Computational fluid dynamics (CFD) has become a significant tool routinely used in design and optimization in aerospace industry. Typical flows may be characterized by high-speed and compressible flow features and, in many cases, by massive flow separation and unsteadiness. Accurate and efficient numerical solution of time-dependent problems is hence required, and the efficiency of standard dual-time stepping methods used for unsteady flows in many CFD codes has been found inadequate for large-scale industrial problems. This has motivated the present work, in which major effort is made to replace the explicit relaxation methods with implicit time integration schemes. The CFD flow solver considered in this work is Edge, a node-based solver for unstructured grids based on a dual, edge-based formulation. Edge is the Swedish national CFD tool for computing compressible flow, used at the Swedish aircraft manufacturer SAAB, and developed at FOI, lately in collaboration with external national and international partners. The work is initially devoted to the implementation of an implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) type of relaxation in Edge with the purpose to speed up the convergence to steady state. The convergence of LU-SGS has been firstly accelerated by basing the implicit operator on a flux splitting method of matrix dissipation type. An increase of the diagonal dominance of the system matrix was the principal motivation. Then the code has been optimized by means of performance tools Intel Vtune and CrayPAT, improving the run time. It was found that the ordering of the unknowns significantly influences the convergence. Thus, different ordering techniques have been investigated. Finding the optimal ordering method is a very hard problem and the results obtained are mostly illustrative. Finally, to improve convergence speed on the stretched computational grids used for boundary layers LU-SGS has been combined with the line-implicit method. / QC 20120626

There is emerging evidence for the potential of occupational back-support exoskeletons (BSEs) to reduce physical demands, and thereby help control/prevent the risk of overexertion injuries associated with manual material handling. However, it is important to understand whether BSEs also introduce any unintended safety challenges. One potential risk associated with BSE use is increased risk of falls, since their extra weight, rigid structure, and external hip extension torque may increase demands on the postural control system. However, there is currently limited evidence on whether, and to what extent, BSE use alters postural stability and/or fall risk. The primary goal of this work was to understand the effects of exoskeleton use, and quantify the effects of exoskeleton design parameters, on balance and postural stability, with a focus on passive BSEs used for repetitive lifting work. A comprehensive evaluation of BSE use was performed under controlled laboratory conditions, focusing on three classes of human activity that form the basis of maintaining postural balance in diverse real-life scenarios: maintenance of a specified posture, voluntary movement, and reaction to an external perturbation. The first study demonstrated that during quiet bipedal stance, BSE use increased median frequency and velocity of the center of pressure in the anterior-posterior direction. In the second study on level walking, BSE use caused an increase in gait step width and gait variability, and decrease in the margin of stability. BSE use with high supportive torque led to adapted gait patterns in early-stance phase. Hip range of motion and peak hip flexion velocity also decreased, and participants exhibited different strategies to increase mechanical energy for propelling the leg in late-stance phase: these effects increased with increasing torque applied by the exoskeleton. In the final study, BSE use did not alter the maximal lean angle from which individuals could successfully execute single step balance recovery, following a forward loss of balance. However, several recovery responses were negatively affected by BSE use, including increased reaction time, impeded hip flexion, and reduced margin of stability in the high-torque condition. This is the first systematical investigation to quantify the effects of passive BSEs with multiple supportive torque levels on balance and postural stability. While exoskeleton effects on static balance were minimal, more substantial changes in gait spatiotemporal parameters, hip joint kinematics, and dynamic margins of stability were observed in the later studies. Our results indicate that postural stability deteriorated with exoskeleton use in dynamic conditions, and provide mechanistic insight into how stability is altered by different exoskeleton design factors such as added mass, restricted range of motion, and external hip extension torque. While our results are suggestive of increased fall risk, especially in the high-torque condition, fall risk in real life is moderated by a complex combination of individual and environmental conditions. Future work should consider more complex, realistic tasks and also include a more diverse sample that is studied under longer exposure durations, to further elucidate these findings. Our characterizations of a wide variety of postural responses as a function of exoskeleton torque settings are expected to contribute to improving both design and practice guidelines to facilitate the safe adoption of BSEs in the workplace. / Doctor of Philosophy / Occupational back-support exoskeletons (BSEs) – wearable mechanical systems designed to support, augment, and/or assist back extension – are expected to serve as an alternative workplace intervention to control and prevent overexertion injuries related to manual material handling tasks. While recent studies have shown the beneficial effects of BSE use in terms of physical load reduction on the low back, some concerns have also been raised on unexpected or unintended effects of exoskeletons. One potential risk associated with exoskeleton use is increased risk of falls, since a BSE's extra weight, rigid structure, and external hip extension torque are expected to place increased demands on the postural control system. Increase in fall risk is a critical safety concern, as occupational falls are a serious problem in terms of injuries, medical/industrial cost, and lost work time. However, there exists limited evidence on whether the use of a BSE alters postural stability and/or increases fall risk. Hence, the goal of our study was to quantify the effects of BSE use on postural stability in various conditions related to real-life scenarios, such as standing balance, walking stability and how one would respond to a loss of balance following an external perturbation. Our results showed that during quiet standing, BSE use slightly increased postural sway. In level walking tasks, BSE use had adverse effects on step length, step width, and dynamic stability. Furthermore, wearing a BSE with high supportive torque led to adapted gait patterns in early-stance phase, whereas participants showed different strategies to increase mechanical energy for propelling the leg in late-stance phase. In the final study investigating single step balance recovery following a forward loss of balance, we found that BSE use negatively affects balance recovery, mainly by impeding hip flexion. Thus, our work suggests that exoskeleton use can deteriorate balance and/or postural stability in situations of static standing, voluntary walking, and reacting to an external perturbation, thereby potentially leading to an increase in fall risk. These effects may be more pronounced among specific population sub-groups such as older workers, and may also affect individuals more severely under conditions of stress or fatigue. Hence, future studies must include more rigorous testing of BSE use using a variety of challenging and realistic scenarios, and also include more diverse population samples. The findings from this work are expected to contribute to improving design and practice guidelines to facilitate the safe adoption of BSEs in the workplace.

