On the numerical solution of differential algebraic equations

A method is proposed to transform a system of differential algebraic equations (D.A.E.) to a system of ordinary differential equations (O.D.E.) which can be solved relatively easily by standard numerical techniques. Two examples, including a model of an absorption tower, are given to illustrate the utility of the method. The example problems reveal that this easily implemented technique offers significant savings in CPU time compared to the numerical solution of the untransformed D.A.E.s particularly when the algebraic equations are nonlinear. Furthermore, it appears to be faster and/or more reliable than other numerical schemes which have been recently developed for equations of this type.     

Optimal selection of orthogonal polynomials applied to the integration of chemical reactor equations by collocation methods

In this paper, we analyse some properties of the orthogonal collocation in the context of its use for reducing PDE (partial differential equations) chemical reactor models for numerical simulation and/or control design. The approximation of the first order derivatives is first considered and analysed with respect to the transfer of the stability properties of the transport component from the PDE model to its approximated ODE (ordinary differential equations) model. Then the choice of the collocation points as zero of Jacobi polynomial is analysed and interpreted as an optimal choice with respect to a weighted norm. Finally, some guidelines for the use of orthogonal collocation are proposed and the results are illustrated on a simulation example.     

A new discretization of space for the solution of multi-dimensional population balance equations

In this work, a novel radial grid is combined with the framework of minimal internal consistency of discretized equations of Chakraborty and Kumar [2007. A new framework for solution of multidimensional population balance equations. Chemical Engineering Science 62, 4112-4125] to solve n-dimensional population balance equations (PBEs) with preservation of (n+1) instead of 2ⁿ properties required in direct extension of the 1-d fixed pivot technique of Kumar and Ramkrishna [1996a. On the solutions of population balance equation by discretization-I. A fixed pivot technique. Chemical Engineering Science 51, 1311-1332]. The radial grids for the solution of 2-d PBEs are obtained by intersecting arbitrarily spaced radial lines with arcs of arbitrarily increasing radii. The quadrilaterals obtained thus are divided into triangles to represent a non-pivot particle in 2-d space through three surrounding pivots by preserving three properties, the number and the two masses of the species that constitute the newly formed particle. Such a grid combines the ease of generating and handling a structured grid with the effectiveness of the framework of minimal internal consistency. A new quantitative measure to supplement visual comparison of two solutions is also introduced. The comparison of numerical and analytical solutions of 2-d PBEs for a number of uniform and selectively refined radial grids shows that the quality of solution obtained with radial grids is substantially better than that obtained with the direct extension of the 1-d fixed pivot technique to higher dimensions for both size independent and size dependent aggregation kernels. The framework of Chakraborty and Kumar combined with the proposed 2-d radial grid, which offers flexibility and achieves both reduced numerical dispersion and the ease of implementation, appears as an effective extension of the widely used 1-d fixed pivot technique to solve 2-d PBEs.     

Anisotropic degradation of polymeric composites: From neat resin to composite

The degradation of polymer matrix composites was investigated through weight loss measurements. A methodology originally developed based on the shrinking core model was extended to account for matrix orientation, lay-up sequence, and differences in neat resin and composite degradation. This methodology was derived based on mass transfer and kinetic considerations taking into account the inherent anisotropy and heterogeneity of polymer composites. The model systems used were a bismaleimide (X5260) and a condensation polyimide (Avimid N). Bismaleimide composites were aged at 250, 260, and 270°C in air, whereas both neat resin and composite Avimid N samples were aged at 371°C. Based on the experimentally observed time exponents, the degradation was modeled as diffusion and reaction controlled. The weight losses of both unidirectional and quasi-isotropic samples were successfully predicted. In addition, correlation between the degradation of neat resin and composite samples was established for the Avimid N system. Finally, this methodology can be used in scaling up weight loss data, providing an important tool in evaluating materials for long-term use at elevated temperatures.     

Neutrophils’ Extracellular Trap Mechanisms: From Physiology to Pathology

Neutrophils are an essential part of the innate immune system and the first line of defense against invading pathogens. They phagocytose, release granular contents, produce reactive oxygen species, and form neutrophil extracellular traps (NETs) to fight pathogens. With the characterization of NETs and their components, neutrophils were identified as players of the innate adaptive crosstalk. This has placed NETs at the center not only of physiological but also pathological processes. Aside from their role in pathogen uptake and clearance, NETs have been demonstrated to contribute to the resolution of inflammation by forming aggregated NETs able to degrade inflammatory mediators. On the other hand, NETs have the potential to foster severe pathological conditions. When homeostasis is disrupted, they occlude vessels and ducts, serve as sources of autoantigens and danger or damage associated molecular patterns, directly damage tissues, and exaggerate complement activity and inflammation. This review focusses on the understanding of NETs from their formation to their functions in both physiological and pathological processes.     

