Alternative Computational Methods Research Articles

Slide track analysis of eight contemporary hip simulator designs

In an earlier paper, the authors presented a new method of computation of slide tracks in the relative motion between femoral head and acetabular cup of total hip prostheses. For the first time, computed tracks were verified experimentally and with an alternative method of computation. Besides being an efficient way to illustrate hip kinematics, the shapes of the slide tracks are known to be of fundamental importance regarding the wear behaviour of prostheses. The verified method was now applied to eight contemporary hip simulator designs. The use of correct motion waveforms and an Euler sequence of rotations in each case was again found to be essential. Considerable differences were found between the simulators. For instance, the shapes of the tracks drawn by the resultant contact force included a circle, ellipse, irregular oval, leaf, twig, and straight line. Computation of tracks correctly for the most widely used hip simulator, known as biaxial, was made possible by the insight that the device is actually three-axial. Slide track patterns have now been computed for virtually all contemporary hip simulators, and both for the heads and for the cups. This comparative analysis forms a valuable basis for studies on the relationship between the type of multidirectional motion and wear. These studies can produce useful information for the design of joint simulators, and improve the understanding of wear phenomena in prosthetic joints.

Accuracy of Numerical Solutions Using the Euler Equation Residuals

In this paper we derive sorne asymptotic properties on the accuracy of numerical solutions. We sIlow tIlat the approximation error of the policy function is of the same order of magnitude as the size of the Euler equation residuals. Moreover, for bounding this approximation error tIle most relevant parameters are the discount factor and the curvature of the return function. These findings provide theoretical foundations for the construction of tests that can assess the performance of alternative computational methods.

New Molecular Mechanics (MM3*) Force Field Parameters for Calculations on (η3-Allyl)palladium Complexes with Nitrogen and Phosphorus Ligands

A force field for (η3-allyl)palladium complexes with phosphorus and/or nitrogen ligands has been developed, based upon both X-ray and quantum chemical reference data. The quality of the force field in structure prediction is checked by comparison to X-ray structures, including several not used in the parametrization. The force field is also compared to alternative computational methods for structure prediction, including earlier force fields and two quantum chemical methods (PM3(tm) and B3LYP/LANL2DZ).

Three-way (PARAFAC) factor analysis: examination and comparison of alternative computational methods as applied to ill-conditioned data

Four different approaches to solving the trilinear three-way factor analysis problem are compared, and their performance with `difficult' (i.e., ill-conditioned) data is tested. These approaches are represented by four different computer programs: one using a simple alternating least squares (ALS) algorithm with only minimal extrapolation (HL-PARAFAC), one in which the ALS is supplemented by a sophisticated extrapolation to speed convergence (TPALS), one using a non-linear curve fitting method (PMF3), and one using a non-iterative closed-form approximation (DTDMR). The options provided by these programs (e.g., with regard to missing values, weighted least squares, non-negativity and other constraints) are compared. Criteria for choosing synthesized test data and a method for synthesizing exponential test data are described. A numerical index is introduced to characterize the ill-conditioning of n-way arrays ( n>2). Two well characterized synthetic data sets serve as `difficult' (ill-conditioned) test data. Intercomparisons among HL-PARAFAC, TPALS, DTDMR and PMF3 were implemented with these test data. Consequently, their limitations and strengths are determined. In addition, these trilinear analysis approaches are applied to a difficult set of ill-conditioned real data: a set of fluorescence spectroscopy measurements that characterize the steady-state fluorescence of an amino acid in aqueous solution. When converged, the results produced by the three least-squares techniques (but not DTDMR) agree. However, there are large differences in convergence speed when these difficult problems are solved: TPALS is faster than PARAFAC by a factor of ten, and PMF3 is faster than TPALS, again by a factor of ten. The program DTDMR is the fastest, but it only solves half of the problems.

Modelling electrode transients: the strongly implicit procedure

The ‘strongly implicit procedure’ is shown to be a general, easy-to-use, stable and computationally efficient method of solving the mass transport equations necessary to predict transient voltammetric responses of electrode processes to which diffusion, convection and homogeneous chemical reaction may all contribute. The method is illustrated with a diversity of problems relating to electrodes of both micro- and milli-dimensions. In all cases excellent agreement with experiment and/or existing analytical or numerical theory is noted. Comparisons are made with alternative computational methods.