Movement of motor proteins along cytoskeletal filaments is fundamental for various cellular processes ranging from muscle contraction over cell division and flagellar movement to intracellular transport. Not surprisingly, the impairment of motility was shown to cause severe diseases. For example, a link between impaired intracellular transport and neurodegenerative diseases, such as Alzheimer’s, has been established. There, the movement of kinesin-1, a neuronal motor protein transporting vesicles along microtubules toward the axonal terminal, is thought to be strongly affected by roadblocks leading to malfunction and death of the nerve cell. Detailed information on how the motility of kinesin-1 deteriorates in the presence of roadblocks and whether the motor has a mechanism to circumvent such obstructions is scarce. In this thesis, kinesin-1 motility was studied in vitro in the presence of rigor kinesin-1 mutants, which served as permanent roadblocks, under controlled single-molecule conditions. The 25 nm wide microtubule track, consisting of 13 individual protofilaments, resembles a multi-lane environment for transport by processive kinesin-1 motors. The existence of multiple traffic-lanes, allows kinesin-1 to utilize different paths for cargo transport and potentially also for the circumvention of roadblocks. However, direct observation of motor encounters with roadblocks has been intricate in the past, mainly due to limitations in both, spatial and temporal resolution. These limitations, intrinsic to fluorescent probes commonly utilized to report on the motor positions, originate from a low rate of photon generation (low brightness) and a limited photostability (short observation time). Thus, studying kinesin-1 encounters with microtubule-associated roadblocks requires alternative labels, which explicitly avoid the shortcomings of fluorescence and consequently allow for a higher localization precision. Promising candidates for replacing fluorescent dyes are gold nanoparticles (AuNPs), which offer an enormous scattering cross-section due to plasmon resonance in the visible part of the optical spectrum. Problematic, however, is their incorporation into conventionally used (fluorescence) microscopes, because illumination and scattered light have the same wavelength and cannot be separated spectrally. Therefore, an approach based on total internal reflection (TIR) utilizing a novel parabolically shaped quartz prism for illumination was developed within this thesis. This approach provided homogenous and spatially invariant illumination profiles in combination with a convenient control over a wide range of illumination angles. Moreover, single-molecule fluorescence as well as single-particle scattering were detectable with high signal-to-noise ratios. Importantly, AuNPs with a diameter of 40 nm provided sub-nanometer localization accuracies within millisecond integration times and reliably reported on the characteristic 8 nm stepping of individual kinesin-1 motors moving along microtubules. These results highlight the potential of AuNPs to replace fluorescent probes in future single-molecule experiments. The newly developed parabolic prism-type TIR microscope is expected to strongly facilitate such approaches in the future. To study how the motility of kinesin-1 is affected by permanent roadblocks on the microtubule lattice, first, conventional objective-type TIRF microscopy was applied to GFP-labeled motors. An increasing density of roadblocks caused the mean velocity, run length, and dwell time to decrease exponentially. This is explained by (i) the kinesin-1 motors showing extended pausing phases when confronted with a roadblock and (ii) the roadblocks causing a reduction in the free path of the motors. Furthermore, kinesin-1 was found to be highly sensitive to the crowdedness of microtubules as a roadblock decoration as low as 1 % sufficed to significantly reduce the landing rate. To study events, where kinesin-1 molecules continued their runs after having paused in front of a roadblock, AuNPs were loaded onto the tails of the motors. When observing the kinesin-1 motors with nanometer-precision, it was interestingly found that about 60 % of the runs continued by movements to the side, with the left and right direction being equally likely. This finding suggests that kinesin-1 is able to reach to a neighboring protofilament in order to ensure ongoing transportation. In the absence of roadblocks, individual kinesin-1 motors stepped sideward with a much lower, but non-vanishing probability (0.2 % per step). These findings suggest that processive motor proteins may possess an intrinsic side stepping mechanism, potentially optimized by evolution for their specific intracellular tasks.

