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Subject of this thesis is introduction to questions of stepping motors control. The thesis characterizes basic principles some types of stepping motor, their features and control methods. These knowledges are consequently used for proposition of controlling circuit for driving stepping motor using microcontroller.

Stepping stones are compromised hosts in a network which can be used by hackers and other malicious attackers to hide the origin of connections. Attackers hop from one compromised host to another to form a chain of stepping stones before launching attack on the actual victim host. Various timing and content based detection techniques have been proposed in the literature to trace back through a chain of stepping stones in order to identify the attacker. This has naturally led to evasive strategies such as shaping the trac di erently at each hop. The evasive techniques can also be detected. Our study aims to adapt some of the existing stepping stone detection and antievasion techniques to software-dened networks which use network function virtualization. We have implemented the stepping-stone detection techniques in a simulated environment and use sFlow for the trac monitoring at the switches. We evaluate the detection algorithms on di erent network topologies and analyze the results to gain insight on the e ectiveness of the detection mechanisms. The selected detection techniques work well on relatively high packet sampling rates. However, new solutions will be needed for large SDN networks where the packet sampling rate needs to be lower.

Problem Statement: Stepping is a common strategy after a perturbation. Stroke survivors display a predilection for stepping with non-paretic leg. Insight into induced stepping between stroke survivors and age-matched control may guide our understanding for reactive postural control training post stroke. Purpose: To investigate the difference in perturbation-induced stepping between chronic stroke survivors and age-matched controls at three phases of the stepping response: preparation, execution, and landing and association with clinical outcome measures. Procedure: Twenty-one community-dwelling chronic stroke survivors (mean age 59y/o ±13yrs) and 17 age- and gender-matched controls (mean age 54.4y/o ±17yrs) completed this study. Clinical measures of gait, balance, range, sensation, and motor control were assessed. A mechanical weight drop of 10% body weight (BW) was used to create the anterior waist pull perturbation during three stance symmetry positions: equal stance (EQ) and two asymmetrical stance (70% BW on dominant leg and 70% BW on nondominant leg). Ten perturbation trials plus two catch trials at 2% BW were given in a standard randomly order at the three stance positions. Kinematic and kinetic data was collected for perturbation steps. Results: The asymmetrical trials resulted in two types of stepping response, steps with the leg bearing 70% BW (loaded steps – LS) and steps with the leg that had 30% BW (unloaded steps – ULS). All subjects initiated steps more often with their unloaded leg (ULS) in the asymmetrical stance trials. In the stroke group the ULS increased paretic leg stepping compared to EQ (p=0.001) and LS (p=0.001). The stroke group had significantly earlier APA onset with both non-paretic leg (p=0.003) and paretic leg (p=0.028), took significantly more steps with paretic (p=0.01) and non-paretic (p=0.07), shorter step length (paretic, p=0.025 and non-paretic p=0.003), and less change in momentum at landing with paretic leg (p=0.01) compared to controls. Conclusion: Reacting to a perturbation is more challenging for chronic stroke survivors than age- and gender-matched control subjects in the preparation, execution, and landing phase of the stepping response regardless of the leg used. Perturbation training should include stepping with both non-paretic and paretic leg.

