rodzaj: materiały konferencyjne w książce

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rodzaj: materiały konferencyjne w książce

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rodzaj: materiały konferencyjne w książce

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rodzaj: materiały konferencyjne w książce

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rodzaj: materiały konferencyjne w książce

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rodzaj: materiały konferencyjne w książce

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rodzaj: artykuł w czasopiśmie

Abstrakt: The fourth-order accurate, three-point finite-difference Numerov spatial discretization provides accurate and efficient solutions to the time-dependent governing differential equations of electrochemical kinetics in one-dimensional space geometry, when the equations contain first time derivatives of the solution, second spatial derivatives, and homogeneous reaction terms only. However, the original Numerov discretization is not applicable when the governing equations involve first spatial derivative terms. To overcome this limitation, an appropriately extended Numerov discretization is required. We examine the utility of one of such extensions, first described by Chawla. Relevant discrete formulae are outlined for systems of linear governing equations involving first derivative terms, and applied to five representative example models of electrochemical transient experiments. The extended Numerov discretization proves to have an accuracy and efficiency comparable to the original Numerov scheme, and its accuracy is typically up to four orders of magnitude higher, compared to the conventional, second-order accurate spatial discretization, commonly used in electrochemistry. This results in a considerable improvement of efficiency. Therefore, the application of the extended Numerov discretization to the electrochemical kinetic simulations can be fully recommended.]]>

rodzaj: materiały konferencyjne w książce

Abstrakt: The current state of development of Computational Electrochemistry is briefly discussed, and a unifying view of the field is proposed, with the aim of stimulating a communication between, and unity of, computationally oriented electrochemists involved in diverse kinds of computations. The most recent work of the author, pertaining to the field, is also reviewed. ]]>

rodzaj: materiały konferencyjne w książce

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rodzaj: artykuł w czasopiśmie

Abstrakt: In the EU there is a pressing need for the change of the current economy into a so-called circular economy in recent years. The rational management of natural resources and the use of waste materials are becoming more and more important. It is also supported by the growing ecological awareness of society, including the consciousness of sustainable development. Nowadays, it is the construction industry that has the most significant impact on pollution. Therefore, numerous attempts are made to reduce energy consumption and the amount of waste generated by it. These are the main issues stimulating the research on new innovative materials such as geopolymer composites. They have a significantly lower carbon footprint than traditional construction materials. Moreover, the synthesis of geopolymers requires 2-3 times less energy than traditional Portland cement, not to mention the fact that 4-8 times less CO2 is generated. In addition, the above process has another environmental benefit i.e. the possibility of using anthropogenic raw materials (minerals) such as slags and fly ashes for the production. One of the limitations for the wide use of such materials is their relatively low brittle fracture behaviour. Nowadays, one of the most important research areas is the improvement of their mechanical properties. To improve the mechanical properties it is possible to reinforce the matrix by fibres addition, especially natural fibres that are renewable resources. The main objective of the article is to analyse the mechanical properties of new composites and assessment the possibility to replace traditional building materials within eco-friendly alternatives.]]>

rodzaj: artykuł w czasopiśmie

Abstrakt: The Directive 2010/31/EU on the energy performance of buildings has introduced the standard of “nearly zero-energy buildings” (NZEBs). European requirements place the obligation to reduce energy consumption on all European Union Member States, particularly in sectors with significant energy consumption indicators. Construction is one such sector, as it is responsible for around 40% of overall energy consumption. Apart from a building’s mass and its material and installation solutions, its energy consumption is also a ected by its placement relative to other buildings. A proper urban layout can also lead to a reduction in project development and occupancy costs. The goal of this article is to present a method of optimising single-family house complexes that takes elements such as direct construction costs, construction site organisation, urban layout and occupancy costs into consideration in the context of sustainability. Its authors have analysed di erent proposals of the placement of 40 NZEBs relative to each other and have carried out a multi-criteria analysis of the complex, determining optimal solutions that are compliant with the precepts of sustainability. The results indicated that the layout composed of semi-detached houses scored the highest among the proposed layouts under the parameter weights set by the developer. This layout also scored the highest when parameter weights were uniformly distributed during a test simulation.]]>

rodzaj: artykuł w czasopiśmie

Abstrakt: The validity for finite-difference electrochemical kinetic simulations, of the extension of the Numerov discretization designed by Chawla and Katti [J Comput Appl Math 1980, 6, 189 –196] for the solution of two-point boundary value problems in ordinary differential equations, is examined. The discretization is adapted to systems of time-dependent reaction-diffusion partial differential equations in one-dimensional space geometry, on nonuniform space grids resulting from coordinate transformations. The equations must not involve first spatial derivatives of the unknowns. Relevant discrete formulae are outlined and tested in calculations on two example kinetic models. The models describe potential step chronoamperometry under limiting current conditions, for the catalytic EC, and Reinert-Berg CE reaction mechanisms. Exponentially expanding space grid is used. The discretization considered proves the most accurate and efficient, out of all the three-point finite-difference discretizations on such grids, that have been used thus far in electrochemical kinetics. Therefore, it can be recommended as a method of choice.]]>

