2,069 research outputs found
Integrals of motion and the shape of the attractor for the Lorenz model
In this paper, we consider three-dimensional dynamical systems, as for
example the Lorenz model. For these systems, we introduce a method for
obtaining families of two-dimensional surfaces such that trajectories cross
each surface of the family in the same direction. For obtaining these surfaces,
we are guided by the integrals of motion that exist for particular values of
the parameters of the system. Nonetheless families of surfaces are obtained for
arbitrary values of these parameters. Only a bounded region of the phase space
is not filled by these surfaces. The global attractor of the system must be
contained in this region. In this way, we obtain information on the shape and
location of the global attractor. These results are more restrictive than
similar bounds that have been recently found by the method of Lyapunov
functions.Comment: 17 pages,12 figures. PACS numbers : 05.45.+b / 02.30.Hq Accepted for
publication in Physics Letters A. e-mails : [email protected] &
[email protected]
The Equity of Public Education Funding in Georgia, 1988-1996
A study of the effect of Quality Basic Education on the level of equity of public education funding in Georgia
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
On the contribution of the benthos to pelagic production
Annual production and consumption of oxygen were compared in large outdoor mesocosms differing only in the presence or absence of an intact benthic community and associated sediments. Both daily apparent production and nighttime respiration of oxygen were greater in tanks with a benthos. The fluxes of oxygen into, and dissolved inorganic nitrogen out of the bottom were also greater in tanks with an intact benthos. In tanks with a benthos, calculated gross system production increased 33% relative to tanks lacking a benthos. Depending on assumed O:N ratios only 45–60% of this increase was attributable to differences in the flux of inorganic nitrogen from the benthos to the water column. Nearly 40% was evidently fueled by higher rates of recycling in the water column. Between 3 and 17% of the difference in production could not be attributed to either source. The benthos apparently affects production in the water column not only by supplying nutrients directly, but also by enhancing rates of pelagic recycling
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 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]
Fuel quality/processing study. Volume 4: On site processing studies
Fuel treated at the turbine and the turbine exhaust gas processed at the turbine site are studied. Fuel treatments protect the turbine from contaminants or impurities either in the upgrading fuel as produced or picked up by the fuel during normal transportation. Exhaust gas treatments provide for the reduction of NOx and SOx to environmentally acceptable levels. The impact of fuel quality upon turbine maintenance and deterioration is considered. On site costs include not only the fuel treatment costs as such, but also incremental costs incurred by the turbine operator if a turbine fuel of low quality is not acceptably upgraded
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
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]
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