N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Computational Analysis of Microarray Data

Most of our knowledge of biodiversity and its causes in the deep-sea benthos derives from regional-scale sampling studies of the macrofauna. Improved sampling methods and the expansion of investigations into a wide variety of habitats have revolutionized our understanding of the deep sea. Local species diversity shows clear geographic variation on spatial scales of 100-1000 km. Recent sampling programs have revealed unexpected complexity in community structure at the landscape level that is associated with large-scale oceanographic processes and their environmental consequences. We review the relationships between variation in local species diversity and the regional-scale phenomena of boundary constraints, gradients of productivity, sediment heterogeneity, oxygen availability, hydrodynamic regimes, and catastrophic physical disturbance. We present a conceptual model of how these interdependent environmental factors shape regional-scale variation in local diversity. Local communities in the deep sea may be composed of species that exist as metapopulations whose regional distribution depends on a balance among global-scale, landscape-scale, and small-scale dynamics. Environmental gradients may form geographic patterns of diversity by influencing local processes such as predation, resource partitioning, competitive exclusion, and facilitation that determine species coexistence. The measurement of deep-sea species diversity remains a vital issue in comparing geographic patterns and evaluating their potential causes. Recent assessments of diversity using species accumulation curves with randomly pooled samples confirm the often-disputed claim that the deep sea supports higher diversity than the continental shelf. However, more intensive quantitative sampling is required to fully characterize the diversity of deep-sea sediments, the most extensive habitat on Earth. Once considered to be constant, spatially uniform, and isolated, deep-sea sediments are now recognized as a dynamic, richly textured environment that is inextricably linked to the global biosphere. Regional studies of the last two decades provide the empirical background necessary to formulate and test specific hypotheses of causality by controlled sampling designs and experimental approaches.

Environmental influences on regional deep-sea species diversity

Strain energy release rate (GIc) of Pinus radiata in the TL opening mode was determined using the compliance crack length relationship. A total of 123 specimens consisting of four sizes of specimen with each size having four different crack lengths were tested. For each specimen, grain and ring angles, density and moisture content were measured. Video imaging, was used to measure crack length during propagation. Since cracks extended in stages, full compliance-crack length relationship was developed for each specimen based on their initial and subsequent crack lengths. No significant differences in GIc, between initial and subsequent crack lengths were found for the smaller specimens by paired sample t-tests, but differences were significant for the largest specimen size. The Average fracture toughness was calculated from GIc and it was 215 kPa.m 0.5 . Three artificial neural networks were developed to predict the: 1) force required to propagate a crack, 2) crack extension, and 3) fracture toughness of an individual specimen. Each was successful, producing respective R 2 of 0.870, 0.865, and 0.621 on validation data. A sensitivity analysis of the networks revealed that the crack length was the most influential with 21% contribution followed by grain angle with 14% contribu tion for predicting the applied force. This was followed by volume and physical properties. For predicting the crack extension, density had the greatest contribution (20%) followed by previous crack length and force contributing 16% equally. Fracture toughness was dominated by the dimensional parameters of the specimen contributing (42%) followed by anisotropy and physical properties.

Neural Networks for predicting fracture toughness of individual wood samples

Preface. I. Modeling solute transport in porous media. II. A brief review of mathematical background. III. Computer simulation of Brownian motion and Ito processes. IV. Solving stochastic differential equations. V. Potential theory approach to SDEs. VI. Stochastic modeling of the velocity. VII. Applying potential theory modeling to solute dispersion. VIII. A stochastic computational model for solute transport in porous media. IX. Solving the eigenvalue problem for a covariance kernel with variable correlation length. X. A stochastic inverse method to estimate parameters in groundwater models.

Stochastic Dynamics. Modeling Solute Transport in Porous Media

Stress intensity factor of radiata pine (Pinus radiata) in Tangential-Longitudinal opening mode was determined from crack-tip displacement fields obtained from digital image correlation in conjunction with orthotropic fracture theory. For lower loads, experiments agreed with the linear elastic fracture theory but for higher loads, stress intensity factor and load relationship was nonlinear. For 41% of the specimens tested, tip-displacement based stress intensity factor agreed with that based on the ASTM standard formula for lower loads but deviated for higher loads closer to failure. The tip displacement plots showed that the nonlinear behaviour is due to large displacements which we attributed to large plastic deformations and/or micro-cracking in this region. The other 59% specimens showed a similar trend except that the crack-tip based stress intensity factor was consistently higher than the value obtained from the standard formula. The fracture toughness from tip displacements was larger than the standard values for all specimens and the two were related by a logarithmic function with an R2 of 0.61. The study also established that fracture toughness increases with the angle of inclination of the original crack plane to the Radial Longitudinal plane.

Stress Intensity Factor of Wood from Crack-Tip Displacement Fields Obtained from Digital Image Processing

This Paper investigates the use of digital image analysis techniques for developing an automated kiwifruit counting system. Three simple counting methods followed by a minimum distance classifier based segmentation technique in L*a*b colour space were studied. Images were taken prior to harvesting at a New Zealand kiwifruit orchard. Accurate counting of kiwifruit in several sample regions of the orchard is required in order to estimate the fruit harvest. At present, the counting is manually done by hired employees. Manual counting has several issues, such as low accuracy, long duration and higher costs. Automated counting technique facilitates a fast, low cost and potentially more accurate way of counting kiwifruit. Several approaches were trialled and validated on different sets of images. Above 90% accuracy on gold image data and above 60% accuracy on green image data were obtained, showing the potential of using the approach for counting kiwifruit for the harvest estimation purpose. The results, limitations and ongoing research in developing a more robust and consistent technique will be discussed.

/pdf/digital-image-analysis-based-automated-kiwifruit-counting-1ifpuecnz0.pdf

Digital image analysis based automated kiwifruit counting technique

Soft (fuzzy) clustering techniques are often used in the study of high-dimensional datasets, such as microarray and other high-throughput bioinformatics data The most widely used method is the fuzzy C-means (FCM) algorithm, but it can present difficulties when dealing with some datasets A fuzzy clustering algorithm, DifFUZZY, which utilises concepts from diffusion processes in graphs and is applicable to a larger class of clustering problems than other fuzzy clustering algorithms is developed Examples of datasets (synthetic and real) for which this method outperforms other frequently used algorithms are presented, including two benchmark biological datasets, a genetic expression dataset and a dataset that contains taxonomic measurements This method is better than traditional fuzzy clustering algorithms at handling datasets that are 'curved', elongated or those which contain clusters of different dispersion The algorithm has been implemented in Matlab and C++ and is available at http://wwwmathsoxacuk/cmb/difFUZZY

/pdf/diffuzzy-a-fuzzy-clustering-algorithm-for-complex-datasets-24e7kdt53c.pdf

Don Kulasiri

Papers

Neural Networks for predicting fracture toughness of individual wood samples

Stochastic Dynamics. Modeling Solute Transport in Porous Media

Stress Intensity Factor of Wood from Crack-Tip Displacement Fields Obtained from Digital Image Processing

Digital image analysis based automated kiwifruit counting technique

DifFUZZY: a fuzzy clustering algorithm for complex datasets