This dissertation investigates the self assembly and automatic oscillation of intelligent poly (N-isopropylacrylamide) [PNIPAM] microgel particles. The equilibrium phase diagram as a function of temperature and concentration was constructed for the charged PNIPAM spheres. The PNIPAM microgel particles display rhythmic size oscillations when covalently coupled to a nonlinear chemical reaction, the Belousov-Zhabotinsky (BZ) reaction. The nonequilibrium dynamics of PNIPAM microgels in the presence of BZ reaction was studied by the systematic variation of substrate concentrations and temperature. In addition, the BZ chemical reaction was modeled to reveal the existence of upper temperature limits for nonlinear chemical systems. The experiments employ environment sensitive PNIPAM particles that are sensitive to temperature, pH, and ionic strength. The PNIPAM particles have been demonstrated here to behave as hard spheres at low pH values and soft spheres at high pH. This is done by measuring the freezing and melting boundary of fluid-crystal coexistence region with a new technique which is simpler and quicker compared to the traditional sedimentation method. A novel method was developed to achieve size uniformity of PNIPAM gel particles with covalently-bound tris(bipyridyl)ruthenium(II) via the coordination chemistry between a ruthenium complex and the monodispersed PNIPAM gel particles bearing bipyridine ligands. The correlation between the dynamic behavior of BZ reaction induced mechanical oscillations of PNIPAM particles and substrate concentrations was presented in a ternary phase diagram. In particular, the dependence of oscillation frequency and induction time on the substrate concentrations was studied. The temperature dependency of the induction time and oscillatory frequency of the BZ reaction in this polymerimmobilized catalyst system were compared to the bulk BZ reaction with the catalyst in the solution phase. Prolonged induction times were observed for the immobilized catalyst, compared with free catalyst, while little difference was observed on the oscillation frequency. A theoretical improvement has been achieved by incorporating the temperature dependence in the BZ Oregonator model. Bifurcation has been calculated in the phase space spanned by initial reagents concentration ratio, stoichiometric factor and temperature. The existence of upper temperature limits has been demonstrated.

An objective in the design of high performance machinery is to minimize weight so magnetic bearings are often designed to operate slightly lower than the magnetic material saturation. Further weight reduction in the bearings requires operation in the nonlinear portion of the B-H curve. This necessitates a more sophisticated analysis at the bearing and rotordynamic system levels during the design stage. This dissertation addresses this problem in a unique manner by developing a fully nonlinear homopolar magnetic bearing model. The nonlinear dynamics of permanent magnet-biased homopolar magnetic bearing (PMB HoMB) system with 2-dof rigid and 4-dof flexible rotor is analyzed. The dynamic behavior of the rotor-bearing system is examined in the feedback control loop that includes low pass filter effects. An analytical magnetization curve model is proposed to predict the nonlinear magnetic force under the influence of the magnetic flux saturation more accurately. The modified Langmuir method with the novel correction terms for the weak flux region is used to curve-fit the experimental magnetization data of Hiperco 50. A new curve fit model of the B-H curve is shown to have significantly better agreement with the measured counterpart than conventional piecewise linear and other models. PMB HoMB characteristics with flux saturation, such as forces depending on the rotor position and bearing stiffness, are compared with these other models. Frequency response curve, bifurcation diagram, Poincare plot, and orbit plot are utilized to demonstrate the effects of the nonlinearities included in the 2-dof rotorbearing system. Due to heavy static loads applied to the rotor, it operates within the magnetic flux saturation region at the bearing clearance. The voltage saturation in the power amplifier of the magnetic bearing introduces lag in the control loop and the response of the heavily loaded 4-dof rotor-bearing system shows that limit cycle stability can be achieved due to the magnetic flux saturation or current saturation in the amplifier; otherwise the system would experience a destructive instability. These simulation results provide the first explanation of this commonly observed limit cycle which is referred to as ‘virtual catcher bearings’.

