Depletion of Nonlinearity in Magnetohydrodynamic Turbulence: Insights from Analysis and Simulations

We build on recent developments in the study of fluid turbulence [Gibbon \textit{et al.} Nonlinearity 27, 2605 (2014)] to define suitably scaled, order-$m$ moments, $D_m^{\pm}$, of $\omega^\pm= \omega \pm j$, where $\omega$ and $j$ are, respectively, the vorticity and current density in three-dimensional magnetohydrodynamics (MHD). We show by mathematical analysis, for unit magnetic Prandtl number $P_M$, how these moments can be used to identify three possible regimes for solutions of the MHD equations; these regimes are specified by inequalities for $D_m^{\pm}$ and $D_1^{\pm}$. We then compare our mathematical results with those from our direct numerical simulations (DNSs) and thus demonstrate that 3D MHD turbulence is like its fluid-turbulence counterpart insofar as all solutions, which we have investigated, remain in \textit{only one of these regimes}; this regime has depleted nonlinearity. We examine the implications of our results for the exponents $q^{\pm}$ that characterize the power-law dependences of the energy spectra $\mathcal{E}^{\pm}(k)$ on the wave number $k$, in the inertial range of scales. We also comment on (a) the generalization of our results to the case $P_M \neq 1$ and (b) the relation between $D_m^{\pm}$ and the order-$m$ moments of gradients of hydrodynamic fields, which are used in characterizing intermittency in turbulent flows.Comment: 14 pages, 3 figure

Exact results and scaling properties of small-world networks

We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance, $\bar{\ell}$, and its variance, $\sigma^2$. We also discuss the scaling properties of the distribution function. Finally, we study the limit of large system sizes and obtain some analytic results.Comment: RevTeX, 4 pages, 5 figures included. Minor corrections and addition

Ekpyrosis and inflationary dynamics in heavy ion collisions: the role of quantum fluctuations

We summarize recent significant progress in the development of a first-principles formalism to describe the formation and evolution of matter in very high energy heavy ion collisions. The key role of quantum fluctuations both before and after a collision is emphasized. Systematic computations are now feasible to address early time dynamics essential to quantifying properties of strongly interacting quark-gluon matter.Comment: Talk by R.V. at Quark Matter 2011, Annecy, France, May 23-28, 2011. LaTex, 4 pages; v2, final version to appear in J. Phys.

Towards Reliable Automatic Protein Structure Alignment

A variety of methods have been proposed for structure similarity calculation, which are called structure alignment or superposition. One major shortcoming in current structure alignment algorithms is in their inherent design, which is based on local structure similarity. In this work, we propose a method to incorporate global information in obtaining optimal alignments and superpositions. Our method, when applied to optimizing the TM-score and the GDT score, produces significantly better results than current state-of-the-art protein structure alignment tools. Specifically, if the highest TM-score found by TMalign is lower than (0.6) and the highest TM-score found by one of the tested methods is higher than (0.5), there is a probability of (42%) that TMalign failed to find TM-scores higher than (0.5), while the same probability is reduced to (2%) if our method is used. This could significantly improve the accuracy of fold detection if the cutoff TM-score of (0.5) is used. In addition, existing structure alignment algorithms focus on structure similarity alone and simply ignore other important similarities, such as sequence similarity. Our approach has the capacity to incorporate multiple similarities into the scoring function. Results show that sequence similarity aids in finding high quality protein structure alignments that are more consistent with eye-examined alignments in HOMSTRAD. Even when structure similarity itself fails to find alignments with any consistency with eye-examined alignments, our method remains capable of finding alignments highly similar to, or even identical to, eye-examined alignments.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

Turbulence and Multiscaling in the Randomly Forced Navier Stokes Equation

We present an extensive pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance $\sim k^{4-d-y}$, where $k$ is the wavevector and the dimension $d = 3$. We present the first evidence for multiscaling of velocity structure functions in this model for $y \geq 4$. We extract the multiscaling exponent ratios $\zeta_p/\zeta_2$ by using extended self similarity (ESS), examine their dependence on $y$, and show that, if $y = 4$, they are in agreement with those obtained for the deterministically forced Navier-Stokes equation ($3d$NSE). We also show that well-defined vortex filaments, which appear clearly in studies of the $3d$NSE, are absent in the RFNSE.Comment: 4 pages (revtex), 6 figures (postscript

