Determination of ion-selective electrode characteristics by non-linear curve fitting

A simple practical method of determining potentiometric selectivity coefficients of ion-selective electrodes (ISEs) is described in which electrode characteristics (slope, potentiometric selectivity coefficients and cell constant) can be determined by fitting the experimental data obtained using the fixed interference (FI) method to an appropriate model by non-linear least-squares regression. The proposed method is simple to implement practically, and data processing can be easily achieved through use of the optimisation add-on, Solver, bundled with Microsoft Excel. The flexibility of the method is demonstrated by modelling the response of a valinomycin potassium-selective electrode with the Nikolskii-Eisenman equation and a recently proposed alternative to the Nikolskii-Eisenman equation for cases where the ionic charges on the primary and interfering ions are unequal.     

Comparative study of different modelling strategies for the dynamic design of cumene reactor in cumene production process

Cumene production is an important intermediate process for the production of phenol and acetone. This paper discusses different modelling strategies to solve the mathematical model of cumene reactor. Five different strategies have been utilised for solving the Partial Differential Equations obtained during the reduction of mathematical model. The schemes include dynamic modelling using Finite Difference Method in OpenModelica, pde solver, FDM in Simulink, MATmol and Orthogonal Collocation Method. A comparative study of the schemes with plant data has been done and it is observed that Orthogonal Collocation Method gives a good agreement with plant data compared to other strategies.     

Highly efficient and exact method for parallelization of grid‐based algorithms and its implementation in DelPhi

The Gauss–Seidel (GS) method is a standard iterative numerical method widely used to solve a system of equations and, in general, is more efficient comparing to other iterative methods, such as the Jacobi method. However, standard implementation of the GS method restricts its utilization in parallel computing due to its requirement of using updated neighboring values (i.e., in current iteration) as soon as they are available. Here, we report an efficient and exact (not requiring assumptions) method to parallelize iterations and to reduce the computational time as a linear/nearly linear function of the number of processes or computing units. In contrast to other existing solutions, our method does not require any assumptions and is equally applicable for solving linear and nonlinear equations. This approach is implemented in the DelPhi program, which is a finite difference Poisson–Boltzmann equation solver to model electrostatics in molecular biology. This development makes the iterative procedure on obtaining the electrostatic potential distribution in the parallelized DelPhi several folds faster than that in the serial code. Further, we demonstrate the advantages of the new parallelized DelPhi by computing the electrostatic potential and the corresponding energies of large supramolecular structures. © 2012 Wiley Periodicals, Inc.     

lipID—a software tool for automated assignment of lipids in mass spectra

A new software tool called lipID is reported, which supports the identification of glycerophospholipids, glycosphingolipids, fatty acids and small oligosaccharides in mass spectra. The user‐extendable software is a Microsoft (MS) Excel Add‐In developed using Visual Basic for Applications and is compatible with all Versions of MS Excel since MS Excel 97. It processes singly given mass‐to‐charge values as well as mass lists considering a number of user‐defined options. The software's mode of operation, usage and options are explained and the benefits and limitations of the tool are illustrated by means of three typical analytical examples of lipid analyses. Copyright © 2009 John Wiley & Sons, Ltd.     

A hybrid genetic algorithm for estimating the equilibrium potential of an ion-selective electrode

Non-linear equations can be used to model the measured potential of ion-selective electrodes (ISEs) as a function of time. This can be done by using non-linear least squares regression to fit parameters of non-linear equations to an ISE response curve. In iterative non-linear least squares regression (which can be considered as local optimisers), the determination of starting parameter estimates that yield convergence to the global optimum can be difficult. Starting values away from the global optimum can lead to either abortive divergence or convergence to a local optimum. To address this issue, a global optimisation technique was used to find initial parameter estimates near the global optimum for subsequent further refinement to the absolute optimum. A genetic algorithm has been applied to two non-linear equations relating the measured potential from selected ISEs to time. The parameter estimates found from the genetic algorithm were used as starting values for non-linear least squares regression, and subsequent refinement to the absolute optimum. This approach was successfully used for both expressions with measured data from three different ISEs; namely, calcium, chloride and lead ISEs.     

