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Register a new userWhy air bubbles in water glow so easily
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Michael Brenner n Dept. of Math
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Sound driven gas bubbles in water can emit light pulses (sonoluminescence). Experiments show a strong dependence on the type of gas dissolved in water. Air is found to be one of the most friendly gases towards this phenomenon. Recently, cite{loh96} have suggested a chemical mechanism to account for the strong dependence on the gas mixture: the dissociation of nitrogen at high temperatures and its subsequent chemical reactions to highly water soluble gases such as NO, NO$_2$, and/or NH$_3$. Here, we analyze the consequences of the theory and offer detailed comparison with the experimental data of Puttermans UCLA group. We can quantitatively account for heretofore unexplained results. In particular, we understand why the argon percentage in air is so essential for the observation of stable SL.
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Experiments are conducted to study the path and shape of single air bubbles (diameter range 0.10- 0.20cm) rising freely in clean water. The experimental results demonstrate that the bubble shape has a bistable state, i. e. the bubble chooses to be in spherical or ellipsoidal shape depending on its generation mechanism. The path of a spherical/ellipsoidal bubble is found to change from a straight path to a zigzag/spiral path via a supercritical/subcritical bifurcation when the Reynolds number of the bubble exceeds a threshold.
Diffusionless phase transitions are at the core of the multifunctionality of (magnetic) shape memory alloys, ferroelectrics and multiferroics. Giant strain effects under external fields are obtained in low symmetric modulated martensitic phases. We outline the origin of modulated phases, their connection with tetragonal martensite and consequences for their functional properties by analysing the martensitic microstructure of epitaxial Ni-Mn-Ga films from the atomic to macroscale. Geometrical constraints at an austenite-martensite phase boundary act down to the atomic scale. Hence a martensitic microstructure of nanotwinned tetragonal martensite can form. Coarsening of twin variants can reduce twin boundary energy, a process we could follow from the atomic to the millimetre scale. Coarsening is a fractal process, proceeding in discrete steps by doubling twin periodicity. The collective defect energy results in a substantial hysteresis, which allows retaining modulated martensite as a metastable phase at room temperature. In this metastable state elastic energy is released by the formation of a twins within twins microstructure which can be observed from the nanometre to millimetre scale. This hierarchical twinning results in mesoscopic twin boundaries which are diffuse, in contrast to the common atomically sharp twin boundaries of tetragonal martensite. We suggest that observed extraordinarily high mobility of such mesoscopic twin boundaries originates from their diffuse nature which renders pinning by atomistic point defects ineffective.
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During the last three decades the Internet has experienced fascinating evolution, both exponential growth in traffic and rapid expansion in topology. The size of the Internet becomes enormous, yet the network is very `small in the sense that it is extremely efficient to route data packets across the global Internet. This paper provides a brief review on three fundamental properties of the Internet topology at the autonomous systems (AS) level. Firstly the Internet has a power-law degree distribution, which means the majority of nodes on the Internet AS graph have small numbers of links, whereas a few nodes have very large numbers of links. Secondly the Internet exhibits a property called disassortative mixing, which means poorly-connected nodes tend to link with well-connected nodes, and vice versa. Thirdly the best-connected nodes, or the rich nodes, are tightly interconnected with each other forming a rich-club. We explain that it is these structural properties that make the global Internet so small.
Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to changes in parameters, and one is left to make adjustments by hand. We explain this difficulty by interpreting the fitting process as a generalized interpretation procedure. By considering the manifold of all model predictions in data space, we find that cross sections have a hierarchy of widths and are typically very narrow. Algorithms become stuck as they move near the boundaries. We observe that the model manifold, in addition to being tightly bounded, has low extrinsic curvature, leading to the use of geodesics in the fitting process. We improve the convergence of the Levenberg-Marquardt algorithm by adding the geodesic acceleration to the usual Levenberg-Marquardt step.
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