Nonlinear effects in buoyancy-driven variable-density turbulence

We consider the time dependence of a hierarchy of scaled L²ᵐ-norms D_m,ω and D_m,θ of the vorticity ω =∇ x u and the density gradient ∇θ, where θ = log.(ρ*/ ρ*₀), in a buoyancy-driven turbulent flow as simulated by Livescu & Ristorcelli (J. Fluid Mech., vol. 591, 2007, pp. 43–71). Here, ρ* (x,t) is the composition density of a mixture of two incompressible miscible fluids with fluid densities ρ*₂ > ρ*₁, and ρ*₀ is a reference normalization density. Using data from the publicly available Johns Hopkins turbulence database, we present evidence that the L²-spatial average of the density gradient can reach extremely large values at intermediate times, even in flows with low Atwood number At = (ρ*₂ - ρ*₁)/(ρ*₂ + ρ*₁) = 0.05, implying that very strong mixing of the density field at small scales can arise in buoyancy-driven turbulence. This large growth raises the possibility that the density gradient ∇θ might blow up in a finite time.We acknowledge, with thanks, the staff of IPAM UCLA where this collaboration began in the Autumn of 2014 on the programme ‘Mathematics of Turbulence’. We would also like to thank C. Doering and D. Livescu for useful discussions. All of the numerical data used are from the JHTDB (Livescu et al. 2014), a publicly available DNS database. For more information, please see http://turbulence.pha.jhu.edu/. We also thank the referees for suggesting substantial improvements

Lessons from dynamic cadaver and invasive bone pin studies: do we know how the foot really moves during gait?

Background: This paper provides a summary of a Keynote lecture delivered at the 2009 Australasian Podiatry Conference. The aim of the paper is to review recent research that has adopted dynamic cadaver and invasive kinematics research approaches to better understand foot and ankle kinematics during gait. It is not intended to systematically cover all literature related to foot and ankle kinematics (such as research using surface mounted markers). Since the paper is based on a keynote presentation its focuses on the authors own experiences and work in the main, drawing on the work of others where appropriate Methods: Two approaches to the problem of accessing and measuring the kinematics of individual anatomical structures in the foot have been taken, (i) static and dynamic cadaver models, and (ii) invasive in-vivo research. Cadaver models offer the advantage that there is complete access to all the tissues of the foot, but the cadaver must be manipulated and loaded in a manner which replicates how the foot would have performed when in-vivo. The key value of invasive in-vivo foot kinematics research is the validity of the description of foot kinematics, but the key difficulty is how generalisable this data is to the wider population. Results: Through these techniques a great deal has been learnt. We better understand the valuable contribution mid and forefoot joints make to foot biomechanics, and how the ankle and subtalar joints can have almost comparable roles. Variation between people in foot kinematics is high and normal. This includes variation in how specific joints move and how combinations of joints move. The foot continues to demonstrate its flexibility in enabling us to get from A to B via a large number of different kinematic solutions. Conclusion: Rather than continue to apply a poorly founded model of foot type whose basis is to make all feet meet criteria for the mechanical 'ideal' or 'normal' foot, we should embrace variation between feet and identify it as an opportunity to develop patient-specific clinical models of foot function

Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications

Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, we propose to describe the interaction forces involving the extracellular matrix via some concepts coming from viscoplasticity. We then apply the model to the description of the growth of tumour cords and the formation of fibrosis

Generation and analysis of expressed sequence tags (ESTs) for marker development in yam (Dioscorea alata L.)

<p>Abstract</p> <p>Background</p> <p>Anthracnose (<it>Colletotrichum </it><it>gloeosporioides</it>) is a major limiting factor in the production of yam (<it>Dioscorea </it>spp.) worldwide. Availability of high quality sequence information is necessary for designing molecular markers associated with resistance. However, very limited sequence information pertaining to yam is available at public genome databases. Therefore, this collaborative project was developed for genetic improvement and germplasm characterization of yams using molecular markers. The current investigation is focused on studying gene expression, by large scale generation of ESTs, from one susceptible (TDa 95-0310) and two resistant yam genotypes (TDa 87-01091, TDa 95-0328) challenged with the fungus. Total RNA was isolated from young leaves of resistant and susceptible genotypes and cDNA libraries were sequenced using Roche 454 technology.</p> <p>Results</p> <p>A total of 44,757 EST sequences were generated from the cDNA libraries of the resistant and susceptible genotypes. Greater than 56% of ESTs were annotated using MapMan Mercator tool and Blast2GO search tools. Gene annotations were used to characterize the transcriptome in yam and also perform a differential gene expression analysis between the resistant and susceptible EST datasets. Mining for SSRs in the ESTs revealed 1702 unique sequences containing SSRs and 1705 SSR markers were designed using those sequences.</p> <p>Conclusion</p> <p>We have developed a comprehensive annotated transcriptome data set in yam to enrich the EST information in public databases. cDNA libraries were constructed from anthracnose fungus challenged leaf tissues for transcriptome characterization, and differential gene expression analysis. Thus, it helped in identifying unique transcripts in each library for disease resistance. These EST resources provide the basis for future microarray development, marker validation, genetic linkage mapping and QTL analysis in <it>Dioscorea </it>species.</p

Exploring the Free Energy Landscape: From Dynamics to Networks and Back

The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers are, how the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times or rate constants, and the hierarchical relationship among basins, complete the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, the dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press

A transformed view of cyclosporine

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62591/1/397471a0.pd

Bianchi Type-II String Cosmological Models in Normal Gauge for Lyra's Manifold with Constant Deceleration Parameter

The present study deals with a spatially homogeneous and anisotropic Bianchi-II cosmological models representing massive strings in normal gauge for Lyra's manifold by applying the variation law for generalized Hubble's parameter that yields a constant value of deceleration parameter. The variation law for Hubble's parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein's modified field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier (1983) is used to construct massive string cosmological models for which we assume that the expansion ($\theta$) in the model is proportional to the component $\sigma^{1}_{~1}$ of the shear tensor $\sigma^{j}_{i}$. This condition leads to $A = (BC)^{m}$, where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector $\beta$ behaves like cosmological term $\Lambda$ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the decelerating universe whereas strings dominate in the accelerating universe. Some physical and geometric behaviour of these models are also discussed.Comment: 24 pages, 10 figure

Genetic determinants of co-accessible chromatin regions in activated T cells across humans.

Over 90% of genetic variants associated with complex human traits map to non-coding regions, but little is understood about how they modulate gene regulation in health and disease. One possible mechanism is that genetic variants affect the activity of one or more cis-regulatory elements leading to gene expression variation in specific cell types. To identify such cases, we analyzed ATAC-seq and RNA-seq profiles from stimulated primary CD4+ T cells in up to 105 healthy donors. We found that regions of accessible chromatin (ATAC-peaks) are co-accessible at kilobase and megabase resolution, consistent with the three-dimensional chromatin organization measured by in situ Hi-C in T cells. Fifteen percent of genetic variants located within ATAC-peaks affected the accessibility of the corresponding peak (local-ATAC-QTLs). Local-ATAC-QTLs have the largest effects on co-accessible peaks, are associated with gene expression and are enriched for autoimmune disease variants. Our results provide insights into how natural genetic variants modulate cis-regulatory elements, in isolation or in concert, to influence gene expression