The classical Laplace plane as a stable disposal orbit for geostationary satellites

The classical Laplace plane is a frozen orbit, or equilibrium solution for the averaged dynamics arising from Earth oblateness and lunisolar gravitational perturbations. The pole of the orbital plane of uncontrolled GEO satellites regress around the pole of the Laplace plane at nearly constant inclination and rate. In accordance with Friesen et al. (1993), we show how this stable plane can be used as a robust long-term disposal orbit. The current graveyard regions for end-of-life retirement of GEO payloads, which is several hundred kilometers above GEO depending on the spacecraft characteristics, cannot contain the newly discovered high area-to-mass ratio debris population. Such objects are highly susceptible to the effects of solar radiation pressure exhibiting dramatic variations in eccentricity and inclination over short periods of time. The Laplace plane graveyard, on the contrary, would trap this debris and would not allow these objects to rain down through GEO. Since placing a satellite in this inclined orbit can be expensive, we discuss some alternative disposal schemes that have acceptable cost-to-benefit ratios.     

可压缩平板边界层转捩的大涡模拟

入口利用层流速度型叠加二维和三维Tollmien-Schliting(T-S)波,应用动态亚格子模型、预处理技术以及高精度算法,采用大涡模拟(Large eddy simulation,LES)数值计算方法,对可压缩平板边界层空间模式的转捩机理及其拟序结构进行了研究。计算结果展示了T-S波经历线性、非线性发展阶段破碎形成发卡涡,最终演化成具有4个涡环的涡链结构的整个过程,并揭示了发卡涡涡腿并非完整对称及低速条带在涡环产生的位置不连续的现象,探讨了主流向涡与壁面相互作用诱导生成次流向涡的机理。     

基于微分Petri网的民机航迹演化通用模型构建

为实现对未来大流量、高密度、小间隔条件下的空域实施管理,在战略航迹规划阶段,提出了一种模块化的战略航迹演化通用模型。建立了不同航段之间航空器状态动态切换的一类宏观Petri网演化模型,以及同一航段内航空器速度和高度两种特征参数值连续变化的3类微观Petri网演化模型。根据航空器特征参数值转化的4种不同形式并基于航空器全飞行剖面的混杂运行特性,运用微分Petri网理论,定义了航空器的4种演化模式,通过组合各种演化模式得到了3种航空器基本演化模型。在满足航空器性能约束的前提下,通过设定10个航段及15个高度和速度预设值,得到了全飞行剖面下各特征参数的演化图。结果表明,所设计的演化模型增强了航迹预测模型的通用性,能够反映航空器在水平剖面和垂直剖面内的状态变化。     

Evolution and History in a new “Mathematical SETI” model

In a recent paper (Maccone, 2011 [15]) and in a recent book (Maccone, 2012 [17]), this author proposed a new mathematical model capable of merging SETI and Darwinian Evolution into a single mathematical scheme. This model is based on exponentials and lognormal probability distributions, called “b-lognormals” if they start at any positive time b (“birth”) larger than zero. Indeed:

