Network Measures of Mixing

Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches, where trajectories serve as nodes and some similarity or distance measure between them is employed to build a (possibly weighted) network, which is then analyzed using spectral methods. Here, we consider the simplest case of an unweighted, undirected network and analytically relate local network measures such as node degree or clustering coefficient to flow structures. In particular, we use these local measures to divide the family of trajectories into groups of similar dynamical behavior via manifold learning methods

Lagrangian heat transport in turbulent three-dimensional convection

Spatial regions that do not mix effectively with their surroundings and thus contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-B\'{e}nard flows are identified by Lagrangian trajectories that stay together for a longer time. These trajectories probe Lagrangian coherent sets (CS) which we investigate here in direct numerical simulations in convection cells with square cross section of aspect ratio $\Gamma = 16$, Rayleigh number $Ra = 10^{5}$, and Prandtl numbers $Pr = 0.1, 0.7$ and $7$. The analysis is based on $N=524,288$ Lagrangian tracer particles which are advected in the time-dependent flow. Clusters of trajectories are identified by a graph Laplacian with a diffusion kernel, which quantifies the connectivity of trajectory segments, and a subsequent sparse eigenbasis approximation (SEBA) for cluster detection. The combination of graph Laplacian and SEBA leads to a significantly improved cluster identification that is compared with the large-scale patterns in the Eulerian frame of reference. We show that the detected CS contribute by a third less to the global turbulent heat transport for all investigated $Pr$ compared to the trajectories in the spatial complement. This is realized by monitoring Nusselt numbers along the tracer trajectory ensembles, a dimensionless local measure of heat transfer.Comment: 8 pages, 5 figure

Lagrangian studies of coherent sets and heat transport in constant heat flux-driven turbulent Rayleigh-B\'enard convection

We explore the mechanisms of heat transfer in a turbulent constant heat flux-driven Rayleigh-B\'enard convection flow, which exhibits a hierarchy of flow structures from granules to supergranules. Our computational framework makes use of time-dependent flow networks. These are based on trajectories of Lagrangian tracer particles that are advected in the flow. We identify coherent sets in the Lagrangian frame of reference as those sets of trajectories that stay closely together for an extended time span under the action of the turbulent flow. Depending on the choice of the measure of coherence, sets with different characteristics are detected. First, the application of a recently proposed evolutionary spectral clustering scheme allows us to extract granular coherent features that are shown to contribute significantly less to the global heat transfer than their spatial complements. Moreover, splits and mergers of these (leaking) coherent sets leave spectral footprints. Secondly, trajectories which exhibit a small node degree in the corresponding network represent objectively highly coherent flow structures and can be related to supergranules as the other stage of the present flow hierarchy. We demonstrate that the supergranular flow structures play a key role in the vertical heat transport and that they exhibit a greater spatial extension than the granular structures obtained from spectral clustering.Comment: 21 pages, 15 figure

Different ascending aortic phenotypes with similar mutations in two patients with Loeys-Dietz-Syndrome type 2

Our goal was to present 2 infants with confirmed Loeys-Dietz syndrome. The missense mutations in exon 7 of the TGFBR2 gene are only 5 codons apart (c.1597T>C and c.1582C>G). Phenotypically, the aneurysms of the ascending aorta were restricted to different segments of the aorta: the suprajunctional segment in 1 patient and the aortic root in another. These cases highlight the complexity of signaling path- ways and gene expression in the pathogenesis of aortic aneurysms

Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I : theoretical formulation and model validation

This paper is first of the two papers dealingwith analytical investigation of resonant multimodal dynamics due to 2:1 internal resonances in the finite-amplitude free vibrations of horizontal/inclined cables. Part I deals with theoretical formulation and validation of the general cable model. Approximate nonlinear partial differential equations of 3-D coupled motion of small sagged cables - which account for both spatio-temporal variation of nonlinear dynamic tension and system asymmetry due to inclined sagged configurations - are presented. A multidimensional Galerkin expansion of the solution ofnonplanar/planar motion is performed, yielding a complete set of system quadratic/cubic coefficients. With the aim of parametrically studying the behavior of horizontal/inclined cables in Part II [25], a second-order asymptotic analysis under planar 2:1 resonance is accomplished by the method of multiple scales. On accounting for higher-order effectsof quadratic/cubic nonlinearities, approximate closed form solutions of nonlinear amplitudes, frequencies and dynamic configurations of resonant nonlinear normal modes reveal the dependence of cable response on resonant/nonresonant modal contributions. Depending on simplifying kinematic modeling and assigned system parameters, approximate horizontal/inclined cable models are thoroughly validated by numerically evaluating statics and non-planar/planar linear/non-linear dynamics against those of the exact model. Moreover, the modal coupling role and contribution of system longitudinal dynamics are discussed for horizontal cables, showing some meaningful effects due to kinematic condensation

A lanostane aldehyde from Momordica charantia

A new lanostane aldehyde, charantal (1), was isolated from the ethanolic leaf extract of Momordica charantia together with the known compound, 2,4-bis(2-phenylpropan-2-yl)phenol (2). The structure of compound 1 was elucidated by extensive 1D and 2D NMR and MS experiments. Compound 2 displayed a moderately strong antitubercular activity against Mycobacterium tuberculosis H37Rv (MIC = 14 μg/mL) according to the MABA susceptibility assay

Quantitative trait loci for sensitivity to ethanol intoxication in a C57BL/6J × 129S1/SvImJ inbred mouse cross

Individual variation in sensitivity to acute ethanol (EtOH) challenge is associated with alcohol drinking and is a predictor of alcohol abuse. Previous studies have shown that the C57BL/6J (B6) and 129S1/SvImJ (S1) inbred mouse strains differ in responses on certain measures of acute EtOH intoxication. To gain insight into genetic factors contributing to these differences, we performed quantitative trait locus (QTL) analysis of measures of EtOH-induced ataxia (accelerating rotarod), hypothermia, and loss of righting reflex (LORR) duration in a B6 × S1 F2 population. We confirmed that S1 showed greater EtOH-induced hypothermia (specifically at a high dose) and longer LORR compared to B6. QTL analysis revealed several additive and interacting loci for various phenotypes, as well as examples of genotype interactions with sex. QTLs for different EtOH phenotypes were largely non-overlapping, suggesting separable genetic influences on these behaviors. The most compelling main-effect QTLs were for hypothermia on chromosome 16 and for LORR on chromosomes 4 and 6. Several QTLs overlapped with loci repeatedly linked to EtOH drinking in previous mouse studies. The architecture of the traits we examined was complex but clearly amenable to dissection in future studies. Using integrative genomics strategies, plausible functional and positional candidates may be found. Uncovering candidate genes associated with variation in these phenotypes in this population could ultimately shed light on genetic factors underlying sensitivity to EtOH intoxication and risk for alcoholism in humans