1,722 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
Exponentially growing solutions in homogeneous Rayleigh-Benard convection
It is shown that homogeneous Rayleigh-Benard flow, i.e., Rayleigh-Benard
turbulence with periodic boundary conditions in all directions and a volume
forcing of the temperature field by a mean gradient, has a family of exact,
exponentially growing, separable solutions of the full non-linear system of
equations. These solutions are clearly manifest in numerical simulations above
a computable critical value of the Rayleigh number. In our numerical
simulations they are subject to secondary numerical noise and resolution
dependent instabilities that limit their growth to produce statistically steady
turbulent transport.Comment: 4 pages, 3 figures, to be published in Phys. Rev. E - rapid
communication
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]
Subdiffusion-limited reactions
We consider the coagulation dynamics A+A -> A and A+A A and the
annihilation dynamics A+A -> 0 for particles moving subdiffusively in one
dimension. This scenario combines the "anomalous kinetics" and "anomalous
diffusion" problems, each of which leads to interesting dynamics separately and
to even more interesting dynamics in combination. Our analysis is based on the
fractional diffusion equation
Phase space dynamics of overdamped quantum systems
The phase space dynamics of dissipative quantum systems in strongly condensed
phase is considered. Based on the exact path integral approach it is shown that
the Wigner transform of the reduced density matrix obeys a time evolution
equation of Fokker-Planck type valid from high down to very low temperatures.
The effect of quantum fluctuations is discussed and the accuracy of these
findings is tested against exact data for a harmonic system.Comment: 7 pages, 2 figures, to appear in Euro. Phys. Let
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]
Distribution of label spacings for genome mapping in nanochannels
In genome mapping experiments, long DNA molecules are stretched by confining
them to very narrow channels, so that the locations of sequence-specific
fluorescent labels along the channel axis provide large-scale genomic
information. It is difficult, however, to make the channels narrow enough so
that the DNA molecule is fully stretched. In practice its conformations may
form hairpins that change the spacings between internal segments of the DNA
molecule, and thus the label locations along the channel axis. Here we describe
a theory for the distribution of label spacings that explains the heavy tails
observed in distributions of label spacings in genome mapping experiments.Comment: 18 pages, 4 figures, 1 tabl
Coherent State path-integral simulation of many particle systems
The coherent state path integral formulation of certain many particle systems
allows for their non perturbative study by the techniques of lattice field
theory. In this paper we exploit this strategy by simulating the explicit
example of the diffusion controlled reaction . Our results are
consistent with some renormalization group-based predictions thus clarifying
the continuum limit of the action of the problem.Comment: 20 pages, 4 figures. Minor corrections. Acknowledgement and reference
correcte
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