<p> Cooper pairs are known to tunnel through a barrier between superconductors in a Josephson junction. The spin states of the pairs can be a mixture of singlet and triplet states when the barrier is an inhomogeneous magnetic material. The purpose of this thesis is to better understand the behavior of pair correlations in the ballistic regime for different magnetic configurations and varying physical parameters. We use a tight-binding Hamiltonian to describe the system and consider singlet-pair conventional superconductors. Using the Bogoliubov-Valatin transformation, we derive the Bogoliubov-de Gennes equations and numerically solve the associated eigenvalue problem. Pair correlations in the magnetic Josephson junction are obtained from the Green's function formalism for a superconductor. This formalism is applied to Josephson junctions composed of discrete and continuous magnetic materials. The differences between representing pair correlations in the time and frequency domain are discussed, as well as the advantages of describing the Gor'kov functions on a log scale rather than the commonly used linear scale, and in a rotating basis as opposed to a static basis. Furthermore, the effects of parameters such as ferromagnetic width, magnetization strength, and band filling will be investigated. Lastly, we compare results in the clean limit with known results in the diffusive regime.</p><p>

<p> In this dissertation, Large Eddy Simulations (LES) are used to model the coupled turbulence-reactive tracer dynamics within the upper mixed layer of the ocean. Prior work has shown that LES works well over the spatial and time scales relevant to both turbulence and reactive biogeochemistry. Additionally, the code intended for use is able to carry an arbitrary number of tracer equations, allowing for easy expansion of the species reactions. Research in this dissertation includes a study of 15 idealized non-reactive tracers within an evolving large-scale temperature front in order determine and understand the fundamental dynamics underlying turbulence-tracer interaction in the absence of reactions. The focus of this study, in particular, was on understanding the evolution of biogeochemically-relevant, non-reactive tracers in the presence of both large (~5 km) submesoscale eddies and smallscale (~100 m) wave-driven Langmuir turbulence. The 15 tracers studied have different initial, boundary, and source conditions and significant differences are seen in their distributions depending on these conditions. Differences are also seen between regions where submesoscale eddies and small-scale Langmuir turbulence are both present, and in regions with only Langmuir turbulence. A second study focuses on the examination of Langmuir turbulence effects on upper ocean carbonate chemistry. Langmuir mixing time scales are similar to those of chemical reactions, resulting in potentially strong tracer-flow coupling effects. The strength of the Langmuir turbulence is varied, from no wave-driven turbulence (i.e., only shear-driven turbulence), to Langmuir turbulence that is much stronger than that found in typical upper ocean conditions. Three different carbonate chemistry models are also used in this study: time-dependent chemistry, equilibrium chemistry, and no-chemistry (i.e., non-reactive tracers). The third and final study described in this dissertation details the development of a reduced-order biogeochemical model with 17 state equations that can accurately reproduce the Bermuda Atlantic Time-series Study (BATS) ecosystem behavior, but that can also be integrated within high-resolution LES.</p><p>

