Exact Second-Order Structure-Function Relationships

Equations that follow from the Navier-Stokes equation and incompressibility but with no other approximations are "exact.". Exact equations relating second- and third-order structure functions are studied, as is an exact incompressibility condition on the second-order velocity structure function. Opportunities for investigations using these equations are discussed. Precisely defined averaging operations are required to obtain exact averaged equations. Ensemble, temporal, and spatial averages are all considered because they produce different statistical equations and because they apply to theoretical purposes, experiment, and numerical simulation of turbulence. Particularly simple exact equations are obtained for the following cases: i) the trace of the structure functions, ii) DNS that has periodic boundary conditions, and iii) an average over a sphere in r-space. The last case (iii) introduces the average over orientations of r into the structure function equations. The energy dissipation rate appears in the exact trace equation without averaging, whereas in previous formulations energy dissipation rate appears after averaging and use of local isotropy. The trace mitigates the effect of anisotropy in the equations, thereby revealing that the trace of the third-order structure function is expected to be superior for quantifying asymptotic scaling laws. The orientation average has the same property.Comment: no figure

Strain measurement at the knee ligament insertion sites

We describe the modification of an existing method of ligament strain measurement at the knee joint in detail. At ten fresh joint specimens we used that technique where strain gauges are attached to the ligamentous insertions and origins. We both improved the preparation of the attachment site and the application of the strain gauges. In a special apparatus the specimens were moved from 0degrees extension to 100degrees flexion while simulating muscle strength and axial force. Testing was performed at the posterior cruciate ligament with both intact and transsected anterior cruciate ligament. In contrast to other existing techniques it does not affect the motion of the joint or the integrity and the function of the ligaments. Unlike the original description of that method we could register a loading behaviour of the posterior cruciate ligament that is similar to those reported in the literature

A tour on Hermitian symmetric manifolds

Hermitian symmetric manifolds are Hermitian manifolds which are homogeneous and such that every point has a symmetry preserving the Hermitian structure. The aim of these notes is to present an introduction to this important class of manifolds, trying to survey the several different perspectives from which Hermitian symmetric manifolds can be studied.Comment: 56 pages, expanded version. Written for the Proceedings of the CIME-CIRM summer course "Combinatorial Algebraic Geometry". Comments are still welcome

Screening and Evaluation of Essential Oils from Mediterranean Aromatic Plants against the Mushroom Cobweb Disease, Cladobotryum mycophilum

The main aim of this study was to evaluate the use of essential oils (EOs) as an alternative to synthetic fungicides used in the control of cobweb disease of button mushroom (Agaricus bisporus) caused by Cladobotryum mycophilum. The EOs used were obtained by hydrodistillation from five Mediterranean aromatic species (Lavandula × intermedia, Salvia lavandulifolia, Satureja montana, Thymus mastichina, and Thymus vulgaris), analyzed by gas chromatography, and tested in vitro for their antifungal activity against C. mycophilum. In vitro bioassays showed that the EOs obtained from T. vulgaris and S. montana (ED50 = 35.5 and 42.8 mg L−1, respectively) were the most effective EOs for inhibiting the mycelial growth of C. mycophilum, and were also the most selective EOs between C. mycophilum and A. bisporus. The in vivo efficacy of T. vulgaris and S. montana EOs at two different concentrations (0.5 and 1%) were evaluated in two mushroom growing trials with C. mycophilum inoculation. The treatments involving T. vulgaris and S. montana EOs at the higher dose (1% concentration) were as effective as fungicide treatment. The effect of these EOs on mushroom productivity was tested in a mushroom cropping trial without inoculation. They had a strong fungitoxic effect at the first flush. However, a compensatory effect was observed by the end of the crop cycle and no differences were observed in biological efficiency between treatments. The main compounds found were carvacrol and p-cymene for S. montana, and p-cymene and thymol for T. vulgaris. These results suggest that T. vulgaris and S. montana EOs may be useful products to manage cobweb disease if used as part of an integrated pest management (IPM) program

Opportunities for use of exact statistical equations

Exact structure function equations are an efficient means of obtaining asymptotic laws such as inertial range laws, as well as all measurable effects of inhomogeneity and anisotropy that cause deviations from such laws. "Exact" means that the equations are obtained from the Navier-Stokes equation or other hydrodynamic equations without any approximation. A pragmatic definition of local homogeneity lies within the exact equations because terms that explicitly depend on the rate of change of measurement location appear within the exact equations; an analogous statement is true for local stationarity. An exact definition of averaging operations is required for the exact equations. Careful derivations of several inertial range laws have appeared in the literature recently in the form of theorems. These theorems give the relationships of the energy dissipation rate to the structure function of acceleration increment multiplied by velocity increment and to both the trace of and the components of the third-order velocity structure functions. These laws are efficiently derived from the exact velocity structure function equations. In some respects, the results obtained herein differ from the previous theorems. The acceleration-velocity structure function is useful for obtaining the energy dissipation rate in particle tracking experiments provided that the effects of inhomogeneity are estimated by means of displacing the measurement location.Comment: accepted by Journal of Turbulenc