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Numerical Techniques (numerical + techniques)
Selected AbstractsComputer programs for estimating substrate flux into steady-state biofilms from pseudoanalytical solutionsCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 1 2002Chetan T. Goudar Abstract Fixed-film processes employing microorganisms attached to an inert surface (biofilms) are widely used for biological treatment of municipal and industrial wastewater. For optimal design and analysis of these processes, mathematical models are necessary that describe the dynamics of contaminant transport within these biofilms and the associated contaminant utilization by the microorganisms. However, these governing equations that typically involve Fickian diffusion for contaminant transport and Monod kinetics for contaminant utilization are inherently nonlinear and have no closed form solutions except under special conditions. This can restrict their use in the classroom as cumbersome numerical techniques must be used for their solution. This problem is well documented in the literature and several authors have presented pseudoanalytical solutions that replace numerical solutions with algebraic equations. In the present study, we present pseudoanalytical solution-based computer programs for estimating substrate flux and biofilm thickness for a steady-state biofilm. Depending upon the intended end use, these programs can either partially or totally automate the solution process. In the partial automation mode, they can serve to enhance student understanding of important concepts related to steady-state biofilms, while complete automation can help bring more challenging and realistic problems associated with steady-state biofilms into the classroom. The programs have been tested on MATLAB version 5.0 and are available as freeware for educational purposes. © 2002 Wiley Periodicals, Inc. Comput Appl Eng Educ 10: 26,32, 2002; Published online in Wiley InterScience (www.interscience.wiley.com.); DOI 10.1002/cae.10017 [source] Direct Manipulation and Interactive Sculpting of PDE SurfacesCOMPUTER GRAPHICS FORUM, Issue 3 2000Haixia Du This paper presents an integrated approach and a unified algorithm that combine the benefits of PDE surfaces and powerful physics-based modeling techniques within one single modeling framework, in order to realize the full potential of PDE surfaces. We have developed a novel system that allows direct manipulation and interactive sculpting of PDE surfaces at arbitrary location, hence supporting various interactive techniques beyond the conventional boundary control. Our prototype software affords users to interactively modify point, normal, curvature, and arbitrary region of PDE surfaces in a predictable way. We employ several simple, yet effective numerical techniques including the finite-difference discretization of the PDE surface, the multigrid-like subdivision on the PDE surface, the mass-spring approximation of the elastic PDE surface, etc. to achieve real-time performance. In addition, our dynamic PDE surfaces can also be approximated using standard bivariate B-spline finite elements, which can subsequently be sculpted and deformed directly in real-time subject to intrinsic PDE constraints. Our experiments demonstrate many attractive advantages of our dynamic PDE formulation such as intuitive control, real-time feedback, and usability to the general public. [source] DEM analysis of bonded granular geomaterialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 17 2008S. Utili Abstract In this paper, the application of the distinct element method (DEM) to frictional cohesive (c, ,) geomaterials is described. A new contact bond model based on the Mohr,Coulomb failure criterion has been implemented in PFC2D. According to this model, the bond strength can be clearly divided into two distinct micromechanical contributions: an intergranular friction angle and a cohesive bond force. A parametric analysis, based on several biaxial tests, has been run to validate the proposed model and to calibrate the micromechanical parameters. Simple relationships between the macromechanical strength parameters (c, ,) and the corresponding micromechanical quantities have been obtained so that they can be used to model boundary value problems with the DEM without need of further calibration. As an example application, the evolution of natural cliffs subject to weathering has been studied. Different weathering scenarios have been considered for an initially vertical cliff. Firstly, the case of uniform weathering has been studied. Although unrealistic, this case has been considered in order to validate the DEM approach by comparison against analytical predictions available from limit analysis. Secondly, non-uniform weathering has been studied. The results obtained clearly show that with the DEM it is possible to realistically model boundary value problems of bonded geomaterials, which would be overwhelmingly difficult to do with other numerical techniques. Copyright © 2008 John Wiley & Sons, Ltd. [source] Frost heave modelling using porosity rate functionINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2006Radoslaw