<p> Low-order numerical methods are widespread in academic solvers and ubiquitous in industrial solvers due to their robustness and usability. High-order methods are less robust and more complicated to implement; however, they exhibit low numerical dissipation and have the potential to improve the accuracy of flow simulations at a lower computational cost when compared to low-order methods. This motivates our development of a high-order compact method using Huynh's flux reconstruction scheme for solving unsteady incompressible flow on unstructured grids. We use Chorin's classic artificial compressibility formulation with dual time stepping to solve unsteady flow problems. In 2D, an implicit non-linear lower-upper symmetric Gauss-Seidel scheme with backward Euler discretization is used to efficiently march the solution in pseudo time, while a second-order backward Euler discretization is used to march in physical time. We verify and validate implementation of the high-order method coupled with our implicit time stepping scheme using both steady and unsteady incompressible flow problems. The current implicit time stepping scheme is proven effective in satisfying the divergence-free constraint on the velocity field in the artificial compressibility formulation. The high-order solver is extended to 3D and parallelized using MPI. Due to its simplicity, time marching for 3D problems is done explicitly. The feasibility of using the current implicit time stepping scheme for large scale three-dimensional problems with high-order polynomial basis still remains to be seen. </p><p> We directly use the aforementioned numerical solver to simulate pulsatile flow of a Newtonian blood-analog fluid through a rigid 180-degree curved artery model. One of the most physiologically relevant forces within the cardiovascular system is the wall shear stress. This force is important because atherosclerotic regions are strongly correlated with curvature and branching in the human vasculature, where the shear stress is both oscillatory and multidirectional. Also, the combined effect of curvature and pulsatility in cardiovascular flows produces unsteady vortices. The aim of this research as it relates to cardiovascular fluid dynamics is to predict the spatial and temporal evolution of vortical structures generated by secondary flows, as well as to assess the correlation between multiple vortex pairs and wall shear stress. We use a physiologically (pulsatile) relevant flow rate and generate results using both fully developed and uniform entrance conditions, the latter being motivated by the fact that flow upstream of a curved artery may not have sufficient straight entrance length to become fully developed. Under the two pulsatile inflow conditions, we characterize the morphology and evolution of various vortex pairs and their subsequent effect on relevant haemodynamic wall shear stress metrics.</p><p>

<p> Computational fluid dynamic (CFD) simulations were conducted on a known low aspect ratio wing design as well as four variant designs incorporating Coanda effect circulation control (CC) for lift generation. The U.S. Navy&rsquo;s Kestrel code was employed to explore the relation of slot height and lip thickness to maximize lift augmentation. Reynolds Averaged Navier-Stokes calculations were performed at a Reynolds number of 2.1 million over wing configurations with a 1 ft span and chord with top slot flow blowing coefficients of 0, 0.005, 0.05, 0.1, and 0.15 over the angles of attack of 0&deg;, 4&deg;, 8&deg;, 14&deg;, and 18&deg;. The computational results were compared to experimental measurements of slot unblown and blown configurations. General findings include higher lift augmentation ratios of modified designs with similar lip thickness and larger slot gap. Greater lift coefficients were found with larger lip thicknesses and smaller slot heights.</p><p>

Soft materials have attracted considerable interest in recent years for predicting the characteristics of phase separation and self-assembly in nanoscale structures. A popular method for demonstrating and simulating the dynamic behaviour of particles (e.g. particle tracking) and to consider effects of simulation parameters is cell dynamic simulation (CDS). This is a cellular computerisation technique that can be used to investigate different aspects of morphological topographies of soft material systems. The acquisition of quantitative data from particles is a critical requirement in order to obtain a better understanding and of characterising their dynamic behaviour. To achieve this objective particle tracking methods considering quantitative data and focusing on different properties and components of particles is essential. Despite the availability of various types of particle tracking used in experimental work, there is no method available to consider uniform computational data. In order to achieve accurate and efficient computational results for cell dynamic simulation method and particle tracking, two factors are essential: computing/calculating time-scale and simulation system size. Consequently, finding available computing algorithms and resources such as sequential algorithm for implementing a complex technique and achieving precise results is critical and rather expensive. Therefore, it is highly desirable to consider a parallel algorithm and programming model to solve time-consuming and massive computational processing issues. Hence, the gaps between the experimental and computational works and solving time consuming for expensive computational calculations need to be filled in order to investigate a uniform computational technique for particle tracking and significant enhancements in speed and execution times. The work presented in this thesis details a new particle tracking method for integrating diblock copolymers in the form of spheres with a shear flow and a novel designed GPU-based parallel acceleration approach to cell dynamic simulation (CDS). In addition, the evaluation of parallel models and architectures (CPUs and GPUs) utilising the mixtures of application program interface, OpenMP and programming model, CUDA were developed. Finally, this study presents the performance enhancements achieved with GPU-CUDA of approximately ~2 times faster than multi-threading implementation and 13~14 times quicker than optimised sequential processing for the CDS computations/workloads respectively.

