Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

Self-Interactions of Strands and Sheets

Physical strands or sheets that can be modelled as curves or surfaces embedded in three dimensions are ubiquitous in nature, and are of fundamental importance in mathematics, physics, biology, and engineering. Often the physical interpretation dictates that self-avoidance should be enforced in the continuum model, i.e., finite energy configurations should not self-intersect. Current continuum models with self-avoidance frequently employ pairwise repulsive potentials, which are of necessity singular. Moreover the potentials do not have an intrinsic length scale appropriate for modelling the finite thickness of the physical systems. Here we develop a framework for modelling self-avoiding strands and sheets which avoids singularities, and which provides a way to introduce a thickness length scale. In our approach pairwise interaction potentials are replaced by many-body potentials involving three or more points, and the radii of certain associated circles or spheres. Self-interaction energies based on these many-body potentials can be used to describe the statistical mechanics of self-interacting strands and sheets of finite thickness.     

Control of the block copolymer morphology in templated epoxy thermosets

It has been found that by the addition of low concentrations of an amphiphilic block copolymer to an epoxy resin, novel disordered morphologies can be formed and preserved through curing. This article will focus on characterizing the influence of the block copolymer and casting solvent on the templated morphology achieved in the thermoset sample. The ultimate goal of this work is to determine the parameters that would control the microphase morphology produced. Epoxy resins blended with a series of amphiphilic block copolymers based on hydrogenated polyisoprene (polyethylene-alt-propylene or PEP) and polyethylene oxide (PEO), specifically, were investigated. In this article, the cure-induced order–order phase transition from the spherical to wormlike micelle morphology will also be discussed. It is proposed that the formation of the wormlike micelle structure from the spherical micelle structure is similar to the phase transition behavior that occurs in dilute block copolymer solutions as a function of the influence of the solvent on micelle morphology. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3338–3348, 2007     

Numerical Modeling of Solitons in a Low Birefringent Optical Fiber

A numerical investigation, based on the split-step Fourier transform algorithm of all optical switching of solitons in a low birefringent optical fiber is presented. The numerical algorithm is described in detail. This revised version was published online in August 2006 with corrections to the Cover Date.     

Selected-area growth of carbon nanotubes by the combination of focused ion beam and chemical vapor deposition techniques.

In this article, we report a technique for growing carbon nanotubes in a more controllable fashion, which enables us to synthesize nanotubes directly in various forms of designed patterns. This nanofabrication process is based on a combination of focused ion beam (FIB) and chemical vapor deposition (CVD) techniques. In this process, arrays of conductive patterns were first deposited on silicon substrates by directing a gaseous compound (C(9)H(16)Pt) via the capillary needle-sized nozzles within a FIB system. The substrates were then coated with catalyst and further modified by the FIB to localize the position of the catalyst. Finally, the growth of carbon nanotubes on the designed substrates was carried out by CVD of hydrocarbon gases. This fabrication technique has the advantage of positioning carbon nanotubes in selected locations. This may open up opportunities for the direct synthesis of carbon nanotubes onto almost any substrate material, thus allowing fabrication of carbon nanotube-based devices.     

Second Dissociation Constant of Bis-[(2-hydroxyethyl)amino]acetic Acid (BICINE) and pH of Its Buffer Solutions from 5 to 55 °C

The values of the second dissociation constant, K ₂, and related thermodynamic quantities of the ampholyte bis[(2-hydroxyethyl)amino]acetic acid (BICINE) have been determined at temperatures from 5 to 55 ^∘C. The pH values of six equimolal buffer solutions, and four buffer solutions having ionic strengths (I = 0.16 mol⋅kg⁻¹) similar to those in blood plasma, have been evaluated at 12 temperatures from 5 to 55 ^∘C using the Bates–Guggenheim convention. The liquid junction potentials (E _j ) between the buffer solutions of BICINE and saturated KCl solution of the calomel electrode at 25 and 37 ^∘C have been estimated by measurement with a flowing junction cell. These values of E _j have been used to ascertain the operational pH values at 25 and 37 ^∘C. The pK ₂ values at 25 and 37 ^∘C are 8.333 and 8.156, respectively. The thermodynamic quantities associated with the second acid dissociation have been calculated from the values of pK ₂ as a function of temperature. The zwitterionic buffer BICINE was shown to be useful as a pH standard in the region close to that of blood serum.     

Ammonium hexafluorosilicate salts

The preparation and characterization of the ammonium hexafluorosilicate salts, 2[R]⁺ [SiF₆]²⁻ (where R=piperidinium (2), methylammonium (3), quinolinium (4), acridinium (5), 2,2,6,6-tetramethylpiperidinium (6), and propylammonium (7)) is described.The salts were prepared from the reaction of the corresponding alkylammonium fluoride with silica gel. The compounds were characterized by NMR, IR, mass spectrometry and in the case of 1 (piperidinium fluoride), 2-4 by X-ray crystallography. Compounds 1-3 crystallize in the orthorhombic crystal system (space groups Iba2, Fdd2, and Pnnm, respectively), with Z=8, 14, and 4, respectively. Compound 4 crystallizes in the triclinic space group P-1, with Z=2. Compounds 1-4 exhibit hydrogen bonding.     

Hamaker constants in integrated circuit metalization

A new method for determining Hamaker constants was examined for materials of interest in integrated circuit manufacture. An ultra-high vacuum atomic force microscope and an atomic force microscope operated in a nitrogen environment were used to measure the interaction forces between metals, dielectrics, and barriers used during the metalization portion of integrated circuit manufacturing. The materials studied included copper, silver, titanium nitride, silicon dioxide, poly(tetrafluoroethylene), and parylene-N. Spheres coated with a material of interest were mounted on AFM cantilevers and brought into contact with substrates of interest. The interaction force was measured as the cantilever approached the substrate but before the two surfaces came into contact, and also when the particle was pulled out of contact with the substrate. The Hamaker constant calculation from the contact measurement is based on an adhesion model that quantifies the contribution of geometrical, morphological and mechanical properties of materials to the measured adhesion force. Hamaker constants determined with this new approach were compared with values found by using the Derjaguin approximation for a sphere to describe the interaction force as the cantilever approaches the surface. Both approaches produced similar values for most of the systems studied, with variations of less than 10%.