Abstract: The nonlinear Schrodinger equation is solved on an infinitesimal thin ring or circle. We obtained the exact real wave functions with their corresponding energies for the ground state and the excited states. Critical values of the circle perimeter are found at which the ground state changes its structure and additional higher excited states appear. Also, the complex wave functions that correspond to energy levels with finite angular momentum are studied.

Abstract: Janus particles present an important class of building blocks for directional assembly. These are compartmentalized colloids with two different hemispheres. Here, we consider a two-dimensional model of Janus disks consisting of a hydrophobic semicircle and an electro-negatively charged one. Placed in a solution, the hydrophobic sides will attract each other while the charged sides will give rise to a repulsive force. Using molecular dynamics simulations, we study the morphology of these particles when confined in a channel-like environment using a one dimensional harmonic confinement potential. The interest to this system is first of all due to the fact that it could serve as a simple model for membrane formation. Indeed, the recently synthesized new class of artificial amphiphiles, known as Janus dendrimers, were shown to self-assemble in bilayer structures mimicking biological membranes. In turn, Janus particles that combine the amphiphilicity and colloidal rigidity serve as a good model for Janus dendrimers. A variety of ordered membrane-like morphologies are found consisting of single and multiple chain configurations with different orientations of the particles with respect to each other that we summarize in a phase diagram.

Abstract: Water confined between two graphene layers with a separation of a few A forms a layered two-dimensional ice structure. Using large scale molecular dynamics simulations with the adoptable ReaxFF interatomic potential we found that flat monolayer ice with a rhombic-square structure nucleates between the graphene layers which is nonpolar and nonferroelectric. We provide different energetic considerations and H-bonding results that explain the interlayer and intralayer properties of two-dimensional ice. The controversial AA stacking found experimentally [Algara-Siller et al., Nature (London) 519, 443 (2015)] is consistent with our minimum-energy crystal structure of bilayer ice. Furthermore, we predict that an odd number of layers of ice has the same lattice structure as monolayer ice, while an even number of ice layers exhibits the square ice AA stacking of bilayer ice.

Abstract: Two-dimensional (2D) honeycomb ferromagnets, such as monolayer chromium trihalides, are predicted to behave as topological magnon insulators, characterized by an insulating bulk and topologically protected edge states, giving rise to a thermal magnon Hall effect. Here we report the behavior of the topological magnons in monolayer CrI3 under external stimuli, including biaxial and uniaxial strain, electric gating, as well as in-plane and out-of-plane magnetic field, revealing that one can thereby tailor the magnetic states as well as the size and the topology of the magnonic bandgap. These findings broaden the perspective of using 2D magnetic materials to design topological magnonic devices.

Abstract: We derive an analytical model for the electrostatics and the drive current in a silicon nanowire operating in JFET mode. We show that there exists a range of nanowire radii and doping densities for which the nanowire JFET satisfies reasonable device characteristics. For thin nanowires we have developed a self-consistent quantum mechanical model to obtain the electronic structure.

Abstract: We theoretically investigate the phonon, surface roughness and ionized impurity limited low-field mobility of ultrathin silicon n-type nanowire junctionless transistors in the long channel approximation with wire radii ranging from 2 to 5 nm, as function of gate voltage. We show that surface roughness scattering is negligible as long as the wire radius is not too small and ionized impurity scattering is the dominant scattering mechanism. We also show that there exists an optimal radius where the ionized impurity limited mobility exhibits a maximum.

Abstract: Using a particle based model, we investigate the skyrmion dynamical behavior in a channel where the upper wall contains divots of one depth and the lower wall contains divots of a different depth. Under an applied driving force, skyrmions in the channels move with a finite skyrmion Hall angle that deflects them toward the upper wall for -x direction driving and the lower wall for +x direction driving. When the upper divots have zero height, the skyrmions are deflected against the flat upper wall for -x direction driving and the skyrmion velocity depends linearly on the drive. For +x direction driving, the skyrmions are pushed against the lower divots and become trapped, giving reduced velocities and a nonlinear velocity-force response. When there are shallow divots on the upper wall and deep divots on the lower wall, skyrmions get trapped for both driving directions; however, due to the divot depth difference, skyrmions move more easily under -x direction driving, and become strongly trapped for +x direction driving. The preferred -x direction motion produces what we call a Magnus diode effect since it vanishes in the limit of zero Magnus force, unlike the diode effects observed for asymmetric sawtooth potentials. We show that the transport curves can exhibit a series of jumps or dips, negative differential conductivity, and reentrant pinning due to collective trapping events. We also discuss how our results relate to recent continuum modeling on a similar skyrmion diode system.

