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published_or_final_version / abstract / toc / Computer Science and Information Systems / Master / Master of Philosophy

The development of localized muscle fatigue has classically been described by the nonlinear intensity - endurance time (ET) curve (Rohmert, 1960; El Ahrache et al., 2006). These empirical intensity-ET relationships have been well-documented and vary between joint regions. Xia and Frey Law (2008) previously proposed a three-compartment biophysical fatigue model, consisting of compartments (i.e. states) for active (MA), fatigued (MF), and resting (MR) muscle, to predict the decay and recovery of muscle force. However the model had yet to be validated for static or intermittent isometric tasks. The purpose of this thesis was to provide validation to the biophysical model. The first goal of this thesis was to determine optimal model parameter values, fatigue (F) and recovery (R), which define the "flow rate" between muscle states and to evaluate the model's accuracy for estimating expected intensity - ET curves. Using a grid-search approach with modified Monte Carlo simulations, over 1 million F and R permutations were used to predict the maximum ET for sustained isometric tasks at 9 intensities ranging from 10 - 90% of maximum in 10% increments (over 9 million simulations total). Optimal F and R values ranged from 0.00589 (Fankle) and 0.0182 (Rankle) to 0.00058 (Fshoulder) and 0.00168 (Rshoulder) , reproducing the intensity-ET curves with low mean RMS errors: shoulder (2.7s), hand/grip (5.6s), knee (6.7s), trunk (9.3s), elbow (9.9s), and ankle (11.2s). Testing the model at different task intensities (15 - 95% maximum in 10% increments) produced slightly higher errors, but largely within the 95% prediction intervals expected for the intensity-ET curves. The second goal of this thesis was to conduct a meta-analysis of available percent torque decline data as a function of duty cycle and intensity from literature. For comparison across studies, decay in MVC (% decline) was extracted at a selected range of time points: 30, 60, 90, and 120 seconds across all joints (shoulder, hand/grip, knee, trunk, elbow, and ankle). Searches of the following databases were performed: PubMed, Cumulative Index to Nursing and Allied Health Literature (CINAHL), Web of Knowledge, and Google Scholar. The inclusion criteria included: studies with healthy human subjects, ages between 18-55 years old, intermittent tasks with force/torque data, a task time of at least 30 seconds, and published in English. Exclusion criteria included: dynamic contractions, simultaneous multi-joint testing (e.g. squat lifts), functional tasks, body/limb weight as primary resistance, and electrically stimulated contractions. The database search strategy resulted in a total of 2781 potential publications. Of these articles 44 met the required inclusion and exclusion criteria. Since there were so few publications that fit the required inclusion and exclusion criteria, static fatigue papers that were used in (Frey Law and Avin, 2010) meta-analysis and fit the inclusion requirements for this study were used to fill in points at the extreme of the surface (DC=1). Of the 194 publications that were used in the prior meta-analysis, only 3 fit the required inclusion and exclusion criteria for this analysis, for a total of 47 studies (torque decline was typically the limiting factor). From these 47 studies, empirical % decline models could be developed for the joint regions with 3 or more data points (ankle, knee, elbow, and hand/grip) and a general model for each of the 4 discrete time points. The total sample size for each joint ranged from 125 (elbow) to 306 (hand/grip). The total number of data points for each joint ranged from 28 (elbow) -to 68 (hand/grip) with a total of 193 data points extracted. The third goal of this thesis was to compare the empirical models developed from the meta-analysis to the predicted surfaces produced by the biophysical model. Each surface was compared to its empirical counterpart qualitatively and quantitatively. Qualitatively the predicted surfaces reasonable resembled the empirical models. Quantitative analysis was performed by calculating the mean RMS and relative errors between the surfaces. The predicted surfaces had reasonably low range of mean RMS errors across each time point: hand/grip (92.66-238s), knee (73.60-186.25s), elbow (23.62-96.31s), and ankle (34.02-129.63s). The quantitative analysis also showed that the percent of the data points found by the meta-analysis that fell within the predicted 95% confidence interval was reasonably high: 52%(hand/grip; 120s) to 100% (elbow; 60, 90, & 120s). This thesis concluded that this three-compartment fatigue model can be used to accurately represent joint-specific static intensity-ET curves and 3D surfaces of percent torque decline as a function of intensity and duty cycle for short intermittent tasks (i.e. <120 seconds). While the intensity-ET curves are currently used for ergonomics analysis. The relative torque decline surfaces for intermittent tasks that were developed in this thesis provide further insight into what occurs at the muscle level (i.e. decline in muscle force production) during intermittent work cycles. This insight could provide a new method for developing rest-work cycles or job rotation cycles in industry.

