Mean- Field Approximation and Extended Self-Similarity in Turbulence

Recent experimental discovery of extended self-similarity (ESS) was one of the most interesting developments, enabling precise determination of the scaling exponents of fully developed turbulence. Here we show that the ESS is consistent with the Navier-Stokes equations, provided the pressure -gradient contributions are expressed in terms of velocity differences in the mean field approximation (Yakhot, Phys.Rev. E{\bf 63}, 026307, (2001)). A sufficient condition for extended self-similarity in a general dynamical systemComment: 8 pages, no figure

Local properties of extended self-similarity in 3D turbulence

Using a generalization of extended self-similarity we have studied local scaling properties of 3D turbulence in a direct numerical simulation. We have found that these properties are consistent with lognormal-like behavior of energy dissipation fluctuations with moderate amplitudes for space scales $r$ beginning from Kolmogorov length $\eta$ up to the largest scales, and in the whole range of the Reynolds numbers: $50 \leq R_{\lambda} \leq 459$. The locally determined intermittency exponent $\mu(r)$ varies with $r$; it has a maximum at scale $r=14 \eta$, independent of $R_{\lambda}$.Comment: 4 pages, 5 figure

Validation of an STR peak area model

In analyzing a DNA mixture sample, the measured peak areas of alleles of STR markers amplified using the polymerase chain-reaction (PCR) technique provide valuable information concerning the relative amounts of DNA originating from each contributor to the mixture. This information can be exploited for the purpose of trying to predict the genetic profiles of those contributors whose genetic profiles are not known. The task is non-trivial, in part due to the need to take into account the stochastic nature of peak area values. Various methods have been proposed suggesting ways in which this may be done. One recent suggestion is a probabilistic expert system model that uses gamma distributions to model the size and stochastic variation in peak area values. In this paper we carry out a statistical analysis of the gamma distribution assumption, testing the assumption against synthetic peak area values computer generated using an independent model that simulates the PCR amplification process. Our analysis shows the gamma assumption works very well when allelic dropout is not present, but performs less and less well as dropout becomes more and more of an issue, such as occurs, for example, in Low Copy Template amplifications

Passive Scalar: Scaling Exponents and Realizability

An isotropic passive scalar field $T$ advected by a rapidly-varying velocity field is studied. The tail of the probability distribution $P(\theta,r)$ for the difference $\theta$ in $T$ across an inertial-range distance $r$ is found to be Gaussian. Scaling exponents of moments of $\theta$ increase as $\sqrt{n}$ or faster at large order $n$, if a mean dissipation conditioned on $\theta$ is a nondecreasing function of $|\theta|$. The $P(\theta,r)$ computed numerically under the so-called linear ansatz is found to be realizable. Some classes of gentle modifications of the linear ansatz are not realizable.Comment: Substantially revised to conform with published version. Revtex (4 pages) with 2 postscript figures. Send email to [email protected]

A scaling theory of 3D spinodal turbulence

A new scaling theory for spinodal decomposition in the inertial hydrodynamic regime is presented. The scaling involves three relevant length scales, the domain size, the Taylor microscale and the Kolmogorov dissipation scale. This allows for the presence of an inertial "energy cascade", familiar from theories of turbulence, and improves on earlier scaling treatments based on a single length: these, it is shown, cannot be reconciled with energy conservation. The new theory reconciles the t^{2/3} scaling of the domain size, predicted by simple scaling, with the physical expectation of a saturating Reynolds number at late times.Comment: 5 pages, no figures, revised version submitted to Phys Rev E Rapp Comm. Minor changes and clarification

Periodically kicked turbulence

Periodically kicked turbulence is theoretically analyzed within a mean field theory. For large enough kicking strength A and kicking frequency f the Reynolds number grows exponentially and then runs into some saturation. The saturation level can be calculated analytically; different regimes can be observed. For large enough Re we find the saturation level to be proportional to A*f, but intermittency can modify this scaling law. We suggest an experimental realization of periodically kicked turbulence to study the different regimes we theoretically predict and thus to better understand the effect of forcing on fully developed turbulence.Comment: 4 pages, 3 figures. Phys. Rev. E., in pres

A new scaling property of turbulent flows

We discuss a possible theoretical interpretation of the self scaling property of turbulent flows (Extended Self Similarity). Our interpretation predicts that, even in cases when ESS is not observed, a generalized self scaling, must be observed. This prediction is checked on a number of laboratory experiments and direct numerical simulations.Comment: Plain Latex, 1 figure available upon request to [email protected]

Dissipative chaotic scattering

We show that weak dissipation, typical in realistic situations, can have a metamorphic consequence on nonhyperbolic chaotic scattering in the sense that the physically important particle-decay law is altered, no matter how small the amount of dissipation. As a result, the previous conclusion about the unity of the fractal dimension of the set of singularities in scattering functions, a major claim about nonhyperbolic chaotic scattering, may not be observable.Comment: 4 pages, 2 figures, revte

ChIP-on-chip significance analysis reveals large-scale binding and regulation by human transcription factor oncogenes

ChIP-on-chip has emerged as a powerful tool to dissect the complex network of regulatory interactions between transcription factors and their targets. However, most ChIP-on-chip analysis methods use conservative approaches aimed to minimize false-positive transcription factor targets. We present a model with improved sensitivity in detecting binding events from ChIP-on-chip data. Biochemically validated analysis in human T-cells reveals that three transcription factor oncogenes, NOTCH1, MYC, and HES1, bind one order of magnitude more promoters than previously thought. Gene expression profiling upon NOTCH1 inhibition shows broad-scale functional regulation across the entire range of predicted target genes, establishing a closer link between occupancy and regulation. Finally, the resolution of a more complete map of transcriptional targets reveals that MYC binds nearly all promoters bound by NOTCH1. Overall, these results suggest an unappreciated complexity of transcriptional regulatory networks and highlight the fundamental importance of genome-scale analysis to represent transcriptional programs