Neural network model predictive control of a styrene polymerization plant: online testing using an electronic worksheet

The batch styrene polymerization process presents transient and nonlinear temperature behavior. In this work, manual control and open loop experiments were carried out in order to build a process knowledge database. Initially, a cascade feedback control loop was implemented by manipulating the thyristor unit of the electrical heater in the thermal fluid tank. Aiming at the MPC development, algebraic equations of a neural network and its adjusted parameters were implemented in an electronic worksheet. Every five seconds, the worksheet was updated with measurements (reactor temperature, thermal fluid temperature and thyristor position) by means of the OLE for the Process Control protocol (OPC). The one-step-ahead temperature prediction was then employed in the objective function of the worksheet solver which used Visual Basic Applications programming. The manipulated variable action was then calculated and sent to the process. A hybrid controller (cascade feedback and MPC) outperformed the pure strategies since the time-integral performance indexes, IAE and ITAE, were reduced by around 22 % and 32 %, respectively. Methodology for the Model Predictive Control presented in this study was considered feasible because the solver of Microsoft Office Excel (2007) is very friendly, easy to understand and ready to implement using VBA.     

Peak shape analysis of core level photoelectron spectra using UNIFIT for WINDOWS

Several approaches used in the peak shape analysis of core level spectra for the purpose of modelling of both peak shapes and background profiles will be discussed. A universal program is presented, which combines options for adequate modelling of the peak shapes and background, implementation of a successful numerical algorithm for an iterative non-linear parameter estimation procedure, and a flexible as well as convenient data handling. The performance of this program code is demonstrated by fitting a synthesized model spectrum. An example for analysis of a complex experimental spectrum is presented, too. An S 2p spectrum recorded from a MBT-treated pyrite surface is successfully analyzed using the presented software and is found to be characterized by five different S 2p contributions.     

Les différentes voies de modélisation macroscopique du procédé de dépôt de SiC par voie gazeuse

The different macroscopic modelling routes and chemical databases are reviewed for the growth of silicon carbide from the vapour phase in the Si-C-H-Ar system. Theses databases have been built up by experts over many years through the critical assessment of primary experimental data and ab-initio calculations. The thermodynamic modelling route addresses several important issues with respect to vapour deposition techniques. This approach is a useful tool in understanding the complex chemistry involved during the growth, but should be used with careful attention to the assumptions underlying the application. The transport modelling approach extends the previous analysis to dynamical systems. It is based on the conservation equations for momentum and heat transfer combined with mass transfer including thermodiffusion and chemical reactions based on thermodynamic and kinetic data. In addition to empirical, lumped chemical kinetic models, we propose a new modelling route linking transfers models with local thermochemical equilibrium (LTCE) computations. The modelling results have been validated with the help of the SiC sublimation technique for the transfer-LTCE concept, and of the chemical vapour deposition technique for lumped chemistry models. The simulated results allow the quantification of the different modelling proposals.     

Artificial neural networks for computer-aided modelling and optimisation in micellar electrokinetic chromatography

The separation process in capillary micellar electrochromatography (MEKC) can be modelled using artificial neural networks (ANNs) and optimisation of MEKC methods can be facilitated by combining ANNs with experimental design. ANNs have shown attractive possibilities for non-linear modelling of response surfaces in MEKC and it was demonstrated that by combining ANN modelling with experimental design, the number of experiments necessary to search and find optimal separation conditions can be reduced significantly. A new general approach for computer-aided optimisation in MEKC has been proposed which, because of its general validity, can also be applied in other separation techniques.     

Kinetic modeling of industrial steam cracker

A comprehensive mathematical model is a very useful tool for the selection of feedstock, optimized cracker product mix, downstream production planning, and optimized plant performance. As a part of achieving this prime objective, a mathematical model has been developed for the simulation of the radiation section of a steam cracker unit. The model involves solving differential component, energy, and momentum balance equations numerically to generate temperature, concentration, and pressure profiles along the length of the reactor tube. The model has been developed in FORTRAN using the lSODE solver. The model considers 19 free radicals and 35 molecules connected over 433 reactions. The model was used to simulate the performance of propane and ethane cracking. The model predicted propane conversion is 95.55 against the plant data of 95% at a coil outlet temperature of 845 ​°C and the corresponding predicted ethylene and propylene yield is 34.49 and 11.53% respectively. The model has been validated for ethane cracking performance. The model predicted ethylene yield is in good agreement with that of plant values for ethane cracking. The model provides a basis for the optimization of process parameters for the given geometry. The model is useful to answer what-if questions and to investigate operational strategies.     

