Crust density in bread baking: Mathematical modelling and numerical solutions

A model for the formation of a “crust” during bread baking is presented. The crust is the outermost part of the loaf where the final bread density is significantly higher than in the “crumb”, the interior of the loaf. The model is based on a collapse mechanism, whereby raised pressures due to thermal expansion and water evaporation squash bubbles in the bread as the dough sets and fractures; the latter process allows vapour within bubbles to escape.     

193nmArF准分子激光剥蚀-等离子体质谱测定富钴结壳中的稀土元素

采用193nm ArF准分子(Excimer)激光剥蚀ICP—MS测定了富钴结壳中痕量稀土元素。比较了^27Al、^49Ti作为内标元素时稀土元素的LA—ICP—MS分析信号的响应行为。结果表明,^27Al与稀土元素具有相似的激光剥蚀行为以及等离子体激发、电离特征;以Al为内标元素,NIST610玻璃标准为外标,可有效抑制基体效应和灵敏度漂移的影响。方法的检出限为1．2～15．8ng／g,用于标准参考物质中稀土元素的测定,测定结果的相对标准偏差(n=5)在2．2％～6．4%,测定值与标准参考值的相对误差小于6．5％。     

Does roughening of rock-fluid-rock interfaces emerge from a stress-induced instability?

Non-planar solid-fluid-solid interfaces under stress are very common in many industrial and natural materials. For example, in the Earth’s crust, many rough and wavy interfaces can be observed in rocks in a wide range of spatial scales, from undulate grain boundaries at the micrometer scale, to stylolite dissolution planes at the meter scale. It is proposed here that these initially flat solid-fluid-solid interfaces become rough by a morphological instability triggered by elastic stress. A model for the formation of these unstable patterns at all scales is thus presented. It is shown that such instability is inherently present due to the uniaxial stress that promotes them, owing to the gain in the total elastic energy: the intrinsic elastic energy plus the work of the external forces. This is shown explicitly by solving the elastic problem in a linear stability analysis, and proved more generally without having resort to the computation of the elastic field.