Numerical analysis of random periodicity of stochastic differential equations

In this thesis, we discuss the numerical approximation of random periodic solutions (r.p.s.) of stochastic differential equations (SDEs) with multiplicative noise. We prove the existence of the random periodic solution as the limit of the pull-back flow when the starting time tends to $-\infty$ along the multiple integrals of the period. As the random periodic solution is not explicitly constructible, it is useful to study the numerical approximation. We discretise the SDE using the Euler-Maruyama scheme and modified Milstein scheme. Subsequently we obtain the existence of the random periodic solution as the limit of the pull-back of the discretised SDE. We prove that the latter is an approximated random periodic solution with an error to the exact one at the rate of $\sqrt {\Delta t}$ in the mean-square sense in Euler-Maruyama method and $\Delta t$ in the modified Milstein method. We obtain the weak convergence result in infinite horizon for the approximation of the average periodic measure

Simulation study on PEM fuel cell gas diffusion layers using x-ray tomography based Lattice Boltzmann method

The Polymer Electrolyte Membrane (PEM) fuel cell has a great potential in leading the future energy generation due to its advantages of zero emissions, higher power density and efficiency. For a PEM fuel cell, the Membrane-Electrode Assembly (MEA) is the key component which consists of a membrane, two catalyst layers and two gas diffusion layers (GDL). The success of optimum PEM fuel cell power output relies on the mass transport to the electrode especially on the cathode side. The carbon based GDL is one of the most important components in the fuel cell since it has one of the basic roles of providing path ways for reactant gases transport to the catalyst layer as well as excess water removal. A detailed understanding and visualization of the GDL from micro-scale level is limited by traditional numerical tool such as CFD and experimental methods due to the complex geometry of the porous GDL structural. In order to take the actual geometry information of the porous GDL into consideration, the x-ray tomography technique is employed which is able to reconstructed the actual structure of the carbon paper or carbon cloth GDLs to three-dimensional digital binary image which can be read directly by the LB model to carry out the simulation. This research work contributes to develop the combined methodology of x-ray tomography based the three-dimensional single phase Lattice Boltzmann (LB) simulation. This newly developed methodology demonstrates its capacity of simulating the flow characteristics and transport phenomena in the porous media by dealing with collision of the particles at pore-scale. The results reveal the heterogeneous nature of the GDL structures which influence the transportation of the reactants in terms of physical parameters of the GDLs such as porosity, permeability and tortuosity. The compression effects on the carbon cloth GDLs have been investigated. The results show that the c applied compression pressure on the GDLs will have negative effects on average pore size, porosity as well as through-plane permeability. A compression pressure range is suggested by the results which gives optimum in-plane permeability to through-plane permeability. The compression effects on one-dimensional water and oxygen partial pressures in the main flow direction have been studied at low, medium and high current densities. It s been observed that the water and oxygen pressure drop across the GDL increase with increasing the compression pressure. Key Words: PEM fuel cell, GDL, LB simulation, SPSC, SPMC, x-ray tomography, carbon paper, carbon cloth, porosity, permeability, degree of anisotropy, tortuosity, flow transport

Polymer electrolyte fuel cell transport mechanisms: simulation study of hydrogen crossover and water content

Hydrogen crossover and membrane hydration are significant issues for polymer electrolyte fuel cells (PEFC). Hydrogen crossover amounts to a quantity of unspent fuel, thereby reducing the fuel efficiency of the cell, but more significantly it also gives rise to the formation of hydrogen peroxide in the cathode catalyst layer which acts to irreversibly degenerate the polymer electrolyte. Membrane hydration not only strongly governs the performance of the cell, most noticeable through its effect on the ionic conductivity of the membrane, it also influences the onset and propagation of internal degradation and failure mechanisms that curtail the reliability and safety of PEFCs. This paper focuses on how hydrogen crossover and membrane hydration are affected by; (a) characteristic cell geometries, and (b) operating conditions relevant to automotive fuel cells. The numerical study is based on the application of a general transport equation developed previously to model multi-species transport through discontinuous materials. The results quantify (1) the effectiveness of different practical mechanisms which can be applied to curtail the effects of hydrogen crossover in automotive fuel cells and (2) the implications on water content within the membrane