A simplex search for conditions giving maximal and/or minimal concentrations of species in distribution plots

A new method is proposed for finding the conditions which maximize or minimize the concentration of a particular species in a multicomponent system. A Simplex procedure is combined with an iterative method for solving mass-balance equations from the total concentrations of the constituents of the system, its pH and the pertinent equilibrium constants. The following examples of application are given: (a) the optimum conditions for maximizing the concentration of mixed-ligand species in systems with more than one ligand; (b) the conditions for maximal or minimal formation of monomeric and dimeric species in the Cu(II)-triethanolamine system; (c) a search for local maximum/minimum in species distribution plots.     

Efficient treatment of solvation shells in 3D molecular theory of solvation

We developed a technique to decrease memory requirements when solving the integral equations of three‐dimensional (3D) molecular theory of solvation, a.k.a. 3D reference interaction site model (3D‐RISM), using the modified direct inversion in the iterative subspace (MDIIS) numerical method of generalized minimal residual type. The latter provides robust convergence, in particular, for charged systems and electrolyte solutions with strong associative effects for which damped iterations do not converge. The MDIIS solver (typically, with 2 × 10 iterative vectors of argument and residual for fast convergence) treats the solute excluded volume (core), while handling the solvation shells in the 3D box with two vectors coupled with MDIIS iteratively and incorporating the electrostatic asymptotics outside the box analytically. For solvated systems from small to large macromolecules and solid–liquid interfaces, this results in 6‐ to 16‐fold memory reduction and corresponding CPU load decrease in MDIIS. We illustrated the new technique on solvated systems of chemical and biomolecular relevance with different dimensionality, both in ambient water and aqueous electrolyte solution, by solving the 3D‐RISM equations with the Kovalenko–Hirata (KH) closure, and the hypernetted chain (HNC) closure where convergent. This core–shell‐asymptotics technique coupling MDIIS for the excluded volume core with iteration of the solvation shells converges as efficiently as MDIIS for the whole 3D box and yields the solvation structure and thermodynamics without loss of accuracy. Although being of benefit for solutes of any size, this memory reduction becomes critical in 3D‐RISM calculations for large solvated systems, such as macromolecules in solution with ions, ligands, and other cofactors. © 2012 Wiley Periodicals, Inc.     

An improved algorithm for the normalized elimination of the small-component method

A new algorithm for the iterative solution of the normalized elimination of the small component (NESC) method is presented that is less costly than previous algorithms and that is based on (1) solving the NESC equations for the uncontracted rather than contracted basis (??First-Diagonalize-then-Contract??), (2) a new iterative procedure for obtaining the NESC Hamiltonian (??iterative TU algorithm??), (3) the renormalization scheme connected to the picture change, and (4) a finite nucleus model with a Gaussian charge distribution. The accuracy of NESC energies, which match those of 4-component Dirac calculations, is demonstrated. Test calculations with CCSD(T), DFT, and large basis sets including high angular momentum basis functions (f,g,h,i) are presented to prove the general applicability of the new NESC algorithm. Comparison with other algorithms of solving the NESC equations are shortly discussed and time savings are presented.     

Iterative Solution Method for the Linearized Poisson-Boltzmann Equation: Indirect Boundary Integral Equation Approach

An iterative solution scheme is proposed for solving the electrical double-layer interactions governed by the linearized Poisson-Boltzmann equation. The method is based on the indirect integral equation formulation with the double-layer potential kernel of the linearized Poisson-Boltzmann equation. In contrast to the conventional direct integral equation approach that yields Fredholm integral equations of the first kind, the indirect integral equation approach yields well-posed Fredholm integral equations of the second kind. The eigenvalue analysis reveals that the spectral radius of the double-layer integral operator is always less than one. Thus, iterative solution schemes can be successfully implemented for solving the electrical double-layer interactions for very large and complex systems. The utility of the iterative indirect method is demonstrated for several examples which include spherical and spheroidal particles. Copyright 2001 Academic Press.     

