Analysis of a stabilized finite element approximation of the transient convection-diffusion-reaction equation using orthogonal subscales

In this paper we analyze a stabilized finite element method to solve the transient convection-diffusion-reaction equation based on the decomposition of the unknowns into resolvable and subgrid scales. We start from the time-discrete form of the problem and obtain an evolution equation for both components of the decomposition. A closed-form expression is proposed for the subscales which, when inserted into the equation for the resolvable scale, leads to the stabilized formulation that we analyze. Optimal error estimates in space are provided for the first order, backward Euler time integration. Received: 31 January 2001 / Accepted: 30 September 2001     

On a viscous-hydrodynamic model for semiconductors: numerical simulation and stability analysis

We deal with a hydrodynamic model for semiconductors with a physical viscosity in the momentum/energy equations. The discretization uses a first-order finite difference scheme with upwinding based on the characteristic variables. We perform a stability analysis of the numerical method applied to a linearized incompletely parabolic system assuming vanishing viscosity in one space dimension although the analysis can be extended to the two dimensional case. A thorough numerical parametric study as a function of the heat conductivity and of the momentum viscosity is carried out in order to investigate their effect on the development of shocks in both one and two space dimensions. Received: 30 January 2001 / Accepted: 30 May 2001     

A simple method for the characterization of thin films during heat treatment

 In this paper, we propose a simple method to characterize thin film during heat treatment with a compact structure as a specimen. By detecting the variation of displacements of the structure, thereby, various kinds of information, such as thermomechanical properties, stress relieving, or microstructure variations of thin films during heat treatment, can be characterized from the record of the displacements of the structure. The measurement of displacements can be done directly under an optical microscope with the specimen placed in a heating stage. Based on this method, the specimen is free from substrate, no mechanical constraints imposed on the specimen, and the characterization can display local conditions on a wafer. To set an example, as-deposited polycrystalline silicon films with phosphorous doping on regular high temperature annealing between 550 and 1100 °C are used as a model system to demonstrate the effectiveness of the proposed method for characterizing variations of stress-levels as function of temperature and time during heat treatment. Received: 30 May 2001/Accepted: 29 August 2001     

Order Reduction Is Invalid for Singularly Perturbed Control Problems with a Vector Fast Variable

The order reduction method for singularly perturbed optimal control systems consists of employing the system obtained while setting the small parameter to zero. In many situations the differential-algebraic system thus obtained indeed provides an appropriate approximation to the singularly perturbed optimal control problem under consideration. In this paper we show, however, that the set of singularly perturbed optimal control systems for which the order reduction approach is invalid is dense (in the L ^∞ norm) in the class of systems which we consider. This is established under the assumption that the fast variable in the singularly perturbed system is not a scalar. Date received: June 8, 2001. Date revised: December 30, 2001.     

High order numerical simulation of sound generated by the Kirchhoff vortex

An improved high order finite difference method for low Mach number computational aeroacoustics (CAA) is described. The improvements involve the conditioning of the Euler equations to minimize numerical cancellation errors, and the use of a stable non-dissipative sixth-order central spatial interior scheme and a third-order boundary scheme. Spurious high frequency oscillations are damped by a third-order characteristic-based filter. The objective of this paper is to apply these improvements in the simulation of sound generated by the Kirchhoff vortex. Received: 31 January 2001 / Accepted: 30 September 2001     

Study of silicon backside damage in deep reactive ion etching for bonded silicon–glass structures

 For devices of bonded silicon and glass structures fabricated by deep reactive ion etching (DRIE), it is important to avoid damage at the silicon sidewall and backside during through-wafer etching in order to ensure reliability of devices. The silicon damage caused by charge accumulation at the glass surface is inhibited by means of an electrically conducting layer patterned onto the glass and connected with the silicon. In this study, indium tin oxide films were applied in order to identify the positions of silicon damage in the structural layout without destruction of samples. From the results, we report that there exists silicon damage caused by charge accumulation at the silicon islands divided by DRIE and we present important rules for mask layout when utilizing this method. Received: 10 August 2001/Accepted: 24 September 2001 This paper was presented at the Fourth International Workshop on high Aspect Ratio Microstructure Technology HARMST 2001 in June 2001.     

