[1] Type II solar radio bursts are produced by shock waves moving through the corona and solar wind. An existing theory predicts Type II dynamic spectra by considering electron acceleration at the shock, growth of Langmuir waves, and their conversion into radiation. Two contributions are presented, both relevant to space weather research and missions like STEREO. First, a more realistic 2-dimensional model for the solar wind is developed, based on spacecraft data at 1 AU, and illustrated for a specific period. It relates time to longitude and extrapolates to different heliocentric distances using MHD style equations and power-law temperature models. Second, the type II theory is combined with the data-driven solar wind model to predict the dynamic spectrum of a specific Type II burst. The results show reasonable semiquantitative agreement with observations. Issues and possible improvements are outlined.
The human tracheobronchial tree is a complex branched distribution system in charge of renewing the air inside the acini, which are the gas exchange units. We present here a systematic geometrical model of this system described as a self-similar assembly of rigid pipes. It includes the specific geometry of the upper bronchial tree and a self-similar intermediary tree with a systematic branching asymmetry. It ends by the terminal bronchioles whose generations range from 8 to 22. Unlike classical models, it does not rely on a simple scaling law. With a limited number of parameters, this model reproduces the morphometric data from various sources (Horsfield K, Dart G, Olson DE, Filley GF, Cumming G. J Appl Physiol 31: 207-217, 1971; Weibel ER. Morphometry of the Human Lung. New York: Academic Press, 1963) and the main characteristics of the ventilation. Studying various types of random variations of the airway sizes, we show that strong correlations are needed to reproduce the measured distributions. Moreover, the ventilation performances are observed to be robust against anatomical variability. The same methodology applied to the rat also permits building a geometrical model that reproduces the anatomical and ventilation characteristics of this animal. This simple model can be directly used as a common description of the entire tree in analytical or numerical studies such as the computation of air flow distribution or aerosol transport.
Most of the studies on optimal transport are done for steady state regime conditions. Yet, there exists numerous examples in living systems where supply tree networks have to deliver products in a limited time due to the pulsatile character of the flow. This is the case for mammals respiration for which air has to reach the gas exchange units before the start of expiration. We report here that introducing a systematic branching asymmetry allows to reduce the average delivery time of the products. It simultaneously increases its robustness against the unevitable variability of sizes related to morphogenesis. We then apply this approach to the human tracheobronchial tree. We show that in this case all extremities are supplied with fresh air, provided that the asymmetry is smaller than a critical threshold which happens to fit with the asymmetry measured in the human lung. This could indicate that the structure is adjusted at the maximum asymmetry level that allows to feed all terminal units with fresh air.
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