L. Michalowski Abstract Frost-susceptible soils are characterized by their sensitivity to freezing that is manifested in heaving of the ground surface. While significant contributions to explaining the nature of frost heave in soils were published in late 1920s, modelling efforts did not start until decades later. Several models describing the heaving process have been developed in the past, but none of them has been generally accepted as a tool in engineering applications. The approach explored in this paper is based on the concept of the porosity rate function dependent on two primary material parameters: the maximum rate, and the temperature at which the maximum rate occurs. The porosity rate is indicative of ice growth, and this growth is also dependent on the temperature gradient and the stress state in the freezing soil. The advantage of this approach over earlier models stems from a formulation consistent with continuum mechanics that makes it possible to generalize the model to arbitrary three-dimensional processes, and use the standard numerical techniques in solving boundary value problems. The physical premise for the model is discussed first, and the development of the constitutive model is outlined. The model is implemented in a 2-D finite element code, and the porosity rate function is calibrated and validated. Effectiveness of the model is then illustrated in an example of freezing of a vertical cut in frost-susceptible soil. Copyright © 2006 John Wiley & Sons, Ltd. [source] Review of validation of the discontinuous deformation analysis (DDA) methodINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2006M. M. MacLaughlin Abstract Over the last decade, researchers in the discontinuous deformation analysis (DDA) community have dedicated a great deal of effort to document the accuracy of the method by performing validation studies. This paper contains a summary of more than 100 published and unpublished validation studies which comprise the body of DDA validation information to which the authors have access. The studies are grouped into three general categories: (a) validation with respect to analytical solutions, (b) validation with respect to results of other numerical techniques, and (c) validation with respect to laboratory and field data. Three general techniques for validation are described: qualitative assessment visually examining runtime behaviour of simulations, semi-quantitative assessment comparing numerical results of simulations, and quantitative where numerical simulation results are evaluated in detail with respect to similar analytical, laboratory or field results. We find that for many of the problems addressed by the papers in this review, DDA performs more than adequately for engineering analysis. Copyright © 2006 John Wiley & Sons, Ltd. [source] Direct assessment of structural resistance against pressurized fractureINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2003G. Bolzon Abstract The determination of the load bearing capacity of hydraulic structures such as dams, reservoirs and retaining walls requires the consideration of mixed-mode fracture, possibly driven by the fluid pressure, in correspondence to artificial and natural joints (or cracks, in the latter case). A friction-cohesive softening interface model with coupled degradation of normal and tangential strength is introduced here to account for the essential features of the joint behaviour; its predictive capability is assessed through extensive calculations. Alternative numerical techniques resting on the discrete-crack approach are considered, focusing on simplified approaches for the direct appraisal of the structural resistance. Comparison is made with the results of evolutionary analyses, based on a priori piecewise linearization of the interface model and on ,exact integration'. Copyright © 2003 John Wiley & Sons, Ltd. [source] A computational model for fracturing porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2007R. Al-Khoury Abstract This paper presents a new computational model for simulating a fracturing process in a porous medium using the finite element method. Two independent numerical techniques are used for describing this process. The partition of unity method is used for describing the fracturing process, and the double porosity model is used for describing the resulting fluid flow. A key feature of the model is the coupling of these two independent numerical techniques, which provide the means for a better simulation of the involved physical and mechanical processes. The paper focuses on the numerical formulation of the model. The capability of the model is illustrated by means of numerical examples, which examine the behaviour of a 1D porous medium under different boundary conditions. The numerical results show that the very complicated physical and mechanical processes of the fracturing porous media can be simulated properly and efficiently. Copyright © 2006 John Wiley & Sons, Ltd. [source] Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedraINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003Seppo Järvenpää Abstract A numerical solution of integral equations typically requires