A robust algorithm for ellipse-based discrete element modelling of granular materials

With recent research indicating the importance of the rolling mechanism of deformation in granular systems consisting of perfectly round particles, it has become popular to use ellipse-shaped particles in the Discrete Element Method (DEM) numerical model. Inherent in this technique is the need for accurately computing ellipse to ellipse intersection, in order to properly detect contact formation and compute relative contact velocities. However, the commonly used algorithms for computing ellipse-ellipse intersection are generally poorly conditioned and can be inaccurate. An alternate method for computing ellipse-ellipse intersection is developed and presented which results in a well-conditioned, stable and accurate contact detection method. These modification are incorporated into the general DEM algorithm.     

The great Minoan eruption of Thera volcano and the ensuing tsunami in the Greek Archipelago

The eastern Mediterranean has been the cradle of many great civilizations. The history of the area consisted of glorious battles, heroic acts, and the rise and fall of great civilizations. But, sometimes, natural hazards became the cause for a new classification of the political, as well as of the military status quo of the region. The enormous eruption of the submarine volcano at the Greek island of Thera (Santorini) during the Bronze Age, around 1500 BC, is such a natural hazard. The tsunami generated by the eruption, literally wiped out the peace-loving Minoan civilization who inhabited the island of Crete. After the sea subsided, the configuration of the area was altered, and the decline of the Minoan principality on the Archipelago began. The present paper introduces evidence concerning the tsunami and states some of the after-effects which were partly responsible for the decline of the Minoan empire. All the information is gathered from historical sources and from recent research works. An effort has been made to include many of the theories introduced by various researchers through time concerning the event. Finally, information has been included from all known research, as well as from the author's own conclusions, in order to make the paper useful to future researchers.     

Feasibility of AFC models for the petrogenesis of calc-alkaline magma series

 One of the most popular petrogenetic concepts is that of simultaneous assimilation and fractional crystallisation (AFC). The equations governing these processes are well known and widely applied. The power and attraction of the model are that, with the minimum of constraints, petrogenetic schemes can be erected for essentially any group of rocks. These models are usually based on the observed variations in a small number of trace elements and/or isotopic systems. In this paper we have generated well-constrained AFC models for the Variscan, calc-alkaline Quérigut complex in the French Pyrénées. Our models are based on geological constraints on the identities of the parent magma and candidate assimilants, and the Sm-Nd and Rb-Sr isotope systematics of the rocks. The modelling is successful in mimicking the isotope array for the actual rocks. However, the results are massively inconsistent with those produced using the major- and trace-element concentrations. Our major conclusion is that AFC modelling should be undertaken only with robust initial constraints on the compositions of the parent magma and the proposed assimilant, with due respect for crystal-liquid partition coefficients, in so far as they are known. The results should then be accepted only if the isotope-based model parameters are consistent with those derived from major- and trace-element variations. Received: 19 August 1994/Accepted: 23 March 1995     

Is the ocean floor a fractal?

The topographic structure of the ocean bottom is investigated at different scales of resolution to answer the question: Can the seafloor be described as a fractal process? Methods from geostatistics, the theory of regionalized variables, are used to analyze the spatial structure of the ocean floor at different scales of resolution. The key to the analysis is the variogram criterion: Self-similarity of a stochastic process implies self-similarity of its variogram. The criterion is derived and proved here: it also is valid for special cases of self-affinity (in a sense adequate for topography). It has been proposed that seafloor topography can be simulated as a fractal (an object of Hausdorff dimension strictly larger than its topological dimension), having scaling properties (self-similarity or self-affinity). The objective of this study is to compare the implications of these concepts with observations of the seafloor. The analyses are based on SEABEAM bathymetric data from the East Pacific Rise at 13°N/104°W and at 9°N/104°W and use tracks that run both across the ridge crest and along the ridge flank. In the geostatistical evaluation, the data are considered as a stochastic process. The spatial continuity of this process is described by variograms that are calculated for different scales and directions. Applications of the variogram criterion to scale-dependent variogram models yields the following results: Although the seafloor may be a fractal in the sense of the definition involving the Hausdorff dimension, it is not self-similar, nor self-affine (in the given sense). Mathematical models of scale-dependent spatial structures are presented, and their relationship to geologic processes such as ridge evolution, crust formation, and sedimentation is discussed.