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Turbulent mixing plays an important role in a variety of applications ranging from astrophysics to combustion and even pollutant dispersion. The Direct Numerical Simulation (DNS) that resolves all scales is not feasible for most engineering applications since the flow has a wide range of length and time scales, which yields extremely high resolution requirements. Large Eddy Simulations (LES) overcome this limitation by modeling the sub‐grid scale effects. In transported Probability Density Function (PDF) methods, the key challenge is to develop an accurate mixing model. At this point, the Hierarchical Parcel‐Swapping (HiPS) model, introduced by A.R. Kerstein [J. Stat. Phys. 153, 142‐161 (2013)], is an attractive candidate. It is characterized by a computationally efficient representation of the effects of turbulence on a time‐evolving structure of diffusive scalar fields. The interpretation of the diffusive scalar fields or a state space as a binary tree structure is an alternative approach compared to the most common mixing models. The characteristic feature of HiPS is that every level of the tree corresponds to a specific length and time scale, which is based on turbulence inertial range scaling. The state variables only reside at the base of the tree and are understood as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub‐trees at rates determined by prevailing turbulent time scales associated with the sub‐trees. The mixing of adjacent fluid parcels is done either instantaneously or at rates consistent with the corresponding diffusion time scales. In this work, HiPS is detailed for the simulation of passive scalar mixing first. Preliminary results for the scalar power spectra, mean square displacement and scalar dissipation rate are shown and reveal a reasonable agreement with experimental findings. Furthermore, the integrated binary tree structure allows to satisfy a large number of criteria for a good mixing model. Considering the reduced order and computational efficiency, HiPS is an attractive candidate for modeling the mixing in transported PDF methods. [ABSTRACT FROM AUTHOR]

In bilaterians, three orthogonal body axes define the animal form, with distinct anterior-posterior, dorsal-ventral and left-right asymmetries. The key signalling factors are Wnt family proteins for the anterior-posterior axis, Bmp family proteins for the dorsal-ventral axis and Nodal for the left-right axis (1). Cnidarians, the sister group to bilaterians, are characterized by one oral-aboral body axis, which exhibits a distinct biradiality of unknown molecular nature. Here we analysed the biradial growth pattern in the radially symmetrical cnidarian polyp Hydra, and we report evidence of Nodal in a pre-bilaterian clade. We identified a Nodal-related gene (Ndr) in Hydra magnipapillata, and this gene is essential for setting up an axial asymmetry along the main body axis. This asymmetry defines a lateral signalling centre, inducing a new body axis of a budding polyp orthogonal to the mother polyp's axis. Ndr is expressed exclusively in the lateral bud anlage and induces Pitx, which encodes an evolutionarily conserved transcription factor that functions downstream of Nodal. Reminiscent of its function in vertebrates (2,3), Nodal acts downstream of β-Catenin signalling. Our data support an evolutionary scenario in which a 'core-signalling cassette' consisting of β-Catenin, Nodal and Pitx pre-dated the cnidarian-bilaterian split. We presume that this cassette was co-opted for various modes of axial patterning: for example, for lateral branching in cnidarians and left-right patterning in bilaterians., An animal body plan can be described by using the axes of a Cartesian coordinate system (1,4). Bilaterian animals, for example, exhibit one major body axis, passing from anterior to [...]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ydbio.2010.08.007 Byline: Kyle A. Gurley, Sarah A. Elliott, Oleg Simakov, Heiko A. Schmidt, Thomas W. Holstein, Alejandro Sanchez Alvarado Keywords: Stem cells; Regeneration; Tissue remodeling; Wnt signaling pathway; Planarians Abstract: Regeneration is widespread throughout the animal kingdom, but our molecular understanding of this process in adult animals remains poorly understood. Wnt/[beta]-catenin signaling plays crucial roles throughout animal life from early development to adulthood. In intact and regenerating planarians, the regulation of Wnt/[beta]-catenin signaling functions to maintain and specify anterior/posterior (A/P) identity. Here, we explore the expression kinetics and RNAi phenotypes for secreted members of the Wnt signaling pathway in the planarian Schmidtea mediterranea. Smed-wnt and sFRP expression during regeneration is surprisingly dynamic and reveals fundamental aspects of planarian biology that have been previously unappreciated. We show that after amputation, a wounding response precedes rapid re-organization of the A/P axis. Furthermore, cells throughout the body plan can mount this response and reassess their new A/P location in the complete absence of stem cells. While initial stages of the amputation response are stem cell independent, tissue remodeling and the integration of a new A/P address with anatomy are stem cell dependent. We also show that WNT5 functions in a reciprocal manner with SLIT to pattern the planarian mediolateral axis, while WNT11-2 patterns the posterior midline. Moreover, we perform an extensive phylogenetic analysis on the Smed-wnt genes using a method that combines and integrates both sequence and structural alignments, enabling us to place all nine genes into Wnt subfamilies for the first time. Article History: Received 11 June 2010; Revised 1 August 2010; Accepted 3 August 2010

Author(s): Arne Kusserow [1]; Kevin Pang [2]; Carsten Sturm [1]; Martina Hrouda [3]; Jan Lentfer [1]; Heiko A. Schmidt [4]; Ulrich Technau [1, 7]; Arndt von Haeseler [4, 5]; Bert [...]