A compact model for the planar rhomboidal 4-body problem

We obtain a compact model for the global study of the planar rhomboidal 4-body problem in a level of constant negative energy. This model is a variation of the non compact model obtained through a McGehee blow up transformation. but compactness permits to obtain results which are not clear in the other case.     

SOFTWARE REVIEWS

software reviews are in this article MACATLAS . Number Cruncher Statistical System (NCSS) TRANSPRO FIRE-ROUTER     

Computing residence times for flow towards a pumping well: nomograph solution and validity of the small draw-down approximation

A recent analytical model developed to compute the residence time of fluid flowing in an unconfined aquifer towards a single pumping well is examined. The solution is scaled and presented practically as a nomograph showing the relationship between the residence time, flow length and draw-down. In addition, a similar scaling process is undertaken for the same problem occurring in a confined aquifer so that the error introduced by approximating an unconfined system as a confined system can be understood over a wide range of conditions.

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Resumen Se examina un modelo analítico, recientemente desarrollado, para calcular el tiempo de residencia de un fluido, el cual está fluyendo dentro de un acuífero libre hacia un pozo de bombeo único. La solución después de ser ajustada, se presenta prácticamente como un nomograma, mostrando la relación entre el tiempo de residencia, la longitud del flujo y el abatimiento. Adicionalmente, un proceso similar de ajuste fue realizado para el mismo problema, pero bajo condiciones de acuífero confinado, por tanto el error causado por hacer la aproximación de un sistema libre como si fuera un sistema confinado, puede llegar a ser entendido para un rango amplio de condiciones.

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Résumé On analyse un modèle analytique récent pour calculer le temps de résidence dun fluide pendant son écoulement vers un puits de pompage dans une nappe libre. La solution a été mise-à-léchelle et présenté dune manière pratique, comme une nomogramme qui exprime la relation entre le temps de résidence, la distance de l› écoulement et le rabattement. De plus, on a utilisé un procédé similaire de mise-à-léchelle pour le même problème dans une nappe captive affin que lerreur introduite par lapproximation dune nappe libre par une nappe captive peut être interprétée pour une grande classe de conditions.

     

The general solution of the HENON–HEILES problem

The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter), which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain (x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε = 0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce the density parameter, say to ε = 10⁻⁶, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary. The stability of all members of each and all families computed was calculated and presented in this paper for both the large solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections. All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received, consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including their stability and is available at request. It is concluded that approximation of the general solution of this system is straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties.     

Ionic association in H2O–CO2 fluids at mid-crustal conditions

The equilibrium constant, K _a, of the association reaction to form ion pairs from charged solute species in supercritical solutions can be calculated from a model based on published equations. Log K _a at constant pressure is a linear function of the inverse in the dielectric constant of the fluid times temperature. The dielectric properties of H₂O and CO₂ at supercritical pressures and temperatures can also be evaluated using the Kirkwood equation. Using Looyenga mixing rules, the dielectric constant of H₂O–CO₂ mixtures can be obtained and the change in log K _a with addition of CO₂ in aqueous solutions evaluated. These changes in log K _a with addition of CO₂ are consistent with measured changes of log K _a with addition of Ar in supercritical H₂O–Ar solutions.
Log K _a of KCl and NaCl increase to an increasing extent as the mole fraction of CO₂ increases in H₂O–CO₂ solutions. For instance, at 2 kbar and constant temperature between 400 and 600° C, log K _a of KCl increases by about two orders of magnitude whilst that of NaCl increases by over four orders of magnitude as the CO₂ mole fraction increases from 0.0 to 0.35. Such changes in log K _a will have dramatic effects on the solubility of minerals in CO₂-rich environments.     

Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem

We describe global bifurcations from the libration points of non-stationary periodic solutions of the restricted three body problem. We show that the only admissible continua of non-stationary periodic solutions of the planar restricted three body problem, bifurcating from the libration points, can be the short-period families bifurcating from the Lagrange equilibria L ₄, L ₅. We classify admissible continua and show that there are possible exactly six admissible continua of non-stationary periodic solutions of the planar restricted three body problem. We also characterize admissible continua of non-stationary periodic solutions of the spatial restricted three body problem. Moreover, we combine our results with the Déprit and Henrard conjectures (see [8]), concerning families of periodic solutions of the planar restricted three body problem, and show that they can be formulated in a stronger way. As the main tool we use degree theory for SO(2)-equivariant gradient maps defined by the second author in [25].This revised version was published online in October 2005 with corrections to the Cover Date.     

一种基于网络拓扑关系的地图匹配算法

地图匹配是车辆导航定位系统中提高定位精度的一种方法,其精度受定位数据、地图数据质量及坐标系转换关系的影响.在分析现有算法的基础上,提出了一种基于网络拓扑关系的地图匹配算法.该算法只需将GPS定位数据和GIS 数据相结合,即可用算法的形式解决地图匹配中一些常见的问题.实验证明:该算法是一种精度高、效率好、实用性强的地图匹配算法,具有较好的实用价值.     

CASIO可编程计算器在线路施工测量中的应用

在线路施工测量中,利用Gauss-Legendre 5点通用公式,采用CASIO可编程计算器编制曲线任意里程中边桩三维坐标正反算程序,只需输入任意里程,即可提供线路该里程的设计中桩坐标和高程,又可通过反算得到任意测点对应的线路里程和偏距。     

关于测绘数字成果数据远程容灾的研究

解决数据本地集中带来的风险,是测绘资料管理部门面临的重要问题。本文通过对容灾关键技术的研究和对测绘数字成果特点的分析,给出了基于远程容灾技术,建立测绘数字成果异地远程容灾体系的思路。