Mathematical model-building is one kind of mathematical thinking, which uses mathematical signs and methods to build a mathematical tool which can describe and solve practical problem. However, System Dynamic is to solve complicated non-linear dynamic problem. It uses the model-building software of diagram interface to make dynamic simulation. Behind the dynamic simulation is the calculation of a set of mathematical equation. The purpose of this research is , by the transition between Mathematics Model and System Dynamic Model, to discuss the mathematical principle of System Dynamic ,and to avoid distorting model and making the model validation harder due to the model-builder's misusing function. Using the conclusion of the transition will help validating the model and raising the reliability and the efficiency of the model. From the conclusion of this research, we find out that System Dynamic is non-linear dynamic mathematical model. Both are exchangeable. From the transition, we also find that the graph function used in the process of System Dynamic model-building is a piecewise-linear- approximate function. The numerical value setting of the graph function can influence the system action. After the transition from System Dynamic model to mathematical model, we can use some other mathematical software to draw the phase-plane-plot or phase-portrait-plot. It will analyze clearly the system action in any situation, and validate the correction of model construction.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-08-28T19:49:36Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Revisão Dilermano V Regis.PDF: 739794 bytes, checksum: d08c982161f7e5a51c6e06ede504f527 (MD5) / Made available in DSpace on 2014-08-28T19:49:36Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Revisão Dilermano V Regis.PDF: 739794 bytes, checksum: d08c982161f7e5a51c6e06ede504f527 (MD5) Previous issue date: 2013-04-11 / O objetivo deste estudo é apresentar uma ferramenta que todos possuem, que é fácil de carregar e que portanto tem alcance popular. Nas primeiras seções apresenta-se algumas operações matemáticas elementares executadas com uma calculadora simples. Começa-se por estudar a operação de divisão de inteiros e como encontrar o resto na calculadora, como operar com frações em uma calculadora e responder na forma de fração, como encontrar a fração geratriz de uma dízima periódica ou ainda como extrair a raíz "n-ésima"de um número real. Para cada operação destas há a preocupação de se expôr também suas devidas aplicações e, quando necessário, de se realizar estudos matemáticos mais profundos como, por exemplo, no caso das congruências módulo m nas dízimas ou derivadas para raízes n-ésima. Em iterações com a adição, por exemplo, trabalha-se o uso adequado de algumas teclas para um procedimento rápido no estudo das progressões aritméticas, juro simples e funções polinomiais do 1o grau. Já na seção de iterações com o produto, propõe-se um estudo das progressões geométricas, funções exponenciais e juro composto. Iterando com as fórmulas de Maclaurin, veremos como é possível utilizar a calculadora simples para encontrar valores das funções trigonométricas circulares e hiperbólicas, bem como os valores dos logaritmos decimais e neperianos. Esse trabalho mostra ao leitor que pelo conhecimento matemático pode se otimizar a calculadora simples, responder questões que antes os cálculos ficariam apenas indicados, ganhar tempo nos cálculos e utilizar o tempo restante para melhor elaborar a estratégia de resolução, e demais vantagens que o leitor descobrirá. / Quero agradecer aos amigos, àqueles que o tempo separou mas as lembranças não, e de forma especial aos 29 novos amigos que o mestrado me proporcionou: Amanda, Viviane, Leozão, Hélio, Flávio, Carlos André, Fabão, Rogério, Marquinhos, Junior César, Paulo César, Edmaldo, Haniel, Simão, Leandro, Kadu, Frederico, Kariton, Marcão, Welington. Àqueles que foram além da amizade e se fizeram irmãos: Túlio, Robison, Alan, Hugo César, César Pereira, Leo Alcântara, Maradona, Eduardo Vasconcelos e Mateus. A esses devo meus reconhecimentos. A esses que leram ou ouviram com cuidado as primeiras versões, que opniram, corrigiram e criticaram, meus sinceros agradecimentos. Desejo agradecer de forma mais pessoal à minha família, pelo apoio incondicional, por me ouvirem mesmo quando nada entendiam. À Dagma e à Dalma pelas lições diárias de força e coragem; a minha esposa Juliana que conseguiu suportar a construção de um livro dentro de casa e por acreditar que eu conseguiria escrevê-lo. Meu maior agradecimento vai aos meus filhos: Priscila pelas horas ao telefone me ouvindo; Pedro, Mariana e Gabriel, pela correção ou reescrita de meu português, pelas brincadeiras, pelas partidas de futebol no vídeo game buscando aliviar meu cansaço, por me obrigarem a ir ao cinema ou por fazermos nada ao final dos meus dias de trabalho. Sem isto, e sem eles, eu não sobreviveria à escrita deste.

