1,095 research outputs found
Model of separated form factors for unilamellar vesicles
New model of separated form factors is proposed for the evaluation of
small-angle neutron scattering curves from large unilamellar vesicles. The
validity of the model was checked by comparison to the model of hollow sphere.
The model of separated form factors and hollow sphere model give reasonable
agreement in the evaluation of vesicle parameters.Comment: LaTeX: 3 pages, 1 figure, 14 references; submitted to Applied Physics
Growing condensate in two-dimensional turbulence
We report a numerical study, supplemented by phenomenological explanations,
of ``energy condensation'' in forced 2D turbulence in a biperiodic box.
Condensation is a finite size effect which occurs after the standard inverse
cascade reaches the size of the system. It leads to emergence of a coherent
vortex dipole. We show that the time growth of the dipole is self-similar, and
it contains most of the injected energy, thus resulting in an energy spectrum
which is markedly steeper than the standard one. Once the coherent
component is subtracted, however, the remaining fluctuations have a spectrum
close to . The fluctuations decay slowly as the coherent part grows.Comment: 4 pages, 4 figures. This version includes some additional
phenomenological explanations of the results, additional references and
improved figure
Large-scale bottleneck effect in two-dimensional turbulence
The bottleneck phenomenon in three-dimensional turbulence is generally
associated with the dissipation range of the energy spectrum. In the present
work, it is shown by using a two-point closure theory, that in two-dimensional
turbulence it is possible to observe a bottleneck at the large scales, due to
the effect of friction on the inverse energy cascade. This large-scale
bottleneck is directly related to the process of energy condensation, the
pile-up of energy at wavenumbers corresponding to the domain size. The link
between the use of friction and the creation of space-filling structures is
discussed and it is concluded that the careless use of hypofriction might
reduce the inertial range of the energy spectrum
Non-equilibrium temperatures in steady-state systems with conserved energy
We study a class of non-equilibrium lattice models describing local
redistributions of a globally conserved quantity, which is interpreted as an
energy. A particular subclass can be solved exactly, allowing to define a
statistical temperature T_{th} along the same lines as in the equilibrium
microcanonical ensemble. We compute the response function and find that when
the fluctuation-dissipation relation is linear, the slope T_{FD}^{-1} of this
relation differs from the inverse temperature T_{th}^{-1}. We argue that T_{th}
is physically more relevant than T_{FD}, since in the steady-state regime, it
takes equal values in two subsystems of a large isolated system. Finally, a
numerical renormalization group procedure suggests that all models within the
class behave similarly at a coarse-grained level, leading to a new parameter
which describes the deviation from equilibrium. Quantitative predictions
concerning this parameter are obtained within a mean-field framework.Comment: 16 pages, 2 figures, submitted to Phys. Rev.
Spectral imbalance and the normalized dissipation rate of turbulence
The normalized turbulent dissipation rate is studied in decaying
and forced turbulence by direct numerical simulations, large-eddy simulations,
and closure calculations. A large difference in the values of is
observed for the two types of turbulence. This difference is found at moderate
Reynolds number, and it is shown that it persists at high Reynolds number,
where the value of becomes independent of the Reynolds number, but
is still not unique. This difference can be explained by the influence of the
nonlinear cascade time that introduces a spectral disequilibrium for
statistically nonstationary turbulence. Phenomenological analysis yields simple
analytical models that satisfactorily reproduce the numerical results. These
simple spectral models also reproduce and explain the increase of
at low Reynolds number that is observed in the simulations
Enstrophy dissipation in two-dimensional turbulence
Insight into the problem of two-dimensional turbulence can be obtained by an
analogy with a heat conduction network. It allows the identification of an
entropy function associated to the enstrophy dissipation and that fluctuates
around a positive (mean) value. While the corresponding enstrophy network is
highly nonlocal, the direction of the enstrophy current follows from the Second
Law of Thermodynamics. An essential parameter is the ratio of the intensity of driving as a function of
wavenumber , to the dissipation strength , where is the
