Mathematical modelling of the catalyst layer of a polymer-electrolyte fuel cell

In this paper we derive a mathematical model for the cathode catalyst layer of a polymer electrolyte fuel cell. The model explicitly incorporates the restriction placed on oxygen in reaching the reaction sites, capturing the experimentally observed fall in the current density to a limiting value at low cell voltages. Temperature variations and interfacial transfer of O2 between the dissolved and gas phases are also included. Bounds on the solutions are derived, from which we provide a rigorous proof that the model admits a solution. Of particular interest are the maximum and minimum attainable values. We perform an asymptotic analysis in several limits inherent in the problem by identifying important groupings of parameters. This analysis reveals a number of key relationships between the solutions, including the current density, and the composition of the layer. A comparison of numerically computed and asymptotic solutions shows very good agreement. Implications of the results are discussed and future work is outlined

Nonlinear asymptotic stability of the semi-strong pulse dynamics in a regularized Gierer-Meinhardt model

We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the semi-strong regime of two-pulse interactions in a regularized Gierer-Meinhardt system. In the semi-strong limit the strongly localized activator pulses interact through the weakly localized inhibitor, the interaction is not tail-tail as in the weak interaction limit, and the pulses change amplitude and even stability as their separation distance evolves on algebraically slow time scales. The RG approach employed here validates the interaction laws of quasi-steady pulse patterns obtained formally in the literature, and establishes that the pulse dynamics reduce to a closed system of ordinary differential equations for the activator pulse locations. Moreover, we fully justify the reduction to the nonlocal eigenvalue problem (NLEP) showing the large difference between the quasi-steady NLEP operator and the operator arising from linearization about the pulse is controlled by the resolven

A SIMPLE THERMAL MODEL OF PEM FUEL CELL STACKS

ABSTRACT A simple model is developed that determines the temperature distribution through a unit fuel cell with straight flow channels, in steady state operation. Using the large aspect ratio of the typical fuel cell geometry, the thermal model approximately decouples cross-plane thermal transport at each channel location. Using the fact that in-plane thermal conductivities are much larger than through-plane in typical bipolar plate construction, it is possible to further approximate the cross-plane thermal transport with a simple, one-dimensional model. We then consider the thermal coupling of several unit cells connected in series. In this way, we can simulate the effect of an anomalously hot cell in a stack environment. We take as inputs to the model the cell voltage and local current density, membrane resistance and condensation rates from a previously developed model. The thermal model outputs the average coolant temperature and the temperature distribution through the bipolar plates and membrane electrode assembly at each location down the channel. Although we are aware that there are significant coupling effects between the thermal distribution and performance, this is not taken into account in this study

Conditional stability of unstable viscous shock waves in compressible gas dynamics and MHD

Extending our previous work in the strictly parabolic case, we show that a linearly unstable Lax-type viscous shock solution of a general quasilinear hyperbolic--parabolic system of conservation laws possesses a translation-invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small $L^1\cap H^3$ perturbations, converging time-asymptotically to a translate of the unperturbed wave. That is, for a shock with $p$ unstable eigenvalues, we establish conditional stability on a codimension-$p$ manifold of initial data, with sharp rates of decay in all $L^p$. For $p=0$, we recover the result of unconditional stability obtained by Mascia and Zumbrun. The main new difficulty in the hyperbolic--parabolic case is to construct an invariant manifold in the absence of parabolic smoothing.Comment: 32p

Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential

The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. All trivial-phase stable solutions are deformations of the ground state of the linear Schr\"odinger equation. Our results show that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Physically, this implies stability of states near the Thomas-Fermi limit.Comment: 12 pages, 17 figure

Stability of Attractive Bose-Einstein Condensates in a Periodic Potential

Using a standing light wave trap, a stable quasi-one-dimensional attractive dilute-gas Bose-Einstein condensate can be realized. In a mean-field approximation, this phenomenon is modeled by the cubic nonlinear Schr\"odinger equation with attractive nonlinearity and an elliptic function potential of which a standing light wave is a special case. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. Trivial-phase solutions are experimentally stable provided they have nodes and their density is localized in the troughs of the potential. Stable time-periodic solutions are also examined.Comment: 12 pages, 18 figure