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Abstrakt: The patch-adaptive strategy for electrochemical kinetic simulations, introduced in Part 5 of the present series of papers, with extensions described in Part 14, is applied to five typical examples of time-dependent models of transient experiments represented by Nernst–Planck–electroneutrality equation systems in one-dimensional space geometry. The models describe: potential step chronoamperometry for a charge neutralisation reaction at a planar electrode in the absence of the supporting electrolyte; potential step chronoamperometry for a planar electrode coated with a polymer film under conditions of migration–diffusion of redox ions; potential step chronoamperometry of uncharged species at a hemispherical electrode in the presence of a low concentration of supporting electrolyte; cyclic voltammetry for an electrode reaction (initially at equilibrium) involving uncharged species, at a planar electrode in the absence of the supporting electrolyte; and current step chronopotentiometry for a liquidjliquid junction between two binary electrolytes. The calculations lead to analogous conclusions, with regard to the performance of the strategy, as in the case of the models represented by the Nernst–Planck–Poisson equations solved in Part 14. New observations reveal that highly non-linear boundary conditions present an additional challenge for the Newton iterative method utilised by the strategy. The ability of the strategy to solve non-local boundary conditions expressing current equality at distant boundaries is also demonstrated. However, formulating such boundary conditions correctly is not straightforward, so that their use is not recommended. Adaptive solutions suggest inaccuracies in the literature solutions for two example models.]]>

rodzaj: artykuł w czasopiśmie

Abstrakt: This review covers developments in digital simulations of electroanalytical experiments, since 1996. Over the period of time considered, a number of new techniques has been applied. Among them are: the method of lines approach using the differential algebraic equations formulation, extrapolation and Rosenbrock time integrators, multipoint and high-order compact spatial discretisations, finite-element-like methods, adaptive techniques and sensitivity analysis. More simulation software is now also available.]]>

rodzaj: artykuł w czasopiśmie

Abstrakt: The vigorous promotion of reuse and recycling activities in Taiwan has solved a number of problems associated with the treatment of industrial waste. Considerable advances have been made in the conversion of waste materials into usable resources, thereby reducing the space required for waste storage and helping to conserve natural resources. This study examined the use of non-alkali activators to create bonded materials. Our aims were to evaluate the feasibility of using ground-granulated blast-furnace slag (S) and circulating fluidized bed co-fired fly ash (F) as non-cement binding materials and determine the optimal mix proportions (including embedded fibers) with the aim of achieving high dimensional stability and good mechanical properties. Under a fixed water/binder ratio of 0.55, we combined S and F to replace 100% of the cement at S:F ratios of 4:6, 5:5, 6:4. Polypropylene fibers (L/d = 375) were also included in the mix at 0.1%, 0.2% and 0.5% of the volume of all bonded materials. Samples were characterized in terms of flowability, compressive strength, tensile strength, water absorption, shrinkage, x-ray diffraction (XRD) and scanning electron microscope (SEM) analysis. Specimens made with an S:F ratio of 6:4 achieved compressive strength of roughly 30 MPa (at 28 days), which is the 80% the strength of conventional cement-based materials (control specimens). The inclusion of 0.2% fibers in the mix further increased compressive strength to 35 MPa and enhanced composite properties.]]>

rodzaj: artykuł w czasopiśmie

Abstrakt: In the second half of the 20th century, asbestos extraction was up to 4 Mt/year. Due to its high strength and insulation properties, this mineral was used as an additive in building materials. Over time these materials were destroyed by the process of weathering and leaching. Asbestos fibers in dust form penetrate the respiratory system causing diseases. This article proposes the binding of hazardous asbestos fibers in a polymer matrix formed from waste cooking oil. Compact materials were produced by heating catalyzed waste cooking oil and asbestos waste, and the process of obtaining these materials was optimized and their physicochemical and strength properties were determined. Oil-asbestos blocks contained sulfuric acid in a mass ratio of 0.05–0.30, being the mass of waste cooking oil, invariable mass of filling and 20% of waste cooking oil to the mass of the whole mixture. The materials were characterized by a compact structure and high hardness. The best mechanical strength above 140 N/mm was obtained for blocks with low acid to oil mass ratio ranging from 0.05 to 0.1125.]]>

rodzaj: artykuł w czasopiśmie

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rodzaj: artykuł w czasopiśmie

