bluuebunny/crossref_metadata_2025 huggingface dataset:
Elimination of spurious pressure and kinematic modes in biquadratic nine‐node plane element
Authors: Sze K. Y. , Fan H. , Chow C. L.
Published: August 2005

In two‐dimensional penalty finite element analysis of incompressible materials, Q9/3P, the 9‐node quadrilateral with three assumed quasi‐pressure modes, is the most popular element not bothered by spurious pressure. In constructing the penalty matrix of Q9/3P, it is necessary to form a 3×18 matrix and a 3×3 symmetric matrix. The inverse of the symmetric matrix is then post‐ and pre‐multiplied by the 3×18 matrix and its transpose, respectively. By employing a rank subtraction technique, a new and more efficient implementation scheme is devised for the penalty matrix. Same as the conventional Q9 element, when Q9/3P is fully integrated, it becomes expensive and too stiff. On the other hand, there are two spurious kinematic modes should the element be sub‐integrated. In the proposed Q9/3P element, the two mechanisms will be annihilated by judiciously chosen higher‐order assumed stress modes in conjunction with a modified Hellinger‐Reissner functional. It will be demonstrated that the element is of good accuracy and high efficiency.
Analysis of time varying errors in quadratic finite element approximation of hyperbolic problems
Authors: Khelifa Ali , Ouellet Yvon
Published: August 2005

A methodology for analysing the numerical errors generated by schemes using high‐order approximation is presented. Based on Fourier analysis, this methodology is illustrated through the study of the θ‐weighting Taylor–Galerkin finite element model applied to an unsteady one‐dimension advection problem with quadratic elements. Results show that the dissipation and dispersion errors may be computed by considering simultaneously the so‐called physical and computational modes and then, contrarily to what is shown when linear approximation is considered, these errors present a transient behaviour. Moreover, it appears that the errors computed at the end node and at the middle node present in general a different behaviour which in some cases may be opposed to one another. Numerical tests are presented to support the validity of the proposed strategy. We recommend strongly the use of this method for studying the behaviour of numerical schemes based on high‐order approximations.
A finite element model for liquid phase electroepitaxy
Authors: Qin Z. , Dost S. , Djilali N. , Tabarrok B.
Published: August 2005

A finite element numerical simulation model for the liquid phase electroepitaxial growth process of gallium arsenide is presented. The basic equations obtained from the fundamental principles of electrodynamics of continua, the constitutive equations for the liquid and solid phases derived from a rational thermodynamic theory, and the associated interface and boundary conditions are presented for a two‐dimensional axisymmetric growth cell configuration.

The field equations are solved numerically by an adaptive finite element procedure. The effect of moving interfaces is taken into account. Numerical simulations are carried out for different convection levels by changing the value of the gravitational constant. Results show that convection has significant effect on the growth process under normal gravity conditions and results in thickness non‐uniformity of the grown layers. The thickness non‐uniformity leads to curved interfaces of growth and dissolution, which enhance convection.
A spectral multipole method for efficient solution of large‐scale boundary element models in elastostatics
Authors: Peirce A. P. , Napier J. A. L.
Published: August 2005

In this paper we introduce a method to reduce the solution cost for Boundary Element (BE) models from O(N3)operations to O(N2logN) operations (where N is the number of elements in the model). Previous attempts to achieve such an improvement in efficiency have been restricted in their applicability to problems with regular geometries defined on a uniform mesh. We have developed the Spectral Multipole Method (SMM) which can be used not only for problems with arbitrary geometries but also with a variety of element types. The memory necessary to store the required influence coefficients for the spectral multipole method is O(N) whereas the memory required for the traditional Boundary Element method is O(N2). We demonstrate the savings in computational speed and fast memory requirements in some numerical examples. We have established that the break‐even point for the method can be as low as 500 elements, which implies that the method is not only suitable for extremely large‐scale problems, but that it also provides a useful bridge between the small‐scale and large‐scale problems. We also demonstrate the performance of the multipole algorithm on the solution of large‐scale granular assembly models. The large‐scale BE capacity provided by this algorithm will not only prove to be useful in large macroscopic models but it will also make it possible to model microscopic damage processes that form the fundamental mechanisms in plastic flow and brittle fracture.
Tracing postbuckling paths of structures containing multi‐loops
Authors: Kuo Shyh‐Rong , Yang Yeong‐Bin
Published: August 2005

Most incremental‐iterative methods for tracing the postbuckling paths of structures have failed to achieve convergent solutions when the paths make sharp turns in regions where nearby equilibrium paths exist. This is largely due to the fact that iterations are not performed along a correct direction in these regions. To overcome this issue, two parameters for detecting the change in direction of loading and for guiding the direction of iteration are proposed. Also, a unit conversion factor is introduced into the constraint (arc length) equation to make it physically consistent. With these modifications, the present method is capable of tracing the postbuckling paths of structures with multi‐loops. A two‐member truss well known for its looping characteristics in the post‐buckling response has been solved as an illustration.
A numerical study of chaos in a reaction‐diffusion equation
Authors: Mitchell A. R. , Bruch J. C.
Published: August 2005

