A. S. Cakmak

Explicit integration method for the time‐dependent Schrodinger equation for collision problems

To date, only the implicit (Crank–Nicholson) integration method has ben used for numerical integration of the Schrodinger equation for collision processes. The standard explicit methods are known to be unstable and a high price is paid for the implicit method due to the inversion of the large matrices involved. Furthermore, the method is prohibitive in more than two dimensions due to restrictions on memory and large computation times. An explicit method (i.e., a method which doesn’t require the solution of simultaneous equations) is presented, and is shown to be stable in n dimensions to the same order of accuracy as the implicit method with the unitarity being secured to two orders higher accuracy than that for the wave function.

Advanced Byzantine cement based composites resisting earthquake stresses: the crushed brick/lime mortars of Justinian's Hagia Sophia

Abstract Structural studies to determine the earthquake worthiness of Hagia Sophia in Istanbul have proved that the monuments static and dynamic behavior depends very strongly on the mechanical, chemical and microstructural properties of the mortars and bricks used for the masonry. Hence, the classification of the crushed brick/lime mortars under the category of advanced cement-based composites is concluded, explaining the fact that the monument still stands, as well as the very large static deformations which it has undergone, since such mortars have a very long curing period. According to the analysis of the dynamic data, the first three natural frequencies of the building were determined. These results show a decrease of approximately 5–10% in the natural frequencies, as the amplitude of the accelerations increases and returns to their initial values, due to the non-linear nature of the masonry. The above-mentioned behavior allows the structure to absorb energy without affecting irreversibly its material properties. The determination of the mortar properties indicated that they are of considerable mechanical strength and longevity. The dated mortar samples examined proved to be resistant to continuous stresses and strains due to the presence of the amorphous hydraulic formations (CSH), investigated by transmission electron microscopy (TEM) at the crushed-brick powder/binder interfaces and at a sufficient content in the binding matrix, as proved by TG-DTA, which allowed for greater energy absorption without initiations of fractures, let alone the transition of the gel to a higher order of formation. Furthermore, the interpretation of the amorphous nature of the hydraulic formations of the crushed brick/lime mortars is attempted by the experimental validation of real chemical interaction between lime and clay and the characterization of the fundamental structural units of the calcium silicate hydrates, produced by mass spectroscopy.

Finite element methods for reactive scattering

Abstract The finite element method is applied to collinear reactive scattering problems. In this way no basis set expansion of the wave function is required and a direct solution of the two-dimensional partial differential equation is achieved. It is shown how to generally formulate this approach and achieve fast and accurate results. As a test calculation the method was applied to H + H 2 , yielding excellent agreement with close coupling results. Since no basis sets are used in the finite element calculation, no question of basis set convergence or closed channel behavior arises. Some discussion on applications to higher dimensions is also included.

SEISMIC DAMAGE ASSESSMENT USING LINEAR MODELS

The problem of earthquake damage assessment is defined. The role of the analysis of strong motion records in damage assessment codes based on expert systems is pointed out. The behavior of some damage indices proposed in the literature is studied using numerical simulations. Global damage indices for complex structures can be computed from the optimal time variant linear model, that is fitted to recorded strong motion accelerograms. Two of these indices are proposed, and their performance is tested both on numerical simulations and on strong motion records. A program for the identification of linear structures, based on strong motion records, has been written and implemented by the authors. The theoretical and computational aspects of the identification algorithm are discussed.

Modelling earthquake ground motions in California using parametric time series methods

Abstract The use of parametric time series analysis to describe strong motion accelerograms has proven to be an efficient method requiring few modelling parameters. In this study, an ARMA model was used to represent accelerograms which were first processed using a variance-stabilizing transformation. By analyzing a large number of recorded accelerograms in the State of California, relationships were found between ARMA parameters and physical variables making it possible to simulate earthquake ground motions throughout the region. The validity of these results was tested by comparing the accelerograms and response spectra of the initial and simulated records.

Flow of Micropolar Fluids between Two Concentric Cylinders

The flow of micropolar fluids between two concentric cylinders, is analyzed first for the use of Couette flow with ∂p/∂θ, then for the case of Poiseuille flow. The results are presented graphically and compared with the classical ones, and the differences are discussed.

A comparison between finite element methods and spectral methods as applied to bound state problems

The finite element and spectral methods are applied to two‐dimensional bound state problems. A comparison of the spectral method, which requires a global basis set expansion of the wave functions, and the finite element method, which requires no such such expansion, is presented. A procedure is given for formulating the finite element approach and for achieving fast and accurate results. The convergence of the finite element calculations is considered and shown to be well behaved. A discussion of the extension of the finite element method to higher dimensions is also included.

Couple Stresses in Fluids

Applications of couple stress and micropolar theories to the problems of Couette and Poiseuille flows between two parallel plates are discussed and the results are compared.

Earthquake resistant construction techniques and materials on Byzantine monuments in Kiev

Abstract The study of the behaviour of historic buildings that have suffered from earthquakes has become a valuable tool for the understanding of earthquake resistant construction techniques and materials. Byzantine monuments of the 11–13th century in Kiev have been studied to provide insights into their effective dynamic properties facing severe earthquake history in the area. The recessed brickworks according to the “concealed course” construction technique of the St. Sophia Cathedral (11th century), the Church of St. Michael in the Vydubytskyi Monastery (11th century), the Tithe Church of the Assumption of the Virgin (10th century) and the Cathedral of Assumption of the Virgin (11th century) in the Monastery of the Caves (Pecherskyi monastery) in Kiev were studied and the material properties of bricks and lime mortars with ceramic fill were investigated (mechanical strength tests, mineralogical, chemical and microstructural analysis). The results show major similarities with those of the Byzantine monuments in Istanbul (Theodosian Walls and Hagia Sophia — 6–11th century construction phases), giving evidence of earthquake resistant construction techniques and materials allowing for continuous stresses and strains. Hence, didactics on proper restoration techniques and materials are deduced aiming at their present safety in the face of future earthquakes.

The use of global wavefunctions in scattering theory

Abstract This paper considers the potential savings associated with the use of global wavefunctions in scattering theory. The normal close coupling approach exp