183 research outputs found
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
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
Lognormal scale invariant random measures
In this article, we consider the continuous analog of the celebrated
Mandelbrot star equation with lognormal weights. Mandelbrot introduced this
equation to characterize the law of multiplicative cascades. We show existence
and uniqueness of measures satisfying the aforementioned continuous equation;
these measures fall under the scope of the Gaussian multiplicative chaos theory
developed by J.P. Kahane in 1985 (or possibly extensions of this theory). As a
by product, we also obtain an explicit characterization of the covariance
structure of these measures. We also prove that qualitative properties such as
long-range independence or isotropy can be read off the equation.Comment: 31 pages; Probability Theory and Related Fields (2012) electronic
versio
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
Extended Self-similarity in Kinetic Surface Roughening
We show from numerical simulations that a limited mobility solid-on-solid
model of kinetically rough surface growth exhibits extended self-similarity
analogous to that found in fluid turbulence. The range over which
scale-independent power-law behavior is observed is significantly enhanced if
two correlation functions of different order, such as those representing two
different moments of the difference in height between two points, are plotted
against each other. This behavior, found in both one and two dimensions,
suggests that the `relative' exponents may be more fundamental than the
`absolute' ones.Comment: 4 pages, 4 postscript figures included (some changes made according
to referees' comments. accepted for publication in PRE Rapid Communication
Exact Resummations in the Theory of Hydrodynamic Turbulence: I The Ball of Locality and Normal Scaling
This paper is the first in a series of three papers that aim at understanding
the scaling behaviour of hydrodynamic turbulence. We present in this paper a
perturbative theory for the structure functions and the response functions of
the hydrodynamic velocity field in real space and time. Starting from the
Navier-Stokes equations (at high Reynolds number Re) we show that the standard
perturbative expansions that suffer from infra-red divergences can be exactly
resummed using the Belinicher-L'vov transformation. After this exact (partial)
resummation it is proven that the resulting perturbation theory is free of
divergences, both in large and in small spatial separations. The hydrodynamic
response and the correlations have contributions that arise from mediated
interactions which take place at some space- time coordinates. It is shown that
the main contribution arises when these coordinates lie within a shell of a
"ball of locality" that is defined and discussed. We argue that the real
space-time formalism developed here offers a clear and intuitive understanding
of every diagram in the theory, and of every element in the diagrams. One major
consequence of this theory is that none of the familiar perturbative mechanisms
may ruin the classical Kolmogorov (K41) scaling solution for the structure
functions. Accordingly, corrections to the K41 solutions should be sought in
nonperturbative effects. These effects are the subjects of papers II and III in
this series, that will propose a mechanism for anomalous scaling in turbulence,
which in particular allows multiscaling of the structure functions.Comment: PRE in press, 18 pages + 6 figures, REVTeX. The Eps files of figures
will be FTPed by request to [email protected]
Variational bound on energy dissipation in plane Couette flow
We present numerical solutions to the extended Doering-Constantin variational
principle for upper bounds on the energy dissipation rate in turbulent plane
Couette flow. Using the compound matrix technique in order to reformulate this
principle's spectral constraint, we derive a system of equations that is
amenable to numerical treatment in the entire range from low to asymptotically
high Reynolds numbers. Our variational bound exhibits a minimum at intermediate
Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a
consequence of a bifurcation of the minimizing wavenumbers, there exist two
length scales that determine the optimal upper bound: the effective width of
the variational profile's boundary segments, and the extension of their flat
interior part.Comment: 22 pages, RevTeX, 11 postscript figures are available as one
uuencoded .tar.gz file from [email protected]
Industrial methodology for process verification in research (IMPROVER): toward systems biology verification
Motivation: Analyses and algorithmic predictions based on high-throughput data are essential for the success of systems biology in academic and industrial settings. Organizations, such as companies and academic consortia, conduct large multi-year scientific studies that entail the collection and analysis of thousands of individual experiments, often over many physical sites and with internal and outsourced components. To extract maximum value, the interested parties need to verify the accuracy and reproducibility of data and methods before the initiation of such large multi-year studies. However, systematic and well-established verification procedures do not exist for automated collection and analysis workflows in systems biology which could lead to inaccurate conclusions
Exact Resummations in the Theory of Hydrodynamic Turbulence: III. Scenarios for Anomalous Scaling and Intermittency
Elements of the analytic structure of anomalous scaling and intermittency in
fully developed hydrodynamic turbulence are described. We focus here on the
structure functions of velocity differences that satisfy inertial range scaling
laws , and the correlation of energy dissipation
. The goal is to understand the
exponents and from first principles. In paper II of this series
it was shown that the existence of an ultraviolet scale (the dissipation scale
) is associated with a spectrum of anomalous exponents that characterize
the ultraviolet divergences of correlations of gradient fields. The leading
scaling exponent in this family was denoted . The exact resummation of
ladder diagrams resulted in the calculation of which satisfies the
scaling relation . In this paper we continue our analysis and
show that nonperturbative effects may introduce multiscaling (i.e.
not being linear in ) with the renormalization scale being the infrared
outer scale of turbulence . It is shown that deviations from K41 scaling of
() must appear if the correlation of dissipation is
mixing (i.e. ). We derive an exact scaling relation . We present analytic expressions for for all
and discuss their relation to experimental data. One surprising prediction is
that the time decay constant of scales
independently of : the dynamic scaling exponent is the same for all
-order quantities, .Comment: PRE submitted, 22 pages + 11 figures, REVTeX. The Eps files of
figures will be FTPed by request to [email protected]
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