A study is made using numerical experiments to see the effect of the parameters in the explicit Euler‐discretized form of a one‐dimensional, nonlinear, reaction‐diffusion equation. Based on a series of these experiments, one of the main results obtained is that diffusion, which is usually perceived as having a stabilizing effect, is able to produce chaotic as well as divergent numerical solutions. Furthermore, the discretization parameters are also able to produce chaotic results. From the results presented herein, it is shown that varying the parameters can produce solutions that are single numbers, periodic, aperiodic (chaos), or divergent.
Unified formulation of numerical methods. I. Green's formulas for operators in discontinuous fields
Authors: Herrera Ismael
Published: August 2005

Applying the method of weighted residuals and then interpreting the resulting equations by means of Green's formulas for discontinuous functions, a direct method of analysis is developed. The scheme includes finite differences, finite elements, and boundary methods. This is the first of a sequence of articles in which the methodology is presented. A fundamental ingredient of the procedure are general Green's formulas for operators defined in discontinuous fields. They are developed in this first article.
Mixed finite element methods for the approximation of time‐dependent problems
Authors: Suri Manil
Published: August 2005

A given elliptic boundary problem can, in general, be approximated by several different mixed finite element methods, depending on what physical unknowns are most desired. The use of certain mixed methods for time‐dependent problems has been proposed by Johnson and Thomee [5]. We analyze here some additional mixed methods for the time‐dependent case which can be used to obtain direct approximations to alternate physical quantities of interest.
Finite element treatment of boundary singularities by augmentation with non‐exact singular functions
Authors: Beagles A. E. , Whiteman J. R.
Published: August 2005

A two‐dimensional Poisson problem which contains both an interface and a reentrant corner is considered. For this problem the singular form of the solution at the reentrant corner is not known explicitly, with the result that a (nonexact) approximation to the singular form has to be calculated. The finite element method is applied to the Poisson problem, with the test and trial function spaces augmented with the nonexact singular functions. An error analysis for the nonexact augmentation is presented.
Finite difference solution of viscoelastic flows by preconditioned conjugate gradients
Authors: Manero O.
Published: August 2005

Attention is given to preconditioned conjugate gradients in the solution of systems of partial differential equations which arise in flows of viscoelastic liquids simulated by rheological implicit models. Finite differences discretization is used together with a generalization of the incomplete Cholesky conjugate‐gradient method to include asymmetric nonsingular matrices, resulted from the discretization of the kinemetic fields and the pressure recovery problem in also considered in a two‐dimensional planar flow.
On a moving boundary problem of transitional ballistics
Authors: Cooke Charlie H. , Hwang Jen‐Ing G.
Published: August 2005

A hybrid algorithm for calculating the flow around a flat‐nosed projectile moving through a fluid is established. At cells of fixed volume away from the projectile, Harten's total variation diminishing (TVD), second‐order accurate, shock capturing scheme is utilized. Due to projectile motion, cells adjacent to the projectile can be treated as compressing or expanding in volume. For such cells, a local finite volume approach has been employed to derive a cell update algorithm.

Proof of concept for the expanding cell scheme is established through calculating the one‐dimensional flow behind a moving piston, whose theoretical solution is well‐known. The resulting hybrid scheme is applied to the problem of blast wave simulation in axisymmetric geometries. Flow around a vertical muzzle brake is calculated for the case of an embedded moving projectile.
A Tensor product generalized ADI method for the method of planes
Authors: Dyksen Wayne R.
Published: August 2005

We consider solving separable, second order, linear elliptic prtial differential equations in three independent variables. If the partial differential opertor separates into two terms, one depending on x and y, and one depending on z, then we use the method of planes to obtain a discrete problem, which we write in tensor product from as

We apply a new interative method, the tensor product generalized alternating direction implicit method, to solve the discrete problem. We study a specific implementation that uses Hermite bicubic collocation in the xy direction and symmetric finite differences in the z direction. We demostrate that this method is a fast and accurate way to solve the large linear systems arising from three‐dimensional elliptic problems.
Downstream implicit schemes for advection
Authors: Bhagwat Satish , Allen Myron B.
Published: August 2005

Downstream‐weighted implicit difference schemes for pure advection are stable for Courant numbers λ ≥ 1. They are numerically diffusive when λ > 1.
The performance of numerical methods for elliptic problems with mixed boundary conditions
Authors: Dyksen Wayne R. , Ribbens Calvin J. , Rice John R.
Published: August 2005

We consider solving linear, second order, elliptic partial differential equations with boundary conditions of types Dirichlet (DIR), mixed (MIX), and nearly Neumann (Neu) by using software modules that implement five numerical methods (one finite element and four finite differences). They represent both the new generation of improved methods and the traditional ones; they are: Hermite collocation plus band Gauss elimination (HC), ordinary finite differences plus band Gauss elimination (5P), ordinary finite differences with Dyaknov iteration (DY), DY with Richardson extrapolation to achieve fourth order convergence (D4), and ordinary finite differences with multigrid iteration (MG). We carry out a performance evaluation in which we measure the grid size and the computer time needed to achieve three significant digits of accuracy in the solution. We compute the changes in these two measures as we change boundary condition types from DIR to MIX and MIX to NEU and then test the following hypotheses: (i) the performance of all the modules is degraded by introducing the derivative terms into the boundary conditions; (ii) finite element collocation (HC) is least affected; (iii) the fourth order modules (HC and D4) are less affected than the other second order modules; and (iv) the traditional 5‐point finite differences (5P) are most affected. We establish these hypotheses with high levels of confidence by using several sample problems. The most significant conclusion is that a high order collocation method is preferred for problems with general operators and derivatives in the boundary conditions. We also establish with considerable confidence that these modules have the following rankings in absolute comparative time performance: MG (best), HC and D4, DY, and 5P (worst).
A fourth‐order difference method for elliptic equations with nonlinear first derivative terms
Authors: Jain M. K. , Jain R. K. , Mohanty R. K.
Published: August 2005

