Gas flows through shallow T-junctions and parallel microchannel networks

We apply a recent extension of the Hele-Shaw scheme to analyze steady compressible viscous flows through micro T-junctions. The linearity of the problem in terms of an appropriately defined quadratic form of the pressure facilitates the definition of the viscous resistance of the configuration, relating the gas mass-flow rate to entrance and exit conditions. Furthermore, under rather mild restrictions, the performance of complex microchannel networks may be estimated through superposition of the contributions of multiple basic junction elements. This procedure is applied to an optimization model problem of a parallel microchannel network. The analysis and results are readily adaptable to incompressible flows

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

GRB afterglow blast wave encountering sudden circumburst density change produces no flares

Afterglows of gamma-ray bursts are observed to produce light curveswith the flux following power law evolution in time. However, recent observations reveal bright flares at times on the order of minutes to days.One proposed explanation for these flares is the interaction of a relativisticblast wave with a circumburst density transition. In this paper, we modelthis type of interaction computationally in one and two dimensions, usinga relativistic hydrodynamics code with adaptive mesh refinement calledram, and analytically in one dimension. We simulate a blast wave travelingin a stellar wind environment that encounters a sudden change indensity, followed by a homogeneous medium, and compute the observedradiation using a synchrotron model. We show that flares are not observablefor an encounter with a sudden density increase, such as a windtermination shock, nor for an encounter with a sudden density decrease.Furthermore, by extending our analysis to two dimensions, we are able toresolve the spreading, collimation, and edge effects of the blast wave as itencounters the change in circumburst medium. In all cases considered inthis paper, we find that a flare will not be observed for any of the densitychanges studied

Quantum versus classical phase-locking transition in a driven-chirped oscillator

Classical and quantum-mechanical phase locking transition in a nonlinear oscillator driven by a chirped frequency perturbation is discussed. Different limits are analyzed in terms of the dimensionless parameters $/\sqrt{2m\hbar \omega_{0}\alpha}$ and $P_{2}=(3\hbar \beta)/(4m\sqrt{\alpha})$ ($\epsilon,$ $\alpha,$ $\beta$ and $\omega_{0}$ being the driving amplitude, the frequency chirp rate, the nonlinearity parameter and the linear frequency of the oscillator). It is shown that for $P_{2}\ll P_{1}+1$, the passage through the linear resonance for $P_{1}$ above a threshold yields classical autoresonance (AR) in the system, even when starting in a quantum ground state. In contrast, for $$, the transition involves quantum-mechanical energy ladder climbing (LC). The threshold for the phase-locking transition and its width in $P_{1}$ in both AR and LC limits are calculated. The theoretical results are tested by solving the Schrodinger equation in the energy basis and illustrated via the Wigner function in phase space

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

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

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

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.

Computational analysis of the synergy among multiple interacting genes

Diseases such as cancer are often related to collaborative effects involving interactions of multiple genes within complex pathways, or to combinations of multiple SNPs. To understand the structure of such mechanisms, it is helpful to analyze genes in terms of the purely cooperative, as opposed to independent, nature of their contributions towards a phenotype. Here, we present an information-theoretic analysis that provides a quantitative measure of the multivariate synergy and decomposes sets of genes into submodules each of which contains synergistically interacting genes. When the resulting computational tools are used for the analysis of gene expression or SNP data, this systems-based methodology provides insight into the biological mechanisms responsible for disease