Efficient simulations with electronic open boundaries

We present a reformulation of the hairy-probe method for introducing electronic open boundaries that is appropriate for steady-state calculations involving nonorthogonal atomic basis sets. As a check on the correctness of the method we investigate a perfect atomic wire of Cu atoms and a perfect nonorthogonal chain of H atoms. For both atom chains we find that the conductance has a value of exactly one quantum unit and that this is rather insensitive to the strength of coupling of the probes to the system, provided values of the coupling are of the same order as the mean interlevel spacing of the system without probes. For the Cu atom chain we find in addition that away from the regions with probes attached, the potential in the wire is uniform, while within them it follows a predicted exponential variation with position. We then apply the method to an initial investigation of the suitability of graphene as a contact material for molecular electronics. We perform calculations on a carbon nanoribbon to determine the correct coupling strength of the probes to the graphene and obtain a conductance of about two quantum units corresponding to two bands crossing the Fermi surface. We then compute the current through a benzene molecule attached to two graphene contacts and find only a very weak current because of the disruption of the π conjugation by the covalent bond between the benzene and the graphene. In all cases we find that very strong or weak probe couplings suppress the current.

Resolved Stars' Insights into Galaxy Physics

Thesis (Ph.D.)--University of Washington, 2016-08

Improving the Accuracy of 3-D Reconstruction in Robotic Vision Applications

Thesis (Ph.D.)--University of Washington, 2016-08

Influência na qualidade final de metais retificados através da variação da velocidade de mergulho

A retificação, processo final de usinagem de uma peça, utiliza fluidos de corte com a finalidade de lubrificação, refrigeração e remoção de cavacos. No entanto, esses fluidos são extremamente agressivos com o meio. Com o avanço tecnológico a tendência mundial é produzir peças cada vez mais sofisticadas, com elevado grau de tolerância geométrica, dimensional, com bom acabamento superficial, com baixo custo e, principalmente, sem causar danos ao meio. Para tanto, ao processo de retificação está intrínseca a reciclagem do fluido de corte, que se destaca pelo seu custo. Através da variação da velocidade de avanço no processo de retificação cilíndrica externa do aço ABNT D6, racionalizando a aplicação de dois fluidos de corte e usando um rebolo superabrasivo de CBN (nitreto de boro cúbico) com ligante vitrificado, avaliaram-se os parâmetros de saída da força tangencial de corte, emissão acústica, rugosidade, circularidade, desgaste da ferramenta, tensão residual e a integridade superficial através da microscopia eletrônica de varredura (MEV) dos corpos-de-prova. Com a análise do desempenho do fluido, do rebolo e da velocidade de mergulho, encontraram-se as melhores condições de usinagem propiciando a diminuição do volume de fluido de corte e a diminuição do tempo de usinagem, sem prejudicar os parâmetros geométricos e dimensionais, o acabamento superficial e a integridade superficial dos componentes.

Landau-Gutzwiller quasi-particles

We define Landau quasiparticles within the Gutzwiller variational theory and derive their dispersion relation for general multiband Hubbard models in the limit of large spatial dimensions D. Thereby we reproduce our previous calculations which were based on a phenomenological effective single-particle Hamiltonian. For the one-band Hubbard model we calculate the frst-order corrections in 1/D and find that the corrections to the quasiparticle dispersions are small in three dimensions. They may be largely absorbed in a rescaling of the total bandwidth, unless the system is close to half band filling. Therefore, the Gutzwiller theory in the limit of large dimensions provides quasiparticle bands which are suitable for a comparison with real, three-dimensional Fermi liquids.

Minimising wave drag for free surface flow past a two-dimensional stern

Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving for the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results found using a forced KdV equation are also presented, as are numerical solutions to the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely.

Surface reconstruction of wheat leaf morphology from three-dimensional scanned data

Realistic virtual models of leaf surfaces are important for a number of applications in the plant sciences, such as modelling agrichemical spray droplet movement and spreading on the surface. In this context, the virtual surfaces are required to be sufficiently smooth to facilitate the use of the mathematical equations that govern the motion of the droplet. While an effective approach is to apply discrete smoothing D2-spline algorithms to reconstruct the leaf surfaces from three-dimensional scanned data, difficulties arise when dealing with wheat leaves that tend to twist and bend. To overcome this topological difficulty, we develop a parameterisation technique that rotates and translates the original data, allowing the surface to be fitted using the discrete smoothing D2-spline methods in the new parameter space. Our algorithm uses finite element methods to represent the surface as a linear combination of compactly supported shape functions. Numerical results confirm that the parameterisation, along with the use of discrete smoothing D2-spline techniques, produces realistic virtual representations of wheat leaves.

Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

Unsteady, three-dimensional, boundary-layer flow due to a stretching surface

Abstract is not available.