Abstract: In this study, reactivity of single-layer GaAs against Ge atoms is studied by means of ab initio density functional theory calculations. Firstly, it is shown that Ge atoms interact quite strongly with the GaAs layer which allows the formation of Ge islands while it hinders the growth of detached germanene monolayers. It is also predicted that adsorption of Ge atoms on GaAs single-layer lead to formation of two novel stable single-layer crystal structures, namely 1H-GaGeAs and 1H(A)-GaGeAs. Both the total energy optimizations and the calculated vibrational spectra indicate the dynamical stability of both single layer structures. Moreover, although both structures crystallize in 1H phase, 1H-GaGeAs and 1H(A)-GaGeAs exhibit distinctive vibrational features in their Raman spectra which is quite important for distinguishing the structures. In contrast to the semiconducting nature of single-layer GaAs, both polytypes of GaGeAs exhibit metallic behavior confirmed by the electronic band dispersions. Furthermore, the linear-elastic constants, in-plane stiffness and Poisson ratio, reveal the ultrasoft nature of the GaAs and GaGeAs structures and the rigidity of GaAs is found to be slightly enhanced via Ge adsorption. With their stable, ultra-thin and metallic properties, predicted single-layer GaGeAs structures can be promising candidates for nanoscale electronic and mechanical applications.

Abstract: Lasers can be used for many applications including determination of size, in addition to the theory of diffraction and material dispersion phenomena. In this paper we calculated the corrections in angular intensity for the Gaussian and uniform particle distributions, the scattering intensity on cylindrical objects. We also evaluated the necessary mathematical summations. In addition, we analyse and Simulate the special positions of detectors using laser Doppler anemometric (LDA) methods, which can be used to determine the particle diameter. The dispersion measurements for actual fibres are given at the end. The geometric and material parameters of these fibres were taken before the evaluation of the angular scattering intensity.

Abstract: Carefully converged calculations are performed for the band gap of ZnO within many-body perturbation theory (G0W0 approximation). The results obtained using four different well-established plasmon-pole models are compared with those of explicit calculations without such models (the contour-deformation approach). This comparison shows that, surprisingly, plasmon-pole models depending on the f-sum rule gives less precise results. In particular, it confirms that the band gap of ZnO is underestimated in the G0W0 approach as compared to experiment, contrary to the recent claim of Shih et al. [ Phys. Rev. Lett. 105 146401 (2010)].

Abstract: Superconductivity is one of the most important discoveries of the last century. With many applications in physics, engineering, and technology, superconductors are crucial to our way of living. Several material and engineering issues however prevent their widespread usage in everyday life. Comprehensive studies are being directed at these materials and their properties to come up with new technologies that will address these challenges and enhance their superconductive capabilities. In this context, numerical modeling plays an important role in the search of new solutions to existing material and engineering issues. The time-dependent Ginzburg-Landau (TDGL) theory is a powerful predictive tool for modeling the macroscopic behavior of superconductors. However most of the numerical algorithms developed so far are incapable of describing many basic properties of real superconducting devices, and are too slow on current hardware for large-scale numerical simulations necessary for their accurate description. Therefore, the purpose of this thesis is to develop high-performing numerical solutions that can correctly describe material features to be used as modeling tools of laboratory experiments. Some important innovations introduced in this work include the numerical modeling of nonrectangular geometrical shapes with complex electrical and insulating components, the inclusion of dynamic heating of the material, and the description of different types of material inhomogeneities. These encompass the principal features necessary for a complete description of the superconductive physics in real material samples. In this thesis a numerical solution is developed for modeling superconducting thin films and used to study the superconductive properties of three experimental configurations: the dynamics of vortex matter in a Corbino disk, the motion of ultrafast vortices in an hourglass-shaped microbridge, and the photon detection process in a meander-patterned nanowire. Moreover, a numerical solution is developed for modeling three-dimensional superconductors which are studied here for the first time in the type-I superconducting regime. These numerical algorithms are optimized to exploit the computational horsepower of graphics processing units (GPUs) and multicore central-processing unit (CPU) clusters such that they can achieve high-performance and be used to model large-scale problems previously impossible on conventional machines. Several computational tools are also designed to assist with the modeling of superconducting devices. These include a numerical library of the TDGL equations, a novel mechanism for the generation of complex geometries, a closed-form solver to conduct numerical simulations, and a graphics user interface (GUI) to visualize the dynamic behavior of superconductors. The contributions in this thesis ultimately push the boundaries on what is possible in state-of-the-art numerical modeling of superconductivity.