Recent studies of the transition metal dichalcogenide niobium diselenide have led to debate in the scientific community regarding the mechanism of the charge density wave (CDW) instability in this material. Moreover, whether or not CDW boosts or competes with superconductivity (SC) is still unknown, as there are experimental measurements which supports both scenarios. Motivated by these measurements we study the interplay of charge density modulations and superconductivity in the context of the Bogoliubov de-Gennes (BdG) equations formulated on a tight-binding lattice. As the BdG equations require large numerical demand, software which utilizes parallel algorithms have been developed to solve these equations directly and numerically. Calculations were performed on a large-scale Beowulf-class PC cluster at the University of Saskatchewan.<p> We first study the effects of inhomogeneity on nanoscale superconductors due to the presence of surfaces or a single impurity deposited in the sample. It is illustrated that CDW can coexist with SC in a finite-size s-wave superconductor. Our calculations show that a weak impurity potential can lead to significant suppression of the superconducting order parameter, more so than a strong impurity. In particular, in a nanoscale d-wave superconductor with strong electron-phonon coupling, the scattering by a weakly attractive impurity can nearly kill superconductivity over the entire sample.<p> Calculations for periodic systems also show that CDW can coexist with s-wave superconductivity. In order to identify the cause of the CDW instability, the BdG equations have been generalized to include the next-nearest neighbour hopping integral. It is shown that the CDW state is strongly affected by the magnitude of the next-nearest neighbour hopping, while superconductivity is not. The difference between the CDW and SC states is a result of the anomalous, or off-diagonal, coupling between particle and hole components of quasiparticle excitations. The Fermi surface is changed as next-nearest neighbour hopping is varied; in particular, the perfect nesting and coincidence of the nesting vectors and the vectors connecting van Hove singularities (vHs) for zero next-nearest neighbor hopping is destroyed, and vHs move away from the Fermi energy. It is found that within our one-band tight-binding model with isotropic s-wave superconductivity, CDW and SC can coexist only for vanishing nearest neighbor hopping and for non-zero hopping, the homogeneous SC state always has the lowest ground-state energy. Furthermore, we find in our model that as the magnitude of the next-nearest neighbor hopping parameter increases, the main cause of the divergence in the dielectric response accompanying the CDW transition changes from nesting to the vHs mechanism proposed by Rice and Scott. It is still an open question as to the origin of CDW and its interplay with SC in multiple-band, anisotropic superconductors such as niobium diselenide, for which fundamental theory is lacking. The work presented in this thesis demonstrates the possible coexistence of charge density waves and superconductivity, and provides insight into the mechanism of electronic instability causing charge density waves.

A fundamental issue in warehouse operations is the storage location of the products it contains. Placing products intelligently within the system can allow for great reductions in order pick costs. This is essential because order picking is a major cost of warehouse operations. For example, a study by Drury conducted in the UK found that 63% of warehouse operating costs are due to order picking. When orders contain a single item, the COI rule of Heskett is an optimal storage policy. This is not true when orders contain multiple line items because no information is used about what products are ordered together. In this situation, products that are frequently ordered together should be stored together. This is the basis of the correlated storage assignment problem. Several previous researchers have considered how to form such clusters of products with an ultimate objective of minimizing travel time. In this dissertation, we focus on the alternate objective of minimizing multi-zone orders. We present a mathematical model and discuss properties of the problem. A Lagrangian relaxation solution approach is discussed. In addition, we both develop and adapt several heuristics from the literature to give upper bounds for the model. A cyclic exchange improvement method is also developed. This exponential size neighborhood can be efficiently searched in polynomial time. Even for poor initial solutions, this method finds solutions which outperform the best approaches from the literature. Different product sizes, stock splitting, and rewarehousing are problem features that our model can handle. The cyclic exchange algorithm is also modified to allow these operating modes. In particular, stock splitting is a difficult issue which most previous research in correlated storage ignores. All of our algorithms are implemented and tested on data from a functioning warehouse. For all data sets, the cyclic exchange algorithm outperforms COI, the standard industry approach, by an average of 15%.

In this thesis, the development and implementation of fluorescence lifetime imaging microscopy that integrates time correlated single photon counting (TCSPC) and a confocal microscope will be described. The TCSPC method has high detection efficiency, with a time resolution limited only by the transit time spread of the detector, and directly delivers the decay functions in the time domain. TCSPC can also be used to obtain images that indicate the fluorescence resonance energy transfer (FRET) effect between critical fluorophores, an important method distinguish the difference between binding and co-localization. Estimation of distances between RET fluorophore pairs can also be established. Additionally, the effects of ion concentration, oxygen concentration, pH value, ..etc. can also be revealed.