On two-fluid equations for dispersed incompressible two-phase flow

This paper deals with the two-fluid formulation for dispersed two-phase flow. In one space dimension the equations with constant viscosity for both phases are shown to result in a locally in time well-posed periodic problem but without viscosity there are regions in phase space where the problem is non-hyperbolic. It is shown that the viscid problem linearized at constant states in the non-hyperbolic region is terribly unstable for small viscosity coefficients. By numerical experiments for the solution to a model problem it is demonstrated that for smooth initial data in the non-hyperbolic region, discontinuities seem to form. Second order artificial dissipation is added, in an effort to regularize the problem. Numerical examples are given, for different types of initial data. For initial data that is smooth in the non-hyperbolic region, the formation of jumps, or viscid layers, is strongly dependent on the amount of artificial dissipation. No convergence is obtained as the amount of artificial dissipation is diminished. On the other hand, if the initial data is smooth only in the hyperbolic region and with jumps through the non-hyperbolic region, then the jumps or viscid layers that later form, can damp the onset of new layers. In this case convergence in the L₂ sense seem to hold, the computed solutions to the regularized problem approach a weak solution as the artificial dissipation is diminished. Received: 30 January 2001 / Accepted: 30 May 2001     

An anisotropic a-posteriori error estimate for a convection-diffusion problem

In this work we develop an a-posteriori error estimation for the finite element simulation of an advection-diffusion problem with anisotropic meshes. The error analysis is carried out by exploiting some recent interpolation error estimates for anisotropic meshes [7, 8] within the a-posteriori analysis framework proposed in [2, 3, 4, 16]. The target application is the transport of a solute (like oxygen or lipids) by the blood stream in a large artery. Received: 30 January 2001 / Accepted: 30 May 2001     

Aeroacoustic modeling of complex flow problems: I-Domain decomposition method for the reduced wave equation

An accurate and efficient method for solving the wave equation on multi-domains is developed for two-dimensional geometries. In this work we treat Cartesian geometries, but the method may be directly extended to more general geometries. As a first step, the one-dimensional problem is investigated. The wave equation is solved in the Fourier space. Three different numerical discretizations are tested, a Pointwise second-order accurate discretization (PT), and two fourth-order schemes: a Padè approximation (HO), and an Equation Based scheme (EB). A consistent discretization of the non reflecting boundary conditions is proposed, which preserves the overall accuracy of the corresponding interior scheme. For the solution of the linear system, it is shown that the preconditioned ILUT-GMRES method is an appropriate choice. In the multi-domain method, an optimal iterative procedure is described, specifying the correct form of the transmission conditions at the interfaces. The numerical tests confirm that the present multi-domain technique retains the same numerical properties of the single domain method. Finally the single and multi domain methods are extended to the two-dimensional case. Received: 31 January 2001 / Accepted: 30 September 2001     

Model Selection by Predictive Validation

: Gaussian mixture modelling is used to provide a semi-parametric density estimate for a given data set. The fundamental problem with this approach is that the number of mixtures required to adequately describe the data is not known in advance. In our previous work , we described an algorithm, termed Predictive Validation, which attempted to automatically select the number of components. The aim of this paper is to investigate the influence of the various parameters in our model selection method in order to develop it into an operational tool. In this paper, we demonstrate the successful application of model validation to three applications in which the selected models are used for supervised classification, unsupervised classification and outlier detection tasks. Received: 23 Novenber 2000, Received in revised form: 24 April 2001, Accepted: 21 May 2001     

A confidence value estimation method for handwritten Kanji character recognition and its application to candidate reduction

This paper describes a method for estimating a confidence value (CV) by which we can express the potential correctness of handwritten Kanji character recognition candidates. An accumulated confidence value (ACV), calculated as the sum of CVs, is also applied to reduce the number of candidates. Such reduction is vital to increasing the speed of such applications as Kanji address recognition, and it also reduces the probability of misreadings in linguistic postprocessing. Sorted sets of character candidates, ranked in increasing order of each candidates distance value, are used as feature vectors. A CV is defined as the a posteriori probability with respect to each rank. To obtain good quality approximations of probability density functions (PDFs), we introduce a subspace within which correct data can easily be separated from erroneous data and then estimate PDF parameters over this subspace. Next, we use an ACV as a measure for expressing a threshold for candidate acceptance in Kanji character recognition. The efficiency of the proposed method is evaluated in an experiment using IPTP CD-ROM2 Japanese address images, and a comparison with the results for a conventional method shows that a roughly 35% reduction in the number of candidates is obtained without reducing the number of correct candidates.Received: 29 October 2001, Accepted: 30 September 2003, Published online: 1 April 2004Correspondence to: Eiki Ishidera     

Consolidation of concentrated suspensions – shear and irreversible floc structure rearrangement

A mathematical model for a consolidation process of a highly concentrated, flocculated suspension is developed. The suspension is treated as a mixture of a fluid and solid particles by an Eulerian two-phase fluid model. We characterize the suspension by constitutive relations correlating the stresses, interaction forces, and inter-particle forces to concentration and velocity gradients. Irreversibility of the permeability and yield stress is modeled by a memory function. A simulation program using finite difference methods in time and space is applied to a two dimensional test case. Numerical experiments are carried out on consolidation under shear and gravity in a 2D box with moving bottom. Received: 30 January 2001 / Accepted: 30 May 2001     