We present a nine‐point fourth‐order finite difference method for the nonlinear second‐order elliptic differential equation Auxx + Buyy = f(x, y, u, ux, uy) on a rectangular region R subject to Dirichlet boundary conditions u(x, y) = g(x, y) on ∂R. We establish, under appropriate conditions O(h4)‐convergence of the finite difference scheme. Numerical examples are given to illustrate the method and its fourth‐order convergence.
Adaptive local grid refinement algorithms for finite‐element collocation
Authors: Allen Myron B. , Curran Mark C.
Published: August 2005

An adaptive grid refinement procedure allows accurate solutions to advection‐dominated, time‐dependent flows using finite‐element collocation. The technique relies on a data structure that is readily amenable to parallel computing. The paper discusses computational aspects of the method.
Some numerical experiments on the splitting of Burgers' equation
Authors: Iskandar Labib , Mohsen Adel
Published: August 2005

The combined approach of linearization and splitting up is used for devising new algorithms to solve a one‐dimensional Burgers' equation. Two schemes are discussed and the computed solutions are compared with the exact solution. For this problem it is found that the schemes proposed yield excellent numerical results for Reynolds number R ranges from 50 up to 1500. The schemes were also tested for another problem whose R = 10000. In this case a filtering technique is used to overcome the nonlinear instability.
Semidiscrete least squares methods for linear hyperbolic systems
Authors: Chen Tsu‐Fen
Published: August 2005

Some approximate methods for solving linear hyperbolic systems are presented and analyzed. The methods consist of discretizing with respect to time and solving the resulting hyperbolic system for fixed time by least squares finite element methods. An analysis of least squares approximations is given, including optimal order estimates for piecewise polynomial approximation spaces. Numerical results for the inviscid Burgers' equation are also presented. © 1992 John Wiley & Sons, Inc.
Multigrid solvers and preconditioners for first kind integral equations
Authors: Von Petersdorff T. , Stephan E. P.
Published: August 2005

We discuss multigrid methods and multilevel preconditioners for first kind boundary integral equations with weakly and hypersingular kernels. We find that the number of iterations needed is bounded or grows no worse than logarithmically in the numbers of unknowns. We also discuss the complexity for parallel implementations.
Modeling of multimaterial interfaces in the finite difference method
Authors: Dow J. O. , Hardaway J. L.
Published: August 2005

This work develops a procedure for representing multimaterial interfaces in finite difference models. The boundary separating the two materials can be on or between a row of nodes. The development is validated by embedding the boundary between two regions in a single, larger region and comparing the results. The development is facilitated by the use of a physically based notation that represents the displacement approximations in terms of rigid‐body rotations and strain gradient quantities that produce the displacements. Four example problems are presented.
Fast numerical method for the solution of the quasigeostrophic vorticity equation
Authors: Dahleh Marie Dillon
Published: August 2005

Particle methods are typically O(N2), where N is the number of computational elements. We present an O(N) particle method for the equations for the conservation of potential vorticity. This method is based on the idea of grouping the particles. The necessary expansions and truncation errors are given. The accuracy and speed of the method are presented for both scalar and vector machines. © 1993 John Wiley & Sons, Inc.
Finite element methods for an acoustic well‐logging problem associated with a porous medium saturated by a two‐phase immiscible fluid
Authors: Sheen Dongwoo
Published: August 2005

A mathematical model is presented concerning wave propagation in a domain that arises in geophysical well‐logging problems. The domain consists of a borehole Ωf surrounded by a porous medium Ωp. Ωf is filled with a compressible inviscid fluid, and Ωp is saturated by a two‐phase immiscible fluid. Absorbing boundary conditions for artificial boundaries and boundary conditions on the interface between Ωf and Ωp are used. The existence and uniqueness theorems are stated for the resulting initial‐boundary value problem. Stability and convergence estimates for a finite element method are also studied. © 1993 John Wiley & Sons, Inc.
Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables
Authors: Fernandes Ryan I. , Fairweather Graeme
Published: August 2005

While alternating direction implicit (ADI) collocation methods have been used for several years to solve parabolic problems in several space variables, no convergence analysis has been derived for any of these methods. We formulate and rigorously analyze ADI collocation schemes applied to the inhomogeneous heat and wave equations on the unit square subject to homogeneous Dirichlet boundary conditions and appropriate initial conditions. We prove that each method is second‐order accurate in time and of optimal accuracy in space in the L2 and H01 norms. Numerical experiments confirm the predicted rates of convergence. © 1993 John Wiley & Sons, Inc.
A computationally efficient modification of mixed finite element methods for flow problems with full transmissivity tensors
Authors: Koebbe Joe
Published: August 2005

