On the periodic solutions of a particular Lame equation     

Makhlouf Amar 《Celestial Mechanics and Dynamical Astronomy》1991,52(4):397-406

We consider the Hill's equation: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGKbWaaWbaaSqabeaacaaIYaaaaOGaeqOVdGhabaGaamizaiaadsha% daahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaacaWGTbGaai% ikaiaad2gacqGHRaWkcaaIXaGaaiykaaqaaiaaikdaaaGaam4qamaa% CaaaleqabaGaaGOmaaaakiaacIcacaWG0bGaaiykaiabe67a4jabg2% da9iaaicdaaaa!4973!\[\frac{{d^2 \xi }}{{dt^2 }} + \frac{{m(m + 1)}}{2}C^2 (t)\xi = 0\]Where C(t) = Cn (t, {frbuilt|1/2}) is the elliptic function of Jacobi and m a given real number. It is a particular case of theame equation. By the change of variable from t to defined by: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaOWaaiqaaq% aabeqaamaalaaajaaybaGaamizaGGaaiab-z6agbqaaiaadsgacaWG% 0baaaiabg2da9OWaaOaaaKaaGfaacaGGOaqcKbaG-laaigdajaaycq% GHsislkmaaleaajeaybaGaaGymaaqaaiaaikdaaaqcaaMaaeiiaiaa% bohacaqGPbGaaeOBaOWaaWbaaKqaGfqabaGaaeOmaaaajaaycqWFMo% GrcqWFPaqkaKqaGfqaaaqcaawaaiab-z6agjab-HcaOiab-bdaWiab% -LcaPiab-1da9iab-bdaWaaakiaawUhaaaaa!51F5!\[\left\{ \begin{array}{l}\frac{{d\Phi }}{{dt}} = \sqrt {(1 - {\textstyle{1 \over 2}}{\rm{ sin}}^{\rm{2}} \Phi )} \\\Phi (0) = 0 \\\end{array} \right.\]it is transformed to the Ince equation: (1 + · cos(2)) y + b · sin(2) · y + (c + d · cos(2)) y = 0 where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaiaadggacq% GH9aqpcqGHsislcaWGIbGaeyypa0JcdaWcgaqaaiaaigdaaeaacaaI% ZaGaaiilaiaabccacaWGJbGaeyypa0Jaamizaiabg2da9aaacaqGGa% WaaSaaaKaaGfaacaWGTbGaaiikaiaad2gacqGHRaWkcaaIXaGaaiyk% aaqaaiaaiodaaaaaaa!4777!\[a = - b = {1 \mathord{\left/{\vphantom {1 {3,{\rm{ }}c = d = }}} \right.\kern-\nulldelimiterspace} {3,{\rm{ }}c = d = }}{\rm{ }}\frac{{m(m + 1)}}{3}\]In the neighbourhood of the poles, we give the expression of the solutions.The periodic solutions of the Equation (1) correspond to the periodic solutions of the Equation (3). Magnus and Winkler give us a theory of their existence. By comparing these results to those of our study in the case of the Hill's equation, we can find the development in Fourier series of periodic solutions in function of the variable and deduce the development of solutions of (1) in function of C(t).  相似文献   

Large eddy simulation of hydrocyclone—prediction of air-core diameter and shape     

M. Narasimha  Mathew Brennan  P.N. Holtham 《International Journal of Mineral Processing》2006

Hydrocyclones are widely used in the mining and chemical industries. An attempt has been made in this study, to develop a CFD (computational fluid dynamics) model, which is capable of predicting the flow patterns inside the hydrocyclone, including accurate prediction of flow split as well as the size of the air-core. The flow velocities and air-core diameters are predicted by DRSM (differential Reynolds stress model) and LES (large eddy simulations) models were compared to experimental results. The predicted water splits and air-core diameter with LES and RSM turbulence models along with VOF (volume of fluid) model for the air phase, through the outlets for various inlet pressures were also analyzed. The LES turbulence model led to an improved turbulence field prediction and thereby to more accurate prediction of pressure and velocity fields. This improvement was distinctive for the axial profile of pressure, indicating that air-core development is principally a transport effect rather than a pressure effect.  相似文献   

Mais comment s'écoule donc un glacier ? Aperçu historique     

Frédérique Rémy  Laurent Testut 《Comptes Rendus Geoscience》2006,338(5):368-385

Ice and snow have often helped physicists understand the world. On the contrary it has taken them a very long time to understand the flow of the glaciers. Naturalists only began to take an interest in glaciers at the beginning of the 19th century during the last phase of glacier advances. When the glacier flow from the upslope direction became obvious, it was then necessary to understand how it flowed. It was only in 1840, the year of the Antarctica ice sheet discovery by Dumont d'Urville, that two books laid the basis for the future field of glaciology: one by Agassiz on the ice age and glaciers, the other one by canon Rendu on glacier theory. During the 19th century, ice flow theories, adopted by most of the leading scientists, were based on melting/refreezing processes. Even though the word ‘fluid’ was first used in 1773 to describe ice, more the 130 years would have to go by before the laws of fluid mechanics were applied to ice. Even now, the parameter of Glen's law, which is used by glaciologists to model ice deformation, can take a very wide range of values, so that no unique ice flow law has yet been defined. To cite this article: F. Rémy, L. Testut, C. R. Geoscience 338 (2006).  相似文献   

Comments on the article “Determination of groundwater availability in shallow arid region aquifers utilizing GIS technology: a case study in Hada Al-Sham, Western Saudi Arabia” by A. S. El-Hames and K. A. Al-Ahmed (Hydrogeology Journal (2005), Volume 13, No.4, p 640–648, and Erratum in Volume 13, No. 4, p 649).     