Injection molding of microstructured components from plastics, metals and ceramics

 Micro injection molding is presently on its way to become an established manufacturing process in commercialising Microsystem Technologies. Enhanced products from plastics for micro optical or medical applications are entering the market. New developments like the different kinds of injection molding for microstructured components from plastics, metals or ceramics will increase the material range available in microdimensions. This will open up opportunities for increasing economic efficiency, for new fields of applications as well as for innovative products in the future. Received: 30 April 2001/Accepted: 30 August 2001     

Implicit treatment of molar mass equations in secondary oil migration

The hydrocarbon migration can be described by a coupled set of partial differential equations describing the dynamics of the temperature, component flow, pressure and velocity. A sequential solution procedure where the component flow is solved explicitly, gives severe restrictions on the time step given by the CFL condition. In this paper an implicit solution procedure is given and results from numerical tests are presented. The results are compared with the explicit solutions. As expected the implicit algorithm allows for substantially larger time steps. Received: 31 January 2001 / Accepted: 30 September 2001     

Injection molding for microstructures controlling mold-core extrusion and cavity heat-flux

 In this work we constructed an injection press molding system with a mold-core extrusion mechanism and a small sensor assembly for effectively duplicating microstructures to the mold products. The mold-core extrusion mechanism is driven by a piezo element to apply force on important area with microstructures. For example, after injection it increases the cavity pressure from 20 to 34 MPa. Small sensors consist of the pressure, displacement, and heat flux sensor assemblies, arranged around the small cavity. The signals showed us the physical phenomena inside the mold and may be further used as control signal. In order to evaluate this injection press molding system, we formed micro triangular grooves of pitch 1 μm and angle 140°. The mold-core extrusion gave better diffraction intensity by several percents. Received: 16 May 2001/Accepted: 24 July 2001 The authors would like to thank FANUC Ltd. for cutting the triangular grooves on the mold-core. This paper was presented at the Conference of Micro System Technologies 2001 in March 2001.     

A model for a viscous preflush prior to gelation in a porous medium

In this paper we propose and analyse a simplified mathematical model on the effect of a fully miscible preflush on gel-placement in an oil reservoir. The approach is based on a segregated flow model even if the two phases are fully miscible. For the rate of a constant injection rate condition, exact solutions are constructed for the scalar conservation law. Saturation profiles consist of shocks and fingering zones. For constant pressure conditions we construct a semi-explicit relation for the shock position and gel penetration depth. Received: 31 January 2001 / Accepted: 30 September 2001     

Vibrational positioning method for optical fibers sliding on a frictional surface

 Open-loop positioning methods for optical fibers on glass substrates are presented. When a slender and flexible object such as an optical fiber is moved on a frictional surface, its position is difficult to control because the object is caught in a frictional dead zone, causing the occurrence of stick-slip. In this paper, first, a positioning method when the friction force is known is derived based on a one-degree-of-freedom model of a sliding optical fiber. Then, a positioning method when the friction force is not known is derived by modifying the method for the case of known friction. Finally, the validity of the theory is verified by experiment and simulation. Received: 5 July 2001/Accepted: 1 November 2001     

A domain decomposition algorithm for inverse welding problems

A mathematical model and a numerical scheme for the inverse determination of heat sources generated by means of a welding process is presented in this paper. The accuracy of the heat source retrieval is discussed. Received: 30 January 2001 / Accepted: 30 May 2001     

A new ultrasonic catheter system with LIGA geared micromotor

 Ultrasonic imaging techniques play an important role in endoscopic pre-operative staging and post operative follow-up of tumour patients as well as for the assessment of cardiac insufficiency. However, cancerous lesions offer only low-contrast targets. Therefore, high sensitivity systems with good contrast as well as flexible and robust handling are required to obtain diagnostic accuracy and confidence. We developed a radial scanning ultrasonic catheter with a total diameter of 2.3 mm, which makes use of a LIGA geared micromotor to turn an ultrasonic transducer directly at the tip of the catheter. Connector rings fitted on a shaft as well as sliding contacts transmit the 20/30 MHz signals from the transmitter/receiver of an ultrasound monitor system (Kretz Technik AG, Austria) to/from the rotating transducer. Due to its excellent performance and easy handling the scanner module will be applied in a number of ultrasonic diagnostic applications. Received: 10 August 2001/Accepted: 24 September 2001 This paper was presented at the Fourth International Workshop on High Aspect Ratio Microstructure Technology HARMST 2001 in June 2001.