Constitutive properties of contacting materials with a finite-sized microstructure

Materials consisting of macro-molecules that are set in a structure and interact via contact interactions are investigated. The analysis is analytical, based on the methodology developed for granular materials by Jenkins J.T. and Koenders M.A. “The incremental response of random aggregates of round particles” European Physics Journal E., 13, 2004 113–123. The stiffness tensor is obtained and the results are screened for auxetic properties. Two-dimensional materials are investigated. For regular packings isotropic and anisotropic structures are examined. It is demonstrated that isotropic materials in this category are never auxetic. Heterogeneous materials are also analysed. It is shown that auxetic behaviour is enhanced when structural variation is present. By contrast, auxetic behaviour is suppressed when constitutive heterogeneity is present. The results of the analysis may be employed to scrutinize numerical simulations.     

On the use of the variogram in checking for independence in spatial data

The variogram is a standard tool in the analysis of spatial data, and its shape provides useful information on the form of spatial correlation that may be present. However, it is also useful to be able to assess the evidence for the presence of any spatial correlation. A method of doing this, based on an assessment of whether the true function underlying the variogram is constant, is proposed. Nonparametric smoothing of the squared differences of the observed variables, on a suitably transformed scale, is used to estimate variogram shape. A statistic based on a ratio of quadratic forms is proposed and the test is constructed by investigating the distributional properties of this statistic under the assumption of an independent Gaussian process. The power of the test is investigated. Reference bands are proposed as a graphical follow-up. An example is discussed.     

The Autocovariance Function for Marked Point Processes: A Comparison between Two Different Approaches

Exploratory analysis of marked point patterns has previously been conducted using two disjoint techniques, namely the mark correlation function and spectral analysis. Our purpose here is to present two alternative autocovariance estimators to the mark correlation function which not only apply in both planar and lattice situations, but which in the lattice case can also be considered in terms of the inverse Fourier transform of the spectrum. Moreover, they can be applied to isotropic or anisotropic marked point patterns. Various examples are presented to show how these estimators perform when applied to data sets possessing different kinds of mark structure, and a rank test procedure is proposed to enable the construction of empirical tests of hypothesis.     

Is echogenicity a viable metric for evaluating tendon properties in vivo?

Material properties of tissue in vivo present an opportunity for clinical analysis of healing progression and pathologies as well as provide an excellent research tool yielding quantified data for longitudinal and cross population studies. Echogenicity is a material?s ability to reflect sound and, using ultrasound, it has been shown to increase with tendon tension in vitro, though this non-invasive measurement technique for determining mechanical properties has not been tested in vivo. The aim of this study was to establish if echogenicity, seen by the increase in image brightness, could be correlated to stress within a tissue. 18 Achilles tendons were imaged in the sagittal and transverse planes while producing a series of isometric contractions starting from rest and producing the torque equivalent of 0.5, 1.0, 1.5, and 2.0× body weights. Manual tracing identified the tendon in each of the images. The cross-sectional area determined from the transverse plane images in conjunction with the tendon force yielded the tendon stress. The echogenicity of the tendon was determined from the mean brightness change from rest to each of the contraction cases, measured from the sagittal plane images. A weak correlation existed between the echogenicity and stress (R=0.25) but it was found that there was no significant change in axial area during contraction (p=0.683) establishing the tendon as incompressible. Echogenicity proved to be non-functional for measuring the mechanical properties of the Achilles tendon due to the additional factors included with in vivo testing e.g. tendon twist and multi-axial loading.     

Wavelet analysis for detecting anisotropy in point patterns

Although many methods have been proposed for analysing point locations for spatial pattern, previous methods have concentrated on clumping and spacing. The study of anisotropy (changes in spatial pattern with direction) in point patterns has been limited by lack of methods explicitly designed for these data and this purpose; researchers have been constrained to choosing arbitrary test directions or converting their data into quadrat counts and using methods designed for continuously distributed data. Wavelet analysis, a booming approach to studying spatial pattern, widely used in mathematics and physics for signal analysis, has started to make its way into the ecological literature. A simple adaptation of wavelet analysis is proposed for the detection of anisotropy in point patterns. The method is illustrated with both simulated and field data. This approach can easily be used for both global and local spatial analysis.