Multiscaling in passive scalar advection as stochastic shape dynamics

The Kraichnan rapid advection model is recast as the stochastic dynamics of tracer trajectories. This framework replaces the random fields with a small set of stochastic ordinary differential equations. Multiscaling of correlation functions arises naturally as a consequence of the geometry described by the evolution of N trajectories. Scaling exponents and scaling structures are interpreted as excited states of the evolution operator. The trajectories become nearly deterministic in high dimensions allowing for perturbation theory in this limit. We calculate perturbatively the anomalous exponent of the third and fourth order correlation functions. The fourth order result agrees with previous calculations.Comment: 14 pages, LaTe

Statistical geometry in scalar turbulence

A general link between geometry and intermittency in passive scalar turbulence is established. Intermittency is qualitatively traced back to events where tracer particles stay for anomalousy long times in degenerate geometries characterized by strong clustering. The quantitative counterpart is the existence of special functions of particle configurations which are statistically invariant under the flow. These are the statistical integrals of motion controlling the scalar statistics at small scales and responsible for the breaking of scale invariance associated to intermittency.Comment: 4 pages, 5 figure

Mapping liver fat female-dependent quantitative trait loci in collaborative cross mice

Non-alcoholic fatty liver disease (NAFLD) is the most common cause of chronic liver disease in the western world, with spectrum from simple steatosis to non-alcoholic steatohepatitis, which can progress to cirrhosis. NAFLD developments are known to be affected by host genetic background. Herein we emphasize the power of collaborative cross (CC) mouse for dissecting this complex trait and revealing quantitative trait loci (QTL) controlling hepatic fat accumulation in mice. 168 female and 338 male mice from 24 and 37 CC lines, respectively, of 18-20 weeks old, maintained on standard rodent diet, since weaning. Hepatic fat content was assessed, using dual DEXA scan in the liver. Using the available high-density genotype markers of the CC line, QTL mapping associated with percentage liver fat accumulation was performed. Our results revealed significant fatty liver accumulation QTL that were specifically, mapped in females. Two significant QTLs on chromosomes 17 and 18, with genomic intervals 3 and 2 Mb, respectively, were mapped. A third QTL, with a less significant P value, was mapped to chromosome 4, with genomic interval of 2 Mb. These QTLs were named Flal1-Flal3, referring to Fatty Liver Accumulation Locus 1-3, for the QTLs on chromosomes 17, 18, and 4, respectively. Unfortunately, no QTL was mapped with males. Searching the mouse genome database suggested several candidate genes involved in hepatic fat accumulation. Our results show that susceptibility to hepatic fat accumulations is a complex trait, controlled by multiple genetic factors in female mice, but not in male

Statistical conservation laws in turbulent transport

We address the statistical theory of fields that are transported by a turbulent velocity field, both in forced and in unforced (decaying) experiments. We propose that with very few provisos on the transporting velocity field, correlation functions of the transported field in the forced case are dominated by statistically preserved structures. In decaying experiments (without forcing the transported fields) we identify infinitely many statistical constants of the motion, which are obtained by projecting the decaying correlation functions on the statistically preserved functions. We exemplify these ideas and provide numerical evidence using a simple model of turbulent transport. This example is chosen for its lack of Lagrangian structure, to stress the generality of the ideas

A Bivariate Measure of Redundant Information

We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual information, redundant information denotes information that is shared about the outcome of a third variable. Formalizing this concept, and being able to measure it, is required for the non-negative decomposition of mutual information into redundant and synergistic information. Previous attempts to formalize redundant or synergistic information struggle to capture some desired properties. We introduce a new formalism for redundant information and prove that it satisfies all the properties necessary outlined in earlier work, as well as an additional criterion that we propose to be necessary to capture redundancy. We also demonstrate the behaviour of this new measure for several examples, compare it to previous measures and apply it to the decomposition of transfer entropy.Comment: 16 pages, 15 figures, 1 table, added citation to Griffith et al 2012, Maurer et al 199

Site-Dilution in quasi one-dimensional antiferromagnet Sr2(Cu1-xPdx)O3: reduction of Neel Temperature and spatial distribution of ordered moment sizes

