17,108 research outputs found
Anomalous scaling of a passive scalar advected by the Navier--Stokes velocity field: Two-loop approximation
The field theoretic renormalization group and operator product expansion are
applied to the model of a passive scalar quantity advected by a non-Gaussian
velocity field with finite correlation time. The velocity is governed by the
Navier--Stokes equation, subject to an external random stirring force with the
correlation function . It is shown that
the scalar field is intermittent already for small , its structure
functions display anomalous scaling behavior, and the corresponding exponents
can be systematically calculated as series in . The practical
calculation is accomplished to order (two-loop approximation),
including anisotropic sectors. Like for the well-known Kraichnan's rapid-change
model, the anomalous scaling results from the existence in the model of
composite fields (operators) with negative scaling dimensions, identified with
the anomalous exponents. Thus the mechanism of the origin of anomalous scaling
appears similar for the Gaussian model with zero correlation time and
non-Gaussian model with finite correlation time. It should be emphasized that,
in contrast to Gaussian velocity ensembles with finite correlation time, the
model and the perturbation theory discussed here are manifestly Galilean
covariant. The relevance of these results for the real passive advection,
comparison with the Gaussian models and experiments are briefly discussed.Comment: 25 pages, 1 figur
Stability of scaling regimes in developed turbulence with weak anisotropy
The fully developed turbulence with weak anisotropy is investigated by means
of renormalization group approach (RG) and double expansion regularization for
dimensions . Some modification of the standard minimal substraction
scheme has been used to analyze stability of the Kolmogorov scaling regime
which is governed by the renormalization group fixed point. This fixed point is
unstable at ; thus, the infinitesimally weak anisotropy destroyes above
scaling regime in two-dimensional space. The restoration of the stability of
this fixed point, under transition from to has been demonstrated
at borderline dimension . The results are in qualitative agreement
with ones obtained recently in the framework of the usual analytical
regularization scheme.Comment: 23 pages, 2 figure
Renormalization group in the infinite-dimensional turbulence: third-order results
The field theoretic renormalization group is applied to the stochastic
Navier-Stokes equation with the stirring force correlator of the form
k^(4-d-2\epsilon) in the d-dimensional space, in connection with the problem of
construction of the 1/d expansion for the fully developed fluid turbulence
beyond the scope of the standard epsilon expansion. It is shown that in the
large-d limit the number of the Feynman diagrams for the Green function (linear
response function) decreases drastically, and the technique of their analytical
calculation is developed. The main ingredients of the renormalization group
approach -- the renormalization constant, beta function and the ultraviolet
correction exponent omega, are calculated to order epsilon^3 (three-loop
approximation). The two-point velocity-velocity correlation function, the
Kolmogorov constant C_K in the spectrum of turbulent energy and the
inertial-range skewness factor S are calculated in the large-d limit to third
order of the epsilon expansion. Surprisingly enough, our results for C_K are in
a reasonable agreement with the existing experimental estimates.Comment: 30 pages with EPS figure
Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence
Statistical model of strongly anisotropic fully developed turbulence of the
weakly compressible fluid is considered by means of the field theoretic
renormalization group. The corrections due to compressibility to the infrared
form of the kinetic energy spectrum have been calculated in the leading order
in Mach number expansion. Furthermore, in this approximation the validity of
the Kolmogorov hypothesis on the independence of dissipation length of velocity
correlation functions in the inertial range has been proved.Comment: REVTEX file with EPS figure
Large Deviation Approach to the Randomly Forced Navier-Stokes Equation
The random forced Navier-Stokes equation can be obtained as a variational
problem of a proper action. By virtue of incompressibility, the integration
over transverse components of the fields allows to cast the action in the form
of a large deviation functional. Since the hydrodynamic operator is nonlinear,
the functional integral yielding the statistics of fluctuations can be
practically computed by linearizing around a physical solution of the
hydrodynamic equation. We show that this procedure yields the dimensional
scaling predicted by K41 theory at the lowest perturbative order, where the
perturbation parameter is the inverse Reynolds number. Moreover, an explicit
expression of the prefactor of the scaling law is obtained.Comment: 24 page
Renormalization group and anomalous scaling in a simple model of passive scalar advection in compressible flow
Field theoretical renormalization group methods are applied to a simple model
of a passive scalar quantity advected by the Gaussian non-solenoidal
(``compressible'') velocity field with the covariance . Convective range anomalous scaling for the structure
functions and various pair correlators is established, and the corresponding
anomalous exponents are calculated to the order of the
expansion. These exponents are non-universal, as a result of the degeneracy of
the RG fixed point. In contrast to the case of a purely solenoidal velocity
field (Obukhov--Kraichnan model), the correlation functions in the case at hand
exhibit nontrivial dependence on both the IR and UV characteristic scales, and
the anomalous scaling appears already at the level of the pair correlator. The
powers of the scalar field without derivatives, whose critical dimensions
determine the anomalous exponents, exhibit multifractal behaviour. The exact
solution for the pair correlator is obtained; it is in agreement with the
result obtained within the expansion. The anomalous exponents for
passively advected magnetic fields are also presented in the first order of the
expansion.Comment: 31 pages, REVTEX file. More detailed discussion of the
one-dimensional case and comparison to the previous paper [20] are given;
references updated. Results and formulas unchange
Medical device innovation in South Africa: Evolution of collaboration networks (2001-2013)
The evolution of medical device development in South Africa was investigated for the period 2001-2013. Collaboration networks for four sectors - academia, healthcare, industry, and science and support - were derived from a bibliometric study. Centrality measures identified dominant institutions. New actors entering the networks either exhibited preferential attachment to these institutions, or joined the network as part of an isolated cluster. Of the new institutions, foreign collaborators seldom stayed beyond five years, while local institutions seldom left after entering the field. Over the 13-year period, local collaboration activity persisted, while local-foreign collaborations were seen to decline. Over time, the network topology became more akin to that of a small-world network. The findings of the study may support innovation management by guiding institutional strategies for effective collaboration
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