This thesis outlines the high intensity tabletop attosecond extreme ultraviolet laser source at the Institute for the Frontier of Attosecond Science and Technology Laboratory. First, a unique Ti:Sapphire chirped pulse amplifier laser system that delivers 14 fs pulses with 300 mJ energy at a 10 Hz repetition rate was designed and built. The broadband spectrum extending from 700 nm to 900 nm was obtained by seeding a two stage Ti:Sapphire chirped pulse power amplifier with mJ-level white light pulses from a gas filled hollow core fiber. It is the highest energy level ever achieved by a broadband pulse in a chirped pulse amplifier up to the current date. Second, using this laser as a driving laser source, the generalized double optical gating method is employed to generate isolated attosecond pulses. Detailed gate width analysis of the ellipticity dependent pulse were performed. Calculation of electron light interaction dynamics on the atomic level was carried out to demonstrate the mechanism of isolated pulse generation. Third, a complete diagnostic apparatus was built to extract and analyze the generated attosecond pulse in spectral domain. The result confirms that an extreme ultraviolet super continuum supporting 230 as isolated attosecond pulses at 35 eV was generated using the generalized double optical gating technique. The extreme ultraviolet pulse energy was ∼100 nJ at the exit of the argon gas target.

Strong Teens is a curriculum designed to help students develop the social-emotional skills needed to manage challenges and become successful socially and academically (Carrizales- Engelmann et al., 2016). Strong Teens has shown promise among adolescents, but this was the first study to evaluate the newly updated version of the intervention in a high school setting. The curriculum was implemented by a special education teacher with students at-risk for emotional and behavioral disorders. A mixed method design was used to evaluate outcomes with 16 ninth grade students. Overall findings suggest that Strong Teens was effective at improving students' social emotional knowledge over a 3-month period. However, there was a worsening of students' internalizing symptoms and teacher-student relationships. The teacher implemented the curriculum with low to moderate fidelity. Students were mostly neutral in their view of Strong Teens, while the teacher held a more favorable view. Future studies should include a larger sample size, offer training to educators on the implementation of Strong Teens, and consider using a more effective collection method to ensure students' anonymity.

The theoretical and experimental investigations presented in this thesis are primarily related to the dynamic response of inelastic multi-storey building frames subjected to strong ground motions. The main purpose is to investigate, both analytically and experimentally, those aspects of the dynamic response characteristics which are of importance in aseismic design. In the first part of the thesis, the various parameters pertaining to the structural system are varied in a systematic manner and an assessment is made of the influence of this variation on the maximum response characteristics of the dynamic system. The second part of the thesis consists of an experimental investigation into the inelastic dynamic response of multi-storey frames. The comparison of experimentally obtained inelastic response and that predicted theoretically indicated a good agreement between the two. / Thesis / Doctor of Philosophy (PhD)

The decision to adopt a formalized charter of rights is a momentous expression of a nations commitment to according and protection certain rights for its citizens. They usually contain complex and ambiguous moral concepts about which people have good faith disagreements. This thesis examines and ultimately rejects the belief put forward by Jeremy Waldron that judicial review is only democratically justifiable if the power of the last word in the interpretation of statutes and charter rights belongs to the democratically appointed legislature instead of the appointed judiciary. This thesis argues that a procedural conception of democracy is too limited and we would do better to base a justification of judicial review using a constitutional conception of democracy. It matters less which party has the authority of the final say with respects to rights-determining decisions and more on whether or not the democratic principle of equal concern for all is satisfied. This thesis introduces the concepts of deference, constitutional conventions, and principles and argues that these, among other things, will inform the constitutional theorists about which powers are actually present in a practice of judicial review. Once the contours of the practice are filled out one can then begin to deliberate about whether a particular conception of judicial review has democratic justification. / Thesis / Master of Arts (MA)

<p>Despite the unprecedented success achieved by Kohn-Sham density functional theory (KS-DFT) in the past few decades, the standard approximations used for the KS exchange-correlation functional typically lead to unacceptably large errors when applied to strongly-correlated electronic systems. Partition-DFT (P-DFT) is a formally exact reformulation of KS-DFT in which the ground-state density and energy of a system are obtained through self-consistent calculations on isolated fragments, with a partition energy introduced to account for the inter-fragment interactions. The unique advantage of this partitioning scheme lies in the fact that it adopts the electron density of fragments as the main variable, in place of the density of the entire system in KS-DFT, so that novel approximations can be constructed in terms of fragment properties. With a simple overlap approximation (OA) of the partition energy proposed for binary-partitioned systems, P-DFT is able to rectify the static correlation error caused by standard density functional approximations for strongly-correlated diatomic molecules. In this work, we first implement P-DFT on a one-dimensional (1D) real-space grid and calculate the ground-state energy and density of a series of 1D hydrogen chains using the local density approximation (LDA) as the density functional approximation for fragments. We then propose the generalized overlap approximation (GOA) and the corrected generalized overlap approximation (cGOA), which extends the applicability of OA to systems partitioned into more than two fragments. Combining LDA with cGOA leads to quantitatively correct dissociation curves of hydrogen chains. The static correlation error of LDA is suppressed by cGOA in the strongly-correlation regime when the calculations are performed in a spin-restricted manner, i.e., without the spin symmetry breaking. Additionally, GOA induces an improvement of the ground-state density upon LDA results, and hence helps P-DFT provide a better description of the density dimerization in hydrogen chains.</p>

