The thermoelastic Hertzian contact problem

AbstractA numerical solution is obtained for the steady-state thermoelastic contact problem in which heat is conducted between two elastic bodies of dissimilar materials at different temperatures with arbitrary quadratic profiles. Thermoelastic deformation causes the initially elliptical contact area to be reduced in size and to become more nearly circular as the temperature difference is increased. There is also a small but identifiable deviation from exact ellipticity at intermediate temperature differences. An approximate analytical solution is obtained, based on approximating the contact area by an ellipse

The NTDs and the matched conditions included in the study.

<p>The reported DALYs were taken from WHO 2004 estimates <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0000576#pntd.0000576-World1" target="_blank">[7]</a>. Estimated DALYs for the NTDs by Hotez et al. <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0000576#pntd.0000576-Hotez2" target="_blank">[10]</a> are also included for comparison (see text for details). The listed DALYs have all been scaled by a factor 1/1,000.</p

Number of publications on NTDs and matched conditions.

<p>(A) The number of publications in PubMed and Web of Science as a function of time for the NTDs and the matched conditions. (B) The ratio between the number of publications in PubMed and Web of science on NTDs and the matched conditions as a function of time. The lines are spline smoothed versions of the ratio data. (C, D) Idem as (A, B) but for the reviews found in the PubMed database. (E) The ratios of the estimated DALYs and number of publications for each NTD-matched condition pair summed across time. The vertical lines indicate a ratio of 1, 2, 4 and 6 respectively. Notice that the x-axis has a logarithmic scaling.</p

Knechtl, Josef

(1771 - 1838), Archiva

Baseline mortality levels and emergency thresholds by region.

<p>Source: Sphere Handbook: Humanitarian Charter and Minimum Standards in Disaster Response, 2011 [<a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.1001887#pmed.1001887.ref009" target="_blank">9</a>]</p><p>Baseline mortality levels and emergency thresholds by region.</p

Simulated prevalences by typology (Scenario 3).

<p>The Scenario 3 introduces the effect of a treatment by psychotherapy. Simulated patterns of elderly depression prevalence by age are generated based on experts' answers, considering several typologies of experts. Empirical Mean and CI 95% of depression prevalence were retrieved from the Belgian Health Interview Survey. They are plotted for comparison together with the regression line on the empirical prevalence.</p

Under-five death rate among internally displaced persons in Duhok governorate, Iraq, September/October 2014.

<p>*The Bayesian estimate is based on a conjugate beta-binomial model. The “high mortality” prior has a mean of 0.64, and the 0.05 percentile is 0.27 (this means we assume there is still a 5% chance that mortality levels are at or even below baseline levels).</p><p>**The Bayesian “confidence interval” is the HDI of the posterior distribution.</p><p>Under-five death rate among internally displaced persons in Duhok governorate, Iraq, September/October 2014.</p

Formal Algorithm at Individual Level.

<p>1) The Historic Variable is checked to see if the individual is widow for only one year; if this is the case, the new widow processes directly step 5. 2) Decision tree leading to the random generation of a Contact with one of the actors (grayed columns of the tables are not used. 3) An Impact is generated at random. 4) This impact is added to the current Depressive State 5) The Age is incremented.</p

Simulated prevalences by typology (Scenario 2).

<p>The Scenario 2 introduces a wedding between husband and wives and defines 3 marital statuses: single, married and widow. Simulated patterns of elderly depression prevalence by age are generated based on experts' answers, considering several typologies of experts. Empirical Mean and CI 95% of depression prevalence were retrieved from the Belgian Health Interview Survey. They are plotted for comparison together with the regression line on the empirical prevalence.</p

Statistical and numerical tests.

<p>Statistical and numerical indices of the comparison between the simulated and empirical data, by scenario and typologies of experts (1st column). The 2nd column indicates the number of times the simulation estimates falls within the empirical confidence interval (CI). The 3rd column indicates the Wilcoxon Signed Rank statistic (WSR). Cases reported with an ‘*’ indicate that the nullity of the difference between the paired two-samples (simulated and empirical) can not be rejected (at the significance level 5%). The 4th column reports the K-S test statistic (K-S) between the simulated sample and the regression line. Cases reported with an ‘*’ indicate that the 2 samples could come from the same distribution (at the significance level 5%). The 5th column indicates the correlation coefficient (r) between the simulated sample and the regression line.</p