The mixed finite element method for approximately solving flow equations in porous media has received a good deal of attention in the literature. The main idea is to solve for the head/pressure and fluid velocity (Darcy velocity) simultaneously to obtain a higher order approximation of the fluid velocity. In the case of a diagonal transmissivity tensor the algebraic equations resulting from the discretization can be reduced to a system of algebraic equations for the head/pressure variable alone. This reduction results in a smaller number of unknows to be solved for in an iterative method such as preconditioned conjugate gradient method. The fluid velocity is then obtained from an algebraic relationship. In the case of full transmissivity tensor, the algebraic reduction is more difficult. This paper investigates some algorithms resulting from the modification of the mixed finite element that take advantage of the mixed finite element method for the diagonal tensor case. The resulting schemes are more efficient implementations that maintain the same order of accuracy as the original schemes. © 1993 John Wiley & Sons, Inc.
Decoupled smooth interfaces for spectral‐element approximations of parabolic or elliptic type
Authors: Black Kelly
Published: August 2005

A method is examined to approximate the interface conditions for Chebyshev polynomial approximations to the solutions of parabolic problems, and a smoothing technique is used to calculate the interface conditions for a domain decomposition method. The methods uses a polynomial of one less degree then the full approximation to calculate the first derivative so that interface values can be calculated by using only the adjacent subdomains. Theoretical results are given for the consistency of the scheme and practical results are presented. Computational results are given for both a fourth‐order Runga‐Kutta methods and an explicit/implicit scheme. © 1993 John Wiley & Sons, Inc.
Eulerian‐Lagrangian localized adjoint method: The theoretical framework
Authors: Herrera Ismael , Ewing Richard E. , Celia Michael A. , Russell Thomas F.
Published: August 2005

This is the second of a sequence of papers devoted to applying the localized adjoint method (LAM), in space‐time, to problems of advective‐diffusive transport. We refer to the resulting methodology as the Eulerian‐Lagrangian localized adjoint method (ELLAM). The ELLAM approach yields a general formulation that subsumes many specific methods based on combined Lagrangian and Eulerian approaches, so‐called characteristic methods (CM). In the first paper of this series the emphasis was placed in the numerical implementation and a careful treatment of implementation of boundary conditions was presented for one‐dimensional problems. The final ELLAM approximation was shown to possess the conservation of mass property, unlike typical characteristic methods. The emphasis of the present paper is on the theoretical aspects of the method. The theory, based on Herrera's algebraic theory of boundary value problems, is presented for advection‐diffusion equations in both one‐dimensional and multidimensional systems. This provides a generalized ELLAM formulation. The generality of the method is also demonstrated by a treatment of systems of equations as well as a derivation of mixed methods. © 1993 John Wiley & Sons, Inc.
On the p version of the finite element method in the presence of numerical integration
Authors: Kim Chang Geun , Suri Manil
Published: August 2005

We analyze the error in the p version of the finite element method when the effect of the quadrature error is taken into account. We extend some results by Banerjee and Suri [Math. Comput. 59, 1–20 (1992)] on the H1‐norm error to the case of the error in the L2 norm. We investigate three sources of quadrature error that can occur: the error due to the numerical integration of the right‐hand side, that due to nonconstant coefficients, and that due to the presence of mapped elements. Presented are various theoretical and computational examples regarding the sharpness of our results. In addition, we make a note on the use of numerical quadrature in conjunction with p‐adaptive procedures and on the necessity of overintegration in the h version with linear elements, when the L2 norm is of interest. © 1993 John Wiley & Sons, Inc.
Optimal m‐stage Runge‐Kutta schemes for steady‐state solutions of hyperbolic equations
Authors: Chen Mei‐Qin , Chiu Chichia
Published: August 2005

A numerical scheme is developed to find optimal parameters and time step of m‐stage Runge‐Kutta (RK) schemes for accelerating the convergence to ‐steady‐state solutions of hyperbolic equations. These optimal RK schemes can be applied to a spatial discretization over nonuniform grids such as Chebyshev spectral discretization. For each m given either a set of all eigenvalues or a geometric closure of all eigenvalues of the discretization matrix, a specially structured nonlinear minimax problem is formulated to find the optimal parameters and time step. It will be shown that each local solution of the minimax problem is also a global solution and therefore the obtained m‐stage RK scheme is optimal. A numerical scheme based on a modified version of the projected Lagrangian method is designed to solve the nonlinear minimax problem. The scheme is generally applicable to any stage number m. Applications in solving nonsymmetric systems of linear equations are also discussed. © 1993 John Wiley & Sons, Inc.
Pseudospectral method for transient viscoelastic flow in an axisymmetric channel
Authors: Xu S. , Davies A. R. , Phillips T. N.
Published: August 2005

