A hybrid moment equation approach to gas-grain chemical modeling

[Context] The stochasticity of grain chemistry requires special care in modeling. Previously methods based on the modified rate equation, the master equation, the moment equation, and Monte Carlo simulations have been used. [Aims] We attempt to develop a systematic and efficient way to model the gas-grain chemistry with a large reaction network as accurately as possible. [Methods] We present a hybrid moment equation approach which is a general and automatic method where the generating function is used to generate the moment equations. For large reaction networks, the moment equation is cut off at the second order, and a switch scheme is used when the average population of certain species reaches 1. For small networks, the third order moments can also be utilized to achieve a higher accuracy. [Results] For physical conditions in which the surface reactions are important, our method provides a major improvement over the rate equation approach, when benchmarked against the rigorous Monte Carlo results. For either very low or very high temperatures, or large grain radii, results from the rate equation are similar to those from our new approach. Our method is faster than the Monte Carlo approach, but slower than the rate equation approach. [Conclusions] The hybrid moment equation approach with a cutoff and switch scheme is applicable to large gas-grain networks, and is accurate enough to be used for astrochemistry studies. The layered structure of the grain mantle could also be incorporated into this approach, although a full implementation of the grain micro-physics appears to be difficult.Comment: 11 pages, 4 figures. Accepted for publication in Astronomy and Astrophysic

"Medien":Mittler beim Lernen und Lehren: nur Bedrohung oder auch Segen?

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Incorporation of stochastic chemistry on dust grains in the PDR code using moment equations

Unlike gas-phase reactions, chemical reactions taking place on interstellar dust grain surfaces cannot always be modeled by rate equations. Due to the small grain sizes and low flux,these reactions may exhibit large fluctuations and thus require stochastic methods such as the moment equations. We evaluate the formation rates of H2, HD and D2 molecules on dust grain surfaces and their abundances in the gas phase under interstellar conditions. We incorporate the moment equations into the Meudon PDR code and compare the results with those obtained from the rate equations. We find that within the experimental constraints on the energy barriers for diffusion and desorption and for the density of adsorption sites on the grain surface, H2, HD and D2 molecules can be formed efficiently on dust grains. Under a broad range of conditions, the moment equation results coincide with those obtained from the rate equations. However, in a range of relatively high grain temperatures, there are significant deviations. In this range, the rate equations fail while the moment equations provide accurate results. The incorporation of the moment equations into the PDR code can be extended to other reactions taking place on grain surfaces

Short term fat feeding rapidly increases plasma insulin but does not result in dyslipidaemia

Although the association between obesity and hypertension is well known, the underlying mechanism remains elusive. Previously, we have shown that 3 week fat feeding in rabbits produces greater visceral adiposity, hypertension, tachycardia and elevated renal sympathetic nerve activity compared to rabbits on a normal diet. Because hyperinsulinaemia, hyperleptinemia and dyslipidaemia are independent cardiovascular risk factors associated with hypertension we compared plasma insulin, leptin and lipid profiles in male New Zealand White rabbits fed a normal fat diet (NFD 4.3% fat, n = 11) or high fat diet (HFD 13.4% fat, n = 13) at days 1, 2, 3 and weeks 1, 2, 3 of the diet. Plasma concentrations of diacylglyceride (DG), triacylglyceride (TG), ceramide and cholesteryl esters (CE) were obtained after analysis by liquid chromatography mass spectrometry. Plasma insulin and glucose increased within the first 3 days of the diet in HFD rabbits (P &lt;0.05) and remained elevated at week 1 (P &lt;0.05). Blood pressure and heart rate followed a similar pattern. By contrast, in both groups, plasma leptin levels remained unchanged during the first few days (P &gt;0.05), increasing by week 3 in fat fed animals alone (P &lt;0.05). Concentrations of total DG, TG, CE and Ceramide at week 3 did not differ between groups (P &gt;0.05). Our data show plasma insulin increases rapidly following consumption of a HFD and suggests that it may play a role in the rapid rise of blood pressure. Dyslipidaemia does not appear to contribute to the hypertension in this animal model

Quantifying the connectivity of a network: The network correlation function method

Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as social networks. Lately, it was found that many of these networks display some common topological features, such as high clustering, small average path length (small world networks) and a power-law degree distribution (scale free networks). The topological features of a network are commonly related to the network's functionality. However, the topology alone does not account for the nature of the interactions in the network and their strength. Here we introduce a method for evaluating the correlations between pairs of nodes in the network. These correlations depend both on the topology and on the functionality of the network. A network with high connectivity displays strong correlations between its interacting nodes and thus features small-world functionality. We quantify the correlations between all pairs of nodes in the network, and express them as matrix elements in the correlation matrix. From this information one can plot the correlation function for the network and to extract the correlation length. The connectivity of a network is then defined as the ratio between this correlation length and the average path length of the network. Using this method we distinguish between a topological small world and a functional small world, where the latter is characterized by long range correlations and high connectivity. Clearly, networks which share the same topology, may have different connectivities, based on the nature and strength of their interactions. The method is demonstrated on metabolic networks, but can be readily generalized to other types of networks.Comment: 10 figure

Stochastic Analysis of Dimerization Systems

The process of dimerization, in which two monomers bind to each other and form a dimer, is common in nature. This process can be modeled using rate equations, from which the average copy numbers of the reacting monomers and of the product dimers can then be obtained. However, the rate equations apply only when these copy numbers are large. In the limit of small copy numbers the system becomes dominated by fluctuations, which are not accounted for by the rate equations. In this limit one must use stochastic methods such as direct integration of the master equation or Monte Carlo simulations. These methods are computationally intensive and rarely succumb to analytical solutions. Here we use the recently introduced moment equations which provide a highly simplified stochastic treatment of the dimerization process. Using this approach, we obtain an analytical solution for the copy numbers and reaction rates both under steady state conditions and in the time-dependent case. We analyze three different dimerization processes: dimerization without dissociation, dimerization with dissociation and hetero-dimer formation. To validate the results we compare them with the results obtained from the master equation in the stochastic limit and with those obtained from the rate equations in the deterministic limit. Potential applications of the results in different physical contexts are discussed.Comment: 10 figure

Reforming state-market relations in rural China 1

Because of the political importance of stable and affordable food prices, governments in transitional economies in Europe and Asia fkequently struggle to balance the desire to maintain state controls in the rural sector with the goal of promoting market development and privatizing or commercializing state agencies involved in rural trade or finance. This paper examines institutional change in China's rural state agencies during the reform period, focusing on the conflict between managerial incentives to maximize profits, on the one hand, and implement policy, on the other. We explain the reasons for changing contractual incentives and authority arrangements over time, assess the effects of new institutional forms on economic performance and policy implementation, and consider reform options.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71599/1/j.1468-0351.1998.tb00059.x.pd