a suitable template for ice growth. However, we show here with the aid of density functional theory calculations that the unreconstructed basal surface is polar. Various mechanisms to eliminate the macroscopic dipole and in so-doing stabilize the basal surface are considered. The most promising option identified so far involves the adsorption of foreign atoms (for example, Na and Cl atoms) on the perfect basal surface, since this yields a non-metallic surface with a cleavage energy lower than the unreconstructed polar basal surface. A quantitative experimental structure determination of the kaolinite basal surface is called for.     

Adsorption of Nd on the Mo(1 1 0) surface

The adsorption of Nd on the Mo(1 1 0) surface has been studied by low energy electron diffraction and Auger electron spectroscopy. It has been found that at low coverages Nd adatoms form a rich amount of dilute (n × 2) commensurate structures, which can be explained as forming zigzag chains oriented along the [1 1 0] direction. Monte Carlo simulations indicate that the formation of the zigzag chain structures is initiated by the indirect lateral interaction between Nd adatoms.     

Singlet and triplet state dynamics of charge and hydride transfer reactions of OD (XΣ) with propyne

We report a crossed beam study of the title reactions in the collision energy range from 0.45 to 1.23 eV (43–119 kJ/mol). Both reactions are exoergic and proceed as direct processes on a time scale much less than the rotational period of the transient association complex of approaching reactants. The charge transfer process takes place with zero momentum transfer. Density Functional Theory calculations of the structures of reactive intermediates show that a plausible pathway for hydride transfer involves initial charge transfer on a triplet surface, followed by intersystem crossing to the singlet manifold. This process is followed by rapid hydrogen atom transfer to form an intermediate that dissociates smoothly to products. The kinematics of the heavy + light-heavy mass combination result in mixed energy release at the lowest collision energy, in which both the breaking and forming bonds are extended, while at higher collision energies, the incremental translational energy in the reactants appears preferentially in product translation, consistent with induced repulsive energy release.     

Crystalline Amyloid Structures at Interfaces

Laying the groundwork : The interfacial self‐assembly properties of an amyloid peptide were used to develop crystalline nanostructures at air–water interfaces, which were studied by both AFM microscopy and X‐ray diffraction (see image). These structures generate regular arrays of functional groups and pave the way to controlled deposition of inorganic materials like that observed in biomineralization.

     

Electrical,Film and Surface Properties of Water-Based Latexes Prepared by Semicontinuous Emulsion Polymerization

Summary: In this study, the results obtained with latexes prepared by semicontinuous emulsion polymerization with conventional anionic and nonionic emulsifiers and their different mixtures were presented. For this study, vinyl acetate-butyl acrylate latexes with a conventional anionic emulsifier (sodium lauril ether sulfate) and a nonionic emulsifier (30 mole nonyl phenol ethoxylate), of which films can be easily cast, were used. The latex properties in terms of mechanical stability, film-water absorption, and film-emulsifier exudation, and surface and electrical properties were assessed and compared.     

Field sensitivity to variations of a scatterer

For the problem of diffraction of harmonic scalar waves by a lossless periodic slab scatterer, we analyze field sensitivity with respect to the material coefficients of the slab. The governing equation is the Helmholtz equation, which describes acoustic or electromagnetic fields. The main theorem establishes the variational (Fréchet) derivative of the scattered field measured in the H¹ (root-mean-square-gradient) norm as a function of the material coefficients measured in an L^p (p-power integral) norm, with 2<p<∞, as long as these coefficients are bounded above and below by positive constants and do not admit resonance. The derivative is Lipschitz continuous. We also establish the variational derivative of the transmitted energy with respect to the material coefficients in L^p.     

New examples of maximal space like surfaces in the anti-de Sitter space

Let be the three-dimensional anti-de Sitter space. In this paper we will construct new examples of complete maximal space like surfaces in . Moreover, we will prove that any complete maximal space like surface in with principal curvatures ±κ bounded away from zero must be isometric to the hyperbolic cylinder. Since the new examples that we have constructed have exactly two principal curvatures everywhere, we conclude that the condition on the principal curvatures on the previous result, i.e. the condition |κ(m)|>c>0, cannot be replaced by the condition |κ(m)|>0.     

Sun-Wong type theorems for second order damped elliptic equations

The oscillation criteria of Sun and Wong [Y.G. Sun, J.S.W. Wong, Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J. Math. Anal. Appl. 334 (2007) 549-560] are extended to the forced second order damped elliptic differential equation with mixed nonlinearities