A new pseudospectral method for simulating transient viscoelastic flows is presented. The governing equations are a system of seven first‐order equations of mixed type. The essential features of the method are (i) all seven independent flow variables are represented on a common Chebyshev‐Gauss‐Lobatto grid; (ii) the pressure is treated in such a way as to give a globally divergence‐free velocity field, i.e., the divergence of the velocity field vanishes globally within the region, and (iii) different time scales pertaining within the hyperbolic constitutive equations are treated using the splitting technique of LeVeque and Yee originally proposed in a finite‐difference context. The method is applied to transient axisymmetric flow of an Oldroyd B fluid in a channel formulated in two ways: (I) as an initial boundary‐value problem, and (II) as a body‐force problem. © 1993 John Wiley & Sons, Inc.
Numerical method for a class of parabolic problems in composite media
Authors: Kačur J. , Van Keer R.
Published: August 2005

This paper deals with a numerical method, viz. a Rothe Galerkin finite element method, for a class of parabolic problems in composite media with jump conditions for the unknown at the interfaces of the subdomains, retaining the continuity of its conormal derivative. Crucial to our approach is a nonstandard variational formulation in a product Sobolev space setting. We begin with the discretization in time by the Rothe method, which, in essence, involves a backward finite difference scheme and which provides a constructive method for proving existence of a (unique) variational exact solution under weak conditions for the data. We are left with a recurrent system of elliptic problems at each subsequent time point which are solved numerically by a Galerkin finite element method. The resulting algorithm may be implemented by adapting standard codes for parabolic problems in one‐component domains, when suitably taking into account the specific transmission conditions at the internal boundaries. The emphasis of the paper is on convergence results and error estimates for both the fully discrete and the semi‐discrete approximation of the exact solution. The effectiveness of the approach is illustrated by means of a 1D and a 2D example, the analytical solution of which is known. © 1993 John Wiley & Sons, Inc.
Solution of the Navier‐Stokes equations by the spectral‐difference method
Authors: Cortes Arturo B. , Miller J. D.
Published: August 2005

The Jacobi polynomial collocation method is extended to two and three dimensions by superimposing the individual one‐dimensional expansions. Two innovative ideas are introduced in this article. The first is the cornerless/edgeless computational grid, and the second is the modified compressibility method, which is an iterative pressure solver. To evaluate the new method's applicability in solving the Navier‐Stokes equation, the lid‐driven cavity flow problem was solved. Two configurations were considered, the square cavity and the rectangular cavity with an aspect ratio of 2. A comparison of the center‐line velocity profiles from two‐ and three‐dimensional simulations at a Reynolds number of 1000 is provided for each of the configurations. The center‐line velocity comparisons showed good quantitative agreement with previous studies. © 1994 John Wiley & Sons, Inc.
Thermally coupled, stationary, incompressible MHD flow; existence, uniqueness, and finite element approximation
Authors: Meir A. J.
Published: August 2005

This article addresses the questions of existence, uniqueness, and finite element approximation (including some computational aspects) of solutions to the equations of steady‐state magnetohy‐drodynamic (MHD) when buoyancy effects due to temperature differences in the flow cannot be neglected. We couple the MHD equations to the heat equation and employ the well‐known Boussinesq approximation. We consider the equations posed on a bounded three‐dimensional domain. The boundary conditions for the velocity are of Dirichlet type; the boundary conditions for the temperature are mixed (of Dirichlet type and of Neumann type); we also specify the normal component of the magnetic field and tangential component of the electric field on the boundary. We point out that these problems are relevant to many physical phenomena such as the cooling of nuclear reactors by electrically conducting fluids, continuous metal casting, crystal growth, and semi‐conductor manufacture. © 1995 John Wiley & Sons, Inc.
Alternative T‐complete systems of shape functions applied in analytical Trefftz finite elements
Authors: Szybiński B. , Zieliński A. P.
Published: August 2005

The authors compare the behavior of hybrid Trefftz p‐elements with two different types of shape functions identically fulfilling governing differential equations. Numerical examples include several boundary problems for Laplace, Poisson, and plane elasticity equations. Accuracy of the solutions, convergence properties, numerical stability and sensitivity for mesh distortion are investigated. It is shown that both systems of the functions can be efficiently applied, although they have different properties. © 1995 John Wiley & Sons, Inc.
Advection‐diffusion equations: Temporal sinc methods
Authors: Bowers Kenneth L. , Carlson Timothy S. , Lund John
Published: August 2005

A fully Sinc–Galerkin method for solving advection–diffusion equations subject to arbitrary radiation boundary conditions is presented. This procedure gives rise to a discretization, which has its most natural representation in the form of a Sylvester system where the coefficient matrix for the temporal discretization is full. The word “full” often implies a computationally more complex method compared to, for example, temporal marching. In a comparison of time‐marching versus this sinc‐temporal procedure, the Sylvester formulation defines a common framework within which these procedures can be evaluated. This framework has been included in the introduction to illustrate an efficiency measure for either method. Similar remarks with regard to fullness versus sparseness in the Sylvester formulation apply when the spatial discretization is spectral or, for example, differencing. Although it is indicated how this sinc‐temporal method can be combined with alternative spatial discretizations, the natural affinity between sinc methods for space and time discretizations motivate carrying out the numerical illustrations using the sinc basis in each. © 1995 John Wiley & Sons, Inc.
A general approach for using a stiff equation solver to integrate a system of partial differential equations
Authors: Zimmerman W. R.
Published: August 2005

