Population responses of four hypothetical species to the scale of spatial autocorrelation in habitat quality <i>S</i>.

<p>(a) population size; (b) mean resource share of individuals; (c) mean mortality rate of individuals; (d) proportion of individuals in high-quality cells (<i>Q</i>≥0.5); (e) proportion of individuals experiencing competition. The figure shows mean±1 SD for 50 replicates for each variable.</p

Flow diagrams of the submodels in the simulation model that determine mortality (a), reproduction (b), and (c) movement for a single individual within a time step.

<p>Flow diagrams of the submodels in the simulation model that determine mortality (a), reproduction (b), and (c) movement for a single individual within a time step.</p

Coefficients of Spearman correlations of the mean resource share of individuals with (a) the proportion of individuals in high-quality cells and (b) the proportion of individuals experiencing competition for four hypothetical species under different landscape scenarios.

<p>Bars marked with an asterisk (*) indicate the coefficients are statistically significant at <i>P</i><0.05.</p

Variables, parameters, and initial conditions used in the model.

<p>Variables, parameters, and initial conditions used in the model.</p

Summary of the percentages of the variation in response variables explained by factors scale of spatial autocorrelation in habitat quality (<i>S</i>), species environmental tolerance (<i>C</i>_envir), and mean moving distance (<i>D</i>_mean). Detailed ANOVAs for each response variable are presented in Table S1.

<p>Summary of the percentages of the variation in response variables explained by factors scale of spatial autocorrelation in habitat quality (<i>S</i>), species environmental tolerance (<i>C</i>_envir), and mean moving distance (<i>D</i>_mean). Detailed ANOVAs for each response variable are presented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0107742#pone.0107742.s003" target="_blank">Table S1</a>.</p

Sample patterns of spatial distribution of individuals under different landscape scenarios.

<p>Hypothetical species are parameterized by environmental tolerance <i>C</i>_envir and mean moving distance <i>D</i>_mean. Black dots represent individuals residing in cells of <i>Q</i>≥0.5 and free of competition, while red dots are individuals residing in cells of <i>Q</i><0.5 or experiencing competition. Greener colour indicates higher habitat quality.</p

A Theoretical Model for Predicting Residual Stress Generation in Fabrication Process of Double-Ceramic-Layer Thermal Barrier Coating System

<div><p>Residual stress arisen in fabrication process of Double-Ceramic-Layer Thermal Barrier Coating System (DCL-TBCs) has a significant effect on its quality and reliability. In this work, based on the practical fabrication process of DCL-TBCs and the force and moment equilibrium, a theoretical model was proposed at first to predict residual stress generation in its fabrication process, in which the temperature dependent material properties of DCL-TBCs were incorporated. Then, a Finite Element method (FEM) has been carried out to verify our theoretical model. Afterwards, some important geometric parameters for DCL-TBCs, such as the thickness ratio of stabilized Zirconia (YSZ, ZrO₂-8%Y₂O₃) layer to Lanthanum Zirconate (LZ, La₂Zr₂O₇) layer, which is adjustable in a wide range in the fabrication process, have a remarkable effect on its performance, therefore, the effect of this thickness ratio on residual stress generation in the fabrication process of DCL-TBCs has been systematically studied. In addition, some thermal spray treatment, such as the pre-heating treatment, its effect on residual stress generation has also been studied in this work. It is found that, the final residual stress mainly comes from the cooling down process in the fabrication of DCL-TBCs. Increasing the pre-heating temperature can obviously decrease the magnitude of residual stresses in LZ layer, YSZ layer and substrate. With the increase of the thickness ratio of YSZ layer to LZ layer, magnitudes of residual stresses arisen in LZ layer and YSZ layer will increase while residual stress in substrate will decrease.</p></div

Comparison of final residual stress generated with different thickness ratios of YSZ to LZ layers.

<p>(A) Different thickness ratios of YSZ to LZ layers are: i.e. YSZ: 250μm, LZ: 50μm; YSZ: 200μm, LZ: 100μm; YSZ: 150μm, LZ: 150μm; YSZ: 100μm, LZ: 200μm; and YSZ: 50μm, LZ: 250μm. (B) (a-c) respect residual stress generated in LZ layer, YSZ layer and the combination of “substrate + BC”, respectively.</p

SEM photo of the cross section of a representative as-sprayed DCL-TBCs.

<p>Thicknesses of LZ layer, YSZ layer, BC and substrate are 220±20μm, 110±20μm, 65±20μm and 3±0.1mm, respectively. BC is fabricated by High-Velocity Oxygen-Fuel (HVOF) method, YSZ and LZ layers are fabricated by APS method.</p

Comparison of residual stress generated during step 1~5 by theoretical model and FEM.

<p>Comparison of residual stress generated during step 1~5 by theoretical model and FEM.</p