Sign-symmetry of temperature structure functions

New scalar structure functions with different sign-symmetry properties are defined. These structure functions possess different scaling exponents even when their order is the same. Their scaling properties are investigated for second and third orders, using data from high-Reynolds-number atmospheric boundary layer. It is only when structure functions with disparate sign-symmetry properties are compared can the extended self-similarity detect two different scaling ranges that may exist, as in the example of convective turbulence.Comment: 18 pages, 5 figures, accepted for publication in Physical Review

Resection and resolution of bone marrow lesions associated with an improvement of pain after total knee replacement: a novel case study using a 3-Tesla metal artefact reduction MRI sequence

We present our case report using a novel metal artefact reduction magnetic resonance imaging (MRI) sequence to observe resolution of subchondral bone marrow lesions (BMLs), which are strongly associated with pain, in a patient after total knee replacement surgery. Large BMLs were seen preoperatively on the 3-Tesla MRI scans in a patient with severe end stage OA awaiting total knee replacement surgery. Twelve months after surgery, using a novel metal artefact reduction MRI sequence, we were able to visualize the bone-prosthesis interface and found complete resection and resolution of these BMLs. This is the first reported study in the UK to use this metal artefact reduction MRI sequence at 3-Tesla showing that resection and resolution of BMLs in this patient were associated with an improvement of pain and function after total knee replacement surgery. In this case it was associated with a clinically significant improvement of pain and function after surgery. Failure to eradicate these lesions may be a cause of persistent postoperative pain that is seen in up to 20% of patients following TKR surgery

Dynamical equations for high-order structure functions, and a comparison of a mean field theory with experiments in three-dimensional turbulence

Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) and R.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] derive, through two different approaches that have the Navier-Stokes equations as the common starting point, a set of steady-state dynamic equations for structure functions of arbitrary order in hydrodynamic turbulence. These equations are not closed. Yakhot proposed a "mean field theory" to close the equations for locally isotropic turbulence, and obtained scaling exponents of structure functions and an expression for the tails of the probability density function of transverse velocity increments. At high Reynolds numbers, we present some relevant experimental data on pressure and dissipation terms that are needed to provide closure, as well as on aspects predicted by the theory. Comparison between the theory and the data shows varying levels of agreement, and reveals gaps inherent to the implementation of the theory.Comment: 16 pages, 23 figure

Closure of two dimensional turbulence: the role of pressure gradients

Inverse energy cascade regime of two dimensional turbulence is investigated by means of high resolution numerical simulations. Numerical computations of conditional averages of transverse pressure gradient increments are found to be compatible with a recently proposed self-consistent Gaussian model. An analogous low order closure model for the longitudinal pressure gradient is proposed and its validity is numerically examined. In this case numerical evidence for the presence of higher order terms in the closure is found. The fundamental role of conditional statistics between longitudinal and transverse components is highlighted.Comment: 4 pages, 2 figures, in press on PR

The Scaling Structure of the Velocity Statistics in Atmospheric Boundary Layer

The statistical objects characterizing turbulence in real turbulent flows differ from those of the ideal homogeneous isotropic model.They containcontributions from various 2d and 3d aspects, and from the superposition ofinhomogeneous and anisotropic contributions. We employ the recently introduceddecomposition of statistical tensor objects into irreducible representations of theSO(3) symmetry group (characterized by $j$ and $m$ indices), to disentangle someof these contributions, separating the universal and the asymptotic from the specific aspects of the flow. The different $j$ contributions transform differently under rotations and so form a complete basis in which to represent the tensor objects under study. The experimental data arerecorded with hot-wire probes placed at various heights in the atmospheric surfacelayer. Time series data from single probes and from pairs of probes are analyzed to compute the amplitudes and exponents of different contributions to the second order statistical objects characterized by $j=0$, $j=1$ and $j=2$. The analysis shows the need to make a careful distinction between long-lived quasi 2d turbulent motions (close to the ground) and relatively short-lived 3d motions. We demonstrate that the leading scaling exponents in the three leading sectors ($j = 0, 1, 2$) appear to be different butuniversal, independent of the positions of the probe, and the large scaleproperties. The measured values of the exponent are $\zeta^{(j=0)}_2=0.68 \pm 0.01$, $\zeta^{(j=1)}_2=1.0\pm 0.15$ and $\zeta^{(j=2)}_2=1.38 \pm 0.10$. We present theoretical arguments for the values of these exponents usingthe Clebsch representation of the Euler equations; neglecting anomalous corrections, the values obtained are 2/3, 1 and 4/3 respectively.Comment: PRE, submitted. RevTex, 38 pages, 8 figures included . Online (HTML) version of this paper is avaliable at http://lvov.weizmann.ac.il

Anomalous and dimensional scaling in anisotropic turbulence

We present a numerical study of anisotropic statistical fluctuations in homogeneous turbulent flows. We give an argument to predict the dimensional scaling exponents, (p+j)/3, for the projections of p-th order structure function in the j-th sector of the rotational group. We show that measured exponents are anomalous, showing a clear deviation from the dimensional prediction. Dimensional scaling is subleading and it is recovered only after a random reshuffling of all velocity phases, in the stationary ensemble. This supports the idea that anomalous scaling is the result of a genuine inertial evolution, independent of large-scale behavior.Comment: 4 pages, 3 figure

Optical pathology of oral tissue: a Raman spectroscopy diagnostic method

Raman and fluorescence spectroscopy methods are being considered as techniques which could be complementary or even alternative to biopsy, and pathology and clinical assays in many medical applications. The present paper discusses the results of Raman spectral studies on oral tissues for optical pathology. It is shown that Raman spectra of oral tissues can be classified into spectra of normal and malignant sets and a model based on such a classification can be used to analyse oral tissue for detection of oral malignancy. Sensitivity and specificity calculated from 90 test spectra are better than 85 and 90 per cent respectively

Inhomogeneous Anisotropic Passive Scalars

We investigate the behaviour of the two-point correlation function in the context of passive scalars for non homogeneous, non isotropic forcing ensembles. Exact analytical computations can be carried out in the framework of the Kraichnan model for each anisotropic sector. It is shown how the homogeneous solution is recovered at separations smaller than an intrinsic typical lengthscale induced by inhomogeneities, and how the different Fourier modes in the centre-of-mass variable recombine themselves to give a ``beating'' (superposition of power laws) described by Bessel functions. The pure power-law behaviour is restored even if the inhomogeneous excitation takes place at very small scales.Comment: 14 pages, 5 figure