Movement of motor proteins along cytoskeletal filaments is fundamental for various cellular processes ranging from muscle contraction over cell division and flagellar movement to intracellular transport. Not surprisingly, the impairment of motility was shown to cause severe diseases. For example, a link between impaired intracellular transport and neurodegenerative diseases, such as Alzheimer’s, has been established. There, the movement of kinesin-1, a neuronal motor protein transporting vesicles along microtubules toward the axonal terminal, is thought to be strongly affected by roadblocks leading to malfunction and death of the nerve cell. Detailed information on how the motility of kinesin-1 deteriorates in the presence of roadblocks and whether the motor has a mechanism to circumvent such obstructions is scarce. In this thesis, kinesin-1 motility was studied in vitro in the presence of rigor kinesin-1 mutants, which served as permanent roadblocks, under controlled single-molecule conditions. The 25 nm wide microtubule track, consisting of 13 individual protofilaments, resembles a multi-lane environment for transport by processive kinesin-1 motors. The existence of multiple traffic-lanes, allows kinesin-1 to utilize different paths for cargo transport and potentially also for the circumvention of roadblocks. However, direct observation of motor encounters with roadblocks has been intricate in the past, mainly due to limitations in both, spatial and temporal resolution. These limitations, intrinsic to fluorescent probes commonly utilized to report on the motor positions, originate from a low rate of photon generation (low brightness) and a limited photostability (short observation time). Thus, studying kinesin-1 encounters with microtubule-associated roadblocks requires alternative labels, which explicitly avoid the shortcomings of fluorescence and consequently allow for a higher localization precision. Promising candidates for replacing fluorescent dyes are gold nanoparticles (AuNPs), which offer an enormous scattering cross-section due to plasmon resonance in the visible part of the optical spectrum. Problematic, however, is their incorporation into conventionally used (fluorescence) microscopes, because illumination and scattered light have the same wavelength and cannot be separated spectrally. Therefore, an approach based on total internal reflection (TIR) utilizing a novel parabolically shaped quartz prism for illumination was developed within this thesis. This approach provided homogenous and spatially invariant illumination profiles in combination with a convenient control over a wide range of illumination angles. Moreover, single-molecule fluorescence as well as single-particle scattering were detectable with high signal-to-noise ratios. Importantly, AuNPs with a diameter of 40 nm provided sub-nanometer localization accuracies within millisecond integration times and reliably reported on the characteristic 8 nm stepping of individual kinesin-1 motors moving along microtubules. These results highlight the potential of AuNPs to replace fluorescent probes in future single-molecule experiments. The newly developed parabolic prism-type TIR microscope is expected to strongly facilitate such approaches in the future. To study how the motility of kinesin-1 is affected by permanent roadblocks on the microtubule lattice, first, conventional objective-type TIRF microscopy was applied to GFP-labeled motors. An increasing density of roadblocks caused the mean velocity, run length, and dwell time to decrease exponentially. This is explained by (i) the kinesin-1 motors showing extended pausing phases when confronted with a roadblock and (ii) the roadblocks causing a reduction in the free path of the motors. Furthermore, kinesin-1 was found to be highly sensitive to the crowdedness of microtubules as a roadblock decoration as low as 1 % sufficed to significantly reduce the landing rate. To study events, where kinesin-1 molecules continued their runs after having paused in front of a roadblock, AuNPs were loaded onto the tails of the motors. When observing the kinesin-1 motors with nanometer-precision, it was interestingly found that about 60 % of the runs continued by movements to the side, with the left and right direction being equally likely. This finding suggests that kinesin-1 is able to reach to a neighboring protofilament in order to ensure ongoing transportation. In the absence of roadblocks, individual kinesin-1 motors stepped sideward with a much lower, but non-vanishing probability (0.2 % per step). These findings suggest that processive motor proteins may possess an intrinsic side stepping mechanism, potentially optimized by evolution for their specific intracellular tasks.