Optimized group contribution methods for predicting chemical biodegradation and eye irritancy

Environmental testing increasingly has emphasized faster, more flexible methods for estimating chemical toxicity. The present work evaluates the use of computational methods to determine chemical biodegradation and to assess irritancy hazards. An optimized strategy begins with structure‐activity relationships between functional groups in a chemical and then generalizes to assess hazards associated with a previously unstudied compound formula. These compound formulas consist of building blocks made from the functional groups, but the effects of these groups are investigated beyond a simple additive method. Both linear sums of these contributions and their corresponding non‐linear fits are compared against known biodegradation and irritancy statistics. In this way, computation of hazards for chemicals not used for modelling, but for which good literature data are available, can grade the method's performance. A correlation is found between existing in vivo databases and proposed computer prediction. These alternative computational methods share the common goal of providing accurate hazard assessments to the chemical industry without using expensive laboratory animal tests.

Dynamic simulations of shear-flow-induced chirality and twisted-texture transitions of a liquid-crystalline polymer.

An alternative computational adaptive method to solve the Leslie-Ericksen equations of nematic hydrodynamics is presented. The method uses adaptive torque balances and is able to accurately compute arbitrary three-dimensional orientation fields. The method is applied, in conjunction with computational bifurcation methods, to solve the governing equations for a model rigid-rod, nonaligning, nematic polymer, in steady and transient rectilinear simple shear flows, using fixed parallel director anchoring. The five-component solution vector consists of the primary and secondary velocity components and the three-dimensional director field n. The parameter space is the line representing the magnitudes of the Ericksen number (scrE). According to the magnitude of scrE, seven types of stable steady-state solutions are found and fully characterized. The seven types of solutions are classified as in-plane solutions if the director remains within the shear plane, defined by the flow direction and the velocity gradient, and as out-of-plane (OP) solutions if the director field is out of the shear plane (three-dimensional orientation). The six OP solutions are three pairs of mirror-image solutions that differ from each other by their rotation number (\ensuremath{\Lambda}). Two pairs of out-of-plane solution branches are achiral (\ensuremath{\Lambda}=0) and display one-way twisting from the shear plane. One pair of out-of-shear-plane solution branches is chiral (\ensuremath{\Lambda}=\ifmmode\pm\else\textpm\fi{}1) and displays a full 2\ensuremath{\pi} director rotation when going from the bottom plate to the top plate.The nucleation mechanisms of these chiral branches are identified using a torque analysis. The main bifurcation phenomena and the local stability of the branches are summarized in a bifurcation diagram. The main structural changes, as the parameter scrE increases, are captured by visualization of the transient director field. The main features of the velocity field are captured by particle tracking visualization, which yields three-dimensional particle motions driven by the combined primary and secondary flows. The main mechanical responses, captured by the transient rheological functions (apparent viscosity and the first normal stress differences), exhibit, at low shear rates, non-Newtonian responses that are usually found in isotropic, viscous, or viscoelastic liquids, at large shear rates. Dynamic simulation in conjunction with the bifurcation diagram is used to construct the stability phase diagram, which yields the adopted stable steady-state solution that results from shearing a monodomain sample with fixed parallel director anchoring. Finally, the strain history is shown to control the finally adopted steady state, thus invalidating linear superposition which is usually valid at small shear rates.

Ellipsometry algorithm for absorbing films

Easy sample preparation and measurement makes ellipsometry attractive for surface and film investigations; however, specialized numerical methods are normally required to relate measurements to unknown physical attributes of reflecting surfaces. Although solution techniques have been developed, the problem of data analysis is by no means solved. This paper presents an alternative method for computation of the thickness and optical properties of an absorbing film overlying a known substrate from ellipsometer data obtained at two light incidence angles. Tests for selected cases required no a priori knowledge of the film, in contrast to other methods.

A model of the volumetrically-controlled hemodialysis circuit.

We developed a model that predicts the hemodynamics of the volumetrically-controlled circuit used to administer high flux hemodialysis. The equations simulate the entire blood side of the circuit so that blood and dialysate pressures can be predicted from a knowledge of circuit component and patient characteristics. An alternative method of computation has also been devised which permits measured circuit pressures to be used to predict patient blood access pressure, dialyzer resistance to flow and membrane hydraulic conductivity. Success of the model was evaluated by measuring both circuit pressure and component characteristics. The model successfully predicted circuit pressures when measured component characteristics were employed as model inputs. Conversely, the model accurately predicted circuit component characteristics when measured pressures were employed as inputs (8 patients, 30 dialyses). Specific predictions of the model include the following. Elevations of patient blood access pressure will cause blood and dialysate pressures to rise equivalently without affecting the rate of back-filtration or location of pressure equilibrium along the dialyzer axis. Elevated hematocrit is predicted to increase circuit pressures to a degree that is similar to a poorly functioning blood access, however, high hematocrit markedly augments back-filtration and moves the point of pressure equilibrium toward the dialyzer entrance. We conclude that the model provides a predictive tool that can be used to optimize circuit design. Alternatively, the model can be used to separate the influence of a poorly functioning patient access from other factors which can elevate circuit pressures.

