This thesis explains and tests a wavelet based implicit numerical method for the solving of partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time discretization into multiple, smaller, systems that can be solved sequentially. Included are tests of this method on linear and non-linear problems, with both its results and the time required to calculate them compared to basic models. It was found that the method requires less computational effort than the high resolution control results. Furthermore, the method showed convergence towards high resolution control results.

This thesis explains and tests a wavelet based implicit numerical method for the solving of partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time discretization into multiple, smaller, systems that can be solved sequentially. Included are tests of this method on linear and non-linear problems, with both its results and the time required to calculate them compared to basic models. It was found that the method requires less computational effort than the high resolution control results. Furthermore, the method showed convergence towards high resolution control results.

This thesis explains and tests a wavelet based implicit numerical method for the solving of partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time discretization into multiple, smaller, systems that can be solved sequentially. Included are tests of this method on linear and non-linear problems, with both its results and the time required to calculate them compared to basic models. It was found that the method requires less computational effort than the high resolution control results. Furthermore, the method showed convergence towards high resolution control results.

Consider the graph induced by Z^d, equipped with uniformly elliptic random conductances on the edges. At time 0, place a Poisson point process of particles on Z^d and let them perform independent simple random walks with jump probabilities proportional to the conductances. It is well known that without conductances (i.e., all conductances equal to 1), an infection started from the origin and transmitted between particles that share a site spreads in all directions with positive speed. We show that a local mixing result holds for random conductance graphs and prove the existence of a special percolation structure called the Lipschitz surface. Using this structure, we show that in the setup of particles on a uniformly elliptic graph, an infection also spreads with positive speed in any direction. We prove the robustness of the framework by extending the result to infection with recovery, where we show positive speed and that the infection survives indefinitely with positive probability.

In recent years the electric power industry has been challenged by a high level of uncertainty and volatility brought on by deregulation and globalization. A power producer must minimize the life cycle cost while meeting stringent safety and regulatory requirements and fulfilling customer demand for high reliability. Therefore, to achieve true system excellence, a more sophisticated system-level decision-making process with a more accurate forecasting support system to manage diverse and often widely dispersed generation units as a single, easily scaled and deployed fleet system in order to fully utilize the critical assets of a power producer has been created as a response. The process takes into account the time horizon for each of the major decision actions taken in a power plant and develops methods for information sharing between them. These decisions are highly interrelated and no optimal operation can be achieved without sharing information in the overall process. The process includes a forecasting system to provide information for planning for uncertainty. A new forecasting method is proposed, which utilizes a synergy of several modeling techniques properly combined at different time-scales of the forecasting objects. It can not only take advantages of the abundant historical data but also take into account the impact of pertinent driving forces from the external business environment to achieve more accurate forecasting results. Then block bootstrap is utilized to measure the bias in the estimate of the expected life cycle cost which will actually be needed to drive the business for a power plant in the long run. Finally, scenario analysis is used to provide a composite picture of future developments for decision making or strategic planning. The decision-making process is applied to a typical power producer chosen to represent challenging customer demand during high-demand periods. The process enhances system excellence by providing more accurate market information, evaluating the impact of external business environment, and considering cross-scale interactions between decision actions. Along with this process, system operation strategies, maintenance schedules, and capacity expansion plans that guide the operation of the power plant are optimally identified, and the total life cycle costs are estimated.

This thesis presents the research results of a correlation and model based on nano and macroindentation hardness measurements. The materials used to develop and test the correlation include bulk tantalum and O1 tool steel. Following the literature review and a detailed description of the experimental techniques, the results of the nanoindentation hardness measurements are presented. After applying the methods and correlation recommended here, the results should give an accurate value of hardness in the Vickers scale for microstructural features that are too small to be precisely and exclusively measured using the traditional macroindentation hardness technique. The phenomena and influential factors in nanoindentation hardness testing are also discussed. These phenomena and theories are consistent with the microstructural behavior predicted in the Nix and Gao model for mechanism-based strain gradients. Implementing the correlation factors and/or correlation curve, accurate results can be found for metals over a broad hardness range. Initially, this research may impact the pipeline division of the petroleum industry by providing a correlation to the Vickers scale for nanoindentation testing of microstructural features. This thesis may also provide a research methodology to develop hardness correlations for materials other than metals. This thesis consists of eight chapters. Following an introduction in Chapter I, the research motivations and objectives are highlighted in Chapter II. Chapter III explains the multi-scale indentation techniques used in this thesis and Chapter IV presents the materials preparation techniques used. Then, the results are presented in Chapter V, followed by the factors affecting nanoindentation hardness in Chapter VI. Finally, Chapters VII and VIII reveal the indentation contact analysis, correlation, and conclusions of this research, respectively.