A general approach for using a stiff ordinary differential equation solver to integrate a system of time‐dependent partial differential equations in one spacial dimension is described. A computer program based upon the algorithm was written and used to solve nonlinear problems in shock hydrodynamics and hydrology as well as a nonlinear system of ordinary differential equations. The approach is global‐implicit and provides an option to the development of specialized computer programs for specific problems of interest. © 1995 John Wiley & Sons, Inc.
Recovery of the optimal mesh density function and near‐optimal meshes with rectangular elements in the mapped domain
Authors: Hugger Jens
Published: August 2005

A method is developed for the recovery and representation of near‐optimal finite‐element meshes of rectangular elements in the mapped domain. The method extends a previously known method, which was restricted to square elements in the mapped domain. The method was developed to obtain a simple, cost‐effective representation of computational meshes for adaptive finite‐element methods solving parametrized problems. © 1995 John Wiley & Sons, Inc.
A Petrov‐Galerkin mixed finite element method with exponential fitting
Authors: Van Nooyen R. R. P.
Published: August 2005

We discuss a Petrov‐Galerkin mixed finite element formulation of the semiconductor continuity equations on a rectangular domain. We give error estimates for equations that are in principle degenerate in the singularly perturbed case. We give arguments that indicate that the method is also effective in the singularly perturbed case. We develop a discretization that gives a higher‐order accurate solution for use in an a posteriori error estimator. © 1995 John Wiley & Sons, Inc.
An adaptive boundary collocation method for linear PDEs
Authors: Golik W. L. , Kolodziej J. A.
Published: August 2005

The article proposes an adaptive algorithm based on a boundary collocation method for linear PDEs satisfying the maximal principle with possibly nonlinear boundary conditions. Given the error tolerance and an initial number of terms in the solution expansion, the algorithm computes expansion coefficients by collocation of boundary conditions and evaluates the maximum absolute error on the boundary. If error exceeds the error tolerance, additional expansion terms and boundary collocation points are added and the process repeated until the tolerance is satisfied. The performance of the algorithm is illustrated by an example of the potential flow past a cylinder placed between parallel walls. © 1995 John Wiley & Sons, Inc.
Array comparative genomic hybridization profiling of first‐trimester spontaneous abortions that fail to grow in vitro
Authors: Benkhalifa M. , Kasakyan S. , Clement P. , Baldi M. , Tachdjian G. , Demirol A. , Gurgan T. , Fiorentino F. , Mohammed M. , Qumsiyeh M. B.
Published: August 2005

Objectives

Cytogenetic analysis of spontaneous abortion samples can be limited by culture failure. Failure to grow in vitro has traditionally been suspected to be due to in vivo death of tissue associated with spontaneous abortion (SAB) or simply technical factors of growth in culture.

Method

We used array comparative genomic hybridization (array CGH) to investigate chromosomal imbalances in products of conception that failed to grow in vitro.

Results

Our data on 26 cases of SABs that failed to grow in culture are compared and contrasted with published data on cytogenetic findings following in vitro culture. The results revealed abnormalities uncommonly seen by classic cytogenetic methods. These abnormalities include high rates of double aneuploidy and autosomal monosomy. The data taken together suggest that classic cytogenetics of spontaneous abortion may yield normal karyotypes or selected abnormal karyotypes that permit cell proliferation in vitro while Array CGH detects other abnormalities.

Conclusion

Array CGH is becoming an important clinical assay for unbalanced chromosome abnormalities whether cells grow in culture or not and in cases of analysis on one or few cells. Copyright © 2005 John Wiley & Sons, Ltd.
Prediction of pregnancy complications by first‐trimester maternal serum PAPP‐A and free β‐hCG and with second‐trimester uterine artery Doppler
Authors: Spencer Kevin , Yu Christina K. H. , Cowans Nicholas J. , Otigbah Chineze , Nicolaides Kypros H.
Published: August 2005

Background

Previous studies have shown an association between low first trimester maternal serum free β‐hCG and PAPP‐A and subsequent development of pregnancy complications. Similarly, uterine artery Doppler in the late second trimester has shown that high impedance to flow is associated with increased risk for preeclampsia and fetal growth restriction. The objective of this study is to determine whether there is an association between the maternal serum concentration of PAPP‐A and free β‐hCG at 11–13+6 weeks with the uterine artery pulsatility index (PI) at 22–24 weeks, and secondly, to compare the screening characteristics of the two methods in the prediction of adverse pregnancy outcome.

Methods

Maternal serum PAPP‐A and free β‐hCG at 11–13+6 weeks and uterine artery PI at 22–24 weeks were measured in 4390 women with singleton pregnancies. Pregnancies with chromosomal defects or fetal anomalies were excluded. The biochemical and Doppler measurements were compared between those with normal outcome and those resulting in spontaneous preterm delivery, pre‐eclampsia and fetal growth restriction (FGR). Detection rates using a combination of the biochemical and Doppler measurements were investigated.

