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A concept of non-commutative Galois extension is introduced and binary and ternary extensions are chosen. Non-commutative Galois extensions of Nonion algebra and su(3) are constructed. Then ternary and binary Clifford analysis are introduced for non-commutative Galois extensions and the corresponding Dirac operators are associated.
The sizing of simple resonators like guitar strings or laser mirrors is directly connected to the wavelength and represents no complex optimisation problem. This is not the case with liquid-filled acoustic resonators of non-trivial geometries, where several masses and stiffnesses of the structure and the fluid have to fit together. This creates a scenario of many competing and interacting resonances varying in relative strength and frequency when design parameters change. Hence, the resonator design involves a parameter-tuning problem with many local optima. As its solution evolutionary algorithms (EA) coupled to a forced-harmonic FE simulation are presented. A new hybrid EA is proposed and compared to two state-of-theart EAs based on selected test problems. The motivating background is the search for better resonators suitable for sonofusion experiments where extreme states of matter are sought in collapsing cavitation bubbles.
Optimum technological solutions must take into account the entire life cycle of structures including design procedures as well as quality assurance, inspection, maintenance, and repair strategies. Unfortunately, current design standards do not provide a satisfactory basis to ensure expected structural lifetimes. The latter may vary from only a few years for temporary structures to over a century for bridges, water dams or nuclear repositories. Consistent scientific concepts are urgently required to cover this wide spectrum of lifetimes in structural design and maintenance. This was a motivation for a group of scientists at the Ruhr-University Bochum (RUB) to start a special research program supported by the German Research Foundation (DFG) within the Cooperative Research Center SFB 398 since 1996. Institutes of the University Wuppertal and of the University Essen-Duisburg joined the research group. The goal of the Center is to study sources of damage and deterioration in materials and structures, to develop consistent models and simulation methods, to predict structural lifetimes and finally to integrate this predictions into new lifetime-oriented design strategies.
Research activities in our center are organised in three Project Groups as follows:
- Modelling of lifetime effects
- Methods for lifetime-oriented structural analyses
- Future lifespan-oriented design strategies.
Information technology plays a key role in the everyday operation of buildings and campuses. Many proprietary technologies and methodologies can assist in effective Building Performance Monitoring (BPM) and efficient managing of building resources. The integration of related tools like energy simulator packages, facility, energy and building management systems, and enterprise resource planning systems is of benefit to BPM. However, the complexity to integrating such domain specific systems prevents their common usage. Service Oriented Architecture (SOA) has been deployed successfully in many large multinational companies to create integrated and flexible software systems, but so far this methodology has not been applied broadly to the field of BPM. This paper envisions that SOA provides an effective integration framework for BPM. Service oriented architecture for the ITOBO framework for sustainable and optimised building operation is proposed and an implementation for a building performance monitoring system is introduced.
The paper is devoted to a study of properties of homogeneous solutions of massless field equation in higher dimensions. We first treat the case of dimension 4. Here we use the two-component spinor language (developed for purposes of general relativity). We describe how are massless field operators related to a higher spin analogues of the de Rham sequence - the so called Bernstein-Gel'fand-Gel'fand (BGG) complexes - and how are they related to the twisted Dirac operators. Then we study similar question in higher (even) dimensions. Here we have to use more tools from representation theory of the orthogonal group. We recall the definition of massless field equations in higher dimensions and relations to higher dimensional conformal BGG complexes. Then we discuss properties of homogeneous solutions of massless field equation. Using some recent techniques for decomposition of tensor products of irreducible $Spin(m)$-modules, we are able to add some new results on a structure of the spaces of homogenous solutions of massless field equations. In particular, we show that the kernel of the massless field equation in a given homogeneity contains at least on specific irreducible submodule.
We consider a structural truss problem where all of the physical model parameters are uncertain: not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process of manufacturing or construction, or round-off errors. In this case the application of the finite element method results in a system of linear equations with numerous interval parameters which cannot be solved conventionally. Applying a suitable variable substitution, an iteration method for the solution of a parametric system of linear equations is firstly employed to obtain initial bounds on the node displacements. Thereafter, an interval tightening (pruning) technique is applied, firstly on the element forces and secondly on the node displacements, in order to obtain tight guaranteed enclosures for the interval solutions for the forces and displacements.
Due to increasing numbers of wind energy converters, the accurate assessment of the lifespan of their structural parts and the entire converter system is becoming more and more paramount. Lifespan-oriented design, inspections and remedial maintenance are challenging because of their complex dynamic behavior. Wind energy converters are subjected to stochastic turbulent wind loading causing corresponding stochastic structural response and vibrations associated with an extreme number of stress cycles (up to 109 according to the rotation of the blades). Currently, wind energy converters are constructed for a service life of about 20 years. However, this estimation is more or less made by rule of thumb and not backed by profound scientific analyses or accurate simulations. By contrast, modern structural health monitoring systems allow an improved identification of deteriorations and, thereupon, to drastically advance the lifespan assessment of wind energy converters. In particular, monitoring systems based on artificial intelligence techniques represent a promising approach towards cost-efficient and reliable real-time monitoring. Therefore, an innovative real-time structural health monitoring concept based on software agents is introduced in this contribution. For a short time, this concept is also turned into a real-world monitoring system developed in a DFG joint research project in the authors’ institute at the Ruhr-University Bochum. In this paper, primarily the agent-based development, implementation and application of the monitoring system is addressed, focusing on the real-time monitoring tasks in the deserved detail.
The concept is presented of the sensitivity analysis of the limit state of the structure with respect to selected basic variables. The sensitivity is presented in the form of the probability distribution of the limit state of the structure. The analysis is performed by the problem-oriented Monte Carlo simulation procedure. The procedure is based on the problem's definition of the elementary event, as a structural limit state. Thus the sample space consists of limit states of the structure. Defined on the sample space the one-dimensional random multiplier is introduced. This multiplier refers to the dominant basic variable (group of variables) of the problem. Numerical procedure results in the set of random numbers. Normalized relative histogram of this set is an estimator of the PDF of the limit state of the structure. Estimators of reliability, or the probability of failure are statistical characteristics of this histogram. The procedure is illustrated by the example of sensitivity analysis of the serviceability limit state of monumental structure. It is the colonnade of Licheń Basilica, situated in central Poland. Limit state of the structure is examined with reference to the upper deck horizontal deflection. Wind actions are taken as dominant variables. An assumption is made that the wind load intensities acting on the lower and on the upper storey of the colonnade, respectively, are identically distributed, but correlated random variables. Three correlation variants of these variables are considered. Relevant limit state histograms are analysed thereafter. The paper ends with the conclusions referring to the method and some general remarks on the fully probabilistic design.
The Bernstein polynomials are used for important applications in many branches of Mathematics and the other sciences, for instance, approximation theory, probability theory, statistic theory, num- ber theory, the solution of the di¤erential equations, numerical analysis, constructing Bezier curves, q-calculus, operator theory and applications in computer graphics. The Bernstein polynomials are used to construct Bezier curves. Bezier was an engineer with the Renault car company and set out in the early 1960’s to develop a curve formulation which would lend itself to shape design. Engineers may …nd it most understandable to think of Bezier curves in terms of the center of mass of a set of point masses. Therefore, in this paper, we study on generating functions and functional equations for these polynomials. By applying these functions, we investigate interpolation function and many properties of these polynomials.