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Seismic vulnerability estimation of existing structures is unquestionably interesting topic of high priority, particularly after earthquake events. Having in mind the vast number of old masonry buildings in North Macedonia serving as public institutions, it is evident that the structural assessment of these buildings is an issue of great importance. In this paper, a comprehensive methodology for the development of seismic fragility curves of existing masonry buildings is presented. A scenario – based method that incorporates the knowledge of the tectonic style of the considered region, the active fault characterization, the earth crust model and the historical seismicity (determined via the Neo Deterministic approach) is used for calculation of the necessary response spectra. The capacity of the investigated masonry buildings has been determined by using nonlinear static analysis. MINEA software (SDA Engineering) is used for verification of the structural safety of the structures Performance point, obtained from the intersection of the capacity of the building and the spectra used, is selected as a response parameter. The thresholds of the spectral displacement are obtained by splitting the capacity curve into five parts, utilizing empirical formulas which are represented as a function of yield displacement and ultimate displacement. As a result, four levels of damage limit states are determined. A maximum likelihood estimation procedure for the process of fragility curves determination is noted as a final step in the proposed procedure. As a result, region specific series of vulnerability curves for structures are defined.
Quantifying and minimizing uncertainty is vital for simulating technically and economically successful geothermal reservoirs. To this end, we apply a stochastic modelling sequence, a Monte Carlo study, based on (i) creating an ensemble of possible realizations of a reservoir model, (ii) forward simulation of fluid flow and heat transport, and (iii) constraining post-processing using observed state variables. To generate the ensemble, we use the stochastic algorithm of Sequential Gaussian Simulation and test its potential fitting rock properties, such as thermal conductivity and permeability, of a synthetic reference model and—performing a corresponding forward simulation—state variables such as temperature. The ensemble yields probability distributions of rock properties and state variables at any location inside the reservoir. In addition, we perform a constraining post-processing in order to minimize the uncertainty of the obtained distributions by conditioning the ensemble to observed state variables, in this case temperature. This constraining post-processing works particularly well on systems dominated by fluid flow. The stochastic modelling sequence is applied to a large, steady-state 3-D heat flow model of a reservoir in The Hague, Netherlands. The spatial thermal conductivity distribution is simulated stochastically based on available logging data. Errors of bottom-hole temperatures provide thresholds for the constraining technique performed afterwards. This reduce the temperature uncertainty for the proposed target location significantly from 25 to 12 K (full distribution width) in a depth of 2300 m. Assuming a Gaussian shape of the temperature distribution, the standard deviation is 1.8 K. To allow a more comprehensive approach to quantify uncertainty, we also implement the stochastic simulation of boundary conditions and demonstrate this for the basal specific heat flow in the reservoir of The Hague. As expected, this results in a larger distribution width and hence, a larger, but more realistic uncertainty estimate. However, applying the constraining post-processing the uncertainty is again reduced to the level of the post-processing without stochastic boundary simulation. Thus, constraining post-processing is a suitable tool for reducing uncertainty estimates by observed state variables.
Anyone who has always wanted to understand the hieroglyphs on Sheldon's blackboard in the TV series The Big Bang Theory or who wanted to know exactly what the fate of Schrödinger's cat is all about will find a short, descriptive introduction to the world of quantum mechanics in this essential. The text particularly focuses on the mathematical description in the Hilbert space. The content goes beyond popular scientific presentations, but is nevertheless suitable for readers without special prior knowledge thanks to the clear examples.