Detection of potential inconsistencies in knowledge bases

We present a new computational approach to the problem of detection of potential inconsistencies in knowledge bases. For such inconsistencies, we characterize the sets of possible input facts that will allow the knowledge based system to derive the contradiction. the state-of-the-art approach to a solution of this problem is represented by the COVADIS system which checks simple rule bases. the COVADIS approach relies on forward chaining and is strongly related to the way ATMS computes labels for deducible facts. Here, we present an alternative computation method that employs backward chaining in a kind of abductive reasoning. This approach gives a more focused reasoning, thus requiring much less computation and memory than COVADIS. Further, since our method is very similar to SLD-resolution, it is suitable for handling the more powerful knowledge base form represented by Horn claause bases. Finally, our method is easily extended to uncertain knowledge bases, assuming that the uncertainty calculus is modeled by possibilistic logic. This extension allows us to model the effect of user defined belief thresholds for inference chains.

A METHOD FOR DETERMINING PLASTOCHRON INDICES DURING HETEROBLASTIC SHOOT GROWTH

A plastochron is defined as the time interval between two successive recurring events during the growth of plant shoots, such as leaf initiation. The plastochron index (PI) formulated by Erickson and Michelini (1957, American Journal of Botany 44: 297–305) provides a method for determining 1) morphological equivalence in a developmentally variable sample of shoots and 2) rates of development in microscopic tissues and organs, by expressing shoot age as a function of plastochron number. The PI assumes that homologous organs at successive nodes grow exponentially, at equal rates, and the plastochron remains constant. These three conditions are not met in many shoots that exhibit heteroblasty in their plastochron and the growth rate of organs at successive nodes. An alternative computational method for the PI is presented that uses two measurements taken at different times from the same organ during its exponential growth phase. The method does not assume that the PI is a linear function of time. Results of an analysis of cyme internode growth in two races of Arenaria uniflora (Caryophyllaceae) demonstrate that the method proposed is in good agreement with Erickson and Michelini's (1957) method when shoot growth is not markedly heteroblastic. The current method is also used to determine the nonlinear relation between PI and time in a race of A. uniflora that has heteroblastic cyme growth. The results generalize the PI for use in studies of heteroblasty, and for shoots where the relative plastochron rate cannot be directly determined.

A Method for Determining Plastochron Indices During Heteroblastic Shoot Growth

A plastochron is defined as the time interval between two successive recurring events during the growth of plant shoots, such as leaf initiation. The plastochron index (PI) formulated by Erickson and Michelini (1957, American Journal of Botany 44: 297–305) provides a method for determining 1) morphological equivalence in a developmentally variable sample of shoots and 2) rates of development in microscopic tissues and organs, by expressing shoot age as a function of plastochron number. The PI assumes that homologous organs at successive nodes grow exponentially, at equal rates, and the plastochron remains constant. These three conditions are not met in many shoots that exhibit heteroblasty in their plastochron and the growth rate of organs at successive nodes. An alternative computational method for the PI is presented that uses two measurements taken at different times from the same organ during its exponential growth phase. The method does not assume that the PI is a linear function of time. Results of an analysis of cyme internode growth in two races of Arenaria uniflora (Caryophyllaceae) demonstrate that the method proposed is in good agreement with Erickson and Michelini's (1957) method when shoot growth is not markedly heteroblastic. The current method is also used to determine the nonlinear relation between PI and time in a race of A. uniflora that has heteroblastic cyme growth. The results generalize the PI for use in studies of heteroblasty, and for shoots where the relative plastochron rate cannot be directly determined.

TE Diffraction by a Pair of Semi-Infinite Material Sheets

The extended spectral ray method (ESRM) is employed in deriving expressions for the multiply diffracted fields by a pair of semi-infinite parallel material sheets/layers. One of the sheets is chosen to satisfy a second order boundary condition simulating a thin dielectric layer and the other is a resistive sheet. Of interest is the computation of the leading edge scattering given as the sum of the singly and multiply diffracted fields with particular attention given to the computation of higher order diffraction fields beyond the second. Their evaluation required a non-traditional approach and up to fifth order diffraction fields are derived and applied in computing the scattering by a pair of half sheets simulating a metal-backed dielectric half plane as thin as 1/20 of a wavelength. Numerical results for other practical simulations are presented and compared with results based on alternative computational methods, where applicable.

Computation of a long-time evolution in a Schrödinger system.

