No description available.

Microfluidic devices have found applications in a number of areas, such as medical analysis, chemical synthesis, biological study, and drug delivery. Because of the small channel dimensions used in these systems, most microchannels exhibit laminar flow due to their low Reynold’s number, making mixing of fluids very challenging. Mixing at this size scale is diffusion-limited, so inducing chaotic flow patterns can increase the interface surface area between two fluids, thereby decreasing overall mixing time. One method to create a chaotic flow within the channel is through the introduction of internal protrusions into the channel. In such an application protrusions that create a rotational flow within the channel are preferred due to their effectiveness in folding the two fluids over one another. The novel mixer outlined in this paper uses a Ti-Ni shape memory alloy for the creation of protrusions that can be turned controlled through material temperature. Controllability of the alloy allows users to turn the chaotic flow created by the protrusions off and on by varying the temperature of the mixer. This ability contributes to the idea of a continuous microfluidic system that can be turned on only when necessary as well as recycle unmixed fluids while turned off.

This work focuses on the use of a genetic algorithm for optimization in a search-based problem. The Genetic Algorithm (GA) is a subset of evolutionary algorithms that models biological processes to optimize highly complex functions. A GA allows a population composed of many individuals to evolve under specified selection rules to a state that maximizes the “fitness” (i.e. minimize the objective function). A major advantage of using GA over most stochastic techniques is its parallelism, which speeds up the simulation results leading to faster convergence. With mutation, the GA is also less likely to get stuck in local minima compared to other stochastic techniques. However, some notable drawbacks of the Standard GA (SGA) include slow convergence and a possibility of being stuck in local optimum solution. The SGA uses a random process to generate parameter values for the initial population generation, crossover and mutation processes. Random number generators are designed to result in either uniform distributions or Gaussian distributions. We conjecture that the evolutionary processes in genetics are driven by a random non-linear deterministic dynamic process rather than a random non-deterministic process. Therefore, in the GA evolutionary process, a chaotic map is incorporated into the initial population generation, the crossover and mutation processes of the SGA; this is termed the Chaotic GA (CGA). The properties of a chaotic system that provides additional benefits over randomly generated solutions are sensitivity to initial conditions, topological density and topological transitivity (robust diversity). These properties ensure that the CGA is able to explore the entire solution space. Introducing chaos into the whole process of a standard genetic algorithm may help improve convergence time and accuracy. Simulation was done using Matlab and Java.

The first line of defence against wireless attacks in Radio Frequency Identi cation (RFID) systems is authentication of tags and readers. RFID tags are very constrained in terms of power, memory and size of circuit. Therefore, RFID tags are not capable of performing sophisticated cryptographic operations. In this dissertation, we have designed light-weight authentication schemes to securely identify the RFID tags to readers and vice versa. The authentication schemes require simple binary operations and can be readily implemented in resource-constrained Radio Frequency Identi cation (RFID) tags. We provide a formal proof of security based on the di culty of solving the Syndrome Decoding (SD) problem. Authentication veri es the unique identity of an RFID tag making it possible to track a tag across multiple readers. We further protect the identity of RFID tags by a light-weight privacy protecting identifi cation scheme based on the di culty of the Learning Parity with Noise (LPN) complexity assumption. To protect RFID tags authentication against the relay attacks, we have designed a resistance scheme in the analog realm that does not have the practicality issues of existing solutions. Our scheme is based on the chaos-suppression theory and it is robust to inconsistencies, such as noise and parameters mismatch. Furthermore, our solutions are based on asymmetric-key algorithms that better facilitate the distribution of cryptographic keys in large systems. We have provided a secure broadcast encryption protocol to effi ciently distribute cryptographic keys throughout the system with minimal communication overheads. The security of the proposed protocol is formally proven in the adaptive adversary model, which simulates the attacker in the real world.

