Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model

We investigate the phase diagram of a spin-$1/2$ Ising model on a cubic lattice, with competing interactions between nearest and next-nearest neighbors along an axial direction, and fully connected spins on the sites of each perpendicular layer. The problem is formulated in terms of a set of noninteracting Ising chains in a position-dependent field. At low temperatures, as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising (ANNNI) model, there are many distinct spatially commensurate phases that spring from a multiphase point of infinitely degenerate ground states. As temperature increases, we confirm the existence of a branching mechanism associated with the onset of higher-order commensurate phases. We check that the ferromagnetic phase undergoes a first-order transition to the modulated phases. Depending on a parameter of competition, the wave number of the striped patterns locks in rational values, giving rise to a devil's staircase. We numerically calculate the Hausdorff dimension $D_{0}$ associated with these fractal structures, and show that $D_{0}$ increases with temperature but seems to reach a limiting value smaller than $D_{0}=1$.Comment: 17 pages, 6 figure

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results

A Role for Frizzled and Their Post-Translational Modifications in the Mammalian Central Nervous System

The Wnt pathway is a key signalling cascade that regulates the formation and function of neuronal circuits. The main receptors for Wnts are Frizzled (Fzd) that mediate diverse functions such as neurogenesis, axon guidance, dendritogenesis, synapse formation, and synaptic plasticity. These processes are crucial for the assembly of functional neuronal circuits required for diverse functions ranging from sensory and motor tasks to cognitive performance. Indeed, aberrant Wnt–Fzd signalling has been associated with synaptic defects during development and in neurodegenerative conditions such as Alzheimer’s disease. New studies suggest that the localisation and stability of Fzd receptors play a crucial role in determining Wnt function. Post-translational modifications (PTMs) of Fzd are emerging as an important mechanism that regulates these Wnt receptors. However, only phosphorylation and glycosylation have been described to modulate Fzd function in the central nervous system (CNS). In this review, we discuss the function of Fzd in neuronal circuit connectivity and how PTMs contribute to their function. We also discuss other PTMs, not yet described in the CNS, and how they might modulate the function of Fzd in neuronal connectivity. PTMs could modulate Fzd function by affecting Fzd localisation and stability at the plasma membrane resulting in local effects of Wnt signalling, a feature particularly important in polarised cells such as neurons. Our review highlights the importance of further studies into the role of PTMs on Fzd receptors in the context of neuronal connectivity

Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity

© 2016 .A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach

Electric LAMP: Virtual Loop-Mediated Isothermal AMPlification

We present eLAMP, a PERL script, with Tk graphical interface, that electronically simulates Loop-mediated AMPlification (LAMP) allowing users to efficiently test putative LAMP primers on a set of target sequences. eLAMP can match primers to templates using either exact (via builtin PERL regular expressions) or approximate matching (via the tre-agrep library). Performance was tested on 40 whole genome sequences of Staphylococcus. eLAMP correctly predicted that the two tested primer sets would amplify from S. aureus genomes and not amplify from other Staphylococcus species. Open source (GNU Public License) PERL scripts are available for download from the New York Botanical Garden’s website

Statistical models of mixtures with a biaxial nematic phase

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like and disc-like molecules. A quenched distribution of shapes leads to the existence of a stable biaxial nematic phase, in qualitative agreement with experimental findings for some ternary lyotropic liquid mixtures. An annealed distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.Comment: 11 pages, 2 figure