2,059 research outputs found
Variational bounds on the energy dissipation rate in body-forced shear flow
A new variational problem for upper bounds on the rate of energy dissipation
in body-forced shear flows is formulated by including a balance parameter in
the derivation from the Navier-Stokes equations. The resulting min-max problem
is investigated computationally, producing new estimates that quantitatively
improve previously obtained rigorous bounds. The results are compared with data
from direct numerical simulations.Comment: 15 pages, 7 figure
Internal heating driven convection at infinite Prandtl number
We derive an improved rigorous bound on the space and time averaged
temperature of an infinite Prandtl number Boussinesq fluid contained
between isothermal no-slip boundaries thermally driven by uniform internal
heating. A novel approach is used wherein a singular stable stratification is
introduced as a perturbation to a non-singular background profile, yielding the
estimate where is the heat Rayleigh
number. The analysis relies on a generalized Hardy-Rellich inequality that is
proved in the appendix
"Ultimate state" of two-dimensional Rayleigh-Benard convection between free-slip fixed temperature boundaries
Rigorous upper limits on the vertical heat transport in two dimensional
Rayleigh-Benard convection between stress-free isothermal boundaries are
derived from the Boussinesq approximation of the Navier-Stokes equations. The
Nusselt number Nu is bounded in terms of the Rayleigh number Ra according to
uniformly in the Prandtl number Pr. This Nusselt
number scaling challenges some theoretical arguments regarding the asymptotic
high Rayleigh number heat transport by turbulent convection.Comment: 4 page
Resonant Activation Phenomenon for Non-Markovian Potential-Fluctuation Processes
We consider a generalization of the model by Doering and Gadoua to
non-Markovian potential-switching generated by arbitrary renewal processes. For
the Markovian switching process, we extend the original results by Doering and
Gadoua by giving a complete description of the absorption process. For all
non-Markovian processes having the first moment of the waiting time
distributions, we get qualitatively the same results as in the Markovian case.
However, for distributions without the first moment, the mean first passage
time curves do not exhibit the resonant activation minimum. We thus come to the
conjecture that the generic mechanism of the resonant activation fails for
fluctuating processes widely deviating from Markovian.Comment: RevTeX 4, 5 pages, 4 figures; considerably shortened version accepted
as a brief report to Phys. Rev.
Energy Dissipation in Fractal-Forced Flow
The rate of energy dissipation in solutions of the body-forced 3-d
incompressible Navier-Stokes equations is rigorously estimated with a focus on
its dependence on the nature of the driving force. For square integrable body
forces the high Reynolds number (low viscosity) upper bound on the dissipation
is independent of the viscosity, consistent with the existence of a
conventional turbulent energy cascade. On the other hand when the body force is
not square integrable, i.e., when the Fourier spectrum of the force decays
sufficiently slowly at high wavenumbers, there is significant direct driving at
a broad range of spatial scales. Then the upper limit for the dissipation rate
may diverge at high Reynolds numbers, consistent with recent experimental and
computational studies of "fractal-forced'' turbulence.Comment: 14 page
Variational bound on energy dissipation in turbulent shear flow
We present numerical solutions to the extended Doering-Constantin variational
principle for upper bounds on the energy dissipation rate in plane Couette
flow, bridging the entire range from low to asymptotically high Reynolds
numbers. Our variational bound exhibits structure, namely a pronounced minimum
at intermediate Reynolds numbers, and recovers the Busse bound in the
asymptotic regime. The most notable feature is a bifurcation of the minimizing
wavenumbers, giving rise to simple scaling of the optimized variational
parameters, and of the upper bound, with the Reynolds number.Comment: 4 pages, RevTeX, 5 postscript figures are available as one .tar.gz
file from [email protected]
Transcription factor search for a DNA promoter in a three-states model
To ensure fast gene activation, Transcription Factors (TF) use a mechanism
known as facilitated diffusion to find their DNA promoter site. Here we analyze
such a process where a TF alternates between 3D and 1D diffusion. In the latter
(TF bound to the DNA), the TF further switches between a fast translocation
state dominated by interaction with the DNA backbone, and a slow examination
state where interaction with DNA base pairs is predominant. We derive a new
formula for the mean search time, and show that it is faster and less sensitive
to the binding energy fluctuations compared to the case of a single sliding
state. We find that for an optimal search, the time spent bound to the DNA is
larger compared to the 3D time in the nucleus, in agreement with recent
experimental data. Our results further suggest that modifying switching via
phosphorylation or methylation of the TF or the DNA can efficiently regulate
transcription.Comment: 4 pages, 3 figure
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