calculation of integrals with singular kernels. The integration of singular terms can be considered either by purely numerical techniques, e.g. Duffy's method, polar co-ordinate transformation, or by singularity extraction. In the latter method the extracted singular integral is calculated in closed form and the remaining integral is calculated numerically. This method has been well established for linear and constant shape functions. In this paper we extend the method for polynomial shape functions of arbitrary order. We present recursive formulas by which we can extract any number of terms from the singular kernel defined by the fundamental solution of the Helmholtz equation, or its gradient, and integrate the extracted terms times a polynomial shape function in closed form over plane triangles or tetrahedra. The presented formulas generalize the singularity extraction technique for surface and volume integral equation methods with high-order basis functions. Numerical experiments show that the developed method leads to a more accurate and robust integration scheme, and in many cases also a faster method than, for example, Duffy's transformation. Copyright © 2003 John Wiley & Sons, Ltd. [source] Instabilities of Boussinesq models in non-uniform depthINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2009F. Løvholt Abstract The von Neumann method for stability analysis of linear waves in a uniform medium is a widely applied procedure. However, the method does not apply to stability of linear waves in a variable medium. Herein we describe instabilities due to variable depth for different Boussinesq equations, including the standard model by Peregrine and the popular generalization by Nwogu. Eigenmodes are first found for bathymetric features on the grid scale. For certain combinations of Boussinesq formulations and bottom profiles stability limits are found in closed form, otherwise numerical techniques are used for the eigenvalue problems. Naturally, the unstable modes in such settings must be considered to be as much a result of the difference method as of the underlying differential (Boussinesq) equations. Hence, modes are also computed for smooth depth profiles that are well resolved. Generally, the instabilities do not vanish with refined resolution. In some cases convergence is observed and we thus have indications of unstable solutions of the differential equations themselves. The stability properties differ strongly. While the standard Boussinesq equations seem perfectly stable, all the other formulations do display unstable modes. In most cases the instabilities are linked to steep bottom gradients and small grid increments. However, while a certain formulation, based on velocity potentials, is very prone to instability, the Boussinesq equations of Nwogu become unstable only under quite demanding conditions. Still, for the formulation of Nwogu, instabilities are probably inherent in the differential equations and are not a result of the numerical model. Copyright © 2008 John Wiley & Sons, Ltd. [source] Liquid vorticity computation in non-spherical bubble dynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2005A. A. Aganin Abstract The purpose of this work is to compare efficiency of a number of numerical techniques of computation of liquid vorticity from non-spherical bubble oscillations. The techniques based on the finite-difference method (FDM), the collocation method (one with differentiating (CMd) the integral boundary condition and another without it (CM)) and the Galerkin method (GM) have been considered. The central-difference approximations are used in FDM. Sinus functions are chosen as the basis in GM. Problems of decaying a small distortion of the spherical shape of a bubble and dynamics of a bubble under harmonic liquid pressure variation with various parameters are used for comparison. The FDM technique has been found to be most efficient in all the cases. Copyright © 2004 John Wiley & Sons, Ltd. [source] Numerical approximation of optimal control of unsteady flows using SQP and time decompositionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004S. S. RavindranArticle first published online: 1 APR 200 Abstract In this paper, we present numerical approximations of optimal control of unsteady flow problems using sequential quadratic programming method (SQP) and time domain decomposition. The SQP method is considered superior due to its fast convergence and its ability to take advantage of existing numerical techniques for fluid flow problems. It iteratively solves a sequence of linear quadratic optimal control problems converging to the solution of the non-linear optimal control problem. The solution to the linear quadratic problem is characterized by the Karush,Kuhn,Tucker (KKT) optimality system which in the present context is a formidable system to solve. As a remedy various time domain decompositions, inexact SQP implementations and block iterative methods to solve the KKT systems are examined. Numerical results are presented showing the efficiency and feasibility of the algorithms. Copyright © 2004 John Wiley & Sons, Ltd. [source] Simulation of transient flow in pipelines for computer-based