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rodzaj: opis bibliograficzny artykułu

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rodzaj: artykuł w czasopiśmie

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rodzaj: opis bibliograficzny artykułu

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rodzaj: artykuł w czasopiśmie

Abstrakt: Transient solutions for potential-step chronoamperometry, obtained by conventional finite-difference simulations, are usually grossly inaccurate in the neighbourhood of temporal discontinuities in boundary conditions. In the case of one-dimensional homogeneous reaction–diffusion systems this problem can be overcome by applying a singularity correction procedure proposed in this work. The procedure is a modification of the approach recently suggested by Flyer and Fornberg [J. Comput. Phys. 184 (2003) 526] for the solution of partial differential equations with incompatible initial/boundary conditions. It consists of decomposing any concentration profile into a sum of two components: an analytically obtainable one that satisfies discontinuous boundary conditions but ignores homogeneous reaction(s), and a numerically obtainable part that satisfies continuous boundary conditions and takes the homogeneous reactions into account. A similar decomposition can also be applied to the electric current. Computational tests performed for four simple examples of electrochemical systems indicate that the most accurate results (close to the discontinuity) are obtained by combining the decomposition of the concentrations, applied at all discrete time levels, with the decomposition of the current.]]>

rodzaj: materiały konferencyjne w książce

Abstrakt: Electrochemical sensors. and other modern devices of electroanalytical chemistry, generate experimental data which should be subject to rapid, real-time, on-line analysis. Digital simulations. commonly used for obtaining theoretical transient responses (such as cyclic voltammograms) of electrochemical systems, are often computationally too expensive to be used in such cases. The large simulation costs also hamper the application of advanced but computationally expensive methods of data analysis. In order to overcome these difficulties, the solution mapping method based on the High-Dimensional Model Representation (HDMR) technique can be applied. Principles of the method will be outlined and illustrative maps for selected electrochemical kinetic models will be demonstrated.]]>

rodzaj: materiały konferencyjne w książce

Abstrakt: A patch-adaptive grid strategy, especially designed for the automatic solution of initial boundary, value problems occurring in the modeling of transient experiments in electrochemical kinetics, is presented. Current work concentrates on the combination of the strategy with a Hermitian (compact) spatial discretization. with the aim of reducing the computational cost of the method. Preliminary results obtained indicate that the Hermitian scheme brings a reduction of the number of grid nodes needed to achieve a target accuracy.]]>

rodzaj: artykuł w czasopiśmie

Abstrakt: Digital simulation costs present an obstacle on the way to high-speed, real-time, on-line theoretical analysis of experimental data in cyclic voltammetry. To overcome this difficulty, we propose to use solution mapping based on a correlated, hierarchical expansion of multivariate functions, known as high-dimensional model representation (HDMR). The nonlinear dependencies of the simulated voltammograms on multiple model parameters are represented in the form of compact look-up tables, from which approximate voltammograms can be calculated rapidly by interpolation, for any model parameter combinations from a predefined domain. Most importantly, the HDMR does not suffer from the problem of the exponential growth of the look-up tables with the number of model parameters. The creation of a solution map requires a single effort of simulating many voltammograms. However, once the map is prepared, it can be stored and reused many times without the need to repeat costly simulations. HDMR maps are created and examined for five examples of cyclic voltammetry models at planar macroelectrodes in a one-dimensional spatial geometry under pure diffusion transport conditions. The usefulness of the maps for rapid visualization and exploration of the effects of the parameters on the voltammograms and for rapid simultaneous estimation of many parameters from cyclic voltammetric data is demonstrated through computational experiments.]]>

rodzaj: materiały konferencyjne w książce

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rodzaj: artykuł w czasopiśmie