With the significant potential of microalgae as a major biofuel source of the future, a considerable scientific attention is attracted towards the field of biotechnology and bioprocess engineering. Nevertheless the current photobioreactor (PBR) design methods are still too empirical. With this work I would like to promote the idea of designing a production system, such as a PBR, completely \emph{in silico}, thus allowing for the in silico optimization and optimal control determination. The thesis deals with the PBR modeling and simulation. It addresses two crucial issues in the current state-of-the-art PBR modeling. The first issue relevant to the deficiency of the currently available models - the incorrect or insufficient treatment of either the transport process modeling, the reaction modeling or the coupling between these two models. A correct treatment of both the transport and the reaction phenomena is proposed in the thesis - in the form of a unified modeling framework consisting of three interconnected parts - (i) the state system, (ii) the fluid-dynamic model and (iii) optimal control determination. The proposed model structure allows prediction of the PBR performance with respect to the modelled PBR size, geometry, operating conditions or a particular microalgae strain. The proposed unified modeling approach is applied to the case of the Couette-Taylor photobioreactor (CTBR) where it is used for the optimal control solution. The PBR represents a complex multiscale problem and especially in the case of the production scale systems, the associated computational costs are paramount. This is the second crucial issue addressed in the thesis. With respect to the computational complexity, the fluid dynamics simulation is the most costly part of the PBR simulation. To model the fluid flow with the classical CFD (Computational Fluid Dynamics) methods inside a production scale PBR leads to an enormous grid size. This usually requires a parallel implementation of the solver but in the parallelization of the classical methods lies another relevant issue - that of the amount of data the individual nodes must interchange with each other. The thesis addresses the performance relevant issues by proposing and evaluation alternative approaches to the fluid flow simulation. These approaches are more suitable to the parallel implementation than the classical methods because of their rather local character in comparison to the classical methods - namely the Lattice Boltzmann Method (LBM) for fluid flow, which is the primary focus of the thesis in this regard and alternatively also the discrete random walk based method (DRW). As the outcome of the thesis I have developed and validated a new Lagrangian general modeling approach to the transport and reaction processes in PBR - a framework based on the Lattice Boltzmann method (LBM) and the model of the Photosynthetic Factory (PSF) that models correctly the transport and reaction processes and their coupling. Further I have implemented a software prototype based on the proposed modeling approach and validated this prototype on the case of the Coutte-Taylor PBR. I have also demonstrated that the modeling approach has a significant potential from the computational costs point of view by implementing and validating the software prototype on the parallel architecture of CUDA (Compute Unified Device Architecture). The current parallel implementation is approximately 20 times faster than the unparallized one and decreases thus significantly the iteration cycle of the PBR design process.