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Tube hydroforming process is a relatively new technology compared to conventional manufacturing via stamping and welding. However there is not much knowledge available for the product or process designers. The objective of this study will determine the flow stress and forming limit diagram of tubular materials to discuss the formability of tubes. Firstly, a mathematical model is proposed to examine the plastic deformation behavior of a thin-walled tube at different process parameters during the bulge hydroforming process without axial feeding. In the formulation of this mathematical model, an ellipsoidal surface and non-uniform thinning in the free bulged region and sticking friction between the tube and die are assumed. In the sticking friction mode, the elements after contact with the die do not move or slide. The effects of various forming parameters, such as the die entry radius, the bulge length, anisotropy, the initial thickness of the tube, etc., upon the forming pressures are discussed systematically. Secondly, an analytical model combined with hydraulic bulge tests is proposed to evaluate the properties of tubular materials considering anisotropy effect. Annealed AA6011 aluminum tubes and SUS409 stainless steel tubes are used for the bulge test. The tube thickness and radius at the pole and the internal forming pressure are measured simultaneously during the bulge test. The anisotropic values are obtained from tensile tests. From above experimental data, the effective stress - effective strain relations can be derived by this analytical model. The finite element method is used to conduct the simulations of hydraulic bulge forming with the flow stresses obtained by the above-mentioned model. The analytical forming pressures versus bulge heights are compared with the experimental results to validate the approach proposed in this study. Finally, this study also establishes the Forming Limit Diagram (FLD) of aluminum tubular material. An experimental system of tube hydroforming in which axial feed is applied to carry out the hydraulic bulge-forming test of the annealed aluminum alloy tubes. Furthermore, Hill¡¦s new yield criterion is also used to predict the Forming Limit Curves of sheets. The predicted forming limit diagrams are compared with the experimental data. The results of this study can provide useful knowledge for process design. In addition, the process parameters of flow stress and forming limit diagram obtained can improve the accuracy of the simulation results in industrial and academic fields.

ABSTRACT The objective of this study is to establish the Forming Limit Diagram (FLD) of tubes. An experimental system of tube hydroforming, the electrical chemical etching method and the image process system are used to carry out the sheet metal forming test and the hydraulic bulge-forming test of annealed aluminum alloy tubes. Furthermore, Hill¡¦s new yield criterion is also used to predict the Forming Limit Curves of sheets. The predicted forming limit diagrams are compared with experimental data. The forming limit diagrams of tubes are coincident with those of sheets. Also, the predicted forming limit curves by Hill¡¦s new yield criterion agree quite well with those by experiments. Therefore, Hill¡¦s new yield criterion can be used to establish the forming limit curves of sheets or tubes.

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A Boolean partition algebra is a pair $(B,F)$ where $B$ is a Boolean algebra and $F$ is a filter on the semilattice of partitions of $B$ where $\bigcup F=B\setminus\{0\}$. In this dissertation, we shall investigate the algebraic theory of Boolean partition algebras and their connection with uniform spaces. In particular, we shall show that the category of complete non-Archimedean uniform spaces is equivalent to a subcategory of the category of Boolean partition algebras, and notions such as supercompleteness of non-Archimedean uniform spaces can be formulated in terms of Boolean partition algebras.