Numerical study of lap joints with composite adhesives and composite adherends subjected to in-plane and transverse loads

In this paper, single lap joints for joining fibre composites were modeled and a three-dimensional finite element method was used to study the joint strength under in-plane tensile and out-of-plane loadings. The behaviour of all the members was assumed to be linear elastic. The adherends were considered to be orthotropic materials while the adhesive could be neat resin or reinforced one. The largest values of shear and peel stresses occurred near the ends of the adhesive region, as expected. The values and the rate of variation in peel stress was more than that of shear stress. By changing the properties and behaviour of adhesive from neat epoxy (isotropic) to fibre composite adhesive (orthotropic) and with various fibre volume fractions of glass fibre, the ultimate bond strength increased as the fibre volume fraction increased, in both tensile and transverse loadings. Also, changing the orientation of fibres in the adhesive region with respect to the global axes influenced the bond strength.     

A new discretization of space for the solution of multi-dimensional population balance equations: Simultaneous breakup and aggregation of particles

In this work, we show that straight forward extensions of the existing techniques to solve 2-d population balance equations (PBEs) for particle breakup result in very high numerical dispersion, particularly in directions perpendicular to the direction of evolution of population. These extensions also fail to predict formation of particles of uniform composition at steady state for simultaneous breakup and aggregation of particles, starting with particles of both uniform and non-uniform compositions. The straight forward extensions of 1-d techniques preserve 2ⁿ properties of non-pivot particles, which are taken to be number, two masses, and product of masses for the solution of 2-d PBEs. Chakraborty and Kumar [2007. A new framework for solution of multidimensional population balance equations. Chemical Engineering Science 62, 4112-4125] have recently proposed a new framework of minimal internal consistency of discretization which requires preservation of only (n+1) properties. In this work, we combine a new radial grid [proposed in 2008. part I, Chemical Engineering Science 63, 2198] with the above framework to solve 2-d PBEs consisting of terms representing breakup of particles. Numerical dispersion with the use of straight forward extensions arises on account of formation of daughter particles of compositions different from that of the parent particles. The proposed technique eliminates numerical dispersion completely with a radial distribution of grid points and preservation of only three properties: number and two masses. The same features also enable it to correctly capture mixing brought about by aggregation of particles. The proposed technique thus emerges as a powerful and flexible technique, naturally suited to simulate PBE based models incorporating simultaneous breakup and aggregation of particles.     

Adaptation of intestine-based microbial functions to bioethanol production

Animal intestine is a favorable habitat to microbes. It facilitates the evolution of dense and diversified microbial communities that are highly active and persistent throughout life span. Here, we stimulate this unique biosystem to develop high-efficient continuous bio-manufacturing processes. The pig small intestine was explored as a novel bioreactor with industrial Saccharomyces cerevisiae for biofuel production. Results showed that the small intestine was a beneficial material for cell adherence. The cells on the intestine exhibited the abilities of self-immobilization, self-duplication and self-repairing. Therefore the intestine-based S. cerevisiae could be continuously used for a long time at high metabolic activities. Both the fermentation speed and ethanol yield were improved. This study provides valuable insights into the functions of intestine-based biosystem and should inspire the development of bionic industrial processes. Future dissection of the interface mechanism and design of more bionic materials will make bioprocesses more economically favorable and environmentally sustainable.     

Smart electrochemical biosensors: From advanced materials to ultrasensitive devices

The specificity, simplicity, and inherent miniaturization afforded by advances in modern electronics have allowed electrochemical sensors to rival the most advanced optical protocols. One major obstacle in implementing electrochemistry for studying biomolecular reaction is its inadequate sensitivity. Recent reports however showed unprecedented sensitivities for biomolecular recognition using enhanced electronic amplification provided by new classes of electrode materials (e.g. carbon nanotubes, metal nanoparticles, and quantum dots). Biosensor technology is one area where recent advances in nanomaterials are pushing the technological limits of electrochemical sensitivities, thus allowing for the development of new sensor chemistries and devices. This work focuses on our recent work, based on metal-enhanced electrochemical detection, and those of others in combining advanced nanomaterials with electrochemistry for the development of smart sensors for proteins, nucleic acids, drugs and cancer cells.     

Solution of stiff convection-diffusion differential equations using marquardt's method

A modified Marquardt method is successfully used to solve a stiff non-linear convection-diffusion problem with chemical reaction. An efficient solution strategy is proposed and comparisons are made with classical iterative solution methods based on loading. The performance of the algorithm is illustrated with an implicit finite difference method.     

Conducting polyaniline composite: From syntheses in waterborne systems to chemical sensor devices

The development of a conducting composite from its one-step synthesis in aqueous dispersed medium to the characterization of its chemical sensor performance is detailed. Composite films of polyaniline and polyacrylate were processed from the crude dispersion with no need for post-formulation. The synthesis has been optimized to be as simple, cheap and transferable as possible. The composite composition is tunable, i.e. the nature of the dopant was varied and its effect on kinetic parameters was observed. Ab initio calculations have been performed on a series of six ionic systems to gain a deeper insight into the contribution of both the stability of the anilinium salts in the composite polymerization. The conductivities of all composites were recorded from room temperature to 150 °C and the thermal stability versus dopant highlighted. The conducting films were then studied as active layers in a chemical sensor. The results showed that these composites, easily synthesized and processed, are ammonia sensitive and exhibit a fast response when exposed to air pollution.     

