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spherical geometry 球面幾何(學)。

spherical trigonometry

At linear stage , the theoretical growth rate for the rt instability in cylindrical and spherical geometries was enhanced ( or reduced ) due to the decrease ( or increase ) in the perturbation wavelength during an implosion ( or explosion ) . even in the absence of an acceleration the perturbation could grow in the convergent geometries . the amplitude growth rate was proportional to the cube of the convergent ratio in spherical geometry and to the square of the convergent ratio in cylindrical geometry 在線性階段,已有的研究表明:一方面,在內爆(或外爆)過程中擾動波長變短(或變長) ,使得不穩定性的增長率變大(或變小) ;另一方面,即使不存在界面加速度,界面運動仍然可能導致擾動幅度的增加,柱幾何中擾動幅度的變化速率正比于界面收縮比的平方,球幾何中擾動幅度的變化速率正比于界面收縮比的三次方,并且擾動幅度的變化方式(增加或減少)只與初始時刻擾動幅度的增長速率(正或負)有關,而與界面的運動方向(向內或向外)無關。

In addition , it was the sign of the initial amplitude growth rate , not the manner of the interface motion that determined whether the amplitude could increase . at weakly nonlinear stage , mode - coupling equations were derived in cylindrical and spherical geometries . it showed that the nonlinear terms were inversely proportional to the position of the interface in cylindrical and spherical geometries 在弱非線性階段,推導了柱和球幾何中模耦合方程,結果表明:非線性作用項反比于界面的位置,界面的位置越小,非線性作用越強,反之越弱;同時柱幾何中模耦合方程的解表明,在收縮幾何中,擾動在界面兩側的發展是不對稱的,在弱非線性階段,不穩定性向內發展的部分受到慣性力的擠壓,而向外發展的部分受到慣性力的拉伸。

Secondly , nonlinear threshold of two - dimensional rt instability was analyzed in planar and cylindrical and spherical geometries . density amplitude was defined relating to instable interface and formulae of nonlinear threshold values for rt instability in three geometries were given , then the lared - s code was used to simulate two - dimensional rt instability in three geometries and simulation results agreed well with the formulae 其次,討論了二維平面、柱和球幾何中rt不穩定性發生非線性偏離的閾值問題,給出了三種幾何中密度擾動振幅的非線性閉值公式,并且用lared一s程序進行了檢驗,計算結果表明柱和球幾何中的模藕合機制與平面幾何不同,存在幾何效應的影響。

The strength of convergent shock was enhanced in cylindrical and spherical geometries than in planar geometry . the bubble became more wide and big and the spike became more narrow and long . it showed in spherical implosion that the spike close to the symmetrical axis grew faster than the ring one away from the symmetrical axis 第四,利用lared一s程序模擬柱和球幾何內爆過程中rt不穩定性增長,表明收縮幾何效應對內爆過程中不穩定性的增長有重要影響,柱和球幾何中聚心沖擊波的強度大于平面情況,氣泡變得更加寬而大,而尖頂變得更加細而長。

Thirdly , multimode - coupling phenomena in cylindrical geometry was analyzed by the simulation . the growth of every mode and its harmonic was qualitatively compared well with the solutions of mode - coupling equation . fourthly , the rt instability in cylindrical and spherical geometries was calculated during an implosion 第三,利用lared一s程序模擬柱幾何中rt不穩定性的多模禍合問題,對各個模及其高次諧波的變化進行了分析,并且與模藕合方程的解定性地進行比較,結果符合得較好。

Many planets ( for example , ganymede , mercury , the earth , jupiter and saturn ) and stars ( for example , the sun ) possess intrinsic magnetic fields . the explanation for their existence and variation remains a great challenge to planetary scientists and astrophysicists . this article attempts to review some recent developments and difficulties in the study of magnetohydrodynamics for the electrically conducting fluid interiors of planets and stars . it is the fluid motions , usually driven by thermal convection , that generate and sustain magnetic fields through magnetohydrodynamic processes in planets and stars . in planets , the magnetohydrodynamic processes are strongly affected by the combined and inseparable effects of rotation , magnetic fields and spherical geometry . the key dynamics involves the interaction between the coriolis and lorentz forces . in the sun , it is the solar tachocline , a thin shear flow layer located at the base of the convection envelope , that plays an essential role in the solar magnetohydrodynamic processes which produce the 11 - year sunspot cycle . some results of a new nonlinear three - dimensional solar dynamo model are also presented 許多行星(如木衛三,水星,地球,木星和土星)和恒星(如太陽)具有內部磁場.對這些磁場的存在和變化的解釋對行星科學家和天體物理學家是一個巨大的挑戰.本文試圖總結行星和恒星的導電流體內部磁流體力學研究的新近發展和困難.一般由熱對流驅動的流動通過磁流體力學過程產生并維持在行星和恒星中的磁場.在行星中磁流體力學過程強烈地受到轉動,磁場和球幾何位型的綜合影響.其動力學的關鍵方面涉及科里奧利力和洛倫茲力間的相互作用.在太陽中其流線,即處于對流層的薄的剪切流層在太陽的磁流體力學過程中扮演了一個基本的角色,并由之產生了11年的太陽黑子周期.本文也給出了一個新的非線性三維太陽發電機模型

In this article , physical equations and relative three - dimensional finite - difference formulae in cylindrical and spherical geometries were derived and two - and three - dimensional code in cylindrical and spherical geometries for direct - drive by laser was made , based on the lared - s code in planar geometry . it consisted of the processes such as the inverse bremsstrahlung absorption , electic heat conduction and fluid dynamics 本論文在lared - s程序平面版本基礎上,推導了三維柱和球幾何中激光驅動的物理方程和相應的差分方程,編制了二維和三維柱和球幾何中激光驅動流體不穩定性的lared - s程序版本,主要物理過程包括:激光逆軔致吸收、電子熱傳導和流體運動。

The rayleigh - taylor ( rt ) instability in cylindrical and spherical geometries was analized in this thesis , based upon velocity potential theory 本論文利用速度勢理論對柱和球幾何中不可壓縮流體的rayleigh - taylor ( rt )不穩定性進行了研究。

Einstein s original cosmological model , introduced by him in 1917 , was a static , homogeneous model with spherical geometry 愛恩斯坦在1917年發表的宇宙模型是一個靜態均勻及具有球狀對稱的宇宙。

Different type methods to survey height by spherical geometry 各類高程測量方法的球面幾何解釋