Parallel-plate electrostatic actuators driven by a voltage difference between two electrodes suffer from an operation range limited to 30% of the gap that has significantly restrained their applications in Microelectromechanical systems (MEMS). In this thesis, the travel range of an electrostatic actuator made of a micro-cantilever beam electrode above a fixed electrode is extended quasi-statically to 90% of the capacitor gap by introducing a voltage regulator (controller) circuit designed for low frequency actuation. The developed large-stroke actuator is valuable contribution to applications in optical filters, optical modulators, digital micro-mirrors and micro-probe based memory disk drives. To implement the low-frequency large-stroke actuator, the beam tip velocity is measured by a vibrometer, the corresponding signal is integrated in the regulator circuit to obtain the displacement feedback, which is used to modify the input voltage of the actuator to reach a target location. The voltage regulator reduces the total voltage, and therefore the electrostatic force, once the beam approaches the fixed electrode so that the balance is maintained between the mechanical restoring force and the electrostatic force that enables the actuator to achieve the desired large stroke. A mathematical model is developed for the actuator based on the mode shapes of the cantilever beam using experimentally identified parameters that yields good accuracy in predicting both the open loop and the closed loop responses. The low-frequency actuator also yields superharmonic resonances that are observed here for the first time in electrostatic actuators. The actuator can also be configured either as a bi-stable actuator using a low-frequency controller or as a chaotic resonator using a high-frequency controller. The high-frequency controller yields large and bounded chaotic attractors for a wide range of excitation magnitudes and frequencies making it suitable for sensor applications. Bifurcation diagrams reveal periodic motions, softening behavior, period doubling cascades, one-well and two-well chaos, superharmonic resonances and a reverse period doubling cascade. To verify the observed chaotic oscillations, Lyapunov exponents are calculated and found to be positive. Furthermore, a chaotic resonator with a quadratic controller is designed that not only requires less voltage, but also produces more robust and larger motions. Another metric of chaos, information entropy, is used to verify the chaotic attractors in this case. It is found that the attractors have a common information entropy of 0.732 independent of the excitation amplitude and frequency.

No description available.

The first part of this work deals with open dynamical systems. A natural question of how the survival probability depends upon a position of a hole was seemingly never addresses in the theory of open dynamical systems. We found that this dependency could be very essential. The main results are related to the holes with equal sizes (measure) in the phase space of strongly chaotic maps. Take in each hole a periodic point of minimal period. Then the faster escape occurs through the hole where this minimal period assumes its maximal value. The results are valid for all finite times (starting with the minimal period), which is unusual in dynamical systems theory where typically statements are asymptotic when time tends to infinity. It seems obvious that the bigger the hole is the bigger is the escape through that hole. Our results demonstrate that generally it is not true, and that specific features of the dynamics may play a role comparable to the size of the hole. In the second part we consider some classes of cellular automata called Deterministic Walks in Random Environments on Z^1. At first we deal with the system with constant rigidity and Markovian distribution of scatterers on Z^1. It is shown that these systems have essentially the same properties as DWRE on Z^1 with constant rigidity and independently distributed scatterers. Lastly, we consider a system with non-constant rigidity (so called process of aging) and independent distribution of scatterers. Asymptotic laws for the dynamics of perturbations propagating in such environments with aging are obtained.

This thesis describes the comparison of time-lapse field observations of suncups on alpine snow with numerical simulations. The simulations consist of solutions to a nonlinear partial differential equation which exhibits spontaneous pattern formation from a low amplitude, random initial surface. Both the field observations and the numerical solutions are found to saturate at a characteristic height and fluctuate chaotically with time. The timescale of these fluctuations is found to be instrumental in determining the full set of parameters for the numerical model such that it mimics the nonlinear dynamics of suncups. These parameters in turn are related to the change in albedo of the snow surface caused by the presence of suncups. This suggests the more general importance of dynamical behaviour in gaining an understanding of pattern formation phenomena.

Doctor of Philosophy / A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.

