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The Syrian civil war is undeniably one of the largest humanitarian crises of modern time. With host countries, such as Lebanon, taking in a disproportionately large influx of refugees in their already fragile national structure, there erupts a complex situation of meeting the needs of the refugee population without compromising the local population. Thus, while education up to the end of secondary school is provided free for refugee children through international and national funding, there are many challenges with regards to not only the access to secondary and higher education, but the role of post grade nine (or post primary school) education for refugee children. This dissertation outlines the post primary school options for Syrian refugee children in Lebanon while at the same time analyzing the perceived options and reasoning behind the choices taken by the refugees themselves. The research will be conducted using an adapted form of grounded theory which does not assume a certain approach to education is ideal and takes on the viewpoints of multiple stakeholders. This two-part analysis includes an open-ended questionnaire sent to policy makers at various governmental and NGO levels in Lebanon as well as a systematic internet search to unveil all post primary school options for Syrian refugees. The second part of the dissertation consists of interviews with refugee children about to finish their primary school years, and refugee teenagers who have made their post primary school choices in Lebanon in an attempt to reveal how refugees view secondary and higher education; what choices they make after primary school and the obstacles they may face in order to meet their educational goals. These are contrasted with interviews of Lebanese students who attend schools in the same areas. The dissertation ends with insights regarding the theoretical implications of education for refugees as well as policy level recommendations.

Periodically correlated time series generally exist in several fields including hydrology, climatology, economics and finance, and are commonly modelled using periodic autoregressive (PAR) model. For a time series with stochastic periodic trend, for which a unit root is expected, a periodically integrated autoregressive PIAR model with periodic and/or seasonal unit root has been shown to be a satisfactory model. The existing theory used the multivariate methodology to study PIAR models. However, this theory is convoluted, majority of it only developed for quarterly time series and its generalisation to time series with larger number of periods is quite cumbersome. This thesis studies the existing theory and highlights its restrictions and flaws. It provides a coherent presentation of the steps for analysing PAR and PIAR models for different number of periods. It presents the different unit roots representations and compares the performance of different unit root tests available in literature. The restrictions of existing studies gave us the impetus to develop a unified theory that gives a clear understanding of the integration and unit roots in the periodic models. This theory is based on the spectral information of the multi-companion matrix of the periodic models. It is more general than the existing theory, since it can be applied to any number of periods whereas the existing methods are developed for quarterly time series. Using the multi-companion method, we specify and estimate the periodic models without the need to extract complicated restrictions on the model parameters corresponding to the unit roots, as required by NLS method. The multi-companion estimation method performed well and its performance is equivalent to the NLS estimation method that has been used in the literature. Analysing integrated multivariate models is a problematic issue in time series. The multi-companion theory provides a more general approach than the error correction method that is commonly used to analyse such time series. A modified state state representation for the seasonal periodically integrated autoregressive (SPIAR) model with periodic and seasonal unit roots is presented. Also an alternative state space representations from which the state space representations of PAR, PIAR and the seasonal periodic autoregressive (SPAR) models can be directly obtained is proposed. The seasons of the parameters in these representations have been clearly specified, which guarantees correct estimated parameters. Kalman filter have been used to estimate the parameters of these models and better estimation results are obtained when the initial values were estimated rather than when they were given.