Partitioning technique procedure revisited: Formalism and first application to atomic problems

Usually the partitioning technique (PT) has been studied under two aspects: (i) as a numerical tool for solving secular equations of high order, and (ii) as a theoretical method related to the infinite‐order perturbation theory and the iteration–variation methods. Here it is shown that there exists a form of the PT equations which allows us to determine explicitly the spectrum and eigenstates of the Hamiltonian operator for different forms of potentials without the utilization of perturbative expansions or iterative equations of the type E=f(E). As a first application of the new approach, we consider the hydrogen‐atom in strong magnetic fields (B ~ 10⁹ G). This revised version was published online in July 2006 with corrections to the Cover Date.     

An approach for simultaneous estimation of reaction kinetics and curve resolution from process and spectral data

Parameter estimation of reaction kinetics from spectroscopic data remains an important and challenging problem. This study describes a unified framework to address this challenge. The presented framework is based on maximum likelihood principles, nonlinear optimization techniques, and the use of collocation methods to solve the differential equations involved. To solve the overall parameter estimation problem, we first develop an iterative optimization‐based procedure to estimate the variances of the noise in system variables (eg, concentrations) and spectral measurements. Once these variances are estimated, we then determine the concentration profiles and kinetic parameters simultaneously. From the properties of the nonlinear programming solver and solution sensitivity, we also obtain the covariance matrix and standard deviations for the estimated kinetic parameters. Our proposed approach is demonstrated on 7 case studies that include simulated data as well as actual experimental data. Moreover, our numerical results compare well with the multivariate curve resolution alternating least squares approach.     

A family of parametric schemes of arbitrary even order for solving nonlinear models: CMMSE2016

Many problems related to gas dynamics, heat transfer or chemical reactions are modeled by means of partial differential equations that usually are solved by using approximation techniques. When they are transformed in nonlinear systems of equations via a discretization process, this system is big-sized and high-order iterative methods are specially useful. In this paper, we construct a new family of parametric iterative methods with arbitrary even order, based on the extension of Ostrowski’ and Chun’s methods for solving nonlinear systems. Some elements of the proposed class are known methods meanwhile others are new schemes with good properties. Some numerical tests confirm the theoretical results and allow us to compare the numerical results obtained by applying new methods and known ones on academical examples. In addition, we apply one of our methods for approximating the solution of a heat conduction problem described by a parabolic partial differential equation.     

Efficient and sample-specific interpretation of ToF-SIMS data by additional postprocessing of principal component analysis results

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) is a powerful tool for surface analysis, but fragmentation of molecular species during the SIMS process may lead to complex mass spectra. While the fragmentation pattern is typically characteristic for each compound, industrial samples are engineered materials, and, thus, may contain a mixture of many compounds, which may result in a variety of overlapping peak patterns in ToF-SIMS spectra. Consequently, the process of data evaluation is challenging and time-consuming. Principal component analysis (PCA) can be used to simplify data analysis for complex sample systems. Especially, correlation loadings were observed as an ideal tool to identify relevant signals in PCA results, which induce the separation of different sample groups. This is because correlation loadings show the relevance of signals independent from their intensity in the raw data. In correlation loadings, however, fragmentation patterns are no longer observed and the identification of peaks' sum formulas is challenging. In this study, a new approach is presented, which simplifies peak identification and assignment in ToF-SIMS spectra after PCA is performed. The approach uses a mathematical transformation that projects PCA results, in particular loadings and correlation loadings, in the direction of specific sample groups. The approach does not change PCA results but rather presents them in a new way. This method allows to visualize characteristic spectra for specific sample groups that contain only relevant signals and, additionally, visualize fragmentation patterns. Data analysis is simplified and helps the user to focus on data interpretation rather than processing.     

化学演讲过程数据的自动分辨: 复杂石油样品的GC－MS分析

基于几种新化学计量学方法,提出了可自动解析化学演进数据的新途径。在该法中,首先选择关键向量。通过子空间比较法确定数据的化学秩。以关键向量为起点,通过初等变换不断迭代而实现对数据的解析。并利用数据非负性等检验解析结果的可靠程度。结合GC－MS数据的特点,选择的关键变量可为关键质谱或关键浓度曲线。该方法能极大地减少人为干预,大大降低数据分析时间,对文中的石油样本共解析出557个成分。