Abstrakt: The conventional determination of model parameter errors in least-squares regression of experimental cyclic voltammetric data assumes validity of local approximations (e.g., linearization) in the parameter space and normal distributions of the data and parameter errors. Such assumptions may not always be satisfied in practice. Bootstrap resampling techniques present a more universally applicable approach to error estimation, which until now has not been used in cyclic voltammetric studies, owing to the high costs of the required voltammogram simulations. We demonstrate that the burden of computing voltammograms can be significantly reduced by the use of high-dimensional model representation (HDMR) solution mapping techniques, thereby making it feasible to apply the bootstrap data analysis in cyclic voltammetry. We perform computational experiments with bootstrap resampling, enhanced by HDMR maps, for a typical cyclic voltammetric model (i.e., the Eqrev Cirr Eqrev reaction mechanism at a planar macroelectrode under semi-infinite, pure diffusion transport conditions). The experiments reveal that the bootstrap distributions of the estimated parameters provide a satisfactory quantification of the parameter errors and can also be used for detecting statistical correlations of the parameters.]]>

rodzaj: materiały konferencyjne w książce

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rodzaj: artykuł w czasopiśmie

Abstrakt: The fourth-order accurate, three-point compact (extended Numerov) finite-difference scheme of Chawla [J. Inst. Math. Appl. 22 (1978) 89] has been recently found superior (in terms of accuracy and efficiency) to the conventional second-order accurate spatial discretisation commonly used in electrochemical kinetic simulations. However, the two-point compact boundary gradient approximation, accompanying the scheme, is difficult to apply in the case of time-dependent kinetic partial differential equations, because it introduces unwanted second temporal derivatives into calculations. The conventional five-point gradient formula is free from this drawback, but it is also not very convenient, owing to the locally increased bandwidth of the matrix of linear equations arising from the spatio-temporal discretisation. A new three-point compact boundary gradient approximation derived in this work, avoids the above inconveniences and economically re-uses expressions utilised by the extended Numerov discretisation. The fourth-order accuracy of the new approximation is proven theoretically and verified in computational experiments performed for examples of kinetic models.]]>

rodzaj: artykuł w czasopiśmie

Abstrakt: The aim of this study was to experimentally determine the creep and shrinkage properties of plain geopolymer and carbon-fiber-reinforced geopolymer concretes. The creep properties of concrete specimens were determined by loading them by 20% of their ultimate stress. The specific creep of the geopolymer concrete was in the same range as that of the ordinary Portland cement — 0.00065 1/MPa. New information on the time-dependent elastic modulus of the concretes was also obtained. The elastic modulus of the plain geopolymer concrete reached, on the average, 32.03 GPa on day 30, 36.29 GPa on day 62, and 45.73 GPa on day 158, but that of the carbon-fiber-reinforced one — 30.12 GPa on day 30, 37.79 GPa on day 62, and 53.35 GPa on day 158 after the production of their specimens.]]>

rodzaj: artykuł w czasopiśmie

Abstrakt: Electrochemical kinetic simulations by the patch-adaptive strategy outlined in the previous parts of this series of papers can be computationally expensive in the extreme cases of very thin boundary layers, moving fronts, or models defined over multiple spatial subintervals having disparate scales. The replacement of the second-order accurate conventional spatial discretisation (thus far used by the strategy) by the fourth-order accurate extended Numerov discretisation of Chawla [M.M. Chawla, J. Inst. Math. Appl. 22 (1978) 89], discussed in this work, allows one to reduce the computational costs. Numerical experiments with five representative examples of difficult-to-simulate kinetic models reveal that the reduction of the computational time, the number of spatial grid nodes needed, and spatial grid refinement levels, is particularly noticeable when a high spatial accuracy of the simulations is requested. At low accuracy demands the conventional spatial discretisation may be more efficient and more convenient to use. The patch-adaptive simulations by the extended Numerov scheme require spatial tolerance parameter TOLX values that are several times larger than the TOLX values that ensure a comparable accuracy by the conventional spatial discretisation.]]>

rodzaj: materiały konferencyjne w książce

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rodzaj: materiały konferencyjne w książce

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rodzaj: materiały konferencyjne w książce

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rodzaj: opis bibliograficzny artykułu

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rodzaj: opis bibliograficzny artykułu

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rodzaj: materiały konferencyjne w książce

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rodzaj: materiały konferencyjne w książce

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rodzaj: materiały konferencyjne w książce

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rodzaj: publikacja w serwisie internetowym

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rodzaj: materiały konferencyjne w książce

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rodzaj: artykuł w czasopiśmie

