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Design and structural optimization has become a very important field in industrial applications over the last years. Due to economical and ecological reasons, the efficient use of material is of highly industrial interest. Therefore, computational tools based on optimization theory have been developed and studied in the last decades. In this work, different structural optimization methods are considered. Special attention lies on the applicability to three-dimensional, large-scale, multiphysic problems, which arise from different areas of the industry. Based on the theory of PDE-constraint optimization, descent methods in structural optimization require knowledge of the (partial) derivatives with respect to shape or topology variations. Therefore, shape and topology sensitivity analysis is introduced and the connection between both sensitivities is given by the Topological-Shape Sensitivity Method. This method leads to a systematic procedure to compute the topological derivative by terms of the shape sensitivity. Due to the framework of moving boundaries in structural optimization, different interface tracking techniques are presented. If the topology of the domain is preserved during the optimization process, explicit interface tracking techniques, combined with mesh-deformation, are used to capture the interface. This techniques fit very well the requirements in classical shape optimization. Otherwise, an implicit representation of the interface is of advantage if the optimal topology is unknown. In this case, the level set method is combined with the concept of the topological derivative to deal with topological perturbation. The resulting methods are applied to different industrial problems. On the one hand, interface shape optimization for solid bodies subject to a transient heat-up phase governed by both linear elasticity and thermal stresses is considered. Therefore, the shape calculus is applied to coupled heat and elasticity problems and a generalized compliance objective function is studied. The resulting thermo-elastic shape optimization scheme is used for compliance reduction of realistic hotplates. On the other hand, structural optimization based on the topological derivative for three-dimensional elasticity problems is observed. In order to comply typical volume constraints, a one-shot augmented Lagrangian method is proposed. Additionally, a multiphase optimization approach based on mesh-refinement is used to reduce the computational costs and the method is illustrated by classical minimum compliance problems. Finally, the topology optimization algorithm is applied to aero-elastic problems and numerical results are presented.
Cortisol exhibits typical ultradian and circadian rhythm and disturbances in its secretory pattern have been described in stress-related pathology. The aim of this thesis was to dissect the underlying structure of cortisol pulsatility and to develop tools to investigate the effects of this pulsatility on immune cell trafficking and the responsiveness of the neuroendocrine system and GR target genes to stress. Deconvolution modeling was set up as a tool for investigation of the pulsatile secretion underlying the ultradian cortisol rhythm. This further allowed us to investigate the role of the single cortisol pulses on the immune cell trafficking and the role of induced cortisol pulses on the kinetics of expression of GR target genes. The development of these three tools, would allow to induce and investigate in future the significance of single cortisol pulses for health and disease.
A big challenge for agriculture in the 21st century is the provision of food safety to fast growing world- population, which not only demands the well utilisation of the available agricultural resources but also to develop new advancements in the mass production of food crops. Wheat is the third largest food crop of the world and Pakistan is the eighth largest wheat producing country globally. Rice is the second most important staple food of Pakistan after wheat, grown in all provinces of the country. Maize is the world- top ranking food crop followed by wheat and rice. The harvested produts have to be stored in different types of storage structures on small or large scale for food as well as seed purpose. In Pakistan, the harvested grains are stored for the whole year till the introduction of fresh produce in order to ensure the regular food supply throughout the year. However, it is this extended storage period making the commodity more vulnerable to insect attacks. Rhyzopertha dominica (Coleoptera: Bostrychidae), Cryptolestes ferrugineus (Coleoptera: Laemophloeidae), Tribolium castaneum (Coleoptera: Tenebrionidae) and Liposcelis spp. (Psocoptera: Liposcelididae) are the major and most damaging insect pests of stored products all around the world. Various management strategies have been adopted for stored grain insect pests mostly relying upon the use of a broad spectrum of insecticides, but the injudicious use of these chemicals raised various environmental and human health related issues, which necessitate the safe use of the prevailing control measures and evaluation of new and alternative control methods. The application of new chemical insecticides, microbial insecticides (particularly entomopathogenic fungi) and the use of inert dusts (diatomaceous earths) is believed amongst the potential alternatives to generally used insecticides in stored grain insect management system. In the current investigations, laboratory bioassays conducted to evaluate the effects of combining Imidacloprid (new chemistry insecticide) with and without Protect-It (diatomaceous