Z-transform implementation of the perfectly matched layer for truncating FDTD domains

A simple algorithm for implementing the perfectly matched layer (PML) is presented for truncating finite difference time domain (FDTD) computational domains. The algorithm is based on incorporating the Z-transform method into the PML FDTD implementation. The main advantage of the algorithm is its simplicity as it allows direct FDTD implementation of Maxwell's equations in the PML region. In addition, the formulations are independent of the material properties of the FDTD computational domain. Numerical examples are included to demonstrate the effectiveness of these formulations.     

A Bound for the Order of Characteristic Set Elements of an Ordinary Prime Differential Ideal and some Applications

With respect to an elimination ordering, we give an upper bound for the order of characteristic set elements of an ordinary prime differential ideal. Using some results of complexity in the algebraic case, we show that computing characteristic sets of ordinary prime differential ideals, by change of ordering, is single exponential time. Received: January 8, 1997; revised version: May 6, 1999     

Teacher beliefs and technology integration practices: A critical relationship

Early studies indicated that teachers’ enacted beliefs, particularly in terms of classroom technology practices, often did not align with their espoused beliefs. Researchers concluded this was due, at least in part, to a variety of external barriers that prevented teachers from using technology in ways that aligned more closely with their beliefs. However, many of these barriers (access, support, etc.) have since been eliminated in the majority of schools. This multiple case-study research was designed to revisit the question, “How do the pedagogical beliefs and classroom technology practices of teachers, recognized for their technology uses, align?”     

A colloidal method for manganese oxide addition to alumina powder and investigation of properties

Various methods can be applied to introduce additives to ceramic materials. Of these methods, mechanical mixing may not always be suitable to obtain a uniform distribution of the small quantities of additive within the structure, requiring colloidal methods to be applied for the purpose. The addition of manganese oxide to alumina powder has been studied using a colloidal method. The effect of the manganese addition on alumina microstructure and the later stages of the densification behaviour was investigated, together with the hardness and mechanical strength. No evidence of secondary phase formation was detected between the manganese cation and alumina powder for up to 0.5wt% manganese addition, suggesting that manganese is in solid solution with alumina. The microstructural evidence presented suggests that small quantities of a manganese addition to alumina enhance the densification process through the formation of fast diffusion paths within the crystalline structure, similar to the effect of TiO₂ addition.     

Numerical and experimental analysis of unsteady heat transfer with periodic variation of inlet temperature in circular ducts

This work focusses on a numerical and experimental analysis of unsteady forced convection in hydrodynamically developed and thermally developing laminar air flow in a circular duct, subjected to a periodic variation of the inlet temperature. The experiments were conducted over a wide range of Reynolds number (281.2 ≤ Re ≤ 1024.3) and inlet frequency (0.01 ≤ β ≤ 0.20 Hz) of the periodic heat input. In the numerical study, the non-uniform inlet temperature amplitude profile derived from the experiments, was included in the numerical model. A fully explicit, second-order accurate finite difference scheme was developed and used for the solution of the unsteady energy equation. Numerical results are obtained with the fully developed parabolic velocity profile under the boundary condition of the first kind, which was verified by the experiments. Temperature variations along the centerline of the circular duct are observed to be thermal oscillations with the same frequency as the inlet periodic heat input and amplitudes that decayed exponentially with distance along the duct. Thermal response along the wall exhibits negligible amplitude variation with changes in Reynolds number and inlet frequency. The variation in the periods and amplitudes of the thermal oscillations are observed to be a function of spacial system variables only. Satisfactory agreement between the numerical and experimental results are obtained.     

Comparing Rasch analyses probability estimates to sensitivity, specificity and likelihood ratios when examining the utility of medical diagnostic tests

INTRODUCTION: Medical diagnostic tests are evaluated based on measures of sensitivity (Sn), specificity (Sp), and likelihood ratios (LR). These procedures are limited in the event of a biased gold standard or missing data. Interpretations of these measures are frequently inappropriate. PURPOSE: The Rasch measurement model (RMM) was examined as a method to provide evidence of diagnostic test utility in order to overcome the limitations of Sn, Sp, and LR. METHODS: Patients suspected of a knee ligament tear (n = 825) were studied, by evaluating four diagnostic tests. The RMM probability estimates for each test were compared to estimates of Sn, Sp, and LR. RESULTS: The RMM provided probability estimates for the diagnosis that were comparable to likelihood ratios. These probability estimates correlated with the estimates of Sn, Sp, and LR. The RMM estimates were not affected by missing data. DISCUSSION: The RMM may provide an alternative means to study the utility of medical diagnostic tests to estimate the probability of disease presence/absence.     