Rydberg-dressed ground state atoms are atoms with an electron off-resonantly excited to a very high energy state, i.e., a state of high principal quantum number n ≫ 1. This thesis investigates the quantum dynamics of interacting Rydberg-dressed ground state atoms trapped in several multi-well potential traps. Rydberg atoms are atoms with exaggerated properties. One of their most interesting properties is that they exhibit a strong and long-ranged interaction that can be tuned leading to a variety of different quantum behaviours. My work focuses on studying the effects of these interacting atoms when loaded in multi-well potential traps. Generally, multi-well systems are considered as the simplest example of a finite optical lattice structure. For this reason, this thesis covers three research topics that examine the effects of long-range interaction on Rydberg-dressed atoms trapped in several potential confinements. I begin, in the introduction, by discussing the theoretical background of relevance to this work. It starts with presenting the physics of Bose-Einstein condensate. Then, the fundamentals of the interaction between two-level atom and light are analytically studied. This study has the purpose of understanding both; the dressed interacting atoms and optical lattices. The definition, characteristics, and the nature of the interaction between Rydberg atoms are analysed afterwards. The second chapter examines the dynamics of an ensemble of interacting Rydberg- dressed atoms trapped in static, i.e., time-independent, multi-well potentials using a mean-field theoretical approach. I choose one-dimensional double- and triple-well in addition to a two-dimensional quadruple-well potentials. The time-dependent non-linear Gross-Pitaevskii equation is used to numerically explore the ensemble's quantum dynamics. Solving the dynamical differential equations along with tuning the strength of the applied long-range interaction shows that the behaviour of non-interacting Rydberg-dressed atoms does not differ conceptually according to the geometry of the trapping potential. However, this changes when the interactions are switched on where the shape of the confinement leads to interesting outcomes especially in the non-linear interacting limit, such as macroscopic quantum self-trapping. After investigating an ensemble of interacting Rydberg-dressed atoms in static multi-well potential traps, the second research topic examines the dynamical evolution of these atoms when loaded in a finite optical lattice using the extended Bose-Hubbard model. In this chapter, the atoms ensemble is assumed to be in a superfluid state where I investigate both, the order parameter when the Rydberg excitation laser is applied and the interference pattern of the condensates in different dimensions. The study shows the emerging long-range interactions lead to a rapid collapse of the superfluid order parameter and in general allow only for partial revivals. In addition, the interference experiments can directly reveal the interaction between Rydberg-dressed atoms. In the fourth chapter, the dynamics of Rydberg-dressed atoms trapped in a dynamical, i.e., time-dependent, potential confinement is presented. The dynamical trap is constructed such that it begins as a harmonic oscillator and ends as a double- well potential. The analysis investigates an ensemble of contact-interacting atoms via the time-dependent non-linear GP equation.

An interdisciplinary study concerning the durability of adhesively elastomer/metal bonded joints in marine environments is reported. The generation of OH⁻ ions at the bondline due to an imposed cathodic current from an external source is suspected to be the predominant cause of failure. A surface analysis study was performed early in this research for the purpose of identifying the cause(s) of failure. Characterization of the rubber and the metal failure surfaces with XPS (X-ray Photoelectron Spectroscopy) showed similar composition on both sides and to that of the bulk degraded primer component of the adhesive. Saponification of the adhesive and the leaching of chlorine (forming HCI that attacks the oxide) are identified as two possible failure mechanisms. The locus of failure is believed to be very close to the . adhesive/oxide interface. The exposure of bulk adhesive free-standing films to different environments showed that the hydroxyl is detrimental in the environmental durability of these specimens judging by the percentage of net mass uptake. An alternate interfacial failure mechanism is also presented where the neutralization of the adhesion-promoting attachment sites (A.S.) at the interface leads to de-adhesion and whereby OH⁻ ions chemically break-up the -COOH-Fe bond forming a non-operative activated complex at the degraded crack tip. Debond, or loss of adhesion, can exist in two modes. Weakening denotes debond growth which takes place undetected to the naked eye, and is governed by a diffusion-control degradation process that gives a straight line when plotted against the square root of time. Delamination, on the other hand, is a "post weakening" process., Debond rates in this mode are influenced by the applied total strain energy release rate, GT, and by the environment and can be described by an exponential function in GT. The effect of shear stress on debond acceleration was determined to be minimal. While compressive stresses seem to be beneficial in slowing the ingression of the bulk hydroxyl into the bondline, no noticeable improvement was detected when an imposed current was used. The use of zinc phosphate-coated steel substrates is shown to improve bond durability significantly at low voltages. Similar trends are observed when silane (γ-aminopropyltrimethoxy) modified primer were used in bonding. Two approaches are used in order to model debonding: empirical and analytical. Statistical Analysis System (SAS) is used to fit the empirical model which draws heavily on the functional dependencies of debond rates on the accelerating parameters, i.e., temperature, stress, and applied voltage. An Arrhenius relationship is shown to model the effect of temperature very well. Also, voltage effect is correlated with the corresponding current densities which, in turn, were found to obey an exponential relationship with debond rates. SAS fits of the experimental data are shown to model the process accurately and could be utilized for life predictions. Integration of delamination rates in real time is a feasible method to predict durability as well. A generalized analytical model for debonding is also developed, and it draws on the similarities between this application and corrosion fatigue of metals. The model is based on the conservation of mass of the involved species and is composed of a system of partial equations and their associated boundary conditions. Furthermore, temperature and voltage-dependent diffusion coefficients and reaction rate constants were used. The resulting boundary value problem amounts to a diffusion-chemical reaction mechanism into which a mechano-chemical failure mechanism is incorporated. A simplified version of the full scale analytical model is solved numerically and some interesting conclusions concerning the failure criterion are drawn. The model also simulates the weakening and delamination behavior and allows for temperature and voltage treatment as well. Delay times are also predicted as a function of the applied voltage and temperature. A particularly important conclusion is that the "marching boundary" phenomena seems to account for most of the accelerating influence of applied G.