operations monitoringINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2004H. E. Emara-Shabaik Abstract Computer models can provide the basis for real-time monitoring and control of fluid flow in pipelines. Problems of fluid flow in pipelines are mathematically represented by a non-linear system of coupled partial differential equations. In this paper, several numerical techniques are evaluated with respect to their suitability for the purpose of real-time monitoring of fluid flow in pipelines. The proposed techniques are evaluated in terms of the L1, the L2, and the L, error norms. Moreover, the developed simulators will be compared in terms of their speed of response and settling time which are essential factors for an effective real-time monitoring scheme. Finally, the selected simulation scheme is further tested under assumed pipeline leak conditions. Copyright © 2004 John Wiley & Sons, Ltd. [source] Performance analysis of a solid oxide fuel cell with reformed natural gas fuelINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 11 2010S. M. Jafarian Abstract In the present study a two-dimensional model of a tubular solid oxide fuel cell operating in a stack is presented. The model analyzes electrochemistry, momentum, heat and mass transfers inside the cell. Internal steam reforming of the reformed natural gas is considered for hydrogen production and Gibbs energy minimization method is used to calculate the fuel equilibrium species concentrations. The conservation equations for energy, mass, momentum and voltage are solved simultaneously using appropriate numerical techniques. The heat radiation between the preheater and cathode surface is incorporated into the model and local heat transfer coefficients are determined throughout the anode and cathode channels. The developed model has been compared with the experimental and numerical data available in literature. The model is used to study the effect of various operating parameters such as excess air, operating pressure and air inlet temperature and the results are discussed in detail. The results show that a more uniform temperature distribution can be achieved along the cell at higher air-flow rates and operating pressures and the cell output voltage is enhanced. It is expected that the proposed model can be used as a design tool for SOFC stack in practical applications. Copyright © 2009 John Wiley & Sons, Ltd. [source] Multiresolution model of electromagnetic wave propagation in dispersive materialsINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 3 2003Ismael Barba Abstract A multiresolution time-domain (MRTD) technique based on Haar wavelets has been applied to model the propagation of waves in dispersive materials, using a discretization of the convolution equation that governs the behaviour of the media. To validate the method, the reflection coefficient at the interface between air and several different linear dispersive media, as well as the propagation of a plane wave towards a non-linear dispersive medium have been calculated and compared with other numerical techniques and theoretical results. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical modelling of equilibrium charge separation in poled devicesINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 6 2001A. De Francesco Abstract We describe an efficient numerical procedure for the equilibrium solution of the internal electric field distribution resulting from poling of photo-refractive materials. This technique has been developed to model the equilibrium state in poled bulk devices requiring bulk charge neutrality to facilitate the modelling of blocking boundaries for a high externally applied voltage (bias) in the kV range for a small number of points. This technique is an improvement on existing conventional numerical techniques employed for modelling semiconductor devices that are intended for low bias. This method can also accommodate the modelling of planar insulators and organic optical materials. We develop an algorithm incorporating the existing Newton,Raphson method for solving Kukhtarev's equations that enforces conservation of charge within the modelled system. We apply this technique to model one-dimensional charge separation in ultraviolet (UV) excited poling of glass and, report numerical equilibrium electric field distribution for a 2 kV bias. The convergence behaviour of the algorithm is investigated and compared against the Newton,Raphson method. Copyright © 2001 John Wiley & Sons, Ltd. [source] Discrimination of dynamical system models for biological and chemical processesJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 8 2007Sönke Lorenz Abstract In technical chemistry, systems biology and biotechnology, the construction of predictive models has become an essential step in process design and product optimization. Accurate modelling of the reactions requires detailed knowledge about the processes involved. However, when concerned with the development of new products and production techniques for example, this knowledge often is not available due to the lack of experimental data. Thus, when one has to work with a selection of proposed models, the main tasks of early development is to discriminate these models. In this article, a new statistical approach to model discrimination is described that ranks models wrt. the probability with which they reproduce the given data. The article introduces the new approach, discusses its statistical background, presents numerical techniques for its implementation and illustrates the application to examples from biokinetics. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 [source] DETERMINATION OF VARIABLE DIFFUSION OF SODIUM DURING DEBITTERING OF GREEN OLIVESJOURNAL OF FOOD PROCESS ENGINEERING, Issue 5 2004MARIELA BEATRIZ MALDONADO ABSTRACT Time-variable average effective diffusion coefficients of sodium in the skin and flesh were determined using Macroscopic Mass Balances from experimental data obtained during debittering of green olives, variety Arauco at temperatures of 15, 20 and 25C and lye concentrations of 1.50, 2.25 and 3.00% of NaOH. The effective diffusion coefficient of sodium increased with treatment time at both surfaces of the skin, while it varied very little within the flesh, and in many cases, remained almost constant during the debittering process. In general, the diffusion coefficients determined in the present study were within an order of magnitude of 10,10 m2/s for the flesh during most of the treatment time, while for the skin, they were of the order of 10,12 m2/s for the initial treatment times. Macroscopic mass balances are a simple mathematical method that can be used in lieu of more common numerical techniques, to evaluate variable diffusion coefficients providing accuracy and greater detail of the whole phenomena. [source] Tracer studies of high-shear granulation: II.AICHE JOURNAL, Issue 9 2001Population balance modeling A population balance framework developed describes the tracer studies in Part I. A two internal coordinate population balance equation (PBE) links the evolution with time of granule-size and tracer-mass distributions to underlying rate processes. A new analytical PBE was developed for the tracer distribution and novel numerical techniques, including a new discretized population balance equation for breakage or grinding. Also developed is a general differential technique for extracting rate constants from measurements of particle-size distributions. Granulation in a high-shear mixer proceeds after nucleation, not studied here, with very high initial breakage rates but a relatively unchanging aggregation rate constant. The breakage function is bimodal on a mass basis and the selection rate decays exponentially over about 20 s. A heterogeneous strength hypothesis was used to account for this time dependence. Aggregation rates are the highest for interactions between small and large granules and may be quantitatively given by the Equipartition of kinetic energy kernel developed from the theory of collisions between gas molecules. The model can describe granule-size and tracer-mass distributions simultaneously with great accuracy. The need to replace time as a driving force variable in the kinetics for these systems is identified. [source] Drug release properties of polymer coated ion-exchange resin complexes: Experimental and theoretical evaluationJOURNAL OF PHARMACEUTICAL SCIENCES, Issue 3 2007Seong Hoon Jeong Abstract Although ion-exchange resins have been used widely as drug delivery systems, their exact release kinetics has not been reported yet. Usually only the rate-limiting step has been taken into account and the rest of the steps have been ignored as instantaneous processes. To investigate the exact release kinetics of polymer-coated drug/ion-exchange resin complexes for sustained drug delivery, the results of new mathematical modeling were compared with experimental results. Drug/resin complexes with a model drug, dextromethorphan, were prepared and used as cores for fluid-bed coating. An aqueous colloidal dispersion of poly(vinyl acetate) was applied for the coating. A comprehensive mathematical model was developed using a mechanistic approach by considering diffusion, swelling, and ion-exchange processes solved by numerical techniques. The rate-limiting factor of the uncoated resin particles was diffusion through the core matrix. Similarly, in the coated particles the rate-limiting factor was diffusion through the coating membrane. The mathematical model has captured the phenomena observed during experimental evaluations and the release dynamics from uncoated and coated (at different coat levels) particles were predicted accurately (maximum RMSE 2.4%). The mathematical model is a useful tool to theoretically evaluate the drug release properties from coated ion-exchange complexes thus can be used for design purposes. © 2006 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci [source] Maximum likelihood estimation in semiparametric regression models with censored dataJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 4 2007D. Zeng Summary., Semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies. The presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models. We present several classes of semiparametric regression models, which extend the existing models in important