The purpose of this research is to study the influence of implementing 9-year compulsory curriculum on students¡¦ mathematical abilities, and to analyze the achievement of students from backgrounds of different educational beliefs and learning practices. Based on this concept, a questionnaire is designed based on papers published both locally and internationally together with analysis of survey results. This study is based on the population of junior high school students graduated during 2003 and 2004 in Kaohsiung City. The method of stratified random sampling is employed to select schools for conducting the survey. A total of 5 schools were selected and 450 sets of questionnaire taken from these schools with 400 successful returns. A total of 16 questionnaires were considered ineffective and 386 were valid returns. The mean, maximum, minimum, and standard deviation of the collected data were analyzed while statistical methods such as equality of means were employed in terms of the heteroschendasticity. The methods of regression analysis and data processing were used to inspect the following questions:

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<p>The dissertation offers a Multiphysics perspective in analyzing emerging metallurgical techniques. Heat transfer, structural deformation, and fluid flow associate with one another in phase-changing materials processing methods. To comprehensively analyze these aspects for an optimized final product, the authors have proposed a numerical mathematical model describing the thermal and geometric progression of the binary alloy casting process. The model is further executed in COMSOL Multiphysics, adapted in two metal manufacturing applications, resistance spot welding (RSW) and binder jet printing (BJP). </p><p>Resistance spot welding is a well-adapted metal sheeting joining technique with comparably limited modeling and simulating research. The heat transfer module and geometric deformation module are applied to the simulation of RSW to discuss the thermal gradient development of the welding zone. The model was further calculated and verified through a case study with Python. </p><p>BJP is a rapidly developing additive manufacturing method. The novel 3D printing technique brings challenges in post-processing geometric control and material selection limitations. Multiphysics simulation serves as an excellent tool in process parameters analysis and quality control. This dissertation focuses on the sintering process of BJP of binary alloy powders. Melting and solidification mathematical models were implemented in COMSOL, where the sintering shrinkage rate could be calculated. The shrinkage rate was further verified through experimental analysis of binder jet printed samples. </p><p>Microstructural analysis on sintered binder jet printed parts was performed to assess the validity of BJP to substitute the die casting method for manufacturing of valvebody. Sintering shrinkage and metallurgical analysis have been performed on the green and sintered BJP samples. After sintering, the final part achieved 98% density, and the integrity of the designed channels was preserved. The shrinkage analysis has indicated the effect of printing orientation and sintering orientation on the geometry and metallurgy of the final products. Microstructure analysis on the cross-sections of the sintered products also indicates the various defects induced from biner jet 3D printing. </p><p>The research aims to provide a systematic rheology analysis of the phase transformation process of binary alloys. The dissertation has connected the physical, mathematical modeling with 15 </p><p><br></p><p>simulative modeling through the rheological evaluation of phase-changing manufacturing techniques. The connections were conclusively verified through empirical studies, including case assessment and experimentation. The research aims to offer universally applicable models that can be applied to phase-changing metal processing techniques. </p>

