Societal Statistics by virtue of the Statistical Drake Equation

The Drake equation, first proposed by Frank D. Drake in 1961, is the foundational equation of SETI. It yields an estimate of the number N of extraterrestrial communicating civilizations in the Galaxy given by the product N=Ns×fp×ne×fl×fi×fc×fL, where: Ns is the number of stars in the Milky Way Galaxy; fp is the fraction of stars that have planetary systems; ne is the number of planets in a given system that are ecologically suitable for life; fl is the fraction of otherwise suitable planets on which life actually arises; fi is the fraction of inhabited planets on which an intelligent form of life evolves; fc is the fraction of planets inhabited by intelligent beings on which a communicative technical civilization develops; and fL is the fraction of planetary lifetime graced by a technical civilization.The first three terms may be called “the astrophysical terms” in the Drake equation since their numerical value is provided by astrophysical considerations. The fourth term, fl, may be called “the origin-of-life term” and entails biology. The last three terms may be called “the societal terms” inasmuch as their respective numerical values are provided by anthropology, telecommunication science and “futuristic science”, respectively.In this paper, we seek to provide a statistical estimate of the three societal terms in the Drake equation basing our calculations on the Statistical Drake Equation first proposed by this author at the 2008 IAC. In that paper the author extended the simple 7-factor product so as to embody Statistics. He proved that, no matter which probability distribution may be assigned to each factor, if the number of factors tends to infinity, then the random variable N follows the lognormal distribution (central limit theorem of Statistics). This author also proved at the 2009 IAC that the Dole (1964) [7] equation, yielding the number of Habitable Planets for Man in the Galaxy, has the same mathematical structure as the Drake equation. So the number of Habitable Planets follows the lognormal distribution as well. But the Dole equation is described by the first FOUR factors of the Drake equation. Thus, we may “divide” the 7-factor Drake equation by the 4-factor Dole equation getting the probability distribution of the last-3-factor Drake equation, i.e. the probability distribution of the SOCIETAL TERMS ONLY. These we study in detail in this paper, achieving new statistical results about the SOCIETAL ASPECTS OF SETI.     

Interaction onde de choc-couche limite laminaire sur un corps de revolution en rotation

(Shock Wave-Laminar Boundary Layer Interaction on a Spinning