Complex interactions between solid, liquid and gas occur in many practical engineering applications, and are often difficult to quantify experimentally. A few examples include boiling over solid heaters, solidification melt-dynamics in metal casting, and convective cooling of electronic components. With the availability of scalable computational tools, high-fidelity simulations can provide new insight into these phenomena and answer open questions. In the present work, a multiphase solver is presented which can simulate problems involving phase transition over complex geometries. The dynamics of liquid-gas interface are modeled using a level-set technique, which utilizes Ghost Fluid Method (GFM) to account for sharp jump in pressure, velocity, and temperature across the multiphase boundary. The fluid-solid interactions are modeled using an Immersed Boundary Method (IBM) which uses a Moving Least Squared (MLS) reconstruction to calculate fluid-flow around the solid, along with an additional GFM forcing to model its effect on pressure, temperature and Conjugate Heat Transfer (CHT). The resulting three dimensional solver is fully explicit in time and uses a fractional step method for Navier-Stokes, energy, and mass transfer equations. Validation and verification cases are presented to demonstrate the accuracy of the solver in comparison to experimental and analytical problems, and results of high fidelity pool boiling simulations in varying gravity environments are discussed in detail.

Quantum revolution has a great potential to impose massive impact on information technology. Point defects in solid-state materials such as NV center in diamond have been demonstrated to be promising qubit candidates. Defect levels in band gaps are analogous to molecular orbitals, serving as an excellent platform for quantum applications. Atomically thin two-dimensional materials are under the spotlight in recent years, as the sheet-like geometry brings advantages for operations of quantum defects. That includes the realization of patterned qubit fabrication, operation at room temperature, and improvement of coherence time through a highly-efficient isotope purification process. Although using point defects in 2D materials is a promising route toward quantum applications, searching for viable defects satisfying the criteria of magneto-optical properties for quantum applications is challenging. Thanks to the continued development of density functional theory, sophisticated multi-electron systems can be accurately simulated on the atomistic level to evaluate multiple ground-state properties, including total energy, magnetic polarization, and atomic orbitals. In addition to that, implementing constrained DFT renders the insight of excited-state properties. Benefited from the application of data-science tools in material science, we are now capable of performing data-driven analysis based on high-throughput computational techniques, including data mining/storage and automatic discovery workflow. Adopting the above tools and physical-principle-enabled symmetry analysis, we are able to identify a large set of quantum defects in a vast material space. We show that antisite defects in 2D transition metal dichalcogenides (TMDs) can provide a general platform for controllable solid-state spin qubit systems. Using high-throughput atomistic simulations that are enabled by a symmetry-based hypothesis, we identify several neutral antisite defects in TMDs that create defect levels deep in the bulk band gaps and host a paramagnetic triplet ground state. Our in-depth analysis reveals the presence of optical transitions and triplet-singlet intersystem crossing processes for fingerprinting these defect qubits. Finally, as an illustrative example, we discuss the initialization and readout principles of an antisite qubit in WS2, which is expected to be stable against interlayer interactions in a multilayer structure for qubit isolation and protection in future qubit-based devices. Motivated by the insight gained from the study of antisite defect qubits in TMDs, we significantly expanded the searching domain to all the binary 2D materials. As mentioned above, searching for defects with triplet ground states is one of the most crucial steps to identify more quantum defects that support multiple quantum functionalities. We design a comprehensive workflow for screening promising quantum defects based on the site-symmetry-based hypothesis. The discovery efforts reveal that the symmetry-enabled discovery workflow of quantum defects significantly increases the probability of finding triplet defects. To identify multiple functionalities for these quantum defects, including qubits and quantum emitters, the magneto-optical properties of triplet defects are comprehensively calculated. We demonstrate that 45 antisite defects in the various hosts, including post-transition metal monochalcogenides (PTMCs) and transition metal dichalcogenides (TMDs) are promising quantum defects. Most importantly, we propose that 16 antisites (both anion and cation based) in PTMCs can serve as the most promising quantum defect platform based on 2D materials, due to their well-defined defect levels, optimal magneto-optical properties, and the availability of host materials. This set of data-driven discovery efforts opens a new pathway for creating scalable, room-temperature spin qubits in 2D materials, including TMDs, PTMCs, and beyond. The comprehensive defect data created in this work, combined with experimental verification and demonstration in the future, will eventually lead to the fertilization of a 2D defect design platform that facilitates the design of point defects in 2D material families for multiple quantum functionalities, including quantum emitters, quantum sensor, transductor, and more. / Physics

No description available.

