5,155 research outputs found
The 3D structure of the Lagrangian acceleration in turbulent flows
We report experimental results on the three dimensional Lagrangian
acceleration in highly turbulent flows. Tracer particles are tracked optically
using four silicon strip detectors from high energy physics that provide high
temporal and spatial resolution. The components of the acceleration are shown
to be statistically dependent. The probability density function (PDF) of the
acceleration magnitude is comparable to a log-normal distribution. Assuming
isotropy, a log-normal distribution of the magnitude can account for the
observed dependency of the components. The time dynamics of the acceleration
components is found to be typical of the dissipation scales whereas the
magnitude evolves over longer times, possibly close to the integral time scale.Comment: accepted for publication in Physical Review Letter
Measurement of Lagrangian velocity in fully developed turbulence
We have developed a new experimental technique to measure the Lagrangian
velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler
tracking. This method yields a direct access to the velocity of a single
particule at a turbulent Reynolds number . Its dynamics is
analyzed with two decades of time resolution, below the Lagrangian correlation
time. We observe that the Lagrangian velocity spectrum has a Lorentzian form
, in agreement
with a Kolmogorov-like scaling in the inertial range. The probability density
function (PDF) of the velocity time increments displays a change of shape from
quasi-Gaussian a integral time scale to stretched exponential tails at the
smallest time increments. This intermittency, when measured from relative
scaling exponents of structure functions, is more pronounced than in the
Eulerian framework.Comment: 4 pages, 5 figures. to appear in PR
Improved Lagrangian mixing models for passive scalars in isotropic turbulence
Lagrangian data for velocity, scalars, and energy and scalar dissipation from direct numerical simulations are used to validate Lagrangian mixing models for inert passive scalars in stationary isotropic turbulence. The scalar fluctuations are nearly Gaussian, and, as a result of production by uniform mean gradients, statistically stationary. Comparisons are made for Taylor-scale Reynolds numbers in the range 38 to about 240 and Schmidt numbers in the range 1/8 to 1. Model predictions for one-point, one-time Eulerian statistics ~Eulerian correspondence! and one-particle, two-time Lagrangian statistics ~Lagrangian correspondence! are examined. Two scalar mixing models, namely the Lagrangian Fokker–Planck model and the Lagrangian colored-noise ~LCN! model, are proposed and written in terms of stochastic differential equations ~SDE! with specified drift and diffusion terms. Both of these models rely on statistics of the scalar field conditioned upon the energy dissipation, as provided by the Lagrangian spectral relaxation ~LSR! model. With the exception of the scalar dissipation, the models are shown to capture the Reynolds and Schmidt-number dependence of the Lagrangian integral time scales. However, the LCN model provides a more realistic description of the Lagrangian scalar fluctuations as differentiable time series having the correct form of the scalar autocorrelation function. Further extensions of the new mixing models to non-Gaussian scalars are conceptually straightforward, but require a closure for the scalar-conditioned scalar dissipation rate matrix. Likewise, accurate prediction of joint statistics for differential diffusion between different scalars with unequal molecular diffusivities will require the formulation of a multiscale SDE similar to the LSR model
Evolution of speckle during spinodal decomposition
Time-dependent properties of the speckled intensity patterns created by
scattering coherent radiation from materials undergoing spinodal decomposition
are investigated by numerical integration of the Cahn-Hilliard-Cook equation.
For binary systems which obey a local conservation law, the characteristic
domain size is known to grow in time as with n=1/3,
where B is a constant. The intensities of individual speckles are found to be
nonstationary, persistent time series. The two-time intensity covariance at
wave vector can be collapsed onto a scaling function , where and . Both analytically and numerically, the covariance
is found to depend on only through in the
small- limit and in the large-
limit, consistent with a simple theory of moving interfaces that applies to any
universality class described by a scalar order parameter. The speckle-intensity
covariance is numerically demonstrated to be equal to the square of the
two-time structure factor of the scattering material, for which an analytic
scaling function is obtained for large In addition, the two-time,
two-point order-parameter correlation function is found to scale as
, even for quite large
distances . The asymptotic power-law exponent for the autocorrelation
function is found to be , violating an upper bound
conjectured by Fisher and Huse.Comment: RevTex: 11 pages + 12 figures, submitted to PR
Optimal Location of Sources in Transportation Networks
We consider the problem of optimizing the locations of source nodes in
transportation networks. A reduction of the fraction of surplus nodes induces a
glassy transition. In contrast to most constraint satisfaction problems
involving discrete variables, our problem involves continuous variables which
lead to cavity fields in the form of functions. The one-step replica symmetry
breaking (1RSB) solution involves solving a stable distribution of functionals,
which is in general infeasible. In this paper, we obtain small closed sets of
functional cavity fields and demonstrate how functional recursions are
converted to simple recursions of probabilities, which make the 1RSB solution
feasible. The physical results in the replica symmetric (RS) and the 1RSB
frameworks are thus derived and the stability of the RS and 1RSB solutions are
examined.Comment: 38 pages, 18 figure
Extracellular electrical signals in a neuron-surface junction: model of heterogeneous membrane conductivity
Signals recorded from neurons with extracellular planar sensors have a wide
range of waveforms and amplitudes. This variety is a result of different
physical conditions affecting the ion currents through a cellular membrane. The
transmembrane currents are often considered by macroscopic membrane models as
essentially a homogeneous process. However, this assumption is doubtful, since
ions move through ion channels, which are scattered within the membrane.
Accounting for this fact, the present work proposes a theoretical model of
heterogeneous membrane conductivity. The model is based on the hypothesis that
both potential and charge are distributed inhomogeneously on the membrane
surface, concentrated near channel pores, as the direct consequence of the
inhomogeneous transmembrane current. A system of continuity equations having
non-stationary and quasi-stationary forms expresses this fact mathematically.
The present work performs mathematical analysis of the proposed equations,
following by the synthesis of the equivalent electric element of a
heterogeneous membrane current. This element is further used to construct a
model of the cell-surface electric junction in a form of the equivalent
electrical circuit. After that a study of how the heterogeneous membrane
conductivity affects parameters of the extracellular electrical signal is
performed. As the result it was found that variation of the passive
characteristics of the cell-surface junction, conductivity of the cleft and the
cleft height, could lead to different shapes of the extracellular signals
Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
The diffusion-limited reaction, with equal initial densities
, is studied by means of a field-theoretic renormalization
group formulation of the problem. For dimension an effective theory is
derived, from which the density and correlation functions can be calculated. We
find the density decays in time as a,b \sim C\sqrt{\D}(Dt)^{-d/4} for , with \D = n_0-C^\prime n_0^{d/2} + \dots, where is a universal
constant, and is non-universal. The calculation is extended to the
case of unequal diffusion constants , resulting in a new
amplitude but the same exponent. For a controlled calculation is not
possible, but a heuristic argument is presented that the results above give at
least the leading term in an expansion. Finally, we address
reaction zones formed in the steady-state by opposing currents of and
particles, and derive scaling properties.Comment: 17 pages, REVTeX, 13 compressed figures, included with epsf. Eq.
(6.12) corrected, and a moderate rewriting of the introduction. Accepted for
publication in J. Stat. Phy
Acceleration and vortex filaments in turbulence
We report recent results from a high resolution numerical study of fluid
particles transported by a fully developed turbulent flow. Single particle
trajectories were followed for a time range spanning more than three decades,
from less than a tenth of the Kolmogorov time-scale up to one large-eddy
turnover time. We present some results concerning acceleration statistics and
the statistics of trapping by vortex filaments.Comment: 10 pages, 5 figure
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