Resonances and Their Relations to Spectral Densities and Scattering Cross Sections in the Schrödinger Formulation

The concept of resonances for a two-body single and many channel Schrödinger problem is discussed with respect to the Titchmarsh–Weyl theory. It is argued that the contributions from the entire set of resonances together with the free particle spectral density build the entire spectrum. The implication of this statement on the influence of resonances on a two-body scattering cross section is discussed. It is described how the residues of the S-matrix at a complex resonance energy, i.e. two complex numbers, is used to define its contribution to the cross section. The limitations of the Breit–Wigner approximation is discussed.     

Pump-free transport of magnetic particles in microfluidic channels

The use of magnetic particles in microfluidic devices offers new possibilities and a new degree of freedom to sequential synthesis and preparative or analytical procedures in very small volumes. In contrast to most of the traditional approaches where the liquid phase is flushed or pumped along a solid phase, the transport of magnetic particles through a microfluidic channel has the advantage of reduced reagent consumption and simpler, smaller systems. By lining up different reservoirs along the transport direction, reactions with different agents can be accomplished. Here, we present a pump and valve-free microfluidic particle transport system. By creating a simple and very effective layout of soft magnetic structures, which concentrate an external homogeneous magnetic field, a passive, thus easy to operate structure was generated. Most importantly, this layout is based on a simple tube by which fluidic and magnetic parts are separated. The tube itself is disposable and can be replaced prior to vital reactions, thus helping reduce sample cross-contaminations without affecting the particle transport properties. The layout of the device was thoroughly examined by a computer simulation of the particle trajectories, and the results were confirmed by experiments on a micro-machined demonstrator, which revealed an effective transport speed of up to 5 mm/s in 30 mT magnetic fields. Thus, we present a microfluidic transport device that combines the advantages of magnetic particles in microfluidic systems with a simple single-use technology for, e.g., bioanalytical purposes.     

A note on bounds for non-linear multivalued homogenized operators

In this paper we study the behaviour of maximal monotone multivalued highly oscillatory operators. We construct Reuss-Voigt-Wiener and Hashin-Shtrikmann type bounds for the minimal sections of G-limits of multivalued operators by using variational convergence and convex analysis.     

Dynamics of the Tippe Top—Properties of numerical solutions versus the dynamical equations

We study the relationship between numerical solutions for inverting Tippe Top and the structure of the dynamical equations. The numerical solutions confirm the oscillatory behavior of the inclination angle θ(t) for the symmetry axis of the Tippe Top, as predicted by the Main Equation for the Tippe Top. They also reveal further fine features of the dynamics of inverting solutions defining the time of inversion. These features are partially understood on the basis of the underlying dynamical equations.     

On the anomalous temperature dependence of cellulose aqueous solubility

The solubility of cellulose in water-based media is promoted by low temperature, which may appear counter-intuitive. An explanation to this phenomenon has been proposed that is based on a temperature-dependent orientation of the hydroxymethyl group. In this paper, this hypothesis is investigated using molecular dynamics computer simulations and NMR spectroscopy, and is discussed in conjunction with alternative explanations based on solvent–solute and solvent–solvent hydrogen bond formation respectively. It is shown that neither simulations nor experiments lend support to the proposed mechanism based on the hydroxymethyl orientation, whereas the two alternative explanations give rise to two distinct contributions to the hydration free energy of cellooligomers.     

An approach to renormalization on the n-torus

The coding theory of rotations (by inspecting closely their relation to flows) and the continued fractions algorithm (by considering even two-coloring of the integers with a given proportion of, say, blue and red) are revisited. Then, even n-coloring of the integers is defined. This allows one to code rotations on the (n-1)-torus by considering linear flows on the n-torus and yields a simple geometric approach to renormalization on tori by first return maps on the coding regions.     

Thermoelectrics from silicon nanoparticles: the influence of native oxide

Thermoelectric materials were synthesized by current-assisted sintering of doped silicon nanoparticles produced in a microwave-plasma reactor. Due to their affinity to oxygen, the nanoparticles start to oxidize when handled in air and even a thin surface layer of native silicon oxide leads to a significant increase in the oxide volume ratio. This results in a considerable incorporation of oxygen into the sintered pellets, thus affecting the thermoelectric performance. To investigate the necessity of inert handling of the raw materials, the thermoelectric transport properties of sintered nanocrystalline silicon samples were characterized with respect to their oxygen content. An innovative method allowing a quantitative silicon oxide analysis by means of electron microscopy was applied: the contrast between areas of high and low electrical conductivity was attributed to the silicon matrix and silicon oxide precipitates, respectively. Thermoelectric characterization revealed that both, electron mobility and thermal conductivity decrease with increasing silicon oxide content. A maximum figure of merit with zT = 0.45 at 950 °C was achieved for samples with a silicon oxide mass fraction of 9.5 and 21.4% while the sample with more than 25% of oxygen clearly indicates a negative impact of the oxygen on the electron mobility.