3,145 research outputs found
Dynamics of spectrally truncated inviscid turbulence
The evolution of the turbulent energy spectrum for the inviscid spectrally
truncated Euler equations is studied by closure calculations. The observed
behavior is similar to the one found in direct numerical simulations
[Cichowlas, Bona\"ititi, Debbasch, and Brachet, Phys. Rev. Lett. 95, 264502
(2005)]. A Kolmogorov spectral range and an equipartition range are observed
simultaneously. Between these two ranges a "quasi-dissipative" zone is present
in the kinetic energy spectrum. The time evolution of the wave number that
marks the beginning of the equipartition range is analyzed and it is shown that
spectral nonlocal interactions are governing this evolution
Modeling Kelvin wave cascades in superfluid helium
We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM
Differential approximation for Kelvin-wave turbulence
I present a nonlinear differential equation model (DAM) for the spectrum of
Kelvin waves on a thin vortex filament. This model preserves the original
scaling of the six-wave kinetic equation, its direct and inverse cascade
solutions, as well as the thermodynamic equilibrium spectra. Further, I extend
DAM to include the effect of sound radiation by Kelvin waves. I show that,
because of the phonon radiation, the turbulence spectrum ends at a maximum
frequency where
is the total energy injection rate, is the speed of sound and
is the quantum of circulation.Comment: Prepared of publication in JETP Letter
Photoelectric measurement of blood flow during hemodialysis
Accurate measurements of blood flow rate during hemodialysis are essential for determinations of hemodialyzer performance. Despite the availability of a variety of electronic blood flow meters, use of such instruments for determination of blood flow in hemodialysis has never been satisfactory, a situation caused by such factors as the need to recalibrate frequently, the necessity of incorporating transducers into the dialyzer blood circuit and the effect which variables such as hematocrit may have on the accuracy of determination. Furthermore, such devices are expensive and often require the periodic services of an electronics specialist to maintain them in an operable condition.An alternative technique for measuring flow rate in the extracorporeal blood tubing consists of timing the passage of an injected air bubble between two points in the tubing. Since the advent of maintenance dialysis, the “racetrack and bubble time” technique [1] has been widely used for routine determinations of blood flow rate. Data derived from research studies in which this method of flow determination was employed have been published widely, in spite of the relative inaccuracies of the method
Predictability in Systems with Many Characteristic Times: The Case of Turbulence
In chaotic dynamical systems, an infinitesimal perturbation is exponentially
amplified at a time-rate given by the inverse of the maximum Lyapunov exponent
. In fully developed turbulence, grows as a power of the
Reynolds number. This result could seem in contrast with phenomenological
arguments suggesting that, as a consequence of `physical' perturbations, the
predictability time is roughly given by the characteristic life-time of the
large scale structures, and hence independent of the Reynolds number. We show
that such a situation is present in generic systems with many degrees of
freedom, since the growth of a non-infinitesimal perturbation is determined by
cumulative effects of many different characteristic times and is unrelated to
the maximum Lyapunov exponent. Our results are illustrated in a chain of
coupled maps and in a shell model for the energy cascade in turbulence.Comment: 24 pages, 10 Postscript figures (included), RevTeX 3.0, files packed
with uufile
Growth of non-infinitesimal perturbations in turbulence
We discuss the effects of finite perturbations in fully developed turbulence
by introducing a measure of the chaoticity degree associated to a given scale
of the velocity field. This allows one to determine the predictability time for
non-infinitesimal perturbations, generalizing the usual concept of maximum
Lyapunov exponent. We also determine the scaling law for our indicator in the
framework of the multifractal approach. We find that the scaling exponent is
not sensitive to intermittency corrections, but is an invariant of the
multifractal models. A numerical test of the results is performed in the shell
model for the turbulent energy cascade.Comment: 4 pages, 2 Postscript figures (included), RevTeX 3.0, files packed
with uufile
Exact solutions in a scalar-tensor model of dark energy
We consider a model of scalar field with non minimal kinetic and Gauss Bonnet
couplings as a source of dark energy. Based on asymptotic limits of the
generalized Friedmann equation, we impose restrictions on the kinetic an
Gauss-Bonnet couplings. This restrictions considerable simplify the equations,
allowing for exact solutions unifying early time matter dominance with
transitions to late time quintessence and phantom phases. The stability of the
solutions in absence of matter has been studied.Comment: 30 pages, 2 figures, to appear in JCA
Improved linear response for stochastically driven systems
The recently developed short-time linear response algorithm, which predicts
the average response of a nonlinear chaotic system with forcing and dissipation
to small external perturbation, generally yields high precision of the response
prediction, although suffers from numerical instability for long response times
due to positive Lyapunov exponents. However, in the case of stochastically
driven dynamics, one typically resorts to the classical fluctuation-dissipation
formula, which has the drawback of explicitly requiring the probability density
of the statistical state together with its derivative for computation, which
might not be available with sufficient precision in the case of complex
dynamics (usually a Gaussian approximation is used). Here we adapt the
short-time linear response formula for stochastically driven dynamics, and
observe that, for short and moderate response times before numerical
instability develops, it is generally superior to the classical formula with
Gaussian approximation for both the additive and multiplicative stochastic
forcing. Additionally, a suitable blending with classical formula for longer
response times eliminates numerical instability and provides an improved
response prediction even for long response times
Quasi-stationary States of Two-Dimensional Electron Plasma Trapped in Magnetic Field
We have performed numerical simulations on a pure electron plasma system
under a strong magnetic field, in order to examine quasi-stationary states that
the system eventually evolves into. We use ring states as the initial states,
changing the width, and find that the system evolves into a vortex crystal
state from a thinner-ring state while a state with a single-peaked density
distribution is obtained from a thicker-ring initial state. For those
quasi-stationary states, density distribution and macroscopic observables are
defined on the basis of a coarse-grained density field. We compare our results
with experiments and some statistical theories, which include the
Gibbs-Boltzmann statistics, Tsallis statistics, the fluid entropy theory, and
the minimum enstrophy state. From some of those initial states, we obtain the
quasi-stationary states which are close to the minimum enstrophy state, but we
also find that the quasi-stationary states depend upon initial states, even if
the initial states have the same energy and angular momentum, which means the
ergodicity does not hold.Comment: 9 pages, 7 figure
On compatibility of string effective action with an accelerating universe
In this paper, we fully investigate the cosmological effects of the moduli
dependent one-loop corrections to the gravitational couplings of the string
effective action to explain the cosmic acceleration problem in early (and/or
late) universe. These corrections comprise a Gauss-Bonnet (GB) invariant
multiplied by universal non-trivial functions of the common modulus
and the dilaton . The model exhibits several features of cosmological
interest, including the transition between deceleration and acceleration
phases. By considering some phenomenologically motivated ansatzs for one of the
scalars and/or the scale factor (of the universe), we also construct a number
of interesting inflationary potentials. In all examples under consideration, we
find that the model leads only to a standard inflation () when the
numerical coefficient associated with modulus-GB coupling is positive,
while the model can lead also to a non-standard inflation (), if
is negative. In the absence of (or trivial) coupling between the GB term and
the scalars, there is no crossing between the phases, while
this is possible with non-trivial GB couplings, even for constant dilaton phase
of the standard picture. Within our model, after a sufficient amount of e-folds
of expansion, the rolling of both fields and can be small. In
turn, any possible violation of equivalence principle or deviations from the
standard general relativity may be small enough to easily satisfy all
astrophysical and cosmological constraints.Comment: 30 pages, 8 figures; v2 significant changes in notations, appendix
and refs added; v3 significant revisions, refs added; v4 appendix extended,
new refs, published versio
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