Khaled S. Balkhair 《Hydrogeology Journal》2006,14(7):1380-1382

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Time domain Gauss–Newton seismic waveform inversion in elastic media     

Dong-Hoon Sheen  Kagan Tuncay  Chang-Eob Baag  Peter J. Ortoleva 《Geophysical Journal International》2006,167(3):1373-1384

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The multilevel fast multipole method for forward modelling the multiply scattered seismic surface waves   总被引：1，自引：0，他引：1  

Özcan Çakir 《Geophysical Journal International》2006,167(2):663-678

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泥石流汇流槽可靠度分析   总被引：2，自引：1，他引：2  

易朋莹  陈洪凯  唐红梅  吴四飞 《中国地质灾害与防治学报》2005,16(3):142-147

汇流槽是泥石流治理工程中常用的工程措施之一。文章基于汇流槽的倾倒破坏、滑移破坏及地基破坏模式，通过对汇流槽设计影响强烈的岩土参数、几何特征、荷载因素等敏感因子的求解方法及分布特征分析，从汇流槽的抗倾稳定、抗滑稳定和基底应力要求三方面建立极限状态方程。对于每个极限状态方程，在泰勒级数对非线性极限状态方程线性化后，运用一次二阶矩的理论，先假定失效点P^＊，求解出相应的均值和方差。然后根据可靠的定义，得到相应的可靠度指标，通过迭代法求解真正失效点的可靠度指标βi。最后根据3个状态方程相互独立的假定，得出整个结构的可靠度指标β。该方法在平川泥石流防治工程中得到了成功的运用。这对于可靠度设计方法在泥石流防治工程中的运用进行了有益的探讨。  相似文献   

大气污染物SO_x输送方程的尺度分析   总被引：5，自引：1，他引：5  

程新金  黄美元  安峻岭  王自发  徐华英  周玲  肖辉 《气象学报》2002,60(4):468-476

文中用量纲分析方法分析了控制大气污染物输送方程的动力学特性。提出了 6种反映大气污染物输送过程中各种动力、物理和化学过程相对重要性的动力学参数。并以硫氧化物为例进行了各参数量级大小分析 ,尤其对 3种起汇作用 (去除机理 )的机理 (化学转化、干沉降和湿清除 )在不同尺度大气污染过程中的作用进行了详细分析。结果表明 :在一般情况下 ,SO2 的气相化学作用小于干沉降和湿清除的作用 ;干沉降作用很依赖于模式最底层厚度的选取 ;在有降雨时湿清除作用一般较大。文中还对大气污染物SOx 输送方程各项特征量的量级作了分析对比 ,得出了控制不同尺度大气污染物输送过程的零级近似方程和一级近似方程 ,并指出了这些方程的基本特征  相似文献   

祁连山林区大气降水特征与森林对降水的截留作用   总被引：30，自引：3，他引：30  

常学向  赵爱芬  王金叶  常宗强  金博文 《高原气象》2002,21(3):274-280

通过对连山寺大隆林区定位站1975－2000年的降水特征与森林对降水的再分配分析，建立了祁连山大隆林区降水与温度，降水与湿度，林冠截留的关系式。该区多年平均降水量为433.5mm，年变幅在326.4-539.7mm;降水量最大出现在夏季，占全年降水量的65．70％；海拔高度每升高100m，年了量平均递增4．55％，林区温度和湿度均与降水有较好的拟合关系。青海云杉林与祁连圆柏林林冠对大气降水的平均截留率分别为37．5％，31．7％，灌木林的截留率平均高达66．5％。青海云杉林林冠层平均截留率随着降雨量的增大逐渐减小，当降雨量为18.67mm时，林冠截留量达到最大，为14.72mm；青海云杉树干径流量占降水量的0．51％，当降雨量超过12.0mm时，才开始产生树干径流。青海云杉林枯枝落叶层对降雨的截留量随降雨量级增加而增大，截留率则随降雨量减小而增大，枯枝落叶层所具有的截留降雨和调蓄降雨作用使祁连山林区基本不发生地表径流。分析结果表明，祁连山林区对水源涵养和水流出山的时间调控有重要意义。  相似文献   

EFG法在土体固结中的应用   总被引：4，自引：0，他引：4  

张延军  唐红兵 《吉林大学学报(地球科学版)》2002,32(1):77-80

EFGM作为一种新的数值计算方法，具有只需节点信息而无段单元的特性，故在解固结方程方面有很大的优势。在计算分析中，此法容易构造固结方程的EFGM刚度矩阵和处理不同边界条件。对单面排水等条件的计算结果表明，EFGM在解决固结变形问题上，精度较高，处理边界准确。  相似文献