Subdivision Schemes for Positive Definite Matrices

The class of symmetric positive definite matrices is an important class both in theory and application. Although this class is well studied, little is known about how to efficiently interpolate such data within the class. We extend the 4-point interpolatory subdivision scheme, as a method of interpolation, to data consisting of symmetric positive definite matrices. This extension is based on an explicit formula for calculating a binary “geodetic average”. Our method generates a smooth curve of matrices, which retain many important properties of the interpolated matrices. Furthermore, the scheme is robust and easy to implement.     

Ferromagnetic bonding: high spin copper clusters (n+1)Cu(n); n = 2-14) devoid of electron pairs but possessing strong bonding

Density functional theoretic studies are performed for the high-spin copper clusters (n)(+1)Cu(n) (n = 2-14), which are devoid of electron pairs shared between atoms, hence no-pair clusters (J. Phys. Chem. 1988, 92, 1352; Isr. J. Chem. 1993, 33, 455; J. Am. Chem. Soc. 1999, 121, 3165). Despite the lack of electron pairing, it is found that the bond dissociation energy per atom (BDE/n) is significant and converges (to within 1 kcal mol(-1)), around a cluster size (11)Cu(10), to a value of BDE/n = 19 kcal mol(-1). This is a very large bonding energy, much larger than has previously been obtained for no-pair clusters of lithium, BDE/n = 12 kcal mol(-1), or sodium clusters, BDE/n = 3 kcal mol(-1). This bonding, so-called ferromagnetic bonding (FM-bonding) is analyzed using a valence bond (VB) model (J. Phys. Chem. A 2002, 106, 4961; Phys. Chem. Chem. Phys. 2003, 5, 158). As such, FM-bonding in no-pair clusters is described as an ionic fluctuation, of the triplet pair, that spreads over all the close neighbors of a given atom in the clusters. Thus, if we refer to each triplet pair and its ionic fluctuations as a local FM-bond, we can regard the electronic structure of a given (n)(+1)M(n) cluster as a resonance hybrid of all the local FM-bonds between close neighbors. The model shows how a weak interaction in the diatomic triplet molecule can become a remarkably strong binding force that binds together mono-valent atoms without even a single electron pair. This is achieved because the growing number of VB structures exerts a cumulative effect of stabilization that is maximized when the cluster has a compact structure with an optimal coordination number for the atoms.     

Dielectric and Calorimetric Characteristics of Bound and Free Water in Surfactant-Based Systems

The hydration behavior of the system polyoxyethylene (10) oleylalcohol [C_18:1 (EO)₁₀ or Brij 97]/water/dodecane/butanol (model system B) was investigated along a dilution line for which the respective weight ratio of dodecane:butanol:Brij 97 is 3:3:4. Two experimental methods were applied: time domain dielectric spectroscopy (TDDS) and sub-zero temperature differential scanning calorimetry (SZT-DSC). Two types of bound water (with melting peaks at -25 and -11°C) were detected by SZT-DSC (using the endothermic mode), whereas TDDS revealed only one such type. Nevertheless, roughly the same total amount of bound water was estimated from these two techniques. The average number of bound water molecules per ethylene oxide (EO) group, N_W/EO is 2.3 (TDDS data) or 2.5 (SZT-DSC data) in good agreement with the observation that 1–2 water layers are formed in the hydration of ethoxylated surfactants. We have also shown that butanol is involved in the formation of the bound water that melts at -25°C. We suggest that butanol molecules occupy binding sites within the second hydration shell, thereby reducing the expected total bound water content.     

Parametric resonance and pattern selection in an array of microcantilevers interacting through fringing electrostatic fields

Nonlinear Dynamics - We investigate collective resonant dynamics of an array of microcantilevers coupled elastically, through a flexible overhang, and electrostatically, through fringing fields....     

Normal and shear forces between a polyelectrolyte brush and a solid surface

The diblock copolymer poly(methyl methacrylate)‐b‐poly(sodium sulfonated glycidyl methacrylate) (PMMA‐b‐PSGMA) was end‐attached by its hydrophobic block (PMMA) onto mica hydrophobized by a stearic trimethylammonium iodide (STAI) layer, to form a polyelectrolyte brush immersed in water. With a surface force balance (SFB), we extended earlier measurements between two such brush layers for the case of normal and shear forces at different shear rates, surface separation, and compressions between one mica surface coated with STAI or a STAI‐diblock layer against a bare mica surface. After coating one of the surfaces with STAI, a long range attraction that results in a jump into an adhesive flat contact between the hydrophobic and hydrophilic surfaces was observed. A very different behavior was seen after forming the polyelectrolyte brush on the STAI‐coated surface. The long range attraction was replaced by repulsion, accompanied by very low friction during shear (ca. three orders of magnitude lower than with adsorbed polyelectrolytes). On further compression, a weak attraction to the adhesive contact was observed. From the final surface–surface contact separation, we deduce that most of the polyelectrolyte diblock brush layer was squeezed out from the gap, leaving the STAI layer and a small amount of the polymer attached to the surface. Stick‐sliding behavior was seen while applying shear, suggesting a dissipation mechanism caused by the trapped polyelectrolyte. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 193–204, 2005     

Visibility preserving terrain simplification— an experimental study

The terrain surface simplification problem has been studied extensively, as it has important applications in geographic information systems and computer graphics. The goal is to obtain a new surface that is combinatorially as simple as possible, while maintaining a prescribed degree of similarity with the original input surface. Generally, the approximation error is measured with respect to distance (e.g., Hausdorff) from the original or with respect to visual similarity. In this paper, we propose a new method of simplifying terrain surfaces, designed specifically to maximize a new measure of quality based on preserving inter-point visibility relationships. Our work is motivated by various problems of terrain analysis that rely on inter-point visibility relationships, such as optimal antenna placement.

We have implemented our new method and give experimental evidence of its effectiveness in simplifying terrains according to our quality measure. We experimentally compare its performance with that of other leading simplification methods.     

Synthesis and characterization of Au102(p-MBA)44 nanoparticles

The synthesis of Au(102)(p-MBA)(44) nanoparticles on a preparative scale in high yield is described. Various analytical methods are shown to give results consistent with the composition and known structure of the particles, showing the preparation is essentially homogeneous, and attesting to the validity of the methods as well. Derivatization of the particles with proteins and DNA is demonstrated, and conditions are described for imaging individual particles by cryo-EM at low electron dose, close to focus, conditions optimal for recording high-resolution details.     

Interaction of viscous drops in a yield stress material

The interaction of Newtonian drops of various volumes moving in yield stress material is investigated experimentally. Tetrachloroethylene drops move in a rectangular reservoir filled with neutralized 0.07% w/w Carbopol gel under the action of gravity. For initially vertically aligned drop pairs, we present time evolution of separation distance, velocities during the interaction and conditions for coalescence of the drops, which depend on the volumes of the drops and the initial separation between them. For the asymmetric interaction of the pairs, we present interaction patterns, which have been used for estimation of the size of the yielded region and its shape around the leading drop.