No description available.

The study of coherent states (CS) for a quantum mechanical system has received a lot of attention. The definition, applications, generalizations of such states have been the subject of work by researchers. A common starting point of all these approaches is the observation of properties of the original CS for the harmonic oscillator. It is well-known that they are described equivalently as (a) eigenstates of the usual annihilation operator, (b) from a displacement operator acting on a fundamental state and (c) as minimum uncertainty states. What we observe in the different generalizations proposed is that the preceding definitions are no longer equivalent and only some of the properties of the harmonic oscillator CS are preserved. In this thesis we propose to study a new class of coherent states and its properties. We note that in one example our CS coincide with the ones proposed by Glauber where a set of three requirements for such states has been imposed. The set of our generalized coherent states remains invariant under the corresponding time evolution and this property is called temporal stability. Secondly, there is no state which is orthogonal to all coherent states (the coherent states form a total set). The third property is that we get all coherent states by acting on one of these states ['fiducial vector'] with operators. They are highly non-classical states, in the sense that in general, their Bargmann functions have zeros which are related to negative regions of their Wigner functions. Examples of these coherent states with Bargmann function that involve the Gamma and also the Riemann ⲝ functions are represented. The zeros of these Bargmann functions and the paths of the zeros during time evolution are also studied.

The differential equations are often used in practice for making different mathematical models of mechanical systems and they are the best help for modelling. The flow, coming around elastic mechanical system, when there are some conditions, awakes the auto-oscillations of it. At my work I onquire the change of auto-oscillations into the electrical signal. If we want to reach it, we must give for mechanical system an extra stimulation by electric network. The purpose of my work - inquire simplification model of this made system; area of existence synchronic processes, when we have relaxed and forced oscillations; to analyse different trajectories of different types this differential equation; to find spectral charakteristics. The analytical and graphical results were forthcoming, let uncover some steady treatments' and their surroundings' attributes of pending system.

In this thesis we are going to study the energy shaping problem on controlled Lagrangian systems with degree of underactuation less than or equal to two. Energy shaping is a method of stabilization by designing a suitable feedback control force on the given controlled Lagrangian system so that the total energy of the feedback equivalent system has a non-degenerate minimum at the equilibrium. The feedback equivalent system can then be stabilized by a further dissipative force. Finding a feedback equivalent system requires solving a system of PDEs. The existence of solutions for this system of PDEs is guaranteed, under some conditions, in the case of one degree of underactuation. Higher degrees of underactuation, however, requires a more careful study on the system of PDEs, and we apply the formal theory of PDEs to achieve this purpose in the case of two degrees of underactuation. The thesis is divided into four chapters. First, we review the basic notion of energy shaping and state the results for the case of one degree of underactuation. We then devise a general scheme to solve the energy shaping problem with degree of underactuation equal to one, together with some examples to illustrate the general procedure. After that we review the tools from the formal theory of PDEs, as a preparation for solving the problem with two degrees of underactuation. We derive an equivalent involutive system of PDEs from which we can deduce the existence of solutions which suit the energy shaping requirement.

Delamination and cracks within the multilayer structure are typical failure modes observed in microelectronic and micro electro mechanical system (MEMS) devices and packages. As destructive detection methods consume large numbers of devices during reliability tests, non-destructive techniques (NDT) are critical for measuring the size and position of internal defects throughout such tests. There are several established NDT methods; however, some of them have significant disadvantages for detecting defects within multilayer structures such as those found in MEMS devices. This thesis presents research into the application of transient infrared thermography as a non-destructive method for detecting and measuring internal defects, such as delamination and cracks, in the multilayer structure of MEMS devices. This technique works through the use of an infrared imaging system to map the changing temperature distribution over the surface of a target object following a sudden change in the boundary conditions, such as the application of a heat source to an external surface. It has previously been utilised in various applications, such as damage assessment in aerospace composites and verification of printed circuit board solder joint manufacture, but little research of its applicability to MEMS structures has previously been reported. In this work, the thermal behaviour of a multilayer structure containing defects was first numerically analysed. A multilayer structure was then successfully modelled using COMSOL finite element analysis (FEA) software with pulse heating on the bottom surface and observing the resulting time varying temperature distribution on the top. The optimum detecting conditions such as the pulse heating energy, pulse duration and heating method were determined and applied in the simulation. The influences of thermal properties of materials, physical dimensions of film, substrate and defect and other factors that will influence the surface temperature gradients were analytically evaluated. Furthermore, a functional relationship between the defect size and the resulting surface temperature was obtained to improve the accuracy of estimating the physical dimensions and location of the internal defect in detection. Corresponding experiments on specimens containing artificially created defects in macro-scale revealed the ability of the thermographic method to detect the internal defect. The precision of the established model was confirmed by contrasting the experimental results and numerical simulations.