earth formulation) against R. dominica, L. paeta, C. ferrugineus and T. castaneum, on three different grain commodities (i.e. wheat, maize and rice) revealed differences in adult mortality levels among grains and insect species tested. Individually, Imidacloprid was more effective as compared with Protect-It alone and the highest numbers of dead adults were recorded in wheat. The insecticidal efficacy of B. bassiana with Protect-It and DEBBM was also assessed against all test insect species under laboratory conditions. The findings of these studies revealed that the more extended exposure period and the higher combined application rate of B. bassiana and DEs provided the highest mortality of the test insect species. The progeny emergence of each insect species was also greatly suppressed where the highest dose rates of the combined treatments were applied. The residual efficacy of all three control measures Imidacloprid, B. bassiana and DEBBM formulation was also evaluated against all test insect species. The bioassays were carried out after grain treatments and monthly for 6 months. The results indicated that the adult mortality of each test insect species was decreased within the six month storage period, and the integarted application of the test grain protectants enhanced the mortality rates than their alone treatments. The maximum mortality was noted in the combined treatment of DEBBM with Imidacloprid. At the end, the effectiveness of B. bassiana, DEBBM and Imidacloprid applied alone as well as in combinations, against all above mentioned test insect species was also evaluated under field conditions in trials conducted in four districts of Punjab, Pakistan. For each district, a significant difference was observed between treatments, while the combined treatments gave better control of test species as compared with them alone. The least number of surviving adults and minimum percentage of grain damage was observed for the DEBBM and Imidacloprid combination, but DEBBM with B. bassiana provided the best long-term protection as compared with the remaining treatments.
Copositive programming is concerned with the problem of optimizing a linear function over the copositive cone, or its dual, the completely positive cone. It is an active field of research and has received a growing amount of attention in recent years. This is because many combinatorial as well as quadratic problems can be formulated as copositive optimization problems. The complexity of these problems is then moved entirely to the cone constraint, showing that general copositive programs are hard to solve. A better understanding of the copositive and the completely positive cone can therefore help in solving (certain classes of) quadratic problems. In this thesis, several aspects of copositive programming are considered. We start by studying the problem of computing the projection of a given matrix onto the copositive and the completely positive cone. These projections can be used to compute factorizations of completely positive matrices. As a second application, we use them to construct cutting planes to separate a matrix from the completely positive cone. Besides the cuts based on copositive projections, we will study another approach to separate a triangle-free doubly nonnegative matrix from the completely positive cone. A special focus is on copositive and completely positive programs that arise as reformulations of quadratic optimization problems. Among those we start by studying the standard quadratic optimization problem. We will show that for several classes of objective functions, the relaxation resulting from replacing the copositive or the completely positive cone in the conic reformulation by a tractable cone is exact. Based on these results, we develop two algorithms for solving standard quadratic optimization problems and discuss numerical results. The methods presented cannot immediately be adapted to general quadratic optimization problems. This is illustrated with examples.
Krylov subspace methods are often used to solve large-scale linear equations arising from optimization problems involving partial differential equations (PDEs). Appropriate preconditioning is vital for designing efficient iterative solvers of this type. This research consists of two parts. In the first part, we compare two different kinds of preconditioners for a conjugate gradient (CG) solver attacking one partial integro-differential equation (PIDE) in finance, both theoretically and numerically. An analysis on mesh independence and rate of convergence of the CG solver is included. The knowledge of preconditioning the PIDE is applied to a relevant optimization problem. The second part aims at developing a new preconditioning technique by embedding reduced order models of nonlinear PDEs, which are generated by proper orthogonal decomposition (POD), into deflated Krylov subspace algorithms in solving corresponding optimization problems. Numerical results are reported for a series of test problems.
In his article, the author asks how legitimacy of law and the concept of rules of law can be described taking into account the interaction between aspects of philosophy and sociology as well as the will of the state in states' constitutions. As the rule of law, versus other kinds of rules in our society, should be regarded as a rule of "three-dimensionality" " an interaction between the will of the state, the social, historical, and economic factors, and the idea or concept of justice ", the author focuses his interest on the examination of these three factors always taking into account that law is the will of the state, but that not every decision of the state can be considered as law.