directions. We construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters. The maximum likelihood estimators are consistent and asymptotically normal with efficient variances. We develop simple and stable numerical techniques to implement the corresponding inference procedures. Extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings. Applications to three medical studies yield important new insights. We conclude that there is no reason, theoretical or numerical, not to use maximum likelihood estimation for semiparametric regression models. We discuss several areas that need further research. [source] When (not) to indulge in ,puffery': the role of consumer expectations and brand goodwill in determining advertised and actual product qualityMANAGERIAL AND DECISION ECONOMICS, Issue 6 2000Praveen K. Kopalle We analyze why some firms advertise product quality at a level different from the actual quality of a product. By considering the interacting effects of product quality and advertising, we develop a dynamic model of consumer expectations about product quality and the development of brand goodwill to determine the optimal values for the decision variables. The model parameters are determined based on prior literature and we use numerical techniques to arrive at the solution. We then derive conditions under which a firm will find it optimal to overstate or understate product quality. The results suggest that quality may be overstated in markets characterized by high price sensitivity, low quality sensitivity, low brand loyalty, and high source credibility, suggesting the need for vigilance on the part of consumers, upper level managers and regulatory authorities in such market conditions. This is important because current regulatory resources are insufficient to reduce deceptive advertising practices (Davis JJ. 1994. Ethics in advertising decision-making: implications for reducing the incidence of deceptive advertising. Journal of Consumer Affairs28: 380,402). Further, the law of deceptive advertising prohibits some advertising claims on the ground that they are likely to harm consumers or competitors (Preston IL, Richards JI. 1993. A role for consumer belief in FTC and Lanham Act deceptive advertising cases. American Business Law Journal31: 1,29). Also, Nagler (1993. Rather bait than switch: deceptive advertising with bounded consumer rationality. Journal of Public Economics51: 359,378) shows that deceptive advertising causes a net social welfare loss and a public policy effectively preventing deception will improve social welfare. Copyright © 2000 John Wiley & Sons, Ltd. [source] Simple models for predicting transmission properties of photonic crystal fibersMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 7 2006Rachad Albandakji Abstract Simple, fast, and efficient 1D models for evaluating the transmission properties of photonic crystal fibers are proposed. Using these models, axial propagation constant, chromatic dispersion, effective area, and leakage loss can be predicted with a reasonable accuracy but much faster than often time-consuming 2D analytical and numerical techniques and with much less computational resources. It is shown that the results are in good agreement with the published data available in the literature. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1286,1290, 2006; Published online in Wiley InterScience (www. interscience.wiley.com). DOI 10.1002/mop.21624 [source] The growth factor of a Hadamard matrix of order 16 is 16NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 9 2009Christos Kravvaritis Abstract In 1968 Cryer conjectured that the growth factor of an n × n Hadamard matrix is n. In 1988 Day and Peterson proved this only for the Hadamard,Sylvester class. In 1995 Edelman and Mascarenhas proved that the growth factor of a Hadamard matrix of order 12 is 12. In the present paper we demonstrate the pivot structures of a Hadamard matrix of order 16 and prove for the first time that its growth factor is 16. The study is divided in two parts: we calculate pivots from the beginning and pivots from the end of the pivot pattern. For the first part we develop counting techniques based on symbolic manipulation for specifying the existence or non-existence of specific submatrices inside the first rows of a Hadamard matrix, and so we can calculate values of principal minors. For the second part we exploit sophisticated numerical techniques that facilitate the computations of all possible (n , j) × (n , j) minors of Hadamard matrices for various values of j. The pivot patterns are obtained by utilizing appropriately the fact that the pivots appearing after the application of Gaussian elimination on a completely pivoted matrix are given as quotients of principal minors of the matrix. Copyright © 2009 John Wiley & Sons, Ltd. [source] Mixing mechanism of three-tip kneading block in twin screw extrudersPOLYMER ENGINEERING & SCIENCE, Issue 1 2000Makoto Yoshinaga In recent years, twin screw extruders have been applied to various kinds of polymer processing. It has been important to find their optimum geometrical configurations and operational processing conditions for the best performance of