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The main limit to the time span of a numerical integration of the planetary orbits is no longer set by the availability of computer resources, but rather by the accumulation of the integration error. By the latter we mean the difference between the computed orbit and the dynamical behaviour of the real physical system, whatever the causes. The analysis of these causes requires an interdisciplinary effort: there are physical model and parameters errors, algorithm and discretisation errors, rounding off errors and reliability problems in the computer hardware and system software, as well as instabilities in the dynamical system. We list all the sources of integration error we are aware of and discuss their relevance in determining the present limit to the time span of a meaningful integration of the orbit of the planets. At present this limit is of the order of 108 years for the outer planets. We discuss in more detail the truncation error of multistep algorithms (when applied to eccentric orbits), the coefficient error, the method of Encke and the associated coordinate change error, the procedures used to test the numerical integration software and their limitations. Many problems remain open, including the one of a realistic statistical model of the rounding off error; at present, the latter can only be described by a semiempirical model based upon the simpleN 2 formula (N=number of steps, =machine accuracy), with an unknown numerical coefficient which is determined only a posteriori.  相似文献   
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Magnetohydrodynamics (MHD) is a fairly recent extension of the field of fluid mechanics. While much remains to be done, it has successfully been applied to the contemporary field of heliospheric space plasma research to evaluate the macroscopic picture of some vital topics via the use of conducting fluid equations and numerical modeling and simulations. Some representative examples from solar and interplanetary physics are described to demonstrate that the continuum approach to global problems (while keeping in mind the assumptions and limitations therein) can be very successful in providing insight and large scale interpretations of otherwise intractable problems in space physics.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.  相似文献   
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Abstract. The secondary production of Spisula subtruncata (somatic production) is calculated in the framework of a benthic monitoring study in a coastal area. The temporal trends of density, biomass and growth increments are examined in the three year-classes present. These are compared to certain physical and chemical parameters.  相似文献   
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Modelers often need to quantify the rates at which zooplankton consume a variety of species, size classes and trophic types. Implicit in the equations used to describe the multiple resource functional response (i.e. how nutritional intake varies with resource densities) are assumptions that are not often stated, let alone tested. This is problematic because models are sensitive to the details of these formulations. Here, we enable modelers to make more informed decisions by providing them with a new framework for considering zooplankton feeding on multiple resources. We define a new classification of multiple resource responses that is based on preference, selection and switching, and we develop a set of mathematical diagnostics that elucidate model assumptions. We use these tools to evaluate the assumptions and biological dynamics inherent in published multiple resource responses. These models are shown to simulate different resource preferences, implied single resource responses, changes in intake with changing resource densities, nutritional benefits of generalism, and nutritional costs of selection. Certain formulations are further shown to exhibit anomalous dynamics such as negative switching and sub-optimal feeding. Such varied responses can have vastly different ecological consequences for both zooplankton and their resources; inappropriate choices may incorrectly quantify biologically-mediated fluxes and predict spurious dynamics. We discuss how our classes and diagnostics can help constrain parameters, interpret behaviors, and identify limitations to a formulation's applicability for both regional (e.g. High-Nitrate-Low-Chlorophyll regions comprising large areas of the Pacific) and large-scale applications (e.g. global biogeochemical or climate change models). Strategies for assessing uncertainty and for using the mathematics to guide future experimental investigations are also discussed.  相似文献   
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We construct a one-dimensional ecosystem model (nitrate, ammonium, phytoplankton, zooplnakton and detritus) with simple physics and biology in order to focus on the structural relations and intrinsic properties of the food web that characterizes the biological regime in the central equatorial Pacific at 140°W. When possible, data collected during the EgPac and other cruises were used to calibrate model parameters for two simulations that differ in the limiting nutrient, i.e. nitrogen or iron. Both simulations show annual results in good agreement with the data, but phytoplankton biomass and primary production show a more pronounced annual variability when iron is used as the limiting nutrient. This more realistically reproduces the variability of biological production and illustrates the greater coupling between vertical physical processes and biological production when the limiting nutrient is iron rather than nitrogen. The iron simulation also illustrates how iron supply controls primary production variability, how grazingbalances primary production and controls phytoplankton biomass, and how both iron supply and grazingcontrol primary production. These results suggest that it is not possible to capture primary production variability in the central equatorial Pacific with biological models using nitrogen as the limiting nutrient. Other indirect results of this modeling study were: (1) partitioning of export production between dissolved and particulate matter is almost equal, suggesting that the importance of DOC export may have been previously overestimated; (2) lateral export of live biomass has to be taken into account in order to balance the nitrogen budget on the equator at 140°W; and (3) preferential uptake of ammonium (i.e. nitrate uptake inhibition by ammonium) associated with high regeneration of nitrogen (low f ratio as a consequence of the food web structure imposed by iron limitation) largely accounts for the surface build-up of upwelled nitrate.  相似文献   
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This special issue is the third and final volume containing results from the JGOFS Process Study in the equatorial Pacific. Most of the Study in the equational Pacific. Most of the contributions evolved either from the US JGOFS workshop in 1994 on the equatorial Pacific in Scottsdale, AZ or from the NATO Advanced Research Workshop on the Carbon Cycle of the Equatorial Pacific in 1995 in Noumea, New Caledonia.  相似文献   
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