As demências na perspectiva do familiar à luz da teoria das incertezas de Mishel

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Ceilândia, Programa de Pós-Graduação em Ciências e Tecnologias em Saúde, 2017.INTRODUÇÃO: A incerteza em relação à doença é considerada como a inabilidade da pessoa em determinar o significado dos eventos relacionados ao fenômeno da doença. A teoria de Mishel trata das incertezas na doença e sugere que as incertezas sejam encaradas como forma de crescimento. O fenômeno das demências, é visto atualmente como um problema de saúde pública e atinge não apena o doente, mas também os familiares, principalmente aqueles que participam diretamente do cuidado. OBJETIVO: Invetigar a incerteza na doença na perspectiva do familiar do individuo com demência sob a ótica da Teoria de Mishel. MÉTODO: Trata-se de um estudo exploratório e descritivo, de corte transversal realizado em em Brasília/DF, na Associação Brasileira de Alzheimer (ABRAz-DF). Participaram os familiares de indivíduos com diagnostico de demência e que participavam das reuniões de apoio da associação. Os dados foram coletados a partir de dois instrumentos, o sócio demográfico e a Escala de Incerteza de Merle Mishel. RESULTADOS: Dentre os quatro domínios da incerteza mensurados (ambiguidade, falta de clareza, falta de informação e imprevisibilidade), constatou-se que 70% (14) dos familiares relataram sentimento de ambiguidade em relação a melhora, ao tratamento, as medicações. Assim como, o sentimento de ambiguidade em relação a quem cuidará do individuo com demência. Da mesma forma em relação ao domínio da imprevisibilidade. O maior grau de incerteza concentrou-se no domínio ambiguidade e imprevisibilidade envolvendo a tomada de decisões e incertezas relacionadas ao futuro do doente. CONCLUSÃO: Pode-se concluir que a incerteza dos familiares estão associados às questões vinculadas ao futuro, pela evolução da doença ser imprevisível, e assim os familiares não conseguem fazer planos futuros de curto e longo prazo, e preocupam-se com a capacidade de desenvolver os cuidados necessários, tais incertezas podem ser amenizadas com esclarecimentos de profissionais de saúde e redes de apoio.INTRODUCTION: The uncertainty regarding the disease is considered as the inability of the person to determine the meaning of the events related to the phenomenon of the disease. Mishel's theory addresses uncertainties in the disease and suggests that uncertainties are viewed as a form of growth. The phenomenon of dementia is currently seen as a public health problem and affects not only the patient, but also the relatives, especially those who participate directly in the care. OBJECTIVE: To investigate the uncertainty in the disease from the family perspective of the individual with dementia from the perspective of the Mishel Theory. METHOD: This is an exploratory and descriptive cross-sectional study carried out in Brasília / DF, at the Brazilian Association of Alzheimer's (ABRAz-DF). Family members of individuals diagnosed with dementia participated in the association's support meetings. Data were collected from two instruments, the demographic partner and the Merle Mishel Uncertainty Scale. RESULTS: Among the four areas of uncertainty measured (ambiguity, lack of clarity, lack of information and unpredictability), it was found that 70% (14) of family members reported a feeling of ambiguity regarding improvement, treatment and medications. As well as the feeling of ambiguity towards who will take care of the individual with dementia. Likewise in relation to the domain of unpredictability. The greater degree of uncertainty focused on the ambiguity and unpredictability domain involving decision-making and uncertainties related to the patient's future. CONCLUSION: It can be concluded that family members' uncertainty is associated with issues related to the future, the evolution of the disease is unpredictable, and thus, family members can not make future plans for the short and long term, and are concerned with the capacity to develop the necessary care, such uncertainties can be softened with clarifications from health professionals and support networks

Threshold fine-tuning and 3D characterisation of porous media using X-ray nanotomography

A common challenge in the X-ray nanotomography of porous media, such as fuel cell gas diffusion layers (GDLs), is to binarize nanotomography greyscale images in order to differentiate between solids and voids for structural characterisation and numerical flow analysis. In the process threshold determination is critical. This paper presents a study on determination of and fine-tuning threshold value based on comparison of material porosity and average fibre diameter obtained from nanotomography images with porosity data from density experiments and average fibre diameter achieved from scanning electron microscopy images respectively. The more accurate 3D reconstructed model is then used to calculate pore size distribution and average pore size, while the gas permeability of the representative 3D binary images are calculated using a single phase Lattice Boltzmann (LB) model in the D3Q19 regime

Nanotomography based study of gas diffusion layers

Nano-computed tomography (nanoCT) was used for non-invasive 3D visualization and characterization of porous gas diffusion layer (GDL) for polymer electrolyte membrane fuel cells (PEMFC). The study was conducted using reconstruction of 3D images of a GDL of polymer electrolyte fuel cell to determine the critical nanostructural parameters of the layer, such as porosity, mean pore radii, structure model index and degrees of anisotropy. Furthermore, permeability of the GDL was obtained through lattice Boltzmann numerical modeling

