Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates

In this paper we show the existence of global minimizers for the geometrically exact, non-linear equations of elastic plates, in the framework of the general 6-parametric shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. We also present a detailed comparison with a previously established Cosserat plate model.Comment: 19 pages, 1 figur

Hydrogen peroxide in exhaled air: A source of error, a paradox and its resolution.

The concentration of hydrogen peroxide (H2O2) in exhaled air has been reported to be elevated in asthma and chronic obstructive pulmonary disease (COPD), but results are inconsistent and difficult to reproduce. As H2O2 occurs in ambient air, we examined its association with exhaled H2 O2 in human subjects. Exhaled breath condensate (EBC) of 12 COPD patients and nine healthy control subjects was collected either with an inhalation filter (efficiency 81%) or without. Ambient air condensate (AAC) was collected in parallel and samples were analysed for H2O2. Additionally, ambient H2O2 was recorded by an atmospheric measuring device (online fluorometric measurement). H2 O2 concentration in AAC was significantly higher (p<0.001) than in EBC. AAC variations were concordant with the data from the atmospheric measuring instrument. In both subjects’ groups, the inhalation filter reduced H2O2 values (p<0.01). Despite generally low levels in exhaled air, analysis by a mathematical model revealed a contribution from endogenous H2O2 production. The low H2O2 levels in exhaled air are explained by the reconditioning of H2O2-containing inhaled air in the airways. Inhaled H2O2 may be one factor in the heterogeneity and limited reproducibility of study results. A valid determination of endogenous H2 O2 production requires inhalation filters

Observed 20th century desert dust variability: impact on climate and biogeochemistry

Desert dust perturbs climate by directly and indirectly interacting with incoming solar and outgoing long wave radiation, thereby changing precipitation and temperature, in addition to modifying ocean and land biogeochemistry. While we know that desert dust is sensitive to perturbations in climate and human land use, previous studies have been unable to determine whether humans were increasing or decreasing desert dust in the global average. Here we present observational estimates of desert dust based on paleodata proxies showing a doubling of desert dust during the 20th century over much, but not all the globe. Large uncertainties remain in estimates of desert dust variability over 20th century due to limited data. Using these observational estimates of desert dust change in combination with ocean, atmosphere and land models, we calculate the net radiative effect of these observed changes (top of atmosphere) over the 20th century to be −0.14 ± 0.11 W/m2 (1990–1999 vs. 1905–1914). The estimated radiative change due to dust is especially strong between the heavily loaded 1980–1989 and the less heavily loaded 1955–1964 time periods (−0.57 ± 0.46 W/m2), which model simulations suggest may have reduced the rate of temperature increase between these time periods by 0.11 °C. Model simulations also indicate strong regional shifts in precipitation and temperature from desert dust changes, causing 6 ppm (12 PgC) reduction in model carbon uptake by the terrestrial biosphere over the 20th century. Desert dust carries iron, an important micronutrient for ocean biogeochemistry that can modulate ocean carbon storage; here we show that dust deposition trends increase ocean productivity by an estimated 6% over the 20th century, drawing down an additional 4 ppm (8 PgC) of carbon dioxide into the oceans. Thus, perturbations to desert dust over the 20th century inferred from observations are potentially important for climate and biogeochemistry, and our understanding of these changes and their impacts should continue to be refined