Vehicle behaviour near the limit of adhesion is studied using linear optimal . control techniques and relatively simple vehicle models. Both time-invariant and time-varying approaches are used. Controllability is applied as a post-processing tool to analyse the resultant vehicle behaviour. First, a 4WS controller is developed using a linear time-invariant method, with a reference model control structure. Two handling objectives are defined, which are thought to provide predictable dynamics. Advantages of using a reference model control are clearly shown. With a developed control structure, it is shown that the prescribed target dynamics is achieved, provided tyre forces are available. It is also found that the controller is robust to small changes in the various vehicle parameter values. As a next step, time-varying modelling approach was used in order to better represent the vehicle operating conditions through the various dynamic range, including the limit of adhesion. An iterative vehicle path optimisation problem is formulated using a linear time-varying control approach. The validity of the optimisation method is studied against the steady-state simulation result at the limit of adhesion. It is shown that the method is capable of finding a trajectory in the vicinity of the friction limit, where the front tyres are used fully whilst retaining some margin at the rears. However, a couple of Issues are discovered. First, due to the quadratic nature of the road geometry cost function, the trajectory could get locked if the vehicle runs very close to the edge of the road. Hence, the . optimisation needs to be formulated such that the level of "optimality" on the trajectory remains consistent throughout the manoeuvre at each iteration. Secondly, it is found that inappropriate control demands are produced if the system matrix becomes poorly conditioned near the limit. This results in optimisation failure. In order to understand the mechanism of this failure, controllability of linear timevarying system was analysed and its properties were discussed in detail. First, the calculation methods of the controllability gramian matrix are investigated and some practical limitations are found. The gramian matrix is then used to define an open loop control sequence. It is found that the damping of the system has a significant influence on the control strategy. Subsequently, "the moving controllability window of a fixed time period" is found to provide the most relevant information of changing dynamics through the time. The study showed that the failure of the optimisation in the vicinity of the friction limit was indeed due to lack of controllability and the optimisation method itself was functioning correctly. The vehicle path optimisation problem is then extended to include longitudinal dynamics, enabling simulation of more general manoeuvres. The single corner simulation showed that the optimisation converges to an "out-in-out" path, with iterative solution improving continuously in a first order manner. Simulations with various controller settings showed that the strategy is reasonably robust provided that the changes in parameter settings are kept within a reasonable magnitude. It is also confirmed that the optimisation is able to drive a vehicle close to the limit under different types of operations required, i.e. braking, cornering and acceleration. The study was then performed with slightly more complex road geometry in order to investigate if the· optimisation is capable of prioritising certain· part of the manoeuvre in order to achieve better overall result. Unfortunately, this problem could not be solved successfully. The optimisation concentrated on the latter part of the manoeuvre as it had higher sensitivity to the final cost. This resulted in clearly sub-optimal overall performance. Finally, relatively simple study is conducted to investigate the correlation between various vehicle settings and optimisation results. Using the path optimisation problem formulation, iris found that the more oversteer vehicles are able to achieve better· result with more margin left in rear tyre force capacity. The handling objective functions used for the 4 WS controller is also calculated for the resultant trajectories. It is found that the neutral steer cost had a strong correlation, whereas the linearity cost showed no noticeable correlation. The controllability analysis was applied on the various vehicle settings using step steer simulation. It showed that more understeering vehicle retains higher controllability throughout the dynamics range. It is also found that higher inertia gives better controllability near the limit, however, it gives less controllability at more moderate operating conditions.

Ο σκοπός της παρούσας έρευνας είναι να εξετάσει, σε μία περίπτωση φοιτητικού πληθυσμού (φοιτητές Τμήματος Γεωλογίας), κατά πόσο οι γνώσεις γύρω από το όριο συνάρτησης και ακολουθίας (ιδιαίτερα και της γεωμετρικής σειράς), τις περισσότερες από τις οποίες έχουν διδαχθεί οι σημερινοί φοιτητές σχολής Θετικών Επιστημών κατά τη διάρκεια της δευτεροβάθμιας εκπαίδευσης είναι γνώσεις οι οποίες έχουν κατανοηθεί σε κάποιο βάθος και αν αυτή η "γνωστική κληρονομιά" μπορεί να αξιοποιηθεί στο χώρο της τριτοβάθμιας εκπαίδευσης. / The purpose of this research is to examine, in one case of student population (Geology students), whether the knowledge about the function limit and the series(specially the geometric series), most of which have been taught to today's "Science's Faculty" students during secondary education, is knowledge which has been understood in sufficient depth and whether this "cognitive legacy" can be used in higher education.

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