An algorithm for the estimation of parameters in models with stochastic differential equations

An algorithm for the estimation of parameters of stochastic differential equations (SDEs) is presented. It is based on a nonlinear weighted least-squares formulation, in which the objective function is evaluated based on mean values of the measured variables predicted through an Euler discretisation of the SDEs and their integration by Monte-Carlo simulation. The problem is solved using a Levenberg-Marquardt algorithm. The presence of simulation noise is handled by choosing a convergence criterion based on the noise level and by ensuring that the optimality criterion is met for a large simulation size and hence a low noise level. In order to increase the reliability of the algorithm and to decrease its computational cost, stochastic sensitivity equations are derived. Furthermore, the number of trajectories used in the Monte-Carlo simulations is changed adaptively throughout the execution of the algorithm. This leads to a significant decrease in computational requirements. These concepts are illustrated on a simple example and a more complex model of polymer rheology. In all cases, parameter estimates close to the true parameter values are identified.     

New Approach to Solve a Model for the Effective Solid Stress Distribution in Conical Spouted Beds

Charbel et al. (1999) have investigated the flow stability in conical spouted beds by modeling the effective solid stress distribution in the annular region as a function of the failure state under which the spout‐annulus interface is formed. However, due to the complexity in solving the momentum balance equations for the solid phase, the model application has been restricted to one case. This work is aimed at developing a new methodology to solve this set of algebraic differential equations, using optimization techniques to determine the model parameter. This methodology has improved the model solution extending its application for any other case.     

Sintering behavior of nanostructured WC-Co composite

Sintering of nanocrystalline WC-Co, retaining the nanoscaled grain sizes is a matter of great interest. Many non traditional methods have been used to achieve this goal as the required result has not been achieved using the traditional method of liquid phase sintering. The present study is an attempt to find out the limitations of traditional sintering method and optimize it to get nanocrystalline WC-Co composites. The effect of temperature, time and composition variation has been studied to see the sintering behavior of nanostructured WC-Co composite. Detailed X-ray diffraction (XRD) analysis as well as microstructural examination showed that sintering at 1350 °C for 1 h with 5% binder composition (Co) is a set of critical temperature, time and composition which can provide the required results. The grain growth is through coalescence. At critical conditions the majorities of WC grains are faceted and attains the shape of prismatic and basal facets.     

A regularization approach to the reconciliation of constrained data sets

A new iterative solution to the statistical adjustment of constrained data sets is derived in this paper. The method is general and may be applied to any weighted least squares problem containing nonlinear equality constraints. Other methods are available to solve this class of problem, but are complicated when unmeasured variables and model parameters are not all observable and the model constraints are not all independent. Of notable exception, however, are the methods of Crowe (1986) and Pai and Fisher (1988), although these implementations require the determination of a matrix projection at each iteration which may be computationally expensive. An alternative solution which makes the pragmatic assumption that the unmeasured variables and model parameters are known with a finite but equal uncertainty is proposed. We then re-formulate the well known data reconciliation solution in the absence of these unknowns to arrive at our new solution; hence the regularization approach. Another procedure for the classification of observable and redundant variables which does not require the explicit computation of the matrix projection is also given. The new algorithm is demonstrated using three illustrative examples previously used in other studies.     

Applying Tikhonov regularization to process the kinetic data of polymerization

Most experimental polymerization kinetic data are in the form of degree of polymerization versus time plots. However, to explore kinetic models it is more useful to have the data as polymerization rate versus degree of polymerization plots. Converting degree of polymerization into rate is an ill‐posed problem in that if inappropriate methods are used the noise in the data will be amplified, leading to unreliable results. This paper describes a procedure, based on Tikhonov regularization, to perform this conversion. The procedure is independent of kinetic models and keeps noise amplification under control. Its performance is demonstrated using several sets of published polymerization kinetic data. In each case the computed rates are used to determine the parameters in the rate expression proposed in the original papers. Modified rate expressions will also be explored. The ease with which such investigations can be performed highlights the advantages of this new procedure. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 1625–1633, 2004     

Determination of hydrogen content of petroleum products using a low resolution pulsed n.m.r. spectrometer: Applications to light cuts,distillates and residues

A low resolution pulsed n.m.r. spectrometer has been used to determine total hydrogen content for a wide range of petroleum cuts. Criteria for selecting experimental conditions are described with respect to three kinds of petroleum-derived products. A hydrogen pulsed n.m.r. instrument was suitable for a small-coil technique (constant volume) experiment when used with a sample of known density. Excellent agreement has been found with microanalysis technique results, and the accuracy is as good as the combustion method. Problems of magnetic contaminants have also been simulated.