Non-destructive testing (NDT) of glass-fibre reinforced polyester (GRP) composite materials has been becoming increasingly important due to their wide applications in engineering components and structures. Electronic Speckle Pattern Interferometry (ESPI) has promising potential in this context because it is a non-contact, whole-field and real-time measurement system. This potential has never been fully exploited and there is only limited knowledge and understanding available in this area. This reality constrains the wide popularity and acceptance of ESPI as a novel NDT technique. Therefore it is of considerable importance to develop an understanding of the capability of ESPI with respect to damage evaluation in GRP composite materials. The research described in this thesis is concerned with an investigation into the applicability of ESPI in the NDT of GRP composite materials. Firstly, a study was carried out to determine excitation techniques in terms of practicality and effectiveness in the ESPI system. Three categories of defects were artificially introduced in GRP composite materials, namely holes, cracks and delaminations each with different geometrical features. ESPI was then employed to evaluate the three kinds of defects individually. It has been found that cracks and holes on back surfaces can be defined when the technique is used in conjunction with thermal excitation. Internal Temperature Differential (ITD) induced fringe patterns were more efficient than External Thermal Source (ETS) induced fringe patterns with regard to detecting the presence of holes and cracks. In the case of delamination, ESPI was found to be capable of detecting the damage when used in combination with mechanical excitation originating from a force transducer hammer. The geometrical features and magnitudes of delaminations were also established as being quantifiable. The validation of ESPI as an NDT technique was carried out in an attempt to establish a better understanding of its suitability and have more confidence in its applications. Four damaged specimens were Subjected to ESPI examination in conjunction with visual inspection, ultrasonic C-scan and sectioning techniques. The geometrical features and magnitudes of damage evaluated using ESPI showed a good correlation with those evaluated by conventional techniques. Poor visibility and readability is an inherent problem associated with ESP! due to an overlapping between the noise and signal frequencies. An improvement of image quality is expected in an attempt to achieve a wide acceptance of ESPI as a novel NDT technique. It has also been demonstrated that this problem can be tackled using optical phase stepping techniques in which optical phase data can be extracted from the intensity fringes. A three-frame optical phase stepping technique was employed to produce the "wrapped" and "unwrapped" phase maps which are capable of indicating internal damage with high visibility and clarity. Finally ESPI was practically employed to evaluate damage in GRP composites introduced by quasi-static and dynamic mechanical loading. It was found that ESP! was capable of monitoring the progressive damage development of specimens subjected to incremental flexural loading. The initial elastic response, damage initiation, propagation and ultimate failure of specimens were clearly characterised by the abnormal fringe pattern variations. In a similar manner, ESPI was employed to evaluate the low velocity falling weight impact induced damage. A correlation was established between the magnitude of damage and the impact event parameters as well as the residual flexural properties.

The aim of this thesis is to deal with teaching of negative numbers in mathematics in lower primary school. The thesis brings an overview of exercises related to negative numbers, which are available in textbooks dedicated to lower and upper primary school. Main part of the thesis is devoted to three different experiments - pupils experiment, teaching experiment and parlour game. The pupils experiment analysis the successes and troubles of pupils attending 4th and 5th class when filling out the worksheets focused on various models of negative numbers. Furthermore, the teaching experiment based on a questionnaire survey describes comments of lower and upper primary school teachers in regards to implementation and usefulness of negative numbers. Parlour game experiment demonstrates the ability of pupils to grasp mathematical phenomenon by playing a game. Key words: ­ additive operations with negative numbers ­ experiment ­ models of negative number: thermometer, floor, surface ­ environment Stepping ­ environment Stairs ­ word problems ­ board game ­ negative numbers