extrusions and products. Many engineers have been evolving numerical and the experimental methods to characterize the mixing performance for twin screw extruders. We have carried out three-dimensional flow simulations of kneading blocks in intermeshing co-rotating twin screw extruders by using the finite element method to quantify their ability in distributive and dispersive mixing. We discuss their performance in distributive mixing for three different type of kneading blocks in terms of the residence time distribution and the nearest distance between markers at various periods of time, by using the marker tracking method. Those numerical techniques and applications of mixing indices have enabled us to quantify and evaluate their abilities in distributive mixing of kneading blocks in twin screw extruders. [source] Modelling electrospinning of nanofibresPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009Tomasz A. Kowalewski Electrospinning is based on so-called bending instability which results in an erratic spiralling motion of the liquid jet as it proceeds towards a collecting electrode, where it is eventually deposited as a mat of micro/nanosized fibres. Most electrospinning models formulated within the slender approximation rely, however, on an inconsistent description of electrostatic interactions which renders them grossly inappropriate whenever the discretization is either too coarse or too fine. The present work aims at proposing a discrete slender model which is numerically consistent (allowing use of arbitrary fine meshes) and remains accurate even for coarse meshes. At the same time, efficient numerical techniques based on hierarchical charge clustering are introduced that drastically decrease computational times. Finally, a versatile boundary value method is implemented to enforce fixed-potential boundary conditions, allowing realistic electrode configurations to be investigated. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Experimental investigation of a moored floating systemPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Daniel Beyer Floating structures are generally excited by a more or less irregular sea state. Therefore the structure undergoes a nonlinear dynamical behaviour which results from hydrodynamic effects or the kinematic coupling of different components. The motions of these structures have been analysed intensively with numerical techniques which predict a wide range of nonlinear effects. On the other hand, experiments are still important when it comes to verifying these theoretical findings. Investigating such a floating structure experimentally requires a complex setup: A wave generator needs to be driven in an appropriate way to yield waves with the required characteristics at the structure. The structure itself is usually designed similar to a real,world system and it has to allow for a comparison with numerical analyses. Sensors which measure the tracks of the individual components not only have to reach a prescribed precision but also need to ensure that the motion is not perturbed as a result of the measurements. Lastly, unwanted disturbances have to be avoided. For experiments in a wave tank this includes that reflections have to be minimized. This talk addresses the development of an experimental setup for the investigation of a floating structure. It highlights components which are found to be critical for the obtained accuracy and proposes techniques to reduce experimental errors. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Mixing symbolic and numerical approaches for the surface-to-surface intersection problemPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007Mario Fioravanti This paper shows how the efficiency of the current methodologies applied to the surface-to-surface intersection problem can be improved by combining an algebraic/symbolic framework with efficient and robust numerical techniques. The algebraic/symbolic framework is used to translate the computation of resultants, subresultants, discriminants, etc. to one or several generalized eigenvalue problems and SVD computations. The framework requires only the values of the involved polynomials at some set of points, and it will guide the numerical computations, providing thus a certificate of the topological correctness of the output. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Coherence of Structural Optimization and Configurational MechanicsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Daniel Materna This contribution is concerned with the similarities of structural optimization and configurational mechanics. In structural optimization sensitivity analysis is used to obtain the sensitivity of continuum mechanical functions with respect to variations of the material body, i.e. the reference configuration. In the same manner in configurational mechanics we are interested in changes of the material body, e.g. crack propagation or phase transition problems. Consequently, variational design sensitivity analysis and the numerical techniques from structural optimization are applicable to problems fromconfigurational mechanics. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||||||||