Friction as Contrast Mechanism in Heterodyne Force Microscopy

The nondestructive imaging of subsurface structures on the nanometer scale has been a long-standing desire in both science and industry. A few impressive images were published so far that demonstrate the general feasibility by combining ultrasound with an Atomic Force Microscope. From different excitation schemes, Heterodyne Force Microscopy seems to be the most promising candidate delivering the highest contrast and resolution. However, the physical contrast mechanism is unknown, thereby preventing any quantitative analysis of samples. Here we show that friction at material boundaries within the sample is responsible for the contrast formation. This result is obtained by performing a full quantitative analysis, in which we compare our experimentally observed contrasts with simulations and calculations. Surprisingly, we can rule out all other generally believed responsible mechanisms, like Rayleigh scattering, sample (visco)elasticity, damping of the ultrasonic tip motion, and ultrasound attenuation. Our analytical description paves the way for quantitative SubSurface-AFM imaging.Comment: 7 pages main paper + 11 pages supplementary material

FOULING MITIGATION WITH SYNTHETIC FIBRES IN A CASO4 SUPERSATURATED SOLUTION

Wood pulp fibre suspensions and model synthetic fibre suspensions have been shown previously to mitigate effectively calcium sulphate fouling in heat exchangers. Fibre flexibility was found to be a decisive fibre property in fouling mitigation. Adding fibres to a fouling fluid is environmentally benign and can be applied during operation without shutting down the heat exchanger. Because polymer fibres are more robust in a hostile environment, further work was initiated with two types of rayon fibre and one acrylic fibre of the same fibre length. Experiments were performed at both constant and varying fibre volume concentrations. The more flexible rayon fibres in suspension produced lower ultimate-fouling resistance values than the stiffer acrylic fibres. Fibres were embedded in the fouling layer and it is believed that this mechanism contributed to the overall fouling resistance and was a counterpart to the positive effects of fibres mitigating fouling. The more flexible fibres momentarily form viscoelastic bundles that can ‘absorb’ hydrodynamic shear forces, modify the turbulent stresses, and lower the fouling matter removal rate. Stiff fibres embedded in the deposit protrude into the bulk flow and entrap more fibres as they are less likely to deflect, bend, and be flattened by the shear stresses near the wall

Inelastic semiclassical Coulomb scattering

We present a semiclassical S-matrix study of inelastic collinear electron-hydrogen scattering. A simple way to extract all necessary information from the deflection function alone without having to compute the stability matrix is described. This includes the determination of the relevant Maslov indices. Results of singlet and triplet cross sections for excitation and ionization are reported. The different levels of approximation -- classical, semiclassical, and uniform semiclassical -- are compared among each other and to the full quantum result.Comment: 9 figure

Semiclassical initial value calculations of collinear helium atom

Semiclassical calculations using the Herman-Kluk initial value treatment are performed to determine energy eigenvalues of bound and resonance states of the collinear helium atom. Both the $eZe$ configuration (where the classical motion is fully chaotic) and the $Zee$ configuration (where the classical dynamics is nearly integrable) are treated. The classical motion is regularized to remove singularities that occur when the electrons collide with the nucleus. Very good agreement is obtained with quantum energies for bound and resonance states calculated by the complex rotation method.Comment: 24 pages, 3 figures. Submitted to J. Phys.

Separation and identification of dominant mechanisms in double photoionization

Double photoionization by a single photon is often discussed in terms of two contributing mechanisms, {\it knock-out} (two-step-one) and {\it shake-off} with the latter being a pure quantum effect. It is shown that a quasi-classical description of knock-out and a simple quantum calculation of shake-off provides a clear separation of the mechanisms and facilitates their calculation considerably. The relevance of each mechanism at different photon energies is quantified for helium. Photoionization ratios, integral and singly differential cross sections obtained by us are in excellent agreement with benchmark experimental data and recent theoretical results.Comment: 4 pages, 5 figure

Pairwise approximation for SIR-type network epidemics with non-Markovian recovery

We present the generalized mean-field and pairwise models for non-Markovian epidemics on networks with arbitrary recovery time distributions. First we consider a hyperbolic partial differential equation (PDE) system, where the population of infective nodes and links are structured by age since infection. We show that the PDE system can be reduced to a system of integro-differential equations, which is analysed analytically and numerically. We investigate the asymptotic behaviour of the generalized model and provide an implicit analytical expression involving the final epidemic size and pairwise reproduction number. As an illustration of the applicability of the general model, we recover known results for the exponentially distributed and fixed recovery time cases. For gamma- and uniformly distributed infectious periods, new pairwise models are derived. Theoretical findings are confirmed by comparing results from the new pairwise model and explicit stochastic network simulation. A major benefit of the generalized pairwise model lies in approximating the time evolution of the epidemic