27,908 research outputs found
Freely-Decaying, Homogeneous Turbulence Generated by Multi-scale Grids
We investigate wind tunnel turbulence generated by both conventional and
multi-scale grids. Measurements were made in a tunnel which has a large
test-section, so that possible side wall effects are very small and the length
assures that the turbulence has time to settle down to a homogeneous shear-free
state. The conventional and multi-scale grids were all designed to produce
turbulence with the same integral scale, so that a direct comparison could be
made between the different flows. Our primary finding is that the behavior of
the turbulence behind our multi-scale grids is virtually identical to that
behind the equivalent conventional grid. In particular, all flows exhibit a
power-law decay of energy, , where is very close to the
classical Saffman exponent of . Moreover, all spectra exhibit
classical Kolmogorov scaling, with the spectra collapsing on the integral
scales at small , and on the Kolmogorov micro-scales at large . Our
results are at odds with some other experiments performed on similar
multi-scale grids, where significantly higher energy decay exponents and
turbulence levels have been reported.Comment: 19 pages, 18 figure
Self-adjoint boundary-value problems on time-scales
In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form on an arbitrary, bounded time-scale , for suitable functions , together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the Hilbert space , in such a way that the resulting operator is self-adjoint, with compact resolvent (here, "self-adjoint" means in the standard functional analytic meaning of this term). Previous discussions of operators of this, and similar, form have described them as self-adjoint, but have not demonstrated self-adjointness in the standard functional analytic sense
Constraints on scalar diffusion anomaly in three-dimensional flows having bounded velocity gradients
This study is concerned with the decay behaviour of a passive scalar
in three-dimensional flows having bounded velocity gradients. Given an
initially smooth scalar distribution, the decay rate of the
scalar variance is found to be bounded in terms of controlled
physical parameters. Furthermore, in the zero diffusivity limit, ,
this rate vanishes as if there exists an
independent of such that for
. This condition is satisfied if in the limit ,
the variance spectrum remains steeper than for large wave
numbers . When no such positive exists, the scalar field may be
said to become virtually singular. A plausible scenario consistent with
Batchelor's theory is that becomes increasingly shallower for
smaller , approaching the Batchelor scaling in the limit
. For this classical case, the decay rate also vanishes, albeit
more slowly -- like , where is the Prandtl or Schmidt
number. Hence, diffusion anomaly is ruled out for a broad range of scalar
distribution, including power-law spectra no shallower than . The
implication is that in order to have a -independent and non-vanishing
decay rate, the variance at small scales must necessarily be greater than that
allowed by the Batchelor spectrum. These results are discussed in the light of
existing literature on the asymptotic exponential decay , where is independent of .Comment: 6-7 journal pages, no figures. accepted for publication by Phys.
Fluid
A Basis for Interactive Schema Merging
We present a technique for merging the schemas of heterogeneous databases that generalizes to several different data models, and show how it can be used in an interactive program that merges Entity-Relationship diagrams. Given a collection of schemas to be merged, the user asserts the correspondence between entities and relationships in the various schemas by defining "isa" relations between them. These assertions are then considered to be elementary schemas, and are combined with the elementary schemas in the merge. Since the method defines the merge to be the join in an information ordering on schemas, it is a commutative and associative operation, which means that the merge is defined independent of the order in which schemas are presented. We briefly describe a prototype interactive schema merging tool that has been built on these principles. Keywords: schemas, merging, semantic data models, entity-relationship data models, inheritance 1 Introduction Schema merging is the proble..
Implications of a new light gauge boson for neutrino physics
We study the impact of light gauge bosons on neutrino physics. We show that
they can explain the NuTeV anomaly and also escape the constraints from
neutrino experiments if they are very weakly coupled and have a mass of a few
GeV. Lighter gauge bosons with stronger couplings could explain both the NuTeV
anomaly and the positive anomalous magnetic moment of the muon. However, in the
simple model we consider in this paper (say a purely vectorial extra U(1)
current), they appear to be in conflict with the precise measurements of \nu-e
elastic scattering cross sections. The surprising agreement that we obtain
between our naive model and the NuTeV anomaly for a Z' mass of a few GeV may be
a coincidence. However, we think it is interesting enough to deserve attention
and perhaps a more careful analysis, especially since a new light gauge boson
is a very important ingredient for the Light Dark Matter scenario.Comment: 9 page
Dirac Quantization of the Pais-Uhlenbeck Fourth Order Oscillator
As a model, the Pais-Uhlenbeck fourth order oscillator with equation of
motion
is a quantum-mechanical prototype of a field theory containing both second and
fourth order derivative terms. With its dynamical degrees of freedom obeying
constraints due to the presence of higher order time derivatives, the model
cannot be quantized canonically. We thus quantize it using the method of Dirac
constraints to construct the correct quantum-mechanical Hamiltonian for the
system, and find that the Hamiltonian diagonalizes in the positive and negative
norm states that are characteristic of higher derivative field theories.
However, we also find that the oscillator commutation relations become singular
in the limit, a limit which corresponds to a prototype
of a pure fourth order theory. Thus the particle content of the theory cannot be inferred from that of the
theory; and in fact in the limit we find that all of
the negative norm states move off shell, with the
spectrum of asymptotic in and out states of the equal frequency theory being
found to be completely devoid of states with either negative energy or negative
norm. As a byproduct of our work we find a Pais-Uhlenbeck analog of the zero
energy theorem of Boulware, Horowitz and Strominger, and show how in the equal
frequency Pais-Uhlenbeck theory the theorem can be transformed into a positive
energy theorem instead.Comment: RevTeX4, 20 pages. Final version, to appear in Phys. Rev.
Growth rate of Rayleigh-Taylor turbulent mixing layers with the foliation approach
For years, astrophysicists, plasma fusion and fluid physicists have puzzled
over Rayleigh-Taylor turbulent mixing layers. In particular, strong
discrepancies in the growth rates have been observed between experiments and
numerical simulations. Although two phenomenological mechanisms (mode-coupling
and mode-competition) have brought some insight on these differences,
convincing theoretical arguments are missing to explain the observed values. In
this paper, we provide an analytical expression of the growth rate compatible
with both mechanisms and is valide for a self-similar, low Atwood
Rayleigh-Taylor turbulent mixing subjected to a constant or time-varying
acceleration. The key step in this work is the introduction of {\it foliated}
averages and {\it foliated} turbulent spectra highlighted in our three
dimensional numerical simulations. We show that the exact value of the
Rayleigh-Taylor growth rate not only depends upon the acceleration history but
is also bound to the power-law exponent of the {\it foliated} spectra at large
scales
Feasibility model of a high reliability five-year tape transport. Volume 3: Appendices
Detailed drawings of the five year tape transport are presented. Analytical tools used in the various analyses are described. These analyses include: tape guidance, tape stress over crowned rollers, tape pack stress program, response (computer) program, and control system electronics description
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