The Ku band microwave remote sensor, SeaWinds, was developed at the National Aeronautics and Space Administration (NASA) Jet Propulsion Laboratory (JPL). Two identical SeaWinds instruments were launched into space. The first was flown onboard NASA QuikSCAT satellite which has been orbiting the Earth since June 1999, and the second instrument flew onboard the Japanese Advanced Earth Observing Satellite II (ADEOS-II) from December 2002 till October 2003 when an irrecoverable solar panel failure caused a premature end to the ADEOS-II satellite mission. SeaWinds operates at a frequency of 13.4 GHz, and was originally designed to measure the speed and direction of the ocean surface wind vector by relating the normalized radar backscatter measurements to the near surface wind vector through a geophysical model function (GMF). In addition to the backscatter measurement capability, SeaWinds simultaneously measures the polarized radiometric emission from the surface and atmosphere, utilizing a ground signal processing algorithm known as the QuikSCAT / SeaWinds Radiometer (QRad / SRad). This dissertation presents the development and validation of a mathematical inversion algorithm that combines the simultaneous active radar backscatter and the passive microwave brightness temperatures observed by the SeaWinds sensor to retrieve the oceanic rainfall. The retrieval algorithm is statistically based, and has been developed using collocated measurements from SeaWinds, the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) rain rates, and Numerical Weather Prediction (NWP) wind fields from the National Centers for Environmental Prediction (NCEP). The oceanic rain is retrieved on a spacecraft wind vector cell (WVC) measurement grid that has a spatial resolution of 25 km. To evaluate the accuracy of the retrievals, examples of the passive-only, as well as the combined active / passive rain estimates from SeaWinds are presented, and comparisons are made with the standard TRMM rain data products. Results demonstrate that SeaWinds rain measurements are in good agreement with the independent microwave rain observations obtained from TMI. Further, by applying a threshold on the retrieved rain rates, SeaWinds rain estimates can be utilized as a rain flag. In order to evaluate the performance of the SeaWinds flag, comparisons are made with the Impact based Multidimensional Histogram (IMUDH) rain flag developed by JPL. Results emphasize the powerful rain detection capabilities of the SeaWinds retrieval algorithm. Due to its broad swath coverage, SeaWinds affords additional independent sampling of the oceanic rainfall, which may contribute to the future NASA's Precipitation Measurement Mission (PMM) objectives of improving the global sampling of oceanic rain within 3 hour windows. Also, since SeaWinds is the only sensor onboard QuikSCAT, the SeaWinds rain estimates can be used to improve the flagging of rain-contaminated oceanic wind vector retrievals. The passive-only rainfall retrieval algorithm (QRad / SRad) has been implemented by JPL as part of the level 2B (L2B) science data product, and can be obtained from the Physical Oceanography Distributed Data Archive (PO.DAAC).

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Flow and reactive transport of chemical species is a very common phenomenon that occurs in natural and artificial systems. However in this study, the topic is related to acid mine drainage in the South African mining environment. Due to the hazards associated with acid mine drainage, prevention or treatment of mine effluent water before discharging to receiving waters and other environments is a necessity. A new time-dependent mathematical model is developed for a passive treatment method, based on multi-scale modelling of the coupled physico-chemical processes such as diffusion, convection, reactions and filtration, that are involved in the treatment process. The time-dependent model is simulated on a two-dimensional domain using finite volume discretization to obtain chemical species distributions. / AFRIKAANSE OPSOMMING: Vloei en reagerende transport van chemiese spesies is ’n baie algemene verskynsel wat in natuurlike en kunsmatige stelsels plaasvind. In hierdie studie is die onderwerp egter verwant aan suurmyndreinering in die Suid-Afrikaanse mynbou-omgewing. As gevolg van die gevare wat verband hou met suurmyndreinering, is die voorkoming of die behandeling van die afval-mynwater voor dit in opvangswaters en ander omgewings beland ’n noodsaaklikheid. ’n Nuwe tydafhanklike wiskundige model vir ’n passiewe behandelingsmetode is ontwikkel. Dit is gebaseer op die multi-skaal modulering van gekoppelde fisies-chemiese prosesse soos diffusie, konveksie, reaksies en filtrasie, wat by die behandelingsproses betrokke is. Die tydafhanklike model word gesimuleer op ’n twee-dimensionele domein met behulp van eindige volume diskretisasie om die verspreiding van chemiese spesies te bepaal.