963 resultados para numerical integration methods
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This thesis presents an investigation into the application of methods of uncertain reasoning to the biological classification of river water quality. Existing biological methods for reporting river water quality are critically evaluated, and the adoption of a discrete biological classification scheme advocated. Reasoning methods for managing uncertainty are explained, in which the Bayesian and Dempster-Shafer calculi are cited as primary numerical schemes. Elicitation of qualitative knowledge on benthic invertebrates is described. The specificity of benthic response to changes in water quality leads to the adoption of a sensor model of data interpretation, in which a reference set of taxa provide probabilistic support for the biological classes. The significance of sensor states, including that of absence, is shown. Novel techniques of directly eliciting the required uncertainty measures are presented. Bayesian and Dempster-Shafer calculi were used to combine the evidence provided by the sensors. The performance of these automatic classifiers was compared with the expert's own discrete classification of sampled sites. Variations of sensor data weighting, combination order and belief representation were examined for their effect on classification performance. The behaviour of the calculi under evidential conflict and alternative combination rules was investigated. Small variations in evidential weight and the inclusion of evidence from sensors absent from a sample improved classification performance of Bayesian belief and support for singleton hypotheses. For simple support, inclusion of absent evidence decreased classification rate. The performance of Dempster-Shafer classification using consonant belief functions was comparable to Bayesian and singleton belief. Recommendations are made for further work in biological classification using uncertain reasoning methods, including the combination of multiple-expert opinion, the use of Bayesian networks, and the integration of classification software within a decision support system for water quality assessment.
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This study analyzes the validity of different Q-factor models in the BER estimation in RZ-DPSK transmission at 40 Gb/s channel rate. The impact of the duty cycle of the carrier pulses on the accuracy of the BER estimates through the different models has also been studied.
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Applying direct error counting, we compare the accuracy and evaluate the validity of different available numerical approaches to the estimation of the bit-error rate (BER) in 40-Gb/s return-to-zero differential phase-shift-keying transmission. As a particular example, we consider a system with in-line semiconductor optical amplifiers. We demonstrate that none of the existing models has an absolute superiority over the others. We also reveal the impact of the duty cycle on the accuracy of the BER estimates through the differently introduced Q-factors.
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This study analyzes the validity of different Q-factor models in the BER estimation in RZ-DPSK transmission at 40 Gb/s channel rate. The impact of the duty cycle of the carrier pulses on the accuracy of the BER estimates through the different models has also been studied.
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Applying direct error counting, we compare the accuracy and evaluate the validity of different available numerical approaches to the estimation of the bit-error rate (BER) in 40-Gb/s return-to-zero differential phase-shift-keying transmission. As a particular example, we consider a system with in-line semiconductor optical amplifiers. We demonstrate that none of the existing models has an absolute superiority over the others. We also reveal the impact of the duty cycle on the accuracy of the BER estimates through the differently introduced Q-factors. © 2007 IEEE.
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MSC subject classification: 65C05, 65U05.
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2000 Mathematics Subject Classification: primary: 60J80, 60J85, secondary: 62M09, 92D40
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We demonstrate an accurate BER estimation method for QPSK CO-OFDM transmission based on the probability density function of the received QPSK symbols. Using a 112Gbs QPSK CO-OFDM transmission as an example, we show that this method offers the most accurate estimate of the system's performance in comparison with other known approaches.
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It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.
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In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.
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The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.
We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.
We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.
The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.
Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.
The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.