Kohn-Sham density functional theory is a widely-used method to predict the ground-state total energies and densities of interacting correlated electrons in atoms, molecules, clusters, solids, and liquids. In principle, exact results for these properties can be found by solving self-consistent one-electron Schrödinger equations based upon density functionals for the energy. In practice, the density functional for the exchange-correlation contribution to the energy must be approximated for the sake of computational efficiency. More accurate but still computationally efficient approximations are being developed by the satisfaction of exact constraints. These include the SCAN (strongly constrained and appropriately normed) semi-local density functional. We used the pressure induced structural phase transition of solids to validate SCAN. To predict an accurate critical pressure, a method must account for a small energy difference between close-lying phases which have very different electronic structures. We computed the critical pressure for the structural phase transition of 25 group IV, III-V, and II-VI compounds using the local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE), and SCAN. LDA systematically underestimates the critical pressures as reported in a previous study. PBE which often improves upon LDA performances yields under- or overestimated pressures in many cases. SCAN, on the other hand, predicts accurate critical pressures with an accuracy comparable to the computationally expensive methods like the quantum Monte Carlo (QMC), random phase approximation (RPA), and the hybrid functional HSE06, in the cases where pressures with these methods are reported. The impressive success of the approximate density functionals, however, comes at a price. There is an incomplete cancellation of the hartree and approximate exchange energies for one-electron densities, giving rise to a spurious interaction of an electron with itself. This is called the self-interaction error (SIE). Perdew-Zunger self-interaction correction (PZ SIC) makes an approximate density functional SIE free for all one-electron density. The transition states, which involve stretched bonds, are poorly described by the semilocal density functionals. Thus LDA, PBE, and SCAN predict too low barrier height for a chemical reaction. We tested the Perdew-Zunger self-interaction correction (PZ SIC) for the barrier heights of the representative test set BH6. We found that the barrier heights are greatly improved when we go from LDA to PBE to SCAN. We also tested the PZ SIC for the atomization energies of the molecular test set AE6. SCAN predicts very accurate atomization energies, whereas SCAN-SIC severely worsens the atomization energies. We attribute such worsening to the noded localized orbitals, over which the PZ energy is minimized. The nodality of the orbital density is a consequence of the orthogonality criterion for overlapping real orbitals, and this nodality increases when free atoms bind to form a molecule. This explains why the error in the atomization energies is reduced when the PZ energy is minimized using complex orbitals, which yield nodeless orbital densities. The complex orbitals, however, do not completely eliminate the error. The remaining error is attributed to the fact that PZ SIC loses the exactness of LDA, PBE, or SCAN for densities that vary slowly over space, calling for a generalization of the PZ theory. / Physics

We calculate the strange quark content of the nucleon, <N|ss|N> − <0|ss|0> using a novel method with the MILC lattice QCD gauge ensembles. The strangeness of the nucleon is related to the interaction cross section between dark matter and ordinary nuclear matter (e.g. in detectors) in many models. Previous results for this quantity suffered from uncontrolled systematic errors and/or large statistical uncertainties. The first result using our methods was the first modern calculation of the strangeness of the nucleon[76] with good control of systematic errors and reasonably small statistical errors, greatly reducing the uncertainty in dark matter detection cross sections. A refinement of this method allows for further reduction of statistical error. On the MILC Asqtad data, we obtain <N|ss|N> = 0.637(55)(stat)(74)(sys). The results obtained from this method are consistent with those obtained from other commonly-used methods applied to the MILC data. We also calculate the disconnected part of the pion-nucleon sigma term and the intrinsic charm of the nucleon using this method. The intrinsic charm has large statistical errors but is consistent with a perturbative calculation.