<p align="justify">The conservation of structures of the historical heritage is an increasing concern nowadays for public authorities. The technical design phase of repair operations for these structures is of prime importance. Such operations usually require an estimation of the residual strength and of the potential structural failure modes of structures to optimize the choice of the repairing techniques.</p> <p align="justify">Although rules of thumb and codes are widely used, numerical simulations now start to emerge as valuable tools. Such alternative methods may be useful in this respect only if they are able to account realistically for the possibly complex failure modes of masonry in structural applications.</p> <p align="justify">The mechanical behaviour of masonry is characterized by the properties of its constituents (bricks and mortar joints) and their stacking mode. Structural failure mechanisms are strongly connected to the mesostructure of the material, with strong localization and damage-induced anisotropy.</p> <p align="justify">The currently available numerical tools for this material are mostly based on approaches incorporating only one scale of representation. Mesoscopic models are used in order to study structural details with an explicit representation of the constituents and of their behaviour. The range of applicability of these descriptions is however restricted by computational costs. At the other end of the spectrum, macroscopic descriptions used in structural computations rely on phenomenological constitutive laws representing the collective behaviour of the constituents. As a result, these macroscopic models are difficult to identify and sometimes lead to wrong failure mode predictions.</p> <p align="justify">The purpose of this study is to bridge the gap between mesoscopic and macroscopic representations and to propose a computational methodology for the analysis of plane masonry walls. To overcome the drawbacks of existing approaches, a multi-scale framework is used which allows to include mesoscopic behaviour features in macroscopic descriptions, without the need for an a priori postulated macroscopic constitutive law. First, a mesoscopic constitutive description is defined for the quasi-brittle constituents of the masonry material, the failure of which mainly occurs through stiffness degradation. The mesoscopic description is therefore based on a scalar damage model. Plane stress and generalized plane state assumptions are used at the mesoscopic scale, leading to two-dimensional macroscopic continuum descriptions. Based on periodic homogenization techniques and unit cell computations, it is shown that the identified mesoscopic constitutive setting allows to reproduce the characteristic shape of (anisotropic) failure envelopes observed experimentally. The failure modes corresponding to various macroscopic loading directions are also shown to be correctly captured. The in-plane failure mechanisms are correctly represented by a plane stress description, while the generalized plane state assumption, introducing simplified three-dimensional effects, is shown to be needed to represent out-of-plane failure under biaxial compressive loading. Macroscopic damage-induced anisotropy resulting from the constituents' stacking mode in the material, which is complex to represent properly using macroscopic phenomenological constitutive equations, is here obtained in a natural fashion. The identified mesoscopic description is introduced in a scale transition procedure to infer the macroscopic response of the material. The first-order computational homogenization technique is used for this purpose to extract this response from unit cells. Damage localization eventually appears as a natural outcome of the quasi-brittle nature of the constituents. The onset of macroscopic localization is treated as a material bifurcation phenomenon and is detected from an eigenvalue analysis of the homogenized acoustic tensor obtained from the scale transition procedure together with a limit point criterion. The macroscopic localization orientations obtained with this type of detection are shown to be strongly related to the underlying mesostructural failure modes in the unit cells.</p> <p align="justify">A well-posed macroscopic description is preserved by embedding localization bands at the macroscopic localization onset, with a width directly deduced from the initial periodicity of the mesostructure of the material. This allows to take into account the finite size of the fracturing zone in the macroscopic description. As a result of mesoscopic damage localization in narrow zones of the order of a mortar joint, the material response computationally deduced from unit cells may exhibit a snap-back behaviour. This precludes the use of such a response in the standard strain-driven multi-scale scheme.</p> <p align="justify">Adaptations of the multi-scale framework required to treat the mesostructural response snap-back are proposed. This multi-scale framework is finally applied for a typical confined shear wall problem, which allows to verify its ability to represent complex structural failure modes.</p>