Elliptic obstacle problems are formulated to find either superharmonic solutions or minimal surfaces that lie on or over the obstacles, by incorporating inequality constraints. This dissertation investigates simple iterative algorithms based on the successive over-relaxation (SOR) method. It introduces subgrid methods to reduce accuracy deterioration occurring near the free boundary when the mesh grid does not match with the free boundary. For nonlinear obstacle problems, a method of gradient-weighting is introduced to solve the problem more conveniently and efficiently. The iterative algorithm is analyzed for convergence for both linear and nonlinear obstacle problems. Parabolic initial-boundary value problems with nonsmooth data show either rapid transitions or reduced smoothness in its solution. For those problems, specific numerical methods are required to avoid spurious oscillations as well as unrealistic smoothing of steep changes in the numerical solution. This dissertation investigates characteristics of the θ-method and introduces a variable-θ method as a synergistic combination of the Crank-Nicolson (CN) method and the implicit method. It suppresses spurious oscillations, by evolving the solution implicitly at points where the solution shows a certain portent of oscillations or reduced smoothness, and maintains as a similar accuracy as the CN method with smooth data. An effective strategy is suggested for the detection of points where the solution may introduce spurious oscillations (the wobble set); the resulting variable-θ method is analyzed for its accuracy and stability. After a theory of morphogenesis in chemical cells was introduced in 1950s, much attention had been devoted to the numerical solution of reaction-diffusion (RD) equations. This dissertation studies a nonoscillatory second-order time-stepping procedure for RD equations incorporating with variable-θ method, as a perturbation of the CN method. We also perform a sensitivity analysis for the numerical solution of RD systems to conclude that it is much more sensitive to the spatial mesh resolution than the temporal one. Moreover, to enhance the spatial approximation of RD equations, this dissertation investigates the averaging scheme, that is, an interpolation of the standard and skewed discrete Laplacian operator and introduce the simple optimizing strategy to minimize the leading truncation error of the scheme.

<p> The analysis of stepping motors using linear models has been simplified through identifications of the constants. Though the existing nonlinear models assuming a smooth air-gap machine may, in some cases, yield a fairly close prediction of the characteristics of a stepping motor, the models do not represent the actual motors which are essentially salient-pole motors. A new salient-pole nonlinear model is introduced. The analysis of permanent-magnet stepping motors using the nonlinear models has been simplified by assuming constant current sources. Dynamic behaviors of a permanent -magnet stepping motor are shown by phase-plane plots and step by step transient response plots.</p> <p> Computer control of stepping motors in both open-loop and closed-loop is discussed. The open-loop control has been demonstrated to be successful and a closed-loop control system using light-sensors as feedback has been designed.</p> / Thesis / Master of Engineering (MEngr)

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The electrical activity of the heart is a well studied process. Mathematical modeling and computer simulations are used to study the cardiac electrical activity: several mathematical models exist, among them the microscopic model, which is based on the explicit representation of individual cells. The cardiac tissue is viewed as two separate domains: the intra-cellular and extra-cellular domains, Ωᵢ and Ωₑ, respectively, separated by cellular membranes Γ. The microscopic model consists of a set of Poisson equations, one for each sub-domain, Ωᵢ and Ωₑ, coupled on interfaces Γ with nonlinear transmission conditions involving a system of ODEs. The unusual transmission conditions on Γ make the model challenging to solve numerically. In this thesis, we first focus on the dimensional analysis of the microscopic model. We then reformulate the problem on the interface Γ using a Steklov-Poincaré operator. We discretize the model in space using finite element methods. We prove the existence of a semi-discrete solution using a reformulation of the model as an ODE system on the interface Γ. We derive stability and error estimates for the finite element method. Afterwards, we consider five numerical schemes including the Godunov splitting method, two implicit methods, (Backward Euler (BE) and second order Backward Differentiation Formula (BDF2)), and two semi-implicit methods (Forward Backward Euler (FBE), and second order Semi-implicit Backward Differentiation Formula (SBDF2)). A convergence analysis of the implicit and semi-implicit methods is performed and the results are compared with manufactured solutions that we have proposed. Numerical results are presented to compare the stability, accuracy and efficiency of the methods. CPU times needed to solve the problem over a single cell using FBE, SBDF2 and Godunov splitting methods are reported. The results show that FBE and Godunov splitting methods achieve better numerical accuracy and efficiency than implicit and SBDF2 schemes, for a given computational time. Finally, we solve the model using FBE and Domain Decomposition Method (DDM) for two cells connected to each other by a gap junction. We investigate the influence of the space discretization and we explore the differences between a conforming and nonconforming mesh on Γ. We compare the solutions obtained with both FBE and DDM methods. The results show that both methods give the same solution. Therefore, the DDM is capable of providing an accurate solution with a minimal number of sub-domain iterations.