No description available.

The study of coherent states (CS) for a quantum mechanical system has received a lot of attention. The definition, applications, generalizations of such states have been the subject of work by researchers. A common starting point of all these approaches is the observation of properties of the original CS for the harmonic oscillator. It is well-known that they are described equivalently as (a) eigenstates of the usual annihilation operator, (b) from a displacement operator acting on a fundamental state and (c) as minimum uncertainty states. What we observe in the different generalizations proposed is that the preceding definitions are no longer equivalent and only some of the properties of the harmonic oscillator CS are preserved. In this thesis we propose to study a new class of coherent states and its properties. We note that in one example our CS coincide with the ones proposed by Glauber where a set of three requirements for such states has been imposed. The set of our generalized coherent states remains invariant under the corresponding time evolution and this property is called temporal stability. Secondly, there is no state which is orthogonal to all coherent states (the coherent states form a total set). The third property is that we get all coherent states by acting on one of these states [¿fiducial vector¿] with operators. They are highly non-classical states, in the sense that in general, their Bargmann functions have zeros which are related to negative regions of their Wigner functions. Examples of these coherent states with Bargmann function that involve the Gamma and also the Riemann ¿ functions are represented. The zeros of these Bargmann functions and the paths of the zeros during time evolution are also studied. / Libyan Cultural Affairs

This article presents a simulation study into effects of compliant (flexible) components (such as the engine subframe and the lower control arm) and their deflections on the characteristics of a vehicle experiencing steering drift during straight-line braking. The vehicle front and rear suspension are modelled using multi-body dynamic analysis software. The front suspension model represents theMacPherson strut design of the vehicle and includes a rack and pinion steering system, brake system, engine subframe, and a powertrain unit. The model has been analysed under two steering control methods: fixed and free control. Suspension characteristics and the effect of deflections arising from the subframe and the lower control arm on these suspension characteristics have been analysed. The simulations confirmed that variation of component stiffness and interactions within components give rise to side-to-side deflections that could affect lateral drift during braking. It is concluded that side-to-side variation of suspension characteristics can have a detrimental effect on lateral drift during braking and that compliant components whose stiffness varies from side to side can cause different side-to-side deflections that can induce and influence variation in suspension characteristics such as toe steer angle that can lead the vehicle during braking.

No description available.

Friction compensation is challenging but imperative for control engineers. For high-performance engineering systems, a friction-model-based controller is typically required to accommodate the nonlinearities arisen from the friction model employed. It is well known that the parameters of the friction model used in the friction compensation are nearly impossible to be accurately identified. Therefore, the objective of this research is to study the effect of these parametric uncertainties on the stability of a set-point position control system. With the above goal in mind, a variety of aspects are investigated in this work. Firstly, several common friction features and friction models are surveyed to provide background knowledge which helps select the friction model with the highest accuracy for our study. Secondly, an experimental setup is proposed and fabricated to validate the levels of accuracy given by the candidate friction models. The comparisons between the numerical and experimental results confirm that the LuGre friction model is the best approximation of the observed friction behaviours among all models selected. Moreover, a series of profound discussions addressing the relation between the candidate models’ structures and their numerical friction feature predictions are provided and followed by a summary table that recapitulates the properties of the candidate friction models. Last but not least, the state space models of the proposed setup formulated by the improved version of the LuGre model and the two controllers of interest, namely input-output linearization controller and nominal characteristic trajectory following (NCTF) controller, are derived for the stability analysis under the parametric uncertainties. Two parameters in the friction model used, σ_0 and σ_1, are perturbed for the stability analysis in which the results applying the concept of Lyapunov exponents (LEs) clearly illustrate the significant effect of the varying σ_0 and σ_1 values on the system stability. The effect of parametric uncertainties can depend quite significantly on the incorporated controller, and the stability results obtained here are applicable to the design and analysis of other systems that are inherently similar to our setup. The stability analysis conducted is this work is recommended for other control systems to avoid unwanted qualitative behaviours under parametric perturbations. / October 2016