Influence of threshold variation on determining the properties of a polymer electrolyte fuel cell gas diffusion layer in X-ray nano-tomography

Morphological parameters of a 3D binary image of a porous carbon gas diffusion layer (GDL) for polymer electrolyte fuel cells (PEFC) reconstructed using X-ray nano-tomography scanning have been obtained, and influence of small alterations in the threshold value on the simulated flow properties of the reconstructed GDL has been determined. A range of threshold values with 0.4% increments on the greyscale map have been applied and the gas permeability of the binary images have been calculated using a single-phase lattice Botlzmann model (LBM), which is based on the treatment of nineteen velocities in the three dimensional domain (D3Q19). The porosity, degrees of anisotropy and the mean pore radius have been calculated directly from segmented voxel representation. A strong relationship between these parameters and threshold variation has been established. These findings suggest that threshold selection can significantly affect some of the flow properties and may strongly influence the computational simulation of micro and nano-scale flows in a porous structure

Multiscale modeling of single-phase multicomponent transport in the cathode gas diffusion layer of a polymer electrolyte fuel cell

This research reports a feasibility study into multiscale polymer electrolyte fuel cell (PEFC) modeling through the simulation of macroscopic flow in the multilayered cell via one-dimensional (1D) electrochemical modeling, and the simulation of microscopic flow in the cathode gas diffusion layer (GDL) via three-dimensional (3D) single-phase multicomponent lattice Boltzmann (SPMC-LB) modeling. The heterogeneous porous geometry of the carbon-paper GDL is digitally reconstructed for the SPMC-LB model using X-ray computer microtomography. Boundary conditions at the channel and catalyst layer interfaces for the SPMC-LB simulations such as specie partial pressures and through-plane flowrates are determined using the validated 1D electrochemical model, which is based on the general transport equation (GTE) and volume-averaged structural properties of the GDL. The calculated pressure profiles from the two models are cross-validated to verify the SPMC-LB technique. The simulations reveal a maximum difference of 2.4% between the thickness-averaged pressures calculated by the two techniques, which is attributable to the actual heterogeneity of the porous GDL structure

Determination of the anisotropic permeability of a carbon cloth gas diffusion layer through X-ray computer micro-tomography and single-phase lattice Boltzmann simulation

An investigation of the anisotropic permeability of a carbon cloth gas diffusion layer (GDL) based on the integration of X-ray micro-tomography and lattice Boltzmann (LB) simulation is presented. The method involves the generation of a 3D digital model of a carbon cloth GDL as manufactured using X-ray shadow images acquired through X-ray micro-tomography at a resolution of 1.74 µm. The resulting 3D model is then split into 21 volumes and integrated with a LB single-phase numerical solver in order to predict three orthogonal permeability tensors when a pressure difference is prescribed in the through-plane direction. The 21 regions exhibit porosity values in the range of 0.910–0.955, while the average fibre diameter is 4 µm. The results demonstrate that the simulated through-plane permeability is about four times higher than the in-plane permeability for the sample imaged and that the corresponding degrees of anisotropy for the two orthogonal off-principal directions are 0.22 and 0.27. The results reveal that flow channelling can play an important role in gas transport through the GDL structure due to the non-homogeneous porosity distribution through the material. The simulated results are also applied to generate a parametric coefficient for the Kozeny–Carman (KC) method of determining permeability. The current research reveals that by applying the X-ray tomography and LB techniques in a complementary manner, there is a strong potential to gain a deeper understanding of the microscopic fluidic phenomenon in representative models of porous fuel cell structures and how this can influence macroscopic transport characteristics which govern fuel cell performance

Simulation of liquid water beakthrough in a nano-tomography reconstruction of a carbon paper gas diffusion layer

This study reports the feasibility of newly simulating liquid water intrusion into the porous gas diffusion layer (GDL) of a polymer electrolyte fuel cell (PEFC) using X-ray nano-tomography and two-phase lattice Boltzmann (LB) simulation. A digital 3D model of the GDL is reconstructed using X-ray nanotomography while two-phase porous flow is simulated at two different levels of surface wettability by applying a newly-developed numerical LB model. The results show liquid infiltration in a hydrophobic GDL is comparatively lower (pore saturation of 0.11 to 0.90) than that for a hydrophilic GDL (pore saturation of 0.36 to 0.96) over the liquid intrusion range of 1 kPa . 100 kPa. Visualisation of simulated results in three dimensions reveal dissimilar liquid infiltration characteristics for the two levels of wettability considered, yet also reveal a general breakthrough of liquid water at a pressure of 10 kPa due to specific structural features of the GDL