Our knowledge of elastic wave propagation in general heterogeneous media with complex geological structures comes principally from numerical simulations. In this dissertation, I demonstrate through rigorous theoretical analyses and comprehensive numerical experiments that the Fourier method is a suitable method of choice for large scale 3D seismic modeling and imaging problems, due to its high accuracy and computational efficiency. The most attractive feature of the Fourier method is its ability to produce highly accurate solutions on relatively coarser grids, compared with other numerical methods for solving wave equations. To further advance the Fourier method, I identify two aspects of the method to focus on in this work, i.e., its implementation on modern clusters of computers and efficient high-order time stepping schemes. I propose two new parallel algorithms to improve the efficiency of the Fourier method on distributed memory systems using MPI. The first algorithm employs non-blocking all-to-all communications to optimize the conventional parallel Fourier modeling workflows by overlapping communication with computation. With a carefully designed communication-computation overlapping mechanism, a large amount of communication overhead can be concealed when implementing different kinds of wave equations. The second algorithm combines the advantages of both the Fourier method and the finite difference method by using convolutional high-order finite difference operators to evaluate the spatial derivatives in the decomposed direction. The high-order convolutional finite difference method guarantees a satisfactory accuracy and provides the flexibility of using non-blocking point-to-point communications for efficient interprocessor data exchange and the possibility of overlapping communication and computation. As a result, this hybrid method achieves an optimized balance between numerical accuracy and computational efficiency. To improve the overall accuracy of time domain Fourier simulations, I propose a family of new high-order time stepping schemes, based on a novel algorithm for designing time integration operators, to reduce temporal derivative discretization errors in a cost-effective fashion. I explore the pseudo-analytical method and propose high-order formulations to further improve its accuracy and ability to deal with spatial heterogeneities. I also extend the pseudo-analytical method to solve the variable-density acoustic and elastic wave equations. I thoroughly examine the finite difference method by conducting complete numerical dispersion and stability analyses. I comprehensively compare the finite difference method with the Fourier method and provide a series of detailed benchmarking tests of these two methods under a number of different simulation configurations. The Fourier method outperforms the finite difference method, in terms of both accuracy and efficiency, for both the theoretical studies and the numerical experiments, which provides solid evidence that the Fourier method is a superior scheme for large scale seismic modeling and imaging problems. / text

This thesis is concerned with the efficient numerical simulation of finite element based flexible multibody systems. Scaling operations are systematically applied to the governing index-3 differential algebraic equations in order to solve the problem of ill conditioning for small time step sizes. The importance of augmented Lagrangian terms is demonstrated. The use of fast sparse solvers is justified for the solution of the linearized equations of motion resulting in significant savings of computational costs. Three time stepping schemes for the integration of the governing equations of flexible multibody systems are discussed in detail. These schemes are the two-stage Radau IIA scheme, the energy decaying scheme, and the generalized-α method. Their formulations are adapted to the specific structure of the governing equations of flexible multibody systems. The efficiency of the time integration schemes is comprehensively evaluated on a series of test problems. Formulations for structural and constraint elements are reviewed and the problem of interpolation of finite rotations in geometrically exact structural elements is revisited. This results in the development of a new improved interpolation algorithm, which preserves the objectivity of the strain field and guarantees stable simulations in the presence of arbitrarily large rotations. Finally, strategies for the spatial discretization of beams in the presence of steep variations in cross-sectional properties are developed. These strategies reduce the number of degrees of freedom needed to accurately analyze beams with discontinuous properties, resulting in improved computational efficiency.

The development of numerical methods for the incompressible Navier-Stokes equations received much attention in the past 50 years. Finite element methods emerged given their robustness and reliability. In our work, we choose the P2-P1 finite element for space approximation which gives 2nd-order accuracy for velocity and 1st-order accuracy for pressure. Our research focuses on the development of several high-order semi-implicit time-stepping methods to compute unsteady flows. The methods investigated include backward difference formulae (SBDF) and defect correction strategy (DC). Using the defect correction strategy, we investigate two variants, the first one being based on high-order artificial compressibility and bootstrapping strategy proposed by Guermond and Minev (GM) and the other being a combination of GM methods with sequential regularization method (GM-SRM). Both GM and GM-SRM methods avoid solving saddle point problems as for SBDF and DC methods. This approach reduces the complexity of the linear systems at the expense that many smaller linear systems need to be solved. Next, we proposed several numerical improvements in terms of better approximations of the nonlinear advection term and high-order initialization for all methods. To further minimize the complexity of the resulting linear systems, we developed several new variants of grad-div splitting algorithms besides the one studied by Guermond and Minev. Splitting algorithm allows us to handle larger flow problems. We showed that our new methods are capable of reproducing flow characteristics (e.g., lift and drag parameters and Strouhal numbers) published in the literature for 2D lid-driven cavity and 2D flow around the cylinder. SBDF methods with grad-div stabilization terms are found to be very stable, accurate and efficient when computing flows with high Reynolds numbers. Lastly, we showcased the robustness of our methods to carry 3D computations.

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