Universal zero-bias conductance for the single electron transistor. II: Comparison with numerical results

A numerical renormalization-group survey of the zero-bias electrical conductance through a quantum dot embedded in the conduction path of a nanodevice is reported. The results are examined in the light of a recently derived linear mapping between the temperature-dependent conductance and the universal function describing the conductance for the symmetric Anderson model. A gate potential applied to the conduction electrons is known to change markedly the transport properties of a quantum dot side-coupled to the conduction path; in the embedded geometry here discussed, a similar potential is shown to affect only quantitatively the temperature dependence of the conductance. As expected, in the Kondo regime the numerical results are in excellent agreement with the mapped conductances. In the mixed-valence regime, the mapping describes accurately the low-temperature tail of the conductance. The mapping is shown to provide a unified view of conduction in the single-electron transistor.Comment: Sequel to arXiv:0906.4063. 9 pages with 8 figure

The least uncomfortable journey from A to B

A short introduction is given about direct variational methods and their relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions to difficult physicalequations. An application of these methods is given in the form of the variational problem of minimizing the discomfort experienced during different journeys, between two fixed horizontal points while keeping the travel time constant. The analysis is shown to provide simple, yet accurate, approximate solutions of the problem and illustrates the usefulness and the power of direct variational and moment methods. It also demonstrates the problem of a priori assessing the accuracy of the approximate solutions and illustrates that the variational solution does not necessarily provide a more accurate solution than that obtained by moment methods

Identification of global modeshape from a few nodal eigenvectors using simple free-form deformation

A new method, different from common eigenvalue extraction methods, was proposed by Li and Kikuchi (in 8th ARC conference, 2002). It consists of explicit finite-element method and eigenvalue-extraction method in time domain. Even though the new method performs well in extracting eigenvalues, it is difficult to identify global modeshape of the given structure due to large size of time history data. Only some eigenvectors of a few nodal points can be extracted. In this paper, we apply computer animation technique to identify the global modeshape from a few nodal eigenvectors. Free-form deformation (FFD) technique is simply modified—simple FFD—and applied to the identification of global modeshapes. The basic concepts that consist of simple FFD algorithm are Delaunay triangulation and barycentric coordinate. Some numerical examples show good performance for the identification of global modeshape of a given structure.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45917/1/366_2005_Article_314.pd