Wetting of a symmetrical binary fluid mixture on a wall

We study the wetting behaviour of a symmetrical binary fluid below the demixing temperature at a non-selective attractive wall. Although it demixes in the bulk, a sufficiently thin liquid film remains mixed. On approaching liquid/vapour coexistence, however, the thickness of the liquid film increases and it may demix and then wet the substrate. We show that the wetting properties are determined by an interplay of the two length scales related to the density and the composition fluctuations. The problem is analysed within the framework of a generic two component Ginzburg-Landau functional (appropriate for systems with short-ranged interactions). This functional is minimized both numerically and analytically within a piecewise parabolic potential approximation. A number of novel surface transitions are found, including first order demixing and prewetting, continuous demixing, a tricritical point connecting the two regimes, or a critical end point beyond which the prewetting line separates a strongly and a weakly demixed film. Our results are supported by detailed Monte Carlo simulations of a symmetrical binary Lennard-Jones fluid at an attractive wall.Comment: submitted to Phys. Rev.

Walks on Apollonian networks

We carry out comparative studies of random walks on deterministic Apollonian networks (DANs) and random Apollonian networks (RANs). We perform computer simulations for the mean first passage time, the average return time, the mean-square displacement, and the network coverage for unrestricted random walk. The diffusions both on DANs and RANs are proved to be sublinear. The search efficiency for walks with various strategies and the influence of the topology of underlying networks on the dynamics of walks are discussed. Contrary to one's intuition, it is shown that the self-avoiding random walk, which has been verified as an optimal strategy for searching on scale-free and small-world networks, is not the best strategy for the DAN in the thermodynamic limit.Comment: 5 pages, 4 figure

Untying a nanoscale knotted polymer structure to linear chains for efficient gene delivery in vitro and to the brain

The purpose of this study was to develop a platform transfection technology, for applications in the brain, which could transfect astrocytes without requiring cell specific functionalization and without the common cause of toxicity through high charge density. Here we show that a simple and scalable preparation technique can be used to produce a “knot” structured cationic polymer, where single growing chains can crosslink together via disulphide intramolecular crosslinks (internal cyclizations). This well-defined knot structure can thus “untie” under reducing conditions, showing a more favorable transfection profile for astrocytes compared to 25 kDa-PEI (48-fold), SuperFect® (39-fold) and Lipofectamine®2000 (18-fold) whilst maintaining neural cell viability at over 80% after four days of culture. The high transfection/lack of toxicity of this knot structured polymer in vitro, combined with its ability to mediate luciferase transgene expression in the adult rat brain, demonstrates its use as a platform transfection technology which should be investigated further for neurodegenerative disease therapies

Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets

A phenomenological theory of magnetic states in noncentrosymmetric tetragonal antiferromagnets is developed, which has to include homogeneous and inhomogeneous terms (Lifshitz-invariants) derived from Dzyaloshinskii-Moriya couplings. Magnetic properties of this class of antiferromagnets with low crystal symmetry are discussed in relation to its first known members, the recently detected compounds Ba2CuGe2O7 and K2V3O8. Crystallographic symmetry and magnetic ordering in these systems allow the simultaneous occurrence of chiral inhomogeneous magnetic structures and weak ferromagnetism. New types of incommensurate magnetic structures are possible, namely, chiral helices with rotation of staggered magnetization and oscillations of the total magnetization. Field-induced reorientation transitions into modulated states have been studied and corresponding phase diagrams are constructed. Structures of magnetic defects (domain-walls and vortices) are discussed. In particular, vortices, i.e. localized non-singular line defects, are stabilized by the inhomogeneous Dzyaloshinskii-Moriya interactions in uniaxial noncentrosymmetric antiferromagnets.Comment: 18 pages RevTeX4, 13 figure