Tuning intermolecular interactions in a rodlike polymer assembled at surfaces and in solution

The isolation of single polyelectrolyte chains of water-soluble poly(isocyanodipeptide)s (PICs) bearing carboxylic acid terminated side chains occurring both at surfaces and in solution was accomplished by reducing the intermolecular interactions through complexation with cations or positively charged surfactants.Scanning force microscopy and viscosity analyses revealed that this method allows to tune the conformation of the macromolecule, which is of importance for tailoring the physicochemical properties of the material.This is particularly significant for the use of these polymer chains as seed for biomineralization processes.     

Stability of films with nanoparticles

Numerous products (such as paints, inks, foods, and beverages) and processes (such as coating, coagulation, sedimentation, lubrication, and paper-making) depend on the stability of the liquid films separating the dispersed phase from the continuous phase in the presence of nanoparticles or surfactant micelles. Nanoparticles exhibit a tendency to form ordered layers (i.e., stratification) and particle in-layer structures in these thin films at a sufficiently high concentration, resulting in a structural force that stabilizes the dispersion. The dispersion stability depends on the film size and the nanoparticle concentration.     

Fixed point formula for holomorphic functions

We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of , we make use of the Bergman kernel of this domain. The Lefschetz number is proved to be the sum of the usual contributions of fixed points of the map in and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points.

     

Molecular origin and dynamic behavior of slip in sheared polymer films

The behavior of the slip length in thin polymer films subject to planar shear is investigated using molecular dynamics simulations. At low shear rates, the slip length extracted from the velocity profiles correlates well with that computed from a Green-Kubo analysis. Beyond chain lengths of about N=10, the molecular weight dependence of the slip length is dominated strongly by the bulk viscosity. The dynamical response of the slip length with increasing shear rate is well captured by a power law up to a critical value where the momentum transfer between wall and fluid reaches its maximum.     

Regenerative amplification of femtosecond laser pulses in Ti:sapphire at multikilohertz repetition rates

We have generated and applied noncoherent x-ray radiation in an all-solid-state laser system operating at repetition rates up to 20 kHz. Based on a model that takes into account the strong thermal loading of the Ti:sapphire rod, a laser cavity with low sensitivity to thermal lensing was chosen. With a maximum pump power of 80 W, an output power as high as 27 W was obtained in gain-switched operation, and, with a seeding from a femtosecond oscillator, 60-fs, 0.8-mJ (8-W) pulses at 10 kHz and 0.32-mJ (6.5-W) pulses at 20 kHz were generated. High power femtosecond output was used to generate x-ray continuum radiation up to 5 keV from a liquid-gallium jet target.     

Continuous-wave lasing of a stoichiometric Yb laser material: KYb(WO4)2

For the first time to the authors' knowledge, continuous-wave laser emission of the stoichiometric crystal KYb(WO4)2 was achieved at 1068 nm. The 125-microm-thin sample was directly water cooled and pumped at 1025 nm by a Ti:sapphire laser. The maximum output power at room temperature was 20 mW.     

Entrapment efficiencies of hydrodynamic boundary layers on rising bubbles

Flotation and separation practice shows that fine hydrophilic solids are often drawn into the froth product. The occurrence of this unwanted event in the classical froth flotation has led to the idea of using it for the separation by size of ground materials. Thus, a method for the extraction of hydrophilic fines by foaming of a suspension was proposed. The aim of the present study is to relate this phenomenon to the residence time of the particles in the vicinities of the rising bubbles. Dynamic interactions of fine solids with rising bubbles cause perturbations in the background flow field. A procedure for the mathematical modeling of these disturbance effects is proposed. The initial idea is that the particles lag behind the background bubble-driven flows. A key point is the possibility of classifying fine entities according to a general criterion, containing only parameters of the outer flow. The basic result is that there exists a range of particle and bubble dimensions for which this entrapment is optimal. The proposed model investigation gives a concise explanation for the observed capture of fine solids in many flotation and separation processes.     

Maximum Norm Resolvent Estimates for Elliptic Finite Element Operators

We study a finite element approximation A _h, based on simplicial Lagrange elements, of a second order elliptic operator A under homogeneous Dirichlet boundary conditions in two and three dimensions, where h is thought of as a meshsize. The main result of the paper is a new resolvent estimate for the operator A _h in the L -norm. This estimate is uniform with respect to h for the case with at least quadratic elements. In the case with linear elements, the estimate contains on the right a factor proportional to (log log ), where = 1 or = in two or three dimensions, respectively.This revised version was published online in October 2005 with corrections to the Cover Date.