On Multi-Dimensional Packets of Surface Waves

By using the method of operators of multiple scales, two coupled nonlinear equations are derived, which govern the slow amplitude modulation of surface gravity waves in two space dimensions. The equations of Davey and Stewartson, which also govern the two-dimensional modulation of the amplitude of gravity waves, are derived as a special case of our equations. For a fully dispersed wave, symmetric about a point which moves with the group velocity, the coupled equations reduce to a nonlinear Schrödinger equation with extra terms representing the effect of the curvature of the wavefront.

Magnetotransport of Dirac fermions on the surface of a topological insulator

We study the properties of Dirac fermions on the surface of a topological insulator in the presence of crossed electric and magnetic fields. We provide an exact solution to this problem and demonstrate that, in contrast to their counterparts in graphene, these Dirac fermions allow relative tuning of the orbital and Zeeman effects of an applied magnetic field by a crossed electric field along the surface. We also elaborate and extend our earlier results on normal-metal-magnetic film-normal metal (NMN) and normal-metal-barrier-magnetic film (NBM) junctions of topological insulators [S. Mondal, D. Sen, K. Sengupta, and R. Shankar, Phys. Rev. Lett. 104, 046403 (2010)]. For NMN junctions, we show that for Dirac fermions with Fermi velocity vF, the transport can be controlled using the exchange field J of a ferromagnetic film over a region of width d. The conductance of such a junction changes from oscillatory to a monotonically decreasing function of d beyond a critical J which leads to the possible realization of magnetic switches using these junctions. For NBM junctions with a potential barrier of width d and potential V-0, we find that beyond a critical J, the criteria of conductance maxima changes from chi=eV(0)d/h upsilon(F)=n pi to chi=(n+1/2)pi for integer n. Finally, we compute the subgap tunneling conductance of a normal-metal-magnetic film-superconductor junctions on the surface of a topological insulator and show that the position of the peaks of the zero-bias tunneling conductance can be tuned using the magnetization of the ferromagnetic film. We point out that these phenomena have no analogs in either conventional two-dimensional materials or Dirac electrons in graphene and suggest experiments to test our theory.

Three-Dimensional Unsteady Flow With Heat and Mass Transfer Over a Continuous Stretching Surface

A numerical solution of the unsteady boundary layer equations under similarity assumptions is obtained. The solution represents the three-dimensional unsteady fluid motion caused by the time-dependent stretching of a flat boundary. It has been shown that a self-similar solution exists when either the rate of stretching is decreasing with time or it is constant. Three different numerical techniques are applied and a comparison is made among them as well as with earlier results. Analysis is made for various situations like deceleration in stretching of the boundary, mass transfer at the surface, saddle and nodal point flows, and the effect of a magnetic field. Both the constant temperature and constant heat flux conditions at the wall have been studied.

Unsteady three-dimensional boundary layer flow due to a stretching surface

In this numerical study, the unsteady laminar incompressible boundary-layer flow over a continuously stretching surface has been investigated when the velocity of the stretching surface varies arbitrarily with time. Both the nodal and the saddle point regions of flow have been considered for the analysis. Also, constant wall temperature/concentration and constant heat/mass flux at the stretching surface have been taken into account. The quasilinearisation method with an implicit finite-difference scheme is used in the nodal point region (0 less-than-or-equal-to c less-than-or-equal-to 1) where c denotes the stretching ratio. This method fails in the saddle point region (-1 less-than-or-equal-to c less-than-or-equal-to 0) due to the occurrence of reverse flow in the y-component of velocity. In order to overcome this difficulty, the method of parametric differentiation with an implicit finite-difference scheme is used, where the values at c = 0 are taken as starting values. Results have been obtained for the stretching velocities which are accelerating and decelerating with time. Results show that the skin friction, the heat transfer and the mass transfer parameters respond significantly to the time dependent stretching velocities. Suction (A > 0) is found to be an important parameter in obtaining convergent solution in the case of the saddle point region of flow. The Prandtl number and the Schmidt number strongly affect the heat and mass transfer of the diffusing species, respectively.

Three-dimensional computational modeling of momentum, heat, and mass transfer in a laser surface alloying process

A three- dimensional, transient model is developed for studying heat transfer, fluid flow, and mass transfer for the case of a single- pass laser surface alloying process. The coupled momentum, energy, and species conservation equations are solved using a finite volume procedure. Phase change processes are modeled using a fixed-grid enthalpy-porosity technique, which is capable of predicting the continuously evolving solid- liquid interface. The three- dimensional model is able to predict the species concentration distribution inside the molten pool during alloying, as well as in the entire cross section of the solidified alloy. The model is simulated for different values of various significant processing parameters such as laser power, scanning speed, and powder feedrate in order to assess their influences on geometry and dynamics of the pool, cooling rates, as well as species concentration distribution inside the substrate. Effects of incorporating property variations in the numerical model are also discussed.