<p>Elastic energy plays important roles in biology across scales, from the molecular to organismal level, and across the tree of life. The ubiquity of elastic systems in biology is partly due to the variety of useful functions they permit such as the simplification of motor control in running cockroaches and the efficient recycling of kinetic energy in hopping kangaroos. Elastic energy is also responsible for ultrafast movements; the fastest movements in animals are not powered directly by muscle, but instead by elastic energy stored in a spring. By demonstrating that the power required to generate ultrafast movements exceeds the limits of muscle, many studies conclude that energy storage is necessary; but, what these studies do not explain is how the properties of a biological structure affect its capacity for energy storage. In this dissertation, I test the general principles of energy storage by investigating elastic systems at three hierarchical levels of organization: a single structure, multiple connected structures, and a spring system connected to muscle. By using a multi-level approach, my aim is to demonstrate, at each of the mentioned levels, how properties of the spring system affect where or how much energy is stored in the system as well as how these conclusions can be combined to inform our understanding of the biomechanics of hierarchical elastic systems.</p><p>When considering spring systems at the level of a single structure, morphology is one major structural aspect that affects mechanics. Continuous changes in morphology are capable of dividing a structure into regions that are responsible for the two contradicting functions that are essential for spring function: energy storage (via deformation) and structural support (via resistance to deformation). Using high quality micro computed tomography scans, I quantify the morphology of the mantis shrimp (Stomatopoda) merus, a single structure of the raptorial appendage hypothesized to store the elastic energy that drives ultrafast strikes. Comparing the morphology among the species, I find that the merus in smashers, species that depend heavily on elastic energy storage, have relatively thicker ventral regions and more eccentric cross-sections than spearers, species that strike relatively slower. I also conclude that differential thickening of a region can provide structural support for resisting spring compression as well as facilitate structural deformation by inducing bending. This multi-level morphological analysis offers a foundation for understanding the evolution and mechanics of monolithic systems in biology.</p><p>When two or more structures are connected, their relative physical properties determine whether the structures store energy, provide structural support, or some combination of both. Although the majority of elastic energy is stored via large deformations of the merus in smashers, some spearer species show relatively little meral deformation, and it is unclear whether elastic energy is stored in these systems. To determine whether the apodeme (arthropod tendon) provides energy storage in species that exhibit low meral deformation, I measure the physical properties of the lateral extensor apodeme and the merus to which it is connected. Comparisons of these properties show that in the spearer species I tested, the merus has a relatively higher spring constant than the apodeme, which results in the merus providing structural support and the apodeme storing the majority of elastic energy. Comparing the material properties of the apodemes with those of other structures reveals that apodemes and other biological spring systems share similar material characteristics. This study demonstrates that in order to understand the biomechanics of spring systems comprised of connected structures, it is necessary to compare their relative mechanical properties.</p><p>Finally, because muscles are responsible for loading spring systems with potential energy, muscle dynamics can affect elastic energy storage in a spring system. Although spring systems can circumvent the limits imposed by muscle via power amplification, they are not entirely independent from muscle dynamics. For example, if an organism has relatively low time to prepare and stretch the spring prior to the onset of movement, the limits of muscle power can dominate energy storage. To test the effects of muscle dynamics on spring loading, I implement a mathematical model that connects a Hookean spring model to a Hill-type muscle model, representing the muscle-tendon complex of the hindlimbs of American bullfrogs, in which the muscle dynamics are well understood and the duration of spring loading is low. I find that the measured spring constants of the tendons nearly maximize energy storage within the duration of in vivo spring loading. Additionally, the measured spring constants are lower than those predicted to produce maximal energy storage when infinite time is available for spring loading. Together, these results suggest that the spring constants of the tendons of American bullfrogs are tuned to maximize elastic energy for small durations of spring loading. This study highlights the importance of assessing muscle dynamics and their effect on energy storage when assessing the functional significance of spring constants.</p> / Dissertation

Flexible pipes are essential components in the subsea oil and gas industry, where they are used to convey fluids under conditions of extreme external pressure and (often) axial load, while retaining low bending stiffness. This is made possible by their complex internal structure, consisting of unbonded components that are, to a certain extent, free to move internally relative to each other. Due to the product's high value and high cost of testing facilities, much e ort has been invested in the development of analytical and numerical models for simulating flexible pipe behaviour, which includes bulk response to various loading actions, calculation of component stresses and use of this data for component fatigue calculations. In this work, it is proposed that the multi-scale methods currently in widespread use for the modelling of composite materials can be applied to the modelling of flexible pipe. This allows the large-scale dynamics of an installed pipe (often several kilometers in length) to be related to the behaviour of its internal components (with characteristic lengths in millimeters). To do this, a formal framework is developed for an extension of the computational homogenisation procedure that allows multiscale models to be constructed in which models at both the large and small scales are composed of different structural elements. Within this framework, a large-scale flexible pipe model is created, using a two-dimensional corotational beam formulation with a constitutive model representative of flexible pipe bulk behaviour, which was obtained by further development of a recently proposed formulation inspired by the analogy between the flexible pipe structural behaviour and that of plastic materials with non-associative flow rules. A three-dimensional corotational formulation is also developed. The model is shown to perform adequately for practical analyses. Next, a detailed finite element (FE) model of a flexible pipe was created, using shell finite elements, generalised periodic boundary conditions and an implicit solution method. This model is tested against two analytical flexible pipe models for several basic load cases. Finally, the two models are used to carry out a sequential multi-scale analysis, in which a set of simulations using the detailed FE model is carried out in order to find the most appropriate coefficients for the large-scale model.