Direct numerical simulation of heat transport in dispersed gas-liquid two-phase flow using a front tracking approach

In this paper a simulation model is presented for the Direct Numerical Simulation (DNS) of heat transport in dispersed gas-liquid two-phase flow using the Front Tracking (FT) approach. Our model extends the FT model developed by van Sint Annaland et al. (2006) to non-isothermal conditions. In FT an unstructured dynamic mesh is used to represent and track the interface explicitly by a number of interconnected marker points. The Lagrangian representation of the interface avoids the necessity to reconstruct the interface from the local distribution of the fractions of the phases and, moreover, allows a direct and accurate calculation of the surface tension force circumventing the (problematic) computation of the interface curvature. The extended model is applied to predict the heat exchange rate between the liquid and a hot wall kept at a fixed temperature. It is found that the wall-to-liquid heat transfer coefficient exhibits a maximum in the vicinity of the bubble that can be attributed to the locally decreased thickness of the thermal boundary layer

The Discrete Frenet Frame, Inflection Point Solitons And Curve Visualization with Applications to Folded Proteins

We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively describe curves that in the limit where the length of line segments vanishes approach fractal structures in lieu of continuous curves. We verify that in the case of differentiable curves the continuum limit of our discrete equation does reproduce the generalized Frenet equation. As an application we consider folded proteins, their Hausdorff dimension is known to be fractal. We explain how to employ the orientation of $C_\beta$ carbons of amino acids along a protein backbone to introduce a preferred framing along the backbone. By analyzing the experimentally resolved fold geometries in the Protein Data Bank we observe that this $C_\beta$ framing relates intimately to the discrete Frenet framing. We also explain how inflection points can be located in the loops, and clarify their distinctive r\^ole in determining the loop structure of foldel proteins.Comment: 14 pages 12 figure

MOTIFATOR: detection and characterization of regulatory motifs using prokaryote transcriptome data

Summary: Unraveling regulatory mechanisms (e.g. identification of motifs in cis-regulatory regions) remains a major challenge in the analysis of transcriptome experiments. Existing applications identify putative motifs from gene lists obtained at rather arbitrary cutoff and require additional manual processing steps. Our standalone application MOTIFATOR identifies the most optimal parameters for motif discovery and creates an interactive visualization of the results. Discovered putative motifs are functionally characterized, thereby providing valuable insight in the biological processes that could be controlled by the motif.

On Hausdorff dimension of the set of closed orbits for a cylindrical transformation

We deal with Besicovitch's problem of existence of discrete orbits for transitive cylindrical transformations $T_\varphi:(x,t)\mapsto(x+\alpha,t+\varphi(x))$ where $Tx=x+\alpha$ is an irrational rotation on the circle \T and \varphi:\T\to\R is continuous, i.e.\ we try to estimate how big can be the set D(\alpha,\varphi):=\{x\in\T:|\varphi^{(n)}(x)|\to+\infty\text{as}|n|\to+\infty\}. We show that for almost every $\alpha$ there exists $\varphi$ such that the Hausdorff dimension of $D(\alpha,\varphi)$ is at least $1/2$. We also provide a Diophantine condition on $\alpha$ that guarantees the existence of $\varphi$ such that the dimension of $D(\alpha,\varphi)$ is positive. Finally, for some multidimensional rotations $T$ on \T^d, $d\geq3$, we construct smooth $\varphi$ so that the Hausdorff dimension of $D(\alpha,\varphi)$ is positive.Comment: 32 pages, 1 figur