The branching graphs of polyhexes: Some elementary theorems,conjectures and open questions

This paper presents a few novel results, and collects together what is known and conjectured about the branching graph of a polyhex.     

Application of negative chemical ionization mass spectrometry to the structure elucidation of perfluorochemicals and related compounds

The negative chemical ionization mass spectra of representative perfluorinated alkanes, cycloalkanes, ethers and tertiary amines have been examined, using Ar at about 0.5 torr as the reagent gas. The compounds chosen are typical of those under study as components of fluorochemical emulsion blood substitutes. Many such PFC's, particularly those with cyclic or branched structures, give intense molecular ions; most give simple spectra with a few major fragment ions at high mass, in marked contrast to the EI spectra which are dominated by m/e 69 (CF₃+) and 131 (C₃F₅+) of no value for structure elucidation. NCI-GC/MS is more sensitive than conventional EI-GC/MS and promises to be more generally useful for structure determination. Specific examples from the various classes will be presented, and their NCI and EI mass spectra compared.     

Microfluidic routing of aqueous and organic flows at high pressures: fabrication and characterization of integrated polymer microvalve elements

This paper presents the first systematic engineering study of the impact of chemical formulation and surface functionalization on the performace of free-standing microfluidic polymer elements used for high-pressure fluid control in glass microsystems. System design, chemical wet-etch processes, and laser-induced polymerization techniques are described, and parametric studies illustrate the effects of polymer formulation, glass surface modification, and geometric constraints on system performance parameters. In particular, this study shows that highly crosslinked and fluorinated polymers can overcome deficiencies in previously-reported microvalve architectures, particularly limited solvent compatibility. Substrate surface modification is shown effective in reducing the friction of the polymer-glass interface and thereby facilitating valve actuation. A microchip one-way valve constructed using this architecture shows a 2 x 10(8) ratio of forward and backward flow rates at 7 MPa. This valve architecture is integrated on chip with minimal dead volumes (70 pl), and should be applicable to systems (including chromatography and chemical synthesis devices) requiring high pressures and solvents of varying polarity.     

Reconstructing phase space from PDE simulations

We propose the Karhunen-Loève (K-L) decomposition as a tool to analyze complex spatio-temporal structures in PDE simulations in terms of concepts from dynamical systems theory. Taking the Kuramoto-Sivashinsky equation as a model problem we discuss the K-L decomposition for 4 different values of its bifurcation parameter . We distinguish two modes of using the K-L decomposition: As an analytic and synthetic tool respectively. Using the analytic mode we find unstable fixed points and stable and unstable manifolds in a parameter regime with structurally stable homoclinic orbits (=17.75). Choosing the data for a K-L analysis carefully by restricting them to certain burst events, we can analyze a more complicated intermittent regime at =68. We establish that the spatially localized oscillations around a so called strange fixed point which are considered as fore-runners of spatially concentrated zones of turbulence are in fact created by a very specific limit cycle (=83.75) which, for =87, bifurcates into a modulated traveling wave. Using the K-L decomposition synthetically by determining an optimal Galerkin system, we present evidence that the K-L decomposition systematically destroys dissipation and leads to blow up solutions.We would like to dedicate this paper to Klaus Kirchgässner on the occasion of his 60th birthday