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Linear Dependency (linear + dependency)

Distribution by Scientific Domains
Engineering60%

Selected Abstracts

Generalized nodes and high-performance elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005
Rong Tian
Abstract The paper concerns the development of robust and high accuracy finite elements with only corner nodes using a partition-of-unity-based finite-element approximation. Construction of the partition-of-unity-based approximation is accomplished by a physically defined local function of displacements. A 4-node quadratic tetrahedral element and a 3-node quadratic triangular element are developed. Eigenvalue analysis shows that linear dependencies in the partition-of-unity-based finite-element approximation constructed for the new elements are eliminable. Numerical calculations demonstrate that the new elements are robust, insensitive to mesh distortion, and offer quadratic accuracy, while also keeping mesh generation extremely simple. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Wavelet Galerkin method in multi-scale homogenization of heterogeneous media

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2006
Shafigh Mehraeen
Abstract The hierarchical properties of scaling functions and wavelets can be utilized as effective means for multi-scale homogenization of heterogeneous materials under Galerkin framework. It is shown in this work, however, when the scaling functions are used as the shape functions in the multi-scale wavelet Galerkin approximation, the linear dependency in the scaling functions renders improper zero energy modes in the discrete differential operator (stiffness matrix) if integration by parts is invoked in the Galerkin weak form. An effort is made to obtain the analytical expression of the improper zero energy modes in the wavelet Galerkin differential operator, and the improper nullity of the discrete differential operator is then removed by an eigenvalue shifting approach. A unique property of multi-scale wavelet Galerkin approximation is that the discrete differential operator at any scale can be effectively obtained. This property is particularly useful in problems where the multi-scale solution cannot be obtained simply by a wavelet projection of the finest scale solution without utilizing the multi-scale discrete differential operator, for example, the multi-scale analysis of an eigenvalue problem with oscillating coefficients. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Oxidative degradation of 4-nitrophenol in UV-illuminated titania suspension

JOURNAL OF CHEMICAL TECHNOLOGY & BIOTECHNOLOGY, Issue 8 2001
Jimmy Lea
Abstract An internally-irradiated annular photoreactor has been used to investigate the oxidative degradation of aqueous 4-nitrophenol with titania as the photocatalyst. Reaction runs were performed over a 3-h period and in practically all cases, complete degradation was possible within about 2,h. The kinetics was determined as a function of nitrophenol concentration, oxygen partial pressure, catalyst loading, pH, temperature and light intensity. The reaction was characterised by a relatively low activation energy of 7.83,kJ,mol,1 although transport intrusions were negligible. Rate decreased almost exponentially with pH while a quadratic (maximum) behaviour with respect to both oxygen pressure and nitrophenol concentration is symptomatic of self-inhibition possibly due to the formation of intermediates which competitively adsorb on similar sites to the reactants. Increased catalyst dosage also improved the reaction rate although the possible effects of light scattering and solution opacity caused a drop at loadings higher than about 1.20,g,dm,3. Rate, however, has a linear dependency on light intensity, suggesting that hole,electron recombination processes were negligible at the conditions investigated. © 2001 Society of Chemical Industry [source]

Modulation of dynamic release of vitamin B2 from a model pH-sensitive terpolymeric hydrogel system

POLYMER INTERNATIONAL, Issue 12 2004
Dr SK Bajpai
Abstract Terpolymeric devices consisting of acrylamide, methacrylamide and acrylic acid were synthesized and the release of the model drug riboflavin from these devices was studied at the physiological temperature 37°C. The gels exhibit a sharp pH-dependent release behavior. The devices released nearly 42.2 ± 2.6% drug at pH 1.0 while nearly 95.3 ± 3.2% drug was released at pH 7.4. With increasing concentration of cross-linker in the gel, the drug released was found to decrease. Moreover, with low content of cross-linker a nearly zero-order profile was obtained. The size of the cylindrical devices also affected the release kinetics and a linear dependency was observed between t1/2 (ie, the time required for 50 % release) and the square of the diameter, thus supporting the Tanaka,Fillmore theory. The molar ratio of acrylamide and methacrylamide also affected the dynamic release of riboflavin. It was found that variation in transit time could also affect the drug-releasing capacity of the devices. Finally, the average and ,late-time' diffusion coefficients for the gels having different initial loads were also evaluated. Copyright © 2004 Society of Chemical Industry [source]

Identification and fine tuning of closed-loop processes under discrete EWMA and PI adjustments

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 6 2001
Rong Pan
Abstract Conventional process identification techniques of a open-loop process use the cross-correlation function between historical values of the process input and of the process output. If the process is operated under a linear feedback controller, however, the cross-correlation function has no information on the process transfer function because of the linear dependency of the process input on the output. In this paper, several circumstances where a closed-loop system can be identified by the autocorrelation function of the output are discussed. It is assumed that a proportional integral controller with known parameters is acting on the process while the output data were collected. The disturbance is assumed to be a member of a simple yet useful family of stochastic models, which is able to represent drift. It is shown that, with these general assumptions, it is possible to identify some dynamic process models commonly encountered in manufacturing. After identification, our approach suggests to tune the controller to a near-optimal setting according to a well-known performance criterion. Copyright © 2001 John Wiley & Sons, Ltd. [source]