• 1.Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f_l in the Drake equation represents the fraction of planets suitable for life on which life actually arose, as it happened on Earth.
• 2.In 2008 (Maccone, 2008 [9]) this author firstly provided a statistical generalization of the Drake equation where the number N of communicating ET civilizations in the Galaxy was shown to follow the lognormal probability distribution. This fact is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution if the number of factors is increased at will, i.e. it approaches infinity.
• 3.Also, in Maccone (2011 [15]), it was shown that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of b-lognormal distributions constrained between the time axis and the exponential growth curve. This was a brand-new result. And one more new and far-reaching idea was to define Darwinian Evolution as a particular realization of a stochastic process called Geometric Brownian Motion (GBM) having the above exponential as its own mean value curve.
• 4.The b-lognormals may be also be interpreted as the lifespan of any living being, let it be a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization. In Maccone, (2012 [17, Chapters 6, 7, 8 and 11]), as well as in the present paper, we give important exact equations yielding the b-lognormal when its birth time, senility-time (descending inflexion point) and death time (where the tangent at senility intercepts the time axis) are known. These also are brand-new results. In particular, the σ=1 b-lognormals are shown to be related to the golden ratio, so famous in the arts and in architecture, and these special b-lognormals we call “golden b-lognormals”.
• 5.Applying this new mathematical apparatus to Human History leads to the discovery of the exponential trend of progress between Ancient Greece and the current USA Empire as the envelope of the b-lognormals of all Western Civilizations over a period of 2500 years.
• 6.We then invoke Shannon's Information Theory. The entropy of the obtained b-lognormals turns out to be the index of “development level” reached by each historic civilization. As a consequence, we get a numerical estimate of the entropy difference (i.e. the difference in the evolution levels) between any two civilizations. In particular, this was the case when Spaniards first met with Aztecs in 1519, and we find the relevant entropy difference between Spaniards an Aztecs to be 3.84 bits/individual over a period of about 50 centuries of technological difference. In a similar calculation, the entropy difference between the first living organism on Earth (RNA?) and Humans turns out to equal 25.57 bits/individual over a period of 3.5 billion years of Darwinian Evolution.
• 7.Finally, we extrapolate our exponentials into the future, which is of course arbitrary, but is the best Humans can do before they get in touch with any alien civilization. The results are appalling: the entropy difference between aliens 1 million years more advanced than Humans is of the order of 1000 bits/individual, while 10,000 bits/individual would be requested to any Civilization wishing to colonize the whole Galaxy (Fermi Paradox).
• 8.In conclusion, we have derived a mathematical model capable of estimating how much more advanced than humans an alien civilization will be when SETI succeeds.

     

Characterization and life prediction of single-pass honing tool for fuel injection nozzle

Single-pass honing is an important machining method for finish machining of holes, which can meet the requirement for high efficiency and consistency of holes. Characterization and life prediction of single-pass honing tool are necessary to improve the machining accuracy of holes honed, especially dimension accuracy. Single-pass honing tool is a single layer abrasive tool with fixed dimension, which still remains problematic for characterization and life prediction. For fuel injection nozzles with bore diameter under 1 mm, the stiffness of the single-pass honing tool is poor. This article presents a novel analytical model that predicts life of the tool with poor stiffness. Firstly, according to the bore diameter and dimension tolerance, the single-pass honing tool is designed and manufactured. Based on the prepared single-pass honing tool, the measurement and characterization methods are established. Furthermore, the tool wear tests are carried out, and the tool contour evolution model is established to predict the tool life.     

Effects of traverse speed on weld formation,microstructure and mechanical properties of ZK60 Mg alloy joint by bobbin tool friction stir welding

ZK60B (Mg-6% Zn-0.6% Zr) alloy joints fabricated by bobbin tool friction stir welding (BTFSW) with various traverse speeds were investigated. The sound joint fabricated by the BTFSW was possible under the appropriate welding parameters. The severe plastic deformation during BTFSW resulted in dispersion and segregation of the Zr-rich particles within the stirred zone (SZ) followed by evolution of a bimodal grain structure with distributed bands of 0.8–1.7 μm ultrafine grains and 4.1–7.1 μm equiaxed grains. Micro-hardness of SZ is substantially reduced in contrast to that of parent metal (PM) in spite of the finer grain size owing to dissolution of Mg-Zn based precipitates having hardening effects on alpha-Mg matrix. With the decrease in traverse speed, randomization degree of the plasticized metal flow increases, which is evidenced by the randomized arc line pattern at the low traverse speed. Among all defect-free joints, the 200 mm/min joint exhibits the weakest isotropy of texture within SZ and the best tensile properties, which has reduced ultimate tensile strength and yield strength by 5.4% and by 22.2%, respectively, as compared to the PM. The randomized texture hinders the joint fracturing within SZ at low elongation. Therefore, a relatively high elongation of 10.8% was achieved, which corresponded to 72% of the PM value.     

