On the solutions of the Schrodinger equation with some molecular potentials: wave function ansatz

Making an ansatz to the wave function, the exact solutions of the $D$% -dimensional radial Schrodinger equation with some molecular potentials like pseudoharmonic and modified Kratzer potentials are obtained. The restriction on the parameters of the given potential, $\delta$ and $\eta$ are also given, where $\eta$ depends on a linear combination of the angular momentum quantum number $\ell$ and the spatial dimensions $D$ and $\delta$ is a parameter in the ansatz to the wave function. On inserting D=3, we find that the bound state eigensolutions recover their standard analytical forms in literature.Comment: 14 page

Exact solutions of the radial Schrodinger equation for some physical potentials

By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and Kratzer potentials in two dimensions. The energy levels of all the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained.Comment: 13 page

A General Approach for the Exact Solution of the Schrodinger Equation

The Schr\"{o}dinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schr\"{o}dinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.Comment: 20 page

Nonequilibrium Kondo Effect in a Multi-level Quantum Dot near singlet-triplet transition

The linear and nonlinear transport through a multi-level lateral quantum dot connected to two leads is investigated using a generalized finite-$U$ slave-boson mean field approach. For a two-level quantum dot, our calculation demonstrates a substantial conductance enhancement near the degeneracy point of the spin singlet and triplet states, a non-monotonic temperature-dependence of conductance and a sharp dip and nonzero bias maximum of the differential conductance. These agree well with recent experiment observations. This two-stage Kondo effect in an out-of-equilibrium situation is attributed to the interference between the two energy levels.Comment: 4 pages, 3 figure

Boundary element simulation of oscillating foil with leading-edge separation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (leaves 107-110).In this thesis, we develop a numerical model to account for the leading-edge separation for the boundary element simulation of the oscillating foil with potential flow assumption. Similar to the trailing-edge separation, the leading-edge separation is modeled by a thin shear layer. Because the leading edge is rounded which is different from the sharp trailing edge, the location for leading-edge separation is extremely difficult to predetermine especially when the flow is unsteady. For unsteady flows, the position of the leading-edge separation may vary with time. However, we present a criterion that is related to the adverse pressure gradient to predict the location for the leading-edge separation. Because of the Lagrange scheme of the wake relaxation in the boundary element simulation, the leading-edge wake sheet goes into or through the thin foil easily. In order to solve the problem of the wake penetration into the foil, we present an algorithm to deal with the penetration of the leading-edge wake into the foil body. We simulate the oscillating foil in heaving-pitching motions with our leading-edge model by the boundary element method to compare with the experiments.(cont.) Without accounting for leading-edge separation, the predictions of the thrust coefficient and the propulsion efficiency of a heaving-pitching foil are good only when the Strouhal number or the maximum angle of attack is small. With our model of the leading-edge separation, the predictions are improved significantly at a larger range of Strouhal numbers or maximum angles of attack because leading-edge separation becomes significant at large Strouhal numbers or maximum angles of attack. Further possible improvements of this leading-edge separation model are discussed.by Xiaoxia Dong.S.M

Biologically-inspired robots for stage performance

Thesis (S.M.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 46-47).Stage performances present many challenges and opportunities in the field of robotics. Onstage robots not only have to function flawlessly, they must interact convincingly with their human counterparts and adhere to a rigid timeline. The scope of this work is to create set pieces that look and behave like organic entities for the production of Tod Machover's new opera, Death and the Powers. With a set of design rules and techniques, I have developed the mechanical and control systems, including their interactive behavior, for several performance-ready robots. A six-legged walking robot and transformable robot were first built to verify the adopted design methodology prior to the prototyping of onstage robots. In addition, the robots were certified as performance-ready according to four criteria: the visual appearance, the overall functionality, the quality of movement, and the fluency of human-robot interaction. Two robots were successfully built and tested for use in the opera of Death and the Powers.by Wei Dong.S.M

Innovative color management methods for RGB printing

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.Includes bibliographical references (leaf 50).Re-calibrating a printer in response to systematic changes is measurement and labor intensive. In this study, a fast correction method with cycle-to-cycle control was proposed. The process includes two steps: the creation of look-up table using a characterization data set, and image color compensation in conjunction with Windows printing architecture. Several types of correction models for determining printer characterization were proposed and evaluated, including polynomial models and neural network models. The most successful of these methods was the quadratic spline interpolation model, which removed most errors introduced by the changes of colorant and printing substrate. A significant reduction in error was realized by incorporating this technique into the color management program.by Wei Dong.M.Eng

Out of equilibrium: understanding cosmological evolution to lower-entropy states

Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing the thermodynamic arrow of time. We study the time development of such fluctuations, especially the very large fluctuations relevant to cosmology. Under fairly general assumptions, the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium. We use this idea to elucidate the spacetime structure of various fluctuations in (stable and metastable) de Sitter space and thermal anti-de Sitter space.Comment: 27 pages, 11 figure

Research on parameters optimization of bilateral ring gear blank-holder in thick-plate fine blanking

To compensate for the poor quality of thick-plate blanking parts in cross-section, this paper suggests using the optimizing bilateral ring gear holder parameters to increase burnish zone and improve cutting precision. With the bilateral gear ring, the hydrostatic pressure of shear deformation zone will increase, plasticity of the material will be lifted to maximum and quality of the cross section will be raised. This paper establishes 8mm AISI-1020 fine blanking model by DEFORM2D, analysis different ring gear parameters and clearance that are influenced the stress-strain and cross section quality to predict forming defects. By using the bilateral gear ring blank holder, the poor quality of thick-plate blanking section is successfully enhanced. Therefore, the bilateral gear ring blank holder is vital to improve the quality of blanking parts and provide the reliable theory basis for the practical engineering application