Results

In the pregnancies resulting in pre‐eclampsia (n = 64) and FGR (n = 172), the median PAPP‐A was lower (0.844 and 0.813 MoM), the median uterine artery mean PI was higher (1.56 and 1.18) but the median free βhCG was not significantly different (0.923 and 0.933 MoM) than in the normal outcome group. In the preterm delivery group (n = 159), the median free β‐hCG (0.944 MoM) and uterine artery mean PI (1.06) were not significantly different from normal but the median PAPP‐A (0.928 MoM) was significantly lower than normal. In screening for pre‐eclampsia, the detection rate, for a 5% false‐positive rate, was 14.1% for PAPP‐A, 54.7% for uterine artery mean PI and 62.1% for a combination of PAPP‐A and uterine artery mean PI.

Conclusion

Maternal serum PAPP‐A at 11–13+6 of gestation is significantly lower in adverse pregnancy outcomes. The combination of first trimester serum PAPP‐A and uterine artery mean PI at 22‐24 weeks improves the screening efficacy for the prediction of pre‐eclampsia. Copyright © 2005 John Wiley & Sons, Ltd.
Interstitial deletion del(10)(q25.2q25.3 ∼ 26.11)—case report and review of the literature
Authors: Kehrer‐Sawatzki Hildegard , Daumiller Eva , Müller‐Navia Jutta , Kendziorra Heidemarie , Rossier Eva , du Bois Gabriele , Barbi Gotthold
Published: August 2005

Objectives

To present the clinical, cytogenetic, and molecular cytogenetic findings of prenatally diagnosed interstitial deletion 10q25.2‐q26.1. The majority of distal 10q deletions are pure terminal deletions with breakpoints in 10q25 and 10q26. Only four patients have been described so far with interstitial deletions involving bands 10q25.2‐q26.1.

Methods

Postmortem physical examination and autopsy of the foetus after medically terminated pregnancy. GTG‐banding, reverse painting, and FISH analysis with BAC clones on amniocyte metaphases were performed to determine the extent of the deletion.

Results

At 20 weeks the eutrophic female foetus showed pronounced microretrogeny and hypertelorism, clubfeet as well as minor internal anomalies like pancreas anulare, atypically lobed liver, and missing choleocystis. Cardiac anomalies were not observed and the genitalia were of a normal female. The deletion encompasses 6‐Mb and is associated with hemizygosity for 30 genes, including the genes for beta‐tectorin, the beta‐1 adrenergic receptor, and the alpha‐2A adrenergic receptor.

Conclusion

An interstitial deletion del(10)(q25.2q25.3 ∼ 26.11) was confirmed by FISH with mapped BAC clones. Clinical and molecular cytogenetic analyses of further interstitial 10q deletions are necessary to assess whether the phenotypic manifestations differ between deletions that are interstitial compared to those that include also the terminal region of chromosome 10. Copyright © 2005 John Wiley & Sons, Ltd.
Synthesis and characterization of a new poly(butadiene(g) acrylamide(g) acrylic acid)
Authors: Spila G. , Bertorello H.
Published: August 2005

Synthetic crosslinked polymers were obtained by reacting oligomers of polybutadiene (av. mol. wt. ∼6000) with acrylamide and acrylic acid. Characterization of these new block‐crosslinked polymers was carried out by FTIR, 1H‐NMR, 13C‐NMR, SEM analyses, DTA, and DTG. The polymers were washed with benzene, ethanol, water, and acetone and then dried at high vacuum. Determinations of the swelling ratio Vs/Vo for the poly (BuAAAm)H, acid form, and poly (BuAAAm)Na, sodium form, were carried out in distilled water, at different pH values and concentrations of electrolytes. Kinetic studies with diffusion of solvents were related to the network structures of the poly (BuAAAm) in acid and sodium forms.
Effect of monofunctional and trifunctional modifiers on a phase mixed polyurethane system
Authors: Fedderly Jeffry J. , Lee Gilbert F. , Ferragut David J. , Hartmann Bruce
Published: August 2005

The dynamic mechanical behavior of a phase mixed polyurethane system modified with trifunctional and monofunctional alcohols was investigated and compared with a typical polyurethane system with a difunctional alcohol. Of interest was verifying that the average functionality of the alcohol would determine the dynamic mechanical properties and not whether that functionality was achieved by an equimolar blend of trifunctional and monofunctional alcohols or by a purely difunctional alcohol. The base system consisted of poly(tetramethylene ether)glycol (PTMG) cured with 4,4′‐diphenylmethane diisocyanate (MDI). The trifunctional alcohol was trimethylol propane (TMP). The monofunctional alcohol was decyl alcohol (DA). Samples with a typical difunctional alcohol, 2,2‐dimethyl‐1,3‐propanediol (DMPD), were prepared and their properties compared with those of the above samples. To a first approximation, the properties of TMP‐DA modified polymers are identical to those of DMPD polymers of the same hard segment concentration. These results confirm our hypothesis that the dynamic properties obtained from a combination of a trifunctional alcohol with a monofunctional alcohol are essentially equivalent to those of a difunctional alcohol.
Epoxy and glass composites in water studied with 2H‐NMR
Authors: Klotz Jürgen , Brostow Witold , Hess Michael , Veeman Wiebren S.
Published: August 2005

