1,720,956 research outputs found
A numerical method based on Runge-Kutta and Gauss-Legendre integration for solving initial value problems in ordinary differential equations
Full text linkM.Sc.A class of numerical methods for solving nonstiff initial value problems in ordinary differential equations has been developed. These methods, designated RKrGLn, are based on a Runge-Kutta method of order r (RKr), and Gauss-Legendre integration over n+ 1 nodes. The interval of integration for the initial value problem is subdivided into an integer number of subintervals. On each of these n + 1 nodes are defined in accordance with the zeros of the Legendre polynomial of degree n. The Runge-Kutta method is used to find an approximate solution at each of these nodes; Gauss-Legendre integration is used to find the solution at the endpoint of the subinterval. The process then carries over to the next subinterval. We find that for a suitable choice of n, the order of the local error of the Runge- Kutta method (r + 1) is preserved in the global error of RKrGLn. However, a poor choice of n can actually limit the order of RKrGLn, irrespective of the choice of r. What is more, the inclusion of Gauss-Legendre integration slightly reduces the number of arithmetical operations required to find a solution, in comparison with RKr at the same number of nodes. These two factors combine to ensure that RKrGLn is considerably more efficient than RKr, particularly when very accurate solutions are sought. Attempts to control the error in RKrGLn have been made. The local error has been successfully controlled using a variable stepsize strategy, similar to that generally used in RK methods. The difference lies in that it is the size of each subinterval that is controlled in RKrGLn, rather than each individual stepsize. Nevertheless, local error has been successfully controlled for relative tolerances ranging from 10 -4 to 10-10 . We have also developed algorithms for estimating and controlling the global error. These algorithms require that a complete solution be obtained for a specified distribution of nodes, after which the global error is estimated and then, if necessary, a new node distribution is determined and another solution obtained. The algorithms are based on Richardson extrapolation and the use of low-order and high-order pairs. The algorithms have successfully achieved desired relative global errors as small as 10-1° . We have briefly studied how RKrGLn may be used to solve stiff systems. We have determined the intervals of stability for several RKrGLn methods on the real line, and used this to develop an algorithm to solve a stiff problem. The algorithm is based on the idea of stepsize/subinterval adjustment, and has been used to successfully solve the van der Pol system. Lagrange interpolation on each subinterval has been implemented to obtain a piecewise continuous polynomial approximation to the numerical solution, with same order error, which can be used to find the solution at arbitrary nodes
Relative Error Control in Bivariate Interpolatory Cubature
Full text linkWe describe an algorithm for controlling the relative error in the numerical
evaluation of a bivariate integral, without prior knowledge of the magnitude of
the integral. In the event that the magnitude of the integral is less than
unity, absolute error control is preferred. The underlying quadrature rule is
positive-weight interpolatory and composite. Some numerical examples
demonstrate the algorithm.Comment: For the 1-D version of this algorithm, available open access at J.
Math. Res., consult reference [10
The development of a one-dimensional numerical simulation of thin-film photovoltaic devices, and an investigation into the properties of Si:H solar cells
Full text linkPh.D.A one-dimensional numerical simulation of photovoltaic (PV) cells has been written, and has been designated RAUPV2. An algorithm for determining the optical generation rate profile, taking into account multiple internal reflections in a multilayer cell has been developed. A method which enables realistic boundary values to be calculated, using RAUPV2 itself, has been developed. This method allows all three boundary values (', Fn and Fp) at each surface, to be determined, without the need to specify any additional input parameters. A comprehensive set of input parameters for aSi:H PV cells has been established, in consultation with the literature. Dangling-bond theory has been described and input parameters for dangling-bond defects have been presented. The effect of surface states in the p-layer on the contact potential at the TCO/p interface has been investigated. It was found that there is an intimate relationship between the contact potential and the parameters pertaining to the surface states. A simple method has been demonstrated, which has allowed RAUPV2 to reproduce the J-V curve of an existing aSi:H PV cell. The method requires that only the dangling-bond concentration in the i-layer and the contact potential at the Sn02/P interface needs to be adjusted. Once the J- V curve had been generated, the simulation results were used to characterise the empirical cell, in both thermodynamic- and steady-state equilibrium. This simulated cell was designated the realistic cell. The effect of asymmetries in the input parameters, under carrier band mobility interchange, on the performance of p-i-n cells has been investigated. The results indicate that, while asymmetries in the gap state distributions do give rise to asymmetrical behaviour in the J- V curve, the effect is slight, and it is the positional asymmetry of the optical generation profile that is mostly responsible for the observed asymmetry in the J- V curve under mobility interchange. An investigation of the limiting carrier effect has led to the conclusion that, in a p-i-n aSi:H cell under forward bias, the electron is the limiting carrier. This has been explained by appealing to the form of the optical generation profile, since most electron-hole pairs (EHPs) are generated near the front of the cell, and it is electrons that must be collected at the back contact. Investigations of the n-i-p aSi:H cell, under forward bias, have shown the hole to be the limiting carrier. It was found that the introduction of positional symmetry into the optical generation rate profile greatly reduced the limiting carrier effect, and it was concluded that the limiting carrier effect arises due to the asymmetries in the material parameters of the cell, particularly the _ positional asymmetry of the optical generation profile. It was observed that the nature of the optical generation profile actually plays an important role in determining the identity of the limiting carrier, in a p-i-n cell. The same effect was not observed in the n-i-p cell. The effective carrier collection length has been defined, and it was seen that the limiting carrier possesses the larger effective collection length. The effect of boron and phosphorous profiling of the i-layer was studied. It was found that boron profiling led to a decrease in cell performance, while phosphorous profiling improved cell performance. It was found that there was a P concentration at which cell performance peaked. The dependence of the spectral response of the realistic cell on device length L, was investigated, showing a general improvement in the spectral response as L was decreased. The spectral response has been interpreted in a novel way. It was assumed that the form of the monochromatic optical generation profiles in the vicinity of the peak in the spectral response represented optimal generation profiles. These profiles were subjected to a linear transformation, such that their form was preserved but that their integrated value was the same as that of the realistic optical generation profile, under global AM1.5 illumination. Using these transformed optical generation profiles, J- V curves were obtained. The maximum power output PM of these J- V curves was seen to exhibit a maximum some 17% greater than that of the realistic cell with a realistic optical generation profile. The spectral response of the phosphorous profiled cell was obtained. In a manner similar to that for the non-P profiled cell, the optimal generation profile was found. The PM for this profile was found to be 7.86mWcm -2 , considerably larger than the 5.60mWcm-2 for the phosphorous profiled cell with a realistic optical generation profile. The effect on the simulation output of variations in numerous dangling-bond defect input parameters has been investigated. It was found that the energy position and concentration of the doped layer defects need not be known to a high degree of precision. On the other hand, it was found that the energy position of the i-layer defects, the standard deviation of the defect distributions, and the defect carrier capture cross-sections, do need to be known with certainty
Incorporation of the first derivative of the objective function into the linear training of a radial basis function neural network for approximation via strict interpolation
Full text linkD.Phil. (Applied mathematics)Please refer to full text to view abstrac
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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