The effects of water and microstructure on the performance of polymer electrolyte fuel cells

n this paper, we present a comprehensive non-isothermal, one-dimensional model of the cathode side of a Polymer Electrolyte Fuel Cell. We explicitly include the catalyst layer, gas diffusion layer and the membrane. The catalyst layer and gas diffusion layer are characterized by several measurable microstructural parameters. We model all three phases of water, with a view to capturing the effect that each has on the performance of the cell. A comparison with experiment is presented, demonstrating excellent agreement, particularly with regard to the effects of water activity in the channels and how it impacts flooding and membrane hydration. We present several results pertaining to the effects of water on the current density (or cell voltage), demonstrating the role of micro-structure, liquid water removal from the channel, water activity, membrane and gas diffusion layer thickness and channel temperature. These results provide an indication of the changes that are required to achieve optimal performance through improved water management and MEA-component design. Moreover, with its level of detail, the model we develop forms an excellent basis for a multi-dimensional model of the entire membrane electrode assembly

Inhomogeneous magnetization in dipolar ferromagnetic liquids

At high densities fluids of strongly dipolar spherical particles exhibit spontaneous long-ranged orientational order. Typically, due to demagnetization effects induced by the long range of the dipolar interactions, the magnetization structure is spatially inhomogeneous and depends on the shape of the sample. We determine this structure for a cubic sample by the free minimization of an appropriate microscopic density functional using simulated annealing. We find a vortex structure resembling four domains separated by four domain walls whose thickness increases proportional to the system size L. There are indications that for large L the whole configuration scales with the system size. Near the axis of the mainly planar vortex structure the direction of the magnetization escapes into the third dimension or, at higher temperatures, the absolute value of the magnetization is strongly reduced. Thus the orientational order is characterized by two point defects at the top and the bottom of the sample, respectively. The equilibrium structure in an external field and the transition to a homogeneous magnetization for strong fields are analyzed, too.Comment: 17 postscript figures included, submitted to Phys. Rev.

Duration of exclusive breastfeeding; validity of retrospective assessment at nine months of age

<p>Abstract</p> <p>Background</p> <p>In cross sectional, case control and retrospective cohort studies, duration of Exclusive Breastfeeding (EBF) usually depends on maternal recall. Retrospective data are often subjected to recall bias and could lead to a potential for exposure misclassification. The purpose of the present paper is to assess the validity of maternal recall of EBF duration during infancy, after cessation of EBF and to evaluate the two methods to collect retrospective data on EBF.</p> <p>Methods</p> <p>A cohort study was carried out in Naula Medical Officer of Health (MOH) area. Study cohort included all infants born during the months of February to April 2008 and currently residing in Naula MOH area. Baseline data collection was carried out using the pregnancy record, the child health development record and by using an interviewer administered structured questionnaire. Data extraction from the pregnancy record and the child health development record were carried out by public health midwives. The interviewer administered structured questionnaire was administered by the MOH during the follow-up visits. Duration of EBF was assessed in three ways; based on prospective data since birth: Retrospective data based on an event calendar: and the Mother reported EBF duration.</p> <p>Results</p> <p>A total of 114 mother-infant pairs were recruited and followed up. Proportion of infants receiving EBF up to the completion of the sixth month by the three methods were; data since birth (actual EBF rate) - 23.9%; mother reported data - 77.7% and event calendar method - 41.3%. Median duration of EBF reported in the three methods was 5, 6, and 5 respectively. A statistically significant difference was observed in these differences from Kaplan-Meire Survival analysis (Log rank test - Chi square-63.4, p < 0.001). Validity of retrospective methods was analysed using data since birth as the gold standard. Sensitivity of both methods to detect exclusively breastfed babies were 100.0%. Specificity of mother recall data was 26.2% (95%CI-17.9, 36.8%) compared to 75.0% (95% CI-64.5, 83.2%) in the event calendar method.</p> <p>Conclusions</p> <p>Retrospective evaluation methods systematically overestimate the duration of EBF. Maternal recall data provide highly unspecific data whereas use of an event calendar provided more valid data. Reporting of data accrual methods in breastfeeding studies will allow the readers to interpret findings accurately and the use of event calendars rather than direct questioning as a valid method of determining EBF is recommended.</p

Evolution of Female Preference for Younger Males

Previous theoretical work has suggested that females should prefer to mate with older males, as older males should have higher fitness than the average fitness of the cohort into which they were born. However, studies in humans and model organisms have shown that as males age, they accumulate deleterious mutations in their germ-line at an ever-increasing rate, thereby reducing the quality of genes passed on to the next generation. Thus, older males may produce relatively poor-quality offspring. To better understand how male age influences female mate preference and offspring quality, we used a genetic algorithm model to study the effect of age-related increases in male genetic load on female mate preference. When we incorporate age-related increases in mutation load in males into our model, we find that females evolve a preference for younger males. Females in this model could determine a male's age, but not his inherited genotype nor his mutation load. Nevertheless, females evolved age-preferences that led them to mate with males that had low mutation loads, but showed no preference for males with respect to their somatic quality. These results suggest that germ-line quality, rather than somatic quality, should be the focus of female preference in good genes models