Comments on 'On the relative dispersion of two particles in homogeneous stationary turbulence and the implication for the size of concentration fluctuations at large times' by D.J. Thomson (1986, 112, 890-894)

1988 ◽  
Vol 114 (480) ◽  
pp. 545-550 ◽  
Author(s):  
H KAPLAN ◽  
N DINAR
Keyword(s):  
Concentration Fluctuations ◽  
Relative Dispersion ◽  
Stationary Turbulence

A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence

1994 ◽  
Vol 279 ◽  
pp. 69-99 ◽  
Author(s):  
M. S. Borgas ◽  
B. L. Sawford
Keyword(s):  
Quadratic Form ◽  
Stochastic Models ◽  
Stokes Equations ◽  
Probability Distributions ◽  
Particle Dispersion ◽  
Relative Dispersion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stationary Turbulence ◽  
Particle Statistics

A family of Lagrangian stochastic models for the joint motion of particle pairs in isotropic homogeneous stationary turbulence is considered. The Markov assumption and well-mixed criterion of Thomson (1990) are used, and the models have quadratic-form functions of velocity for the particle accelerations. Two constraints are derived which formally require that the correct one-particle statistics are obtained by the models. These constraints involve the Eulerian expectation of the ‘acceleration’ of a fluid particle with conditioned instantaneous velocity, given either at the particle, or at some other particle's position. The Navier-Stokes equations, with Gaussian Eulerian probability distributions, are shown to give quadratic-form conditional accelerations, and models which satisfy these two constraints are found. Dispersion calculations show that the constraints do not always guarantee good one-particle statistics, but it is possible to select a constrained model that does. Thomson's model has good one-particle statistics, but is shown to have unphysical conditional accelerations. Comparisons of relative dispersion for the models are made.

Concentration fluctuations and relative dispersion PDF

2005 ◽  
Vol 39 (11) ◽  
pp. 2135-2143 ◽  
Author(s):  
E FERRERO ◽  
L MORTARINI
Keyword(s):  
Concentration Fluctuations ◽  
Relative Dispersion

Heterogeneity of Cerebral Blood Flow: a Fractal Approach

2000 ◽  
Vol 39 (02) ◽  
pp. 37-42 ◽  
Author(s):  
P. Hartikainen ◽  
J. T. Kuikka
Keyword(s):  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Fractal Dimension ◽  
Frontal Lobe ◽  
Fractal Analysis ◽  
Relative Dispersion ◽  
Emission Computed Tomography ◽  
Brain Blood Flow ◽  
Healthy Controls ◽  
Fractal Approach

Summary Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and singlephoton emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (= coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17 ± 0.05 (mean ± SD) for the left hemisphere and 1.15 ± 0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04 ± 0.03 than in healthy controls. Conclusion: Within the limits of spatial resolution of SPECT, the heterogeneity of brain blood flow is well characterized by a fractal dimension. Fractal analysis may help brain scientists to assess age-, sex- and laterality-related anatomic and physiological changes of brain blood flow and possibly to improve precision of diagnostic information available for patient care.

Sign in / Sign up

Export Citation Format

Share Document