抛物化稳定性方程在曲面边界层中的应用

为了研究抛物化稳定性方程在曲面边界层中的应用,选取了等曲率圆环管道、等曲率板和NACA0012翼型3种典型的曲面边界层.通过计算小幅值扰动波的演化,抛物化稳定性方程的计算结果和线性稳定性理论、数值模拟扰动方程结果相符,说明可以使用抛物化稳定性方程研究曲面边界层的小幅值扰动波的演化和稳定性分析;通过计算有限幅值扰动波的演化,线性阶段抛物化稳定性方程计算结果和扰动方程相符,在非线性很强的阶段,抛物化稳定性方程计算发散,发散的位置可作为转捩位置.      

Medium Earth Orbit dynamical survey and its use in passive debris removal

The Medium Earth Orbit (MEO) region hosts satellites for navigation, communication, and geodetic/space environmental science, among which are the Global Navigation Satellites Systems (GNSS). Safe and efficient removal of debris from MEO is problematic due to the high cost for maneuvers needed to directly reach the Earth (reentry orbits) and the relatively crowded GNSS neighborhood (graveyard orbits). Recent studies have highlighted the complicated secular dynamics in the MEO region, but also the possibility of exploiting these dynamics, for designing removal strategies. In this paper, we present our numerical exploration of the long-term dynamics in MEO, performed with the purpose of unveiling the set of reentry and graveyard solutions that could be reached with maneuvers of reasonable $\mathrm{\Delta }V$ cost. We simulated the dynamics over 120–200?years for an extended grid of millions of fictitious MEO satellites that covered all inclinations from 0 to 90°, using non-averaged equations of motion and a suitable dynamical model that accounted for the principal geopotential terms, 3rd-body perturbations and solar radiation pressure (SRP). We found a sizeable set of usable solutions with reentry times that exceed $～40$ years, mainly around three specific inclination values: 46°, 56°, and 68°; a result compatible with our understanding of MEO secular dynamics. For $\mathrm{\Delta }V?300$ m/s (i.e., achieved if you start from a typical GNSS orbit and target a disposal orbit with $e<0.3$), reentry times from GNSS altitudes exceed $～70$ years, while low-cost ($\mathrm{\Delta }V?5–35$ m/s) graveyard orbits, stable for at lest 200?years, are found for eccentricities up to $e\approx 0.018$. This investigation was carried out in the framework of the EC-funded “ReDSHIFT” project.     

Continuum Model for Space Debris Evolution with Account of Collisions and Orbital Breakups

The paper discusses the mathematical modeling of long-term orbital debris evolution taking into account mutual collisions of space debris particles of different sizes. Investigations and long-term forecasts of orbital debris environment evolution in low Earth orbits are essential for future space mission hazard evaluation and for adopting rational space policies and mitigation measures. The paper introduces a new approach to space debris evolution mathematical modeling based on continuum mechanics incorporating partial differential equations. This is an alternative to the traditional approaches of celestial mechanics incorporating ordinary differential equations to model fragments evolution. The continuum approach to orbital debris evolution modeling has essential advantages for describing the evolution of a large number of particles, because it replaces the traditional tracking of space objects by modeling the evolution of their density of distribution.     

航天器空间碎片防护结构设计优化技术研究

航天器空间碎片防护结构设计优化在国际上属前沿研究课题,也是我国载人航天后续工程急需突破的技术。文章研究了防护优化理论方法,建立了适用于各类典型防护结构的两类防护优化数学模型,介绍了所采用的优化算法;完成了防护结构设计优化软件系统的重要模块防护优化算法库及防护优化求解器的设计开发;还对防护优化求解器进行了测试考核,验证了求解器的有效性、稳定性及高效性。