We compare different techniques for the computation of a long-time evolution and the S matrix in a Schr\"odinger system. As an application we consider a two-nucleon system interacting via the Yamaguchi potential. We suggest computation of the time evolution for a very short time using Pad\'e approximants, the long-time evolution being obtained by iterative squaring. Within the technique of strong approximation of Moller wave operators (SAM) we compare our calculation with computation of the time evolution in the eigenrepresentation of the Hamiltonian and with the standard Lippmann-Schwinger solution for the S matrix. We find numerical agreement between these alternative methods for time-evolution computation up to half the number of digits of internal machine precision, and fairly rapid convergence of both techniques towards the Lippmann-Schwinger solution.

COMPUTATION OF TSUNAMI WAVEFORMS BY A SUPERPOSITION OF NORMAL MODES

Computation of tsunami waveforms for actual topography is usually made by a time-stepping finite-difference method which needs a long computation time and must be repeated for different initial conditions. We propose here an alternative computation method by a superposition of normal modes. Although the eigenvalue problem to obtain the normal mode solutions needs more memories, once we get the solution, the waveforms can be computed by merely summing up the normal modes with weights determined by the initial condition. We present the waveforms for a simple water basin computed by both methods. The results show that the new method is useful for a completely or almost closed basin including the tsunami source.

Qualitative Student Models

Abstract : Instructional programs were among the earliest applications of computer programming. The original vision remains strong today: Instruction by computer offers the potential of better attention to individual student needs and interests that can be met in the typical classroom. Individualized instruction, modeled after the idea of a private tutor, allows a student to proceed at his own pace, to explore his interests, and to receive personal, detailed evaluation and direction. Realized as an interactive computer program, such instruction might be more effective, faster, and possibly less costly than traditional teaching. In addition, computer technology provides opportunities for new forms of instruction based on interactive graphics and programming itself, which foster intuition for abstract and creative thinking. The goal of this review is to provide a comprehensive, but critical review of qualitative student models. A student model is the set of records in an instructional program that describe a student's knowledge about what is being taught and allow the program to adapt its presentations to his needs. A qualitative student model describes a student's knowledge structurally, in terms of relations among concepts and a problem solving procedure. I use the concept of a qualitative model as the focus of this review in order to compare alternative computational methods and to contrast domain requirements.

Algorithm for Autocorrelation Analysis of Secular Trends

An algorithm for autocorrelation analysis of time series data was presented and compared with two alternative computational methods. The algorithm was based on continuous variance adjustment following withdrawal of an element from the lagged series. The algorithm not only reduces the number of computations during the repeated passes through the data vector but also avoids a dampening effect toward the end of the series.

High-frequency propagation in an elevated tropospheric duct

High-frequency propagation in an elevated tropospheric duct above the earth is analyzed conventionally by normal mode summation, which may be inefficient and often of questionable accuracy because of the large number of modes required. Ray-optical methods, which have been employed, are likewise subject to limitations. The present study explores a new method that combines a judiciously chosen mixture of ray-optical and normal mode fields plus a remainder field that is usually small. The modes may be guided along the concave side of the duct boundary or between this boundary and the earth's surface. By retaining the advantages of both the modal and ray formulations, the hybrid scheme generally requires far fewer rays and modes than the number of modes in a conventional normal mode representation. The hybrid method is applied here to the Green's function problem for a two-dimensional model of the duct formed by a refractive index discontinuity above a perfectly conducting earth. Field values for various locations of source and observation points are computed from the normal mode formulation, which is used as a reference solution, and from the hybrid formulation. The features of these alternative computational methods are discussed in detail and reveal the advantages of the hybrid scheme. Physical interpretation of the hybrid ray-mode field is emphasized throughout and grants new insight into various wave processes.

ANALYSIS OF WASTE LOAD ALLOCATION PROCEDURES1

ABSTRACTA study was made to analyze and modify procedures used for stream assimilation capacity and point source wasteload allocation calculations. This paper describes the sources and types of information collected and the analysis of alternative computation methods developed during the study. The calculation of stream assimilation capacity or Total Maximum Daily Load (TMDL), will depend upon assumed stream flows, quality standards, reaction rates, and modeling procedures. The “critical conditions” selected for TMDL calculations usually are low flows and warm temperatures. The complexity of water quality models used for TMDL and allocation calculations can range from simple, complete mixing to calibrated and verified mathematical models. A list of 20 wasteload allocation (WLA) methods was developed. Five of these WLA's were applied to an example stream to permit comparisons based on cost, equity, efficient use of stream assimilation capacity, and sensitivity to fundamental stream quality data. Based on insensitivity to data errors and current use by several states, the WLA method of “equal percent treatment” was preferable in the example stream.

An alternative computational method for the approximation of random functions

This paper shows that a computational procedure for approximation of random functions can be accomplished using purely linear programming techniques. This contrasts with previous results which use a twostage approach for the computation, one of which requires linear programming techniques. Computational results are given.