Contact Dynamics of Masonry Block Structures Using Mathematical Programming

A simple variational formulation for contact dynamics is adopted to investigate the dynamic behavior of planar masonry block structures subjected to seismic events. The numerical model is a two-dimensional assemblage of rigid blocks interacting at potential contact points located at the vertices of the interfaces. A no-tension and associative frictional behavior with infinite compressive strength is considered for joints. The dynamic contact problem is formulated as a quadratic programming problem (QP) and an iterative procedure is implemented for time integration. Applications to analytical and numerical case studies are presented for validation. Comparisons with the experimental results of a masonry wall under free rocking motion and of a small scale panel with opening subjected to in-plane loads are also carried out to evaluate the accuracy and the computational efficiency of the formulation adopted.     

Duncan F. Gregory and Robert Leslie Ellis: second-generation reformers of British mathematics

The paper discusses some of the contributions of Duncan Farquharson Gregory and Robert Leslie Ellis to symbolical algebra and their views on the philosophy of mathematics with the aim of revisiting the accepted characterisation of the second generation of reformers of British mathematics found in Crosbie Smith and Norton Wise’s seminal Energy and Empire. It is argued that at least some of the features brought to the fore in their treatment of the work of Gregory and Ellis – namely “geometrical methods” in mathematics and “anti-metaphysical”, “non-hypothetical” and “practical” knowledge – cannot be straightforwardly upheld. On the one hand, Gregory’s generalisation of George Peacock’s symbolical algebra was connected to several natural philosophical considerations underlying the Scottish Newtonians’ “abstractionism” and “geometrical fluxional analysis”. On the other hand, Ellis’s idealist philosophy of mathematics and science insisted that the a priori necessary truths of mathematics could inform the “hypothetical part of scientific induction”. A more nuanced understanding of the place of the second generation of reformers within the analytical revolution in Victorian Britain should thus take into account the eclectic foundational position that arises from the work of Gregory and Ellis.     

Historical mosque orientation in Turkey: Central-Western Anatolia Region, 1150–1590

The orientation of buildings in the ancient civilisations has been referred to the movements of several celestial bodies above the horizon on characteristics dates (two solstices and equinoxes). However, Muslims have used a sacred direction (qibla) towards Kaaba located in the courtyard in the Sacred Mosque in Mecca to pray and to perform various ritual acts in their daily lives since the early days of Islam. Thus, the mosques had then to orientate towards the qibla direction, being indicated by a niche in the focal point of the qibla-wall wherever they were building on the Earth. This article focuses on the mosque orientation in Turkey before the seventeenth century with regard to the astronomical knowledge derived from Arabic sources before Islam, mathematical theory and spherical computation derived from Greek sources and traditions based on the early Islamic period. The mosque orientations are compared to the qibla directions that are used in sacred geography which was determined by the producers of folk astronomy and in the application of the geometric or trigonometric formulae in mathematical astronomy.     

Modelling the Neolithic transition in a heterogeneous environment

The Neolithic transition, involving the change of subsistence from foraging to agriculture, can fruitfully be modelled mathematically, as, e.g., in the three-population model of Aoki et al. (1996). Here that model is modified to include some features of population dynamics in a realistic, two-dimensional environment, and including population pressure, competition for resources between farmers and foragers, and the dependence of the population carrying capacities and diffusivities on the environmental conditions. This modified model allows for the survival of foragers in regions where environmental conditions do not favour farming. The model is tentatively applied to the Indian subcontinent, which is a complicated example of this transition involving multiple domestication centres. The results are briefly compared with published archaeological data.