Radial basis function partition of unity method for modelling water flow in porous media

Water flow in variably-saturated porous media is modelled by using the highly nonlinear parabolic Richards’ equation. The nonlinearity is due to the hydraulic conductivity and moisture content variables. The latter were estimated by using experimental models, including Gardner, Burdine, Mualem and van Genuchten models. The aim of this work is to develop a new technique based on the radial basis function partition of unity method (RBFPUM) and Gardner model in order to solve Richards’ equation in one and two dimensions. We have used Gardner model to handle the nonlinearity issue and the RBFPUM is used to approximate the solution of the linearized Richards’ equation. Our proposed algorithm is based on testing many configurations of the partitions number and selecting the optimal shape parameter for each case. Then we pick up the optimal configuration (partitions number-shape parameter) that yields the best solution in terms of error and conditioning number. By following this procedure, an optimal solution is ensured for our given problem. As numerical tests, we consider the vertical infiltration of water in soils in order to validate our proposed method.     

On the improvement of a scalable sparse direct solver for unsymmetrical linear equations

This paper focuses on the application level improvements in a sparse direct solver specifically used for large-scale unsymmetrical linear equations resulting from unstructured mesh discretization of coupled elliptic/hyperbolic PDEs. Existing sparse direct solvers are designed for distributed server systems taking advantage of both distributed memory and processing units. We conducted extensive numerical experiments with three state-of-the-art direct linear solvers that can work on distributed-memory parallel architectures; namely, MUMPS (MUMPS solver website, http://graal.ens-lyon.fr/MUMPS), WSMP (Technical Report TR RC-21886, IBM, Watson Research Center, Yorktown Heights, 2000), and SUPERLU_DIST (ACM Trans Math Softw 29(2):110–140, 2003). The performance of these solvers was analyzed in detail, using advanced analysis tools such as Tuning and Analysis Utilities (TAU) and Performance Application Programming Interface (PAPI). The performance is evaluated with respect to robustness, speed, scalability, and efficiency in CPU and memory usage. We have determined application level issues that we believe they can improve the performance of a distributed-shared memory hybrid variant of this solver, which is proposed as an alternative solver [SuperLU_MCDT (Many-Core Distributed)] in this paper. The new solver utilizing the MPI/OpenMP hybrid programming is specifically tuned to handle large unsymmetrical systems arising in reservoir simulations so that higher performance and better scalability can be achieved for a large distributed computing system with many nodes of multicore processors. Two main tasks are accomplished during this study: (i) comparisons of public domain solver algorithms; existing state-of-the-art direct sparse linear system solvers are investigated and their performance and weaknesses based on test cases are analyzed, (ii) improvement of direct sparse solver algorithm (SuperLU_MCDT) for many-core distributed systems is achieved. We provided results of numerical tests that were run on up to 16,384 cores, and used many sets of test matrices for reservoir simulations with unstructured meshes. The numerical results showed that SuperLU_MCDT can outperform SuperLU_DIST 3.3 in terms of both speed and robustness.     

Low-frequency electrophoretic actuation of nanoscale optoentropic transduction mechanisms

Inherent bistabilities within DNA-assembled fluorescent resonant energy transfer systems demonstrated time-varying optical signals in response to an electrophoretic driving force. Frequency responses of electrophoretically driven FRET systems were shown to be sequence specific. Integration of these signals over time gave near single-molecule sensitivity within a high background of autofluorescence. This research suggests that externally driven nanoscale mechanical systems may help improve information flow within morphologically intact specimens.     

Numerical simulation of oscillatory flow in melt during InSb single crystal growth by RF heating Czochralski method

Oscillatory flow present in the melt during InSb single crystal growth using an RF-heating Czochralski method has been numerically investigated by means of the finite difference method using the HSMAC algorithm. The thermal boundary conditions required for the numerical simulation model were obtained experimentally by measuring the temperature profile along the crucible of a Czochralski system by means of thermocouples mounted in the crucible. Results of numerical simulations showed that the use of a third-order upwind discretization scheme was necessary to catch the oscillatory behaviour of the fluid flow in the melt. It was shown that this oscillatory behaviour strongly depends on the crystal rotation rate. Indeed, the oscillation period increases when the crystal rotation rate is above a critical rotation rate. In order to avoid such oscillations, crystal rotation rates lower than this critical value of crystal rotation rate must be selected for the growth of high quality crystals free of striations. © 1998 John Wiley & Sons, Ltd.