We investigate the Neel temperature of Sr2CuO3 as a function of the site dilution at the Cu (S=1/2) sites with Pd (S=0), utilizing the muon spin relaxation (muSR) technique. The Neel temperature, which is Tn=5.4K for the undoped system, becomes significantly reduced for less than one percent of doping Pd, giving a support for the previous proposal for the good one-dimensionality. The Pd concentration dependence of the Neel temperature is compared with a recent theoretical study (S. Eggert, I. Affleck and M.D.P. Horton, Phys. Rev. Lett. 89, 47202 (2002)) of weakly coupled one-dimensional antiferromagnetic chains of S=1/2 spins, and a quantitative agreement is found. The inhomogeneity of the ordered moment sizes is characterized by the muSR time spectra. We propose a model that the ordered moment size recovers away from the dopant S=0 sites with a recovery length of \xi = 150-200 sites. The origin of the finite recovery length \xi for the gapless S=1/2 antiferromagnetic chain is compared to the estimate based on the effective staggered magnetic field from the neighboring chains.Comment: 10 pages, 9 figures, submitted to PR

Doping and temperature dependence of electron spectrum and quasiparticle dispersion in doped bilayer cuprates

Within the t-t'-J model, the electron spectrum and quasiparticle dispersion in doped bilayer cuprates in the normal state are discussed by considering the bilayer interaction. It is shown that the bilayer interaction splits the electron spectrum of doped bilayer cuprates into the bonding and antibonding components around the $(\pi,0)$ point. The differentiation between the bonding and antibonding components is essential, which leads to two main flat bands around the $(\pi,0)$ point below the Fermi energy. In analogy to the doped single layer cuprates, the lowest energy states in doped bilayer cuprates are located at the $(\pi/2,\pi/2)$ point. Our results also show that the striking behavior of the electronic structure in doped bilayer cuprates is intriguingly related to the bilayer interaction together with strong coupling between the electron quasiparticles and collective magnetic excitations.Comment: 9 pages, 4 figures, updated references, added figures and discussions, accepted for publication in Phys. Rev.

Muon Spin Relaxation and Susceptibility Studies of Pure and Doped Spin 1/2 Kagom\'{e}-like system (Cux_xZn1−x_{1-x})3_{3}V2_{2}O7_7(OH)2_{2} 2H2_2O

Muon spin relaxation ($\mu$SR) and magnetic susceptibility measurements have been performed on the pure and diluted spin 1/2 kagom\'{e} system (Cu$_x$Zn$_{1-x}$)$_{3}$V$_{2}$O$_7$(OH)$_{2}$ 2H$_2$O. In the pure $x=1$ system we found a slowing down of Cu spin fluctuations with decreasing temperature towards $T \sim 1$ K, followed by slow and nearly temperature-independent spin fluctuations persisting down to $T$ = 50 mK, indicative of quantum fluctuations. No indication of static spin freezing was detected in either of the pure ($x$=1.0) or diluted samples. The observed magnitude of fluctuating fields indicates that the slow spin fluctuations represent an intrinsic property of kagom\'e network rather than impurity spins.Comment: 4 pges, 4 color figures, Phys. Rev. Lett. in pres

Scotland, Catalonia and the “right” to self-determination: a comment suggested by Kathryn Crameri’s “Do Catalans Have the Right to Decide?

No abstract available

Active and passive fields face to face

The statistical properties of active and passive scalar fields transported by the same turbulent flow are investigated. Four examples of active scalar have been considered: temperature in thermal convection, magnetic potential in two-dimensional magnetohydrodynamics, vorticity in two-dimensional Ekman turbulence and potential temperature in surface flows. In the cases of temperature and vorticity, it is found that the active scalar behavior is akin to that of its co-evolving passive counterpart. The two other cases indicate that this similarity is in fact not generic and differences between passive and active fields can be striking: in two-dimensional magnetohydrodynamics the magnetic potential performs an inverse cascade while the passive scalar cascades toward the small-scales; in surface flows, albeit both perform a direct cascade, the potential temperature and the passive scalar have different scaling laws already at the level of low-order statistical objects. These dramatic differences are rooted in the correlations between the active scalar input and the particle trajectories. The role of such correlations in the issue of universality in active scalar transport and the behavior of dissipative anomalies is addressed.Comment: 36 pages, 20 eps figures, for the published version see http://www.iop.org/EJ/abstract/1367-2630/6/1/07