Direct simulation of liquid-gas-solid flow with a free surface lattice Boltzmann method

Direct numerical simulation of liquid-gas-solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary -- in particular if the bubble-particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble-particle interaction at a size ratio of 1-2 orders of magnitude that makes simulations feasible on currently available super-computing resources. With the presented approach, simulations of bubbles in suspension columns consisting of more than $100\,000$ fully resolved particles become possible. Furthermore, we demonstrate the significance of particle-resolved simulations by comparison to previous unresolved solutions. The results indicate that fully-resolved direct numerical simulation is indeed necessary to predict the flow structure of bubble-particle interaction problems correctly.Comment: submitted to International Journal of Computational Fluid Dynamic

Effects of disorder in striped phases of cuprate superconductors and in planar vortex arrays

Effects of disorder on planar periodic structures in superconductors are examined in the present work. In part one we analyse the role of impurities in the striped phases of cuprate high-temperature superconductors. The geometrical degrees of freedom of the combined charge and spin superstructure in the two-dimensional (2D) copper-oxide planes are first discussed. Pinning by the atomic lattice - which might give rise to commensuration effects - is irrelevant on large length scales in the presence of quenched disorder. As a consequence, the stripes have divergent displacement fluctuations and topological defects are present at all temperatures, implying short-ranged positional order of the stripe array with a finite correlation length even at zero temperature. Lock-in phenomena can exist only as crossovers but not as transitions. These results are in agreement with the glassy nature of stripes observed in experiments. Secondly, we study the effect of disorder on coupled planar arrays of Luttinger liquids (LLs) as a model for the electronic degrees of freedom of the stripes. In the framework of a renormalisation group analysis, we find that weak inter-LL charge-density-wave couplings are always irrelevant as opposed to the pure system. By varying either disorder strength, intra- or inter-LL interactions, the system can undergo a delocalisation transition between an insulator and a strongly anisotropic metallic state with LL-like transport. The delocalised state can exist other than in one dimension even for a purely repulsive interactions and it is characterised by short-ranged charge-density-wave order, quasi-long-ranged superconducting order along the stripes and short-ranged superconducting order in the transversal direction. In part two the random (1+1)-dimensional fluxline lattice as a model system for vortex glasses (VG) is examined. Using the recently found exact Replica Bethe Ansatz solution by Emig et al. for a special vortex interaction, we argue against the existence of the transition to a thermally unpinned phase above the VG. The argument is generalised to arbitrary repulsive interactions via the mapping to one-dimensional repulsive fermions. A small window for the transition sharply below the superconducting critical temperature is opened by the introduction of a finite persistence length of a single vortex line. In the phenomenologically related random-field XY model the transition under debate is present but does not leave any signature in the free energy as we calculate in a sideline of the reasoning. Finally, the relation of the vortex system to the random-bond dimer model is explored in detail. The latter can be simulated with a recently developed polynomial algorithm at a precision far beyond any previous Monte Carlo approach. Data from simulations, which are provided by the collaborating group of C. Zeng (Washington, D.C.), and theory do not only show qualitative but also excellent quantitative agreement for a wide range of observables: the large scale lattice stiffness; the average free energy, internal energy and entropy; moments of the disorder distributed free energy; specific heat. The special model character of the planar VG as a genuine glassy and yet in many aspects solvable system is highlighted

"Trees live on soil and sunshine!" : Coexistence of scientific and alternative conception of tree assimilation

Successful learning is the integration of new knowledge into existing schemes, leading to an integrated and correct scientific conception. By contrast, the co-existence of scientific and alternative conceptions may indicate a fragmented knowledge profile. Every learner is unique and thus carries an individual set of preconceptions before classroom engagement due to prior experiences. Hence, instructors and teachers have to consider the heterogeneous knowledge profiles of their class when teaching. However, determinants of fragmented knowledge profiles are not well understood yet, which may hamper a development of adapted teaching schemes. We used a questionnaire-based approach to assess conceptual knowledge of tree assimilation and wood synthesis surveying 885 students of four educational levels: 6th graders, 10th graders, natural science freshmen and other academic studies freshmen. We analysed the influence of learner's characteristics such as educational level, age and sex on the coexistence of scientific and alternative conceptions. Within all subsamples well-known alternative conceptions regarding tree assimilation and wood synthesis coexisted with correct scientific ones. For example, students describe trees to be living on "soil and sunshine", representing scientific knowledge of photosynthesis mingled with an alternative conception of trees eating like animals. Fragmented knowledge profiles occurred in all subsamples, but our models showed that improved education and age foster knowledge integration. Sex had almost no influence on the existing scientific conceptions and evolution of knowledge integration. Consequently, complex biological issues such as tree assimilation and wood synthesis need specific support e.g. through repeated learning units in class- and seminar-rooms in order to help especially young students to handle and overcome common alternative conceptions and appropriately integrate scientific conceptions into their knowledge profile

Liquid-gas-solid flows with lattice Boltzmann: Simulation of floating bodies

This paper presents a model for the simulation of liquid-gas-solid flows by means of the lattice Boltzmann method. The approach is built upon previous works for the simulation of liquid-solid particle suspensions on the one hand, and on a liquid-gas free surface model on the other. We show how the two approaches can be unified by a novel set of dynamic cell conversion rules. For evaluation, we concentrate on the rotational stability of non-spherical rigid bodies floating on a plane water surface - a classical hydrostatic problem known from naval architecture. We show the consistency of our method in this kind of flows and obtain convergence towards the ideal solution for the measured heeling stability of a floating box.Comment: 22 pages, Preprint submitted to Computers and Mathematics with Applications Special Issue ICMMES 2011, Proceedings of the Eighth International Conference for Mesoscopic Methods in Engineering and Scienc

Controlled Stark shifts in Er3+^{3+}-doped crystalline and amorphous waveguides for quantum state storage

We present measurements of the linear Stark effect on the $^{4}$I$_{15/2} \to$ $^{4}$I$_{13/2}$ transition in an Er$^{3+}$-doped proton-exchanged LiNbO$_{3}$ crystalline waveguide and an Er$^{3+}$-doped silicate fiber. The measurements were made using spectral hole burning techniques at temperatures below 4 K. We measured an effective Stark coefficient $(\Delta\mu_{e}\chi)/(h)=25\pm1$kHz/Vcm$^{-1}$ in the crystalline waveguide and $(\bar{\Delta\mu_{e}}\chi)/(h)=15\pm1$kHz/Vcm$^{-1}$ in the silicate fiber. These results confirm the potential of Erbium doped waveguides for quantum state storage based on controlled reversible inhomogeneous broadening.Comment: 4 pages, 2 figures v2. typo in formula correcte

Delocalization in Coupled Luttinger Liquids with Impurities

We study effects of quenched disorder on coupled two-dimensional arrays of Luttinger liquids (LL) as a model for stripes in high-T_c compounds. In the framework of a renormalization-group analysis, we find that weak inter-LL charge-density-wave couplings are always irrelevant as opposed to the pure system. By varying either disorder strength, intra- or inter-LL interactions, the system can undergo a delocalization transition between an insulator and a novel strongly anisotropic metallic state with LL-like transport. This state is characterized by short-ranged charge-density-wave order, the superconducting order is quasi long-ranged along the stripes and short-ranged in the transversal direction.Comment: 6 pages, 5 figures, substantially extended and revised versio