A plethora of physical phenomena are modelled by hyperbolic partial differential equations, for which the exact solution is usually not known. Numerical methods are employed to approximate the solution to hyperbolic problems; however, in many cases it is difficult to satisfy certain physical properties while maintaining high order of accuracy. In this thesis, we develop high-order time-stepping methods that are capable of maintaining stability constraints of the solution, when coupled with suitable spatial discretizations. Such methods are called strong stability preserving (SSP) time integrators, and we mainly focus on perturbed methods that use both upwind- and downwind-biased spatial discretizations. Firstly, we introduce a new family of third-order implicit Runge–Kuttas methods with arbitrarily large SSP coefficient. We investigate the stability and accuracy of these methods and we show that they perform well on hyperbolic problems with large CFL numbers. Moreover, we extend the analysis of SSP linear multistep methods to semi-discretized problems for which different terms on the right-hand side of the initial value problem satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain augmented monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding non-additive SSP linear multistep methods. Furthermore, we develop the first SSP linear multistep methods of order two and three with variable step size, and study their optimality. We describe an optimal step-size strategy and demonstrate the effectiveness of these methods on various one- and multi-dimensional problems. Finally, we establish necessary conditions to preserve the total variation of the solution obtained when perturbed methods are applied to boundary value problems. We implement a stable treatment of nonreflecting boundary conditions for hyperbolic problems that allows high order of accuracy and controls spurious wave reflections. Numerical examples with high-order perturbed Runge–Kutta methods reveal that this technique provides a significant improvement in accuracy compared with zero-order extrapolation.

In calculus the concept of an infinite derivative – i.e. DF(x) = ±∞ – is seldom studied due to a plethora of complications that arise from this definition. For instance, in this extended sense, algebraic expressions involving derivatives are generally undefined; and two continuous functions possessing identical derivatives at every point of an interval generally differ by a non-constant function. These problems are fundamentally irremediable insofar as calculus is concerned and must therefore be addressed in a more general setting. This is quite difficult since the literature on infinite derivatives is rather sparse and seldom accessible to non-specialists. Therefore we supply a self-contained thesis on continuous functions with infinite derivatives aimed at graduate students with a background in real analysis and measure theory.  Predominately we study continuous primitives which satisfy the Luzin condition (N) by establishing a deep connection with the strong Luzin condition – a weak form of absolute continuity which has its origins in the Henstock–Kurzweil theory of integration. The main result states that a function satisfies the strong Luzin condition if and only if it can be expressed as a sum of two such primitives. Furthermore, we establish some pathological properties of continuous primitives which fail to satisfy the Luzin condition (N).

In this thesis, we study six Ginzburg-Landau minimization problems in the context of two-dimensional nematic liquid crystals with the intention of finding conditions for the existence of boundary vortices. The first minimization problem consists of the standard Ginzburg-Landau energy on bounded, simply connected domains Ω ⊂ R2 with boundary energy penalizing minimizers who stray from being parallel to some smooth S1-valued boundary function g of degree D ≥ 1. The second and third minimization problems consider the same Ginzburg-Landau energy but now with divergence and curl penalization in the interior and boundary function taken to be g = τ, the positively oriented unit tangent vector to the boundary. The remaining three problems involve minimizing the same energies, but now over the set for which all functions are precisely parallel to the given boundary data (up to a set for which their norms can be zero). These six problems are classified under two categories called the weak and strong orthogonal problems. In each of the six problems, we show that conditions exist for which sequences of minimizers converge to a limiting S1-valued vector field describing an equilibrium configuration for nematic material with defects. In some cases, energy estimates are obtained that show vortices belong to the boundary exclusively and the exact number of these vortices are known. A special case is also studied in the strong orthogonality setting. The analysis here suggests that geometries exist for which boundary vortices may be energetically preferable to interior vortices in the case where interior and boundary vortices have similar energy contributions. / Thesis / Doctor of Philosophy (PhD)

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