Time-averaged Mean Square Research Articles

Non-Gaussian Fluctuations Resulting from Power-Law Trapping in a Lipid Bilayer

Anomalous diffusion in lipid bilayers is usually attributed to viscoelastic behavior. We compute the scaling exponent of relative fluctuations of the time-averaged mean square displacement in a lipid bilayer, by using a molecular dynamics simulation. According to the continuous time random walk theory, this exponent indicates non-Gaussian behavior caused by a power-law trapping time. Our results provide the first evidence that a lipid bilayer has not only viscoelastic properties but also trapping times distributed according to a power law.

Role of infinite invariant measure in deterministic subdiffusion

Statistical properties of the transport coefficient for deterministic subdiffusion are investigated from the viewpoint of infinite ergodic theory. We find that the averaged diffusion coefficient is characterized by the infinite invariant measure of the reduced map. We also show that when the time difference is much smaller than the total observation time, the time-averaged mean square displacement depends linearly on the time difference. Furthermore, the diffusion coefficient becomes a random variable and its limit distribution is characterized by the universal law called the Mittag-Leffler distribution.

Spatial structure of a confined swirling flow using planar elastic scatter imaging and laser Doppler velocimetry

This paper reports the results of a study of the instantaneous spatial structure of a confined swirling flow after a sudden expansion. The flow chosen corresponds to the cold flow conditions of an axisymmetric laboratory-scale research furnace. The swirl number of the flow is 0.7 at the inlet plane and the expansion diameter ratio is 6:1. The flow has a centre hub-to-throat diameter ratio of 1:4. Data are reported for the instantaneous spatial structure of the flow via transient planar elastic scattering imaging. This technique allows for unambiguous visualization of the spatial structure of the flow by slicing through it with a thin sheet (≅ 1.5 mm) of light at various locations in the axial/radial and radial/azimuthal planes. By varying the time delay between introduction of the seeding material and data acquisition, features of the flow that would ordinarily be inaccessible are revealed. Laser Doppler velocimetry is used to measure the time-averaged and root mean square velocity components in all three coordinate directions. Using these data, we construct a model of the flow from the viewpoint of the vorticity fed into the flow and its subsequent dynamics. This viewpoint suggests different reasons for the development of the observable features of the flow and shows promise for helping to deconvolve the apparent complexity of this flowfield.