Quantum scattering in the strip: From ballistic to localized regimes

Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition between the ballistic and the localized regimes. By considering the cylinder geometry and introducing the magnetic flux we are able to study time reversal symmetry breaking in the system. Both macroscopic (conductance) and microscopic (eigenphases distribution, statistics of S-matrix elements) characteristics of the system are examined. Received: 28 January 1998 / Revised: 16 June 1998 / Accepted: 6 July 1998     

Multiple Cuts with a Homogeneous Analytic Center Cutting Plane Method

This paper analyzes the introduction of multiple central cuts in a conic formulation of the analytic center cutting plane method (in short ACCPM). This work extends earlier work on the homogeneous ACCPM, and parallels the analysis of the multiple cut process in the standard ACCPM. The main issue is the calculation of a direction that restores feasibility after introducing p new cutting planes at the query point. We prove that the new analytic center can be recovered in O(p log p) damped Newton iterations, where is a parameter depending of the data. We also present two special cases where the complexity can be decreased to O (p log p). Finally, we show that the number of calls to the oracle is the same as in the single cut case, up to a factor .     

Two Workload Properties for Brownian Networks

As one approach to dynamic scheduling problems for open stochastic processing networks, J.M. Harrison has proposed the use of formal heavy traffic approximations known as Brownian networks. A key step in this approach is a reduction in dimension of a Brownian network, due to Harrison and Van Mieghem [21], in which the queue length process is replaced by a workload process. In this paper, we establish two properties of these workload processes. Firstly, we derive a formula for the dimension of such processes. For a given Brownian network, this dimension is unique. However, there are infinitely many possible choices for the workload process. Harrison [16] has proposed a canonical choice, which reduces the possibilities to a finite number. Our second result provides sufficient conditions for this canonical choice to be valid and for it to yield a non-negative workload process. The assumptions and proofs for our results involve only first-order model parameters.     

Model management systems: A survey

This paper provides a survey of model management literature within the mathematical modeling domain. The first part of the survey is a review and a summary of the literature. After giving some basic definitions of modeling, modeling life cycle, and model management, two representative algebraic modeling languages followed by three approaches to modeling are introduced. These approaches are database, graph-based, and knowledge-based. The discussion is followed by a review of two specialized model management systems. The second part of the survey is a categorization of various modeling systems based on the modeling functions they provide and some of their features. These functions include life cycle support and model base administration. The degree of model independence provided by model management systems and the implemented environment systems is also summarized. The last part of the paper provides directions for future research.     

High-order compact exponential finite difference methods for convection–diffusion type problems

A class of high-order compact (HOC) exponential finite difference (FD) methods is proposed for solving one- and two-dimensional steady-state convection–diffusion problems. The newly proposed HOC exponential FD schemes have nonoscillation property and yield high accuracy approximation solution as well as are suitable for convection-dominated problems. The O(h⁴) compact exponential FD schemes developed for the one-dimensional (1D) problems produce diagonally dominant tri-diagonal system of equations which can be solved by applying the tridiagonal Thomas algorithm. For the two-dimensional (2D) problems, O(h⁴ + k⁴) compact exponential FD schemes are formulated on the nine-point 2D stencil and the line iterative approach with alternating direction implicit (ADI) procedure enables us to deal with diagonally dominant tridiagonal matrix equations which can be solved by application of the one-dimensional tridiagonal Thomas algorithm with a considerable saving in computing time. To validate the present HOC exponential FD methods, three linear and nonlinear problems, mostly with boundary or internal layers where sharp gradients may appear due to high Peclet or Reynolds numbers, are numerically solved. Comparisons are made between analytical solutions and numerical results for the currently proposed HOC exponential FD methods and some previously published HOC methods. The present HOC exponential FD methods produce excellent results for all test problems. It is shown that, besides including the excellent performances in computational accuracy, efficiency and stability, the present method has the advantage of better scale resolution. The method developed in this article is easy to implement and has been applied to obtain the numerical solutions of the lid driven cavity flow problem governed by the 2D incompressible Navier–Stokes equations using the stream function-vorticity formulation.     

Modified mixed Ritz-DQ formulation for free vibration of thick rectangular and skew plates with general boundary conditions

Recently, the present authors proposed a simple mixed Ritz-differential quadrature (DQ) methodology for free and forced vibration, and buckling analysis of rectangular plates. In this technique, the Ritz method is first used to discretize the spatial partial derivatives with respect to a coordinate direction of the plate. The DQ method is then employed to analogize the resulting system of ordinary or partial differential equations. The mixed method was shown to work well for vibration and buckling problems of rectangular plates with simple boundary conditions. But, due to the use of conventional Ritz method in one coordinate direction of the plate, the geometric boundary conditions of the problem can only be satisfied in that direction. Therefore, the conventional mixed Ritz-DQ methodology may encounter difficulties when dealing with rectangular plates involving adjacent free edges and skew plates. To overcome this difficulty, this paper presents a modified mixed Ritz-DQ formulation in which all the natural boundary conditions are exactly implemented. The versatility, accuracy and efficiency of the proposed method for free vibration analysis of thick rectangular and skew plates are tested against other solution procedures. It is revealed that the proposed method can produce highly accurate solutions for the natural frequencies of thick rectangular plates involving adjacent free edges and skew plates using a small number Ritz terms and DQ sampling points.