Abstrakt: The extended Numerov scheme of Chawla is one of high-order compact finite-difference discretisations applicable to BVPs in second-order ODEs, and to PDEs. The use of such discretisations in connection with adaptive grids remains largely unexplored. In order to make up this deficiency, we study the combination of the extended Numerov discretisation with the iterative local adaptive grid h-refinement previously tested by the present author at the assumption of the conventional finite-difference discretisation. A detailed formalism enabling a posteriori error analysis of the extended Numerov scheme is developed, together with several alternative choices for error estimators, grid refinement indicators, and regridding strategies. The adaptive algorithms obtained are examined in calculations on a collection of 15 examples of singularly perturbed ODEs, including equations relevant for electrochemistry. The most satisfactory algorithm involves: deferred approach to error estimation, based on virtual grid coarsening for truncation error evaluation; local discretisation errors as refinement indicators; and regridding strategy that uses the mean indicator values as the indicator thresholds for refinement. The extended Numerov scheme proves more efficient than the conventional discretisation, when used together with the iterative h-refinement.]]>

rodzaj: artykuł w czasopiśmie

Abstrakt: Clouds are a kind of atmospheric factor that most effectively scatters the artificial light coming from the ground. Therefore, they have the most significant impact on the brightness of the night sky. The paper analyses the influence of both the level of cloudiness, as well as the genera of clouds and altitude of its base, on amplifying of the light pollution. The impact of cloudiness on the brightness of the night sky in places with different levels of light pollution was researched. Measurements of meteorological elements were used together with clouds genera assessments. The introduction of an innovative method of identifying some genera of clouds on the base of the all-night continuous measurements of the sky’s brightness allowed for a similar analysis in the absence of observational data specifying the genera of clouds. A linear correlation between the cloudiness and the brightness of the night sky was found. The deter- mined linear correlation parameters allow for specifying the three types of light-polluted areas, possibly related to the density of population. It was found that among the nine genera of the identified night clouds, the Altocumulus, Cirrocumulus, and Cumulonimbus ones are responsible for this correlation. No dependence of the brightness of the night sky on the clouds’ albedo was found. In case of overcast sky, there was a clear relationship between the average altitude of the individual genus of clouds and the brightness of the night sky. Most of the night sky brightness comes from the light scattered on the low- est altitude clouds genera, while the least contribution comes from the light scattered on the high-level clouds. It was also found that at the freezing temperatures, the layer of aerosols forms below the level of the genera Nimbostratus or Stratus. This layer, thickening with the decreasing temperature, additionally scatters the artificial light.]]>

rodzaj: artykuł w czasopiśmie

Abstrakt: This article discusses living environment determinants in Central and Eastern Europe. It is based on a case study of the city of Radzionków, which has 16 thousand inhabitants and is located in the Silesian agglomeration in southern Poland. Hard coal has been mined in this area for almost two hundred years, and it is the main fuel used for central heating. A total of 360 buildings, divided into groups of 60 buildings each, were investigated in the selected city. Three distinct areas were distinguished in terms of living environment quality, depending on building technical condition, heating method and location. These qualities were found to be largely determined by site-speciﬁc spatial and geophysical conditions. A signiﬁcant portion of the literature was found to ignore the spatial factors mentioned in this paper, instead focusing primarily on statistical data concerning pollution. This study examines site-speciﬁc variables and presents diﬀerences in air pollution levels as examined in relation to the morphological structure of development, the degree of building modernisation and heating system types.]]>

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Abstrakt: The extended Numerov scheme of Chawla, adopted for nonuniform grids, is a useful compact finite-difference discretisation, suitable for the numerical solution of boundary value problems in singularly perturbed second order non-linear ordinary differential equations. A new set of three-point compact approximations to first and second derivatives, related to the Chawla scheme and valid for nonuniform grids, is developed in the present work. The approximations economically re-use intermediate quantities occurring in the Chawla scheme. The theoretical orders of accuracy are equal four for the central and one-sided first derivative approximations obtained, whereas the central second derivative formula is either fourth, third, or second order accurate, depending on the grid ratio. The approximations can be used for accurate a posteriori derivative evaluations. A Hermitian interpolation polynomial, consistent with the derivative approximations, is also derived. The values of the polynomial can be used, among other things, for guiding adaptive grid refinement. Accuracy orders of the new derivative approximations, and of the interpolating polynomial, are verified by computational experiments.]]>