We study timing effects of carbon mitigation and solar radiation management (SRM) policies for correlated pollutants, CO₂ and SO₂. We show that national levels of carbon and sulfur emissions quotas and SRM implementation are positively correlated with each other. First-mover advantages exist when deciding both carbon quotas and SRM levels. Moreover, we use an example to illustrate that if international equity is considered, governments would be willing to choose SRM levels before carbon quotas since it yields higher payoffs and less acid rain and droughts damages. This timing was neglected by all previous theoretical economic models on geoengineering.

This thesis focuses on the construction and role of benchmark quality computations in the area of non-covalent interactions. We have provided a detailed error analysis of focal-point schemes commonly used in benchmark quality computations, as well as provide error and speedup analysis of commonly used approximations to these methods. An analysis of basis set effects on higher-order corrections to MP2/CBS has been carried out, providing the community error bounds on future benchmarks. We demonstrate how these high-level computations can elucidate a better understanding of non-bonded interactions in chemistry as well as provide high-quality reference data to refit existing methods against to increase the overall accuracy of the method.

This thesis represents a systematic study of electronic structure of the modulation-free Pb-doped Bi2212 superconducting cuprates with respect to interlayer coupling done by using the angle-resolved photoemission spectroscopy (ARPES), which is a leading technique in the experimental investigation of the single particle excitations in solids. The results presented in this work indicate a very different origin for the observed complex spectra lineshape. Specifically, the peak-dip-hump lineshape can be easily understood in terms of the superposition of spectral features due to bilayer band splitting, namely the splitting of the CuO2 plane derived electronic structure in bonding and antibonding bands due to the interlayer coupling of CuO2 bilayer blocks within the unit cell of Bi2212. By performing experiments at synchrotron beamlines where the energy of the incoming photons can be tuned over a very broad range, the detailed matrix elements energy dependence for both bonding and antibonding bands was determined. This gave the opportunity to study the electronic properties these two bands separately. For the first time, it was proved that the superconducting gap has the same value and symmetry for both bands. Furthermore, having recognized and sorted out the bilayer splitting effects, it became possible to identify more subtle effects hidden in the details of the ARPES lineshapes. On underdoped samples an &amp;quot;intrinsic&amp;quot; peak-dip-hump structure due to the interaction between electrons and a bosonic mode was observed. Studying the doping, temperature, and momentum dependence of the photoemission spectra it was established that: the mode has a characteristic energy of 38-40 meV and causes strong renormalization of the electronic structure only in the superconducting state; the electron-mode coupling is maximal around the (?à,0) point in momentum space and is strongly doping dependent (being greatly enhanced in the underdoped regime). From the above, it was concluded that the bosonic mode must correspond to the sharp magnetic resonance mode observed in inelastic neutron scattering experiments, and that this coupling is relevant to superconductivity and the pairing mechanism in the cuprates.

In the paper asymptotic expansions for second-order moments of integral functionals of a class of random functions are considered. The random functions are assumed to be $\epsilon$-correlated, i.e. the values are not correlated excluding a $\epsilon$-neighbourhood of each point. The asymptotic expansions are derived for $\epsilon \to 0$. With the help of a special weak assumption there are found easier expansions as in the case of general weakly correlated functions.

This paper is devoted to the computation of statistical characteristics of the response of discrete vibration systems with a random external excitation. The excitation can act at multiple points and is modeled by a time-shifted random process and its derivatives up to the second order. Statistical characteristics of the response are given by expansions as to the correlation length of a weakly correlated random process which is used in the excitation model. As the main result analytic expressions of some integrals involved in the expansion terms are derived.

The paper considers approximations of time-continuous epsilon-correlated random processes by interpolation of time-discrete Moving-Average processes. These approximations are helpful for Monte-Carlo simulations of the response of systems containing random parameters described by epsilon-correlated processes. The paper focuses on the approximation of stationary epsilon-correlated processes with a prescribed correlation function. Numerical results are presented.

Empirical autocorrelation functions of returns of stochastic price processes show phenomena of correlation on small intervals of time, which decay to zero after a short time. The paper deals with the concept of weakly correlated random processes to describe a mathematical model which takes into account this behaviour of statistical data. Weakly correlated functions have been applied to model numerous problems of physics and engineering. The main idea is, that the values of the functions at two points are uncorrelated if the distance between the points exceeds a certain quantity epsilon > 0. In contrast to the white noise model, for distances smaller than epsilon a correlation between the values is permitted.