The amount, behavior, and localization of water in epoxy resin composites largely influence the mechanical properties and aging. Gravimetric analysis combined with 2H‐NMR of heavy water in epoxy resin glass fabric composites provides direct information about types of water, which can be distinguished by their mobility. Three different epoxy composites were analyzed with this technique. The results are correlated with mechanical properties.
Thermally stimulated oxidative degradation of high impact polystyrene with nitric acid
Authors: Hace Drago , Kovacevic Vera , Pajc‐Liplin Davorka
Published: August 2005

The practical application of high impact polystyrene (HIPS) depends on the resistance to aging in aggressive environments. The investigation of morphological, mechanical, and chemical properties was made on HIPS samples of various thickness. The property deterioration of HIPS caused by concentrated nitric acid and heat was studied. The diffusion through micropores formed visible cracks that finally led to the complete destruction into a powder. The rapid loss in mechanical properties was explained in terms of scission reaction of the graft polybutadiene (PB) with the homopolystyrene (PS) matrix. Comparative measurements of pure PS and PB under the same conditions were helpful in resolving parallel reactions that preferentially take place in PS and/or in PB sequences. It was established that higher degree of nitration caused by higher temperature results in increased insolubility owing to parallel crosslinking reactions. The nitric acid attack on HIPS caused scission reactions, which also led to the oxidative degradation, more pronounced in the PS phase in the soluble part of HIPS.
Stereochemical analysis of acrylic copolymers with large polar side groups by NMR spectroscopy
Authors: Román Julio San , Gallardo Alberto
Published: August 2005

NMR spectra give abundant information at the microstructural level. When pseudoasymmetric carbon atoms are present in the monomeric repeating units, it is possible to obtain valuable information about the relative stereochemical configuration of the side substituents of the pseudoasymmetric center. This is the best way to know the tacticity of a polymer and the cotacticity parameters of copolymers, as well as the average distribution of comonomeric units along the chains, according to the polymerization mechanism. In this work, we present the microstructural and stereochemical characterization of acrylic copolymers prepared by free radical copolymerization of 2‐hydroxyethyl methacrylate with a methacrylic ester or methacrylamide derivative, bearing polar side groups of biomedical interest. These copolymer systems were analyzed by 1H‐NMR spectroscopy to determine the average molar composition, and the corresponding reactivity ratios, and by 13C‐NMR to study the microstructural and stereochemical configuration of comonomer sequences in terms of triads and pentads. Analyses account for the mechanism of polymerization, which fits first order Markov statistics for the addition of comonomers to free radical growing ends. The stereochemical distribution is described by a Bernoullian trial.
Don't fill a position; recruit talent
Authors: Freeman Gail L.
Published: August 2005

The process of recruitment for nonprofit institutions is an opportunity for the institution to further define its culture and community, as well as its fundraising goals.
Synthesis, characterization and properties evaluation of copolymers of 2,3,4,5,6‐pentafluorostyrene and N‐phenylmaleimide
Authors: Agarwal Seema , Becker Mathias , Tewes Friederike
Published: August 2005

Copolymers of 2,3,4,5,6‐pentafluorostyrene (PFS) having a combination of high hydrophobicity and high glass transition temperature (Tg) are reported here for the first time. The copolymerization was carried out using N‐phenylmaleimide (NPM) as the comonomer and azobisisobutyronitrile (AIBN) as the initiator under both conventional thermal heating and microwave heating. The initial copolymerization rate was found to be higher under microwave heating than under thermal heating. The copolymerization parameters were determined using the Fineman–Ross method and were found to be r1 (NPM) = 0.28 and r2 (PFS) = 0.86. Increased incorporation of NPM in the copolymers led to an increase in Tg of the copolymers without significantly affecting the hydrophobicity of poly(2,3,4,5,6‐pentafluorostyrene). Thermal stability of the copolymers is also reported. Copyright © 2005 Society of Chemical Industry
Synthesis and evaluation of new ditopic cyclophane receptors for benzoic acid
Authors: Stetson Christopher M. , Nishikawa Shiro , Purkiss David W. , Dalley N. Kent , Bartsch Richard A.
Published: August 2005

As potential receptors for a benzoic acid guest, new ditopic cyclophane host molecules, each with a π electron‐rich portion and a pyridine ring‐containing portion, are synthesized. Complexation of benzoic acid guest by the potential molecular receptors is probed by infrared spectroscopy, proton magnetic resonance titration experiments and solid‐state structure determination. Copyright © 2005 John Wiley & Sons, Ltd.
Heat capacity and chemical equilibria of liquid selenium
Authors: Shu Hua‐Cheng , Gaur Umesh , Wunderlich Bernhard
Published: August 2005

Heat capacities of liquid selenium have been measured by computer interfaced differential scanning calorimetry in the metastable region with an accuracy of ± 1% from 330 to 520°K. To avoid crystallization, the measurements were done on cooling. A semiquantitative fitting of the heat capacity to vibrational energy contributions, free volume (hole) effects, and heats of reaction from the changes in the ring‐chain and depolymerization equilibria was possible to within ±5% of the newly measured and literature data between the glass transition temperature (ca. 303°K) and 1000°K. It could be established that the shift in the ring‐chain equilibrium is not the major reason for the overall decrease in heat capacity above the glass transition temperature. The floor temperature, which was earlier placed at about 356°K, is possibly below the glass transition temperature. The increase in heat capacity beyond 800°K has been linked with the depolymerization reaction.