viscosity. The enstrophy current flows from higher to lower values of ,
similar to a heat current from higher to lower temperature. Our probabilistic
analysis of the enstrophy dissipation and the analogy with heat conduction thus
complements and visualizes the more traditional spectral arguments for the
direct enstrophy cascade. We also show a fluctuation symmetry in the
distribution of the total entropy production which relates the probabilities of
direct and inverse enstrophy cascades.Comment: 8 pages, revtex
Marangoni shocks in unobstructed soap-film flows
It is widely thought that in steady, gravity-driven, unobstructed soap-film
flows, the velocity increases monotonically downstream. Here we show
experimentally that the velocity increases, peaks, drops abruptly, then lessens
gradually downstream. We argue theoretically and verify experimentally that the
abrupt drop in velocity corresponds to a Marangoni shock, a type of shock
related to the elasticity of the film. Marangoni shocks induce locally intense
turbulent fluctuations and may help elucidate the mechanisms that produce
two-dimensional turbulence away from boundaries.Comment: 4 pages, 5 figures, published in PR
A Multiresolution Census Algorithm for Calculating Vortex Statistics in Turbulent Flows
The fundamental equations that model turbulent flow do not provide much
insight into the size and shape of observed turbulent structures. We
investigate the efficient and accurate representation of structures in
two-dimensional turbulence by applying statistical models directly to the
simulated vorticity field. Rather than extract the coherent portion of the
image from the background variation, as in the classical signal-plus-noise
model, we present a model for individual vortices using the non-decimated
discrete wavelet transform. A template image, supplied by the user, provides
the features to be extracted from the vorticity field. By transforming the
vortex template into the wavelet domain, specific characteristics present in
the template, such as size and symmetry, are broken down into components
associated with spatial frequencies. Multivariate multiple linear regression is
used to fit the vortex template to the vorticity field in the wavelet domain.
Since all levels of the template decomposition may be used to model each level
in the field decomposition, the resulting model need not be identical to the
template. Application to a vortex census algorithm that records quantities of
interest (such as size, peak amplitude, circulation, etc.) as the vorticity
field evolves is given. The multiresolution census algorithm extracts coherent
structures of all shapes and sizes in simulated vorticity fields and is able to
reproduce known physical scaling laws when processing a set of voriticity
fields that evolve over time
Field theory of the inverse cascade in two-dimensional turbulence
A two-dimensional fluid, stirred at high wavenumbers and damped by both
viscosity and linear friction, is modeled by a statistical field theory. The
fluid's long-distance behavior is studied using renormalization-group (RG)
methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732
(1977)]. With friction, which dissipates energy at low wavenumbers, one expects
a stationary inverse energy cascade for strong enough stirring. While such
developed turbulence is beyond the quantitative reach of perturbation theory, a
combination of exact and perturbative results suggests a coherent picture of
the inverse cascade. The zero-friction fluctuation-dissipation theorem (FDT) is
derived from a generalized time-reversal symmetry and implies zero anomalous
dimension for the velocity even when friction is present. Thus the Kolmogorov
scaling of the inverse cascade cannot be explained by any RG fixed point. The
beta function for the dimensionless coupling ghat is computed through two
loops; the ghat^3 term is positive, as already known, but the ghat^5 term is
negative. An ideal cascade requires a linear beta function for large ghat,
consistent with a Pad\'e approximant to the Borel transform. The conjecture
that the Kolmogorov spectrum arises from an RG flow through large ghat is
compatible with other results, but the accurate k^{-5/3} scaling is not
explained and the Kolmogorov constant is not estimated. The lack of scale
invariance should produce intermittency in high-order structure functions, as
observed in some but not all numerical simulations of the inverse cascade. When
analogous RG methods are applied to the one-dimensional Burgers equation using
an FDT-preserving dimensional continuation, equipartition is obtained instead
of a cascade--in agreement with simulations.Comment: 16 pages, 3 figures, REVTeX 4. Material added on energy flux,
intermittency, and comparison with Burgers equatio
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