This dissertation is concerned with identification of nonlinear instabilities in rotating multibody systems and subsequent control to eliminate the vibrations. Three nonlinear mechanical systems of this type are investigated and instabilities arising from their inherent nonlinearities are shown to exist for a range of system parameters and conditions. Subsequently, various nonlinear methods of vibration control have been employed to eliminate or suppress the instabilities. Analytical and numerical models have been designed to demonstrate various unstable dynamical behaviour with consistent results. The motion is studied by means of time history, phase space, frequency spectrum, Poincare map, Lyapunov characteristic exponents and Correlation Dimension. Numerical simulations have also shown the effectiveness and robustness of the control techniques over a range of instability conditions for each model. The dynamics of a rotating body with internal energy dissipation is first investigated. Such a model may be considered to be representative of a simplified spinning spacecraft. A comprehensive stability analysis is performed and regions of highly nonlinear behaviour are identified for more rigorous investigation. Numerical simulations using typical satellite parameter values are performed and the system is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. Analysis of this model using Melnikov’s method is performed and a sufficient criterion for chaotic instabilities is obtained in terms of system parameters. Evidence is also presented, indicating that the onset of chaotic motion is characterised by period doubling as well as intermittency. Subsequently, Control of chaotic vibrations in this model is achieved using three techniques. The control methods are implemented on the model under instability conditions. The first two control techniques, recursive proportional feedback (RPF) and continuous delayed feedback are recently developed model independent methods for control of chaotic motion in dynamical systems. As such these methods are employed on all three rotating multibody systems in this dissertation. Control of chaotic instability in this model is also achieved using an algorithm derived using Lyapunov’s second method. Each technique is outlined and the effectiveness of the three strategies in controlling chaotic motion exhibited by the present system is compared and contrasted. The dynamics of a dual-spin spacecraft with internal energy dissipation in the form of an axial nutational damper is also investigated for non-linear phenomena. The problem involves the study of a body with internal moving parts that is characterised by a coupling of the motions of the damper mass and the angular rotations of the platform and rotor of the spacecraft. Two realistic spacecraft parameter configurations are investigated and each is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft rotor for a range of forcing amplitude and frequency. Onset of chaotic motion was shown to be characterised by period doubling and Hopf bifurcations. An investigation of the effects of damping upon the configuration is also performed. Predicted instabilities indicate the range of rotor speeds, perturbation amplitudes and damping coefficients to be avoided in the design of dual-spin spacecraft. Control of chaotic vibrations in this model is also achieved using recursive proportional feedback (RPF) and continuous delayed feedback. Subsequently a more effective model dependent method based on energy considerations is derived and implemented. The effectiveness and robustness of each technique is shown using numerical simulations. Another rotating multibody system that is physically distinct from the previously described models is also investigated for nonlinear instabilities and control. The model is in the form of a driveline which incorporates a commonly used coupling called a Hooke’s joint. In particular, torsional instabilities due to fluctuating angular velocity ratio across the joint are examined. Linearised equations are used for the prediction of critical speed ranges where parametric instabilities characterised by exponential build up of torsional response amplitudes occur. Predicted instabilities indicate the range of driveshaft speeds to be avoided during the design of a driveline which employs a Hooke's joint. Numerical simulations further demonstrate the existence of parametric, quasi-periodic and chaotic instabilities. Subsequently, suppression of these vibrations is achieved using the previously described model independent techniques. Chaotic vibrations have also been observed in a range of simple mechanical systems such as a periodically kicked rotor, forced pendulum, synchronous rotor, aeroelastic panel flutter and impact print hammer to name but a few. It is thus becoming of increasing importance to engineers to be aware of chaotic phenomena and be able to recognise, quantify and eliminate these undesirable vibrations. The analytical and numerical methods described in this dissertation may be usefully employed by engineers for detecting as well as controlling chaotic vibrations in an extensive range of physical systems.