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Abstrakt: Despite many years of the development of adaptive grid methods, there is still a need for re-evaluation, tuning, and comparisons of the various approaches to grid adaptation. In this study we seek to identify the most reliable and computationally inexpensive variant of the iterative grid refinement/de-refinement algorithm for the finite difference solution of singularly perturbed BVPs in second-order ODEs, that is also easily extendable to evolutionary PDEs. Conventional threepoint discretisations of the first and second derivatives are used. Errors of the discrete solution and its first derivative are simultaneously controlled. The grid refinement is accomplished by adding nodes at inter-nodal positions, and de-refinement by removing previously added nodes in reverse order. Computational experiments are performed for 15 examples of ODEs, assuming several alternative choices of the a posteriori error estimators, grid refinement indicators, and regridding strategies. The most satisfactory results are obtained by combining: deferred approach to error estimation, based on higher-order reference derivative approximations for truncation error evaluation; interpolation-based indicator for grid refinement; and regridding strategy that uses the mean indicator value as the indicator threshold for refinement.]]>

rodzaj: artykuł w czasopiśmie

Abstrakt: The mathematical model of Abdekhodaie and Wu (J Membr Sci 335:21–31, 2009) of glucose-responsive composite membranes for closed-loop insulin delivery is discussed. The glucose composite membrane contains nanoparticles of an anionic polymer, glucose oxidase and catalase embedded in a hydrophobic polymer. The model involves the system of nonlinear steady-state reaction–diffusion equations. Analytical expressions for the concentration of glucose, oxygen and gluconic acid are derived from these equations using the Adomian decomposition method. A comparison of the analytical approximation and numerical simulation is also presented. An agreement between analytical expressions and numerical results is observed.]]>

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Abstrakt: Digital simulation of transient experiments at channel and tubular electrodes can be performed approximately but relatively cheaply, by means of the integral equation based approach introduced by Singh and Dutt [J. Electroanal. Chem. 182 (1985) 259]. Unfortunately, the use of the series expansion for the relevant integral transformation kernel, suggested by Singh and Dutt, makes such calculations overly slow. A new series expansion is proposed in the present study, which, when combined with the former expansion, yields inexpensive approximations to the kernel and its moment integrals. The relative error of these approximations is at the level of 10−16. The approximations are incorporated into the adaptive Huber method, developed by the present author. The method is shown to provide automatic solutions to the representative integral equations describing chronoamperometry for irreversible charge transfer and cyclic voltammetry for irreversible and reversible charge transfer. Desired accuracy of the solutions is selected simply by specifying a value of the error tolerance parameter. Errors corresponding to the range from about 10−2 of the maximum solution value, down to about 10−7 or even smaller, can be easily obtained at a modest computational cost.]]>

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Abstrakt: Integral equations describing controlled-potential transient experiments at planar interfaces, and under conditions of diffusion in one dimensional finite space, occur in various areas of electrochemistry. Former simulation methods used to solve such equations were rather crudely approximate and non-automatic. In the present work computationally inexpensive approximations to the integral transformation kernels occurring in these equations are determined, that possess the best accuracy achievable within the standard floating point arithmetic. The approximations are combined with the recently developed adaptive Huber method for solving electrochemical integral equations of the Volterra type. The resulting algorithm is tested on representative examples of transient experiments: potential step chronoamperometry for irreversible electron transfer, and cyclic voltammetry for irreversible and reversible electron transfers. The performance of the method is found similar to that previously reported for integral equations involving kernels specific for semi-infinite diffusion. Desired accuracy of the solutions is achieved automatically, depending on user-selected values of the error tolerance parameter. Errors corresponding to the range from about 10−2 of the maximum solution value, down to about 10−7 or even smaller, can be easily achieved at a modest computational cost.]]>

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Abstrakt: Diffusion of reactants inside spherical spatial domains, in the absence of homogeneous reactions, is characteristic of some electrochemical systems, such as amalgam mercury drop electrodes. Simulation of transient experiments in such systems can be performed by the classical integral equation method [see, for example, R.S. Nicholson, I. Shain, Anal. Chem. 36 (1964) 706]. This requires an accurate computation of a specific integral transformation kernel function and its moment integrals. Based on formerly known series expansions, highly accurate (16 digits) and cost-optimised procedures serving for this purpose have been designed in this work. The procedures have been combined with the adaptive Huber method developed by the present author. The resulting simulation technique has been tested on simple examples of relevant integral equations, including models of potential step chronoamperometry and cyclic voltammetry. The method is shown to provide automatic solutions, with a user-selected target accuracy. Errors corresponding to the range from about 10-2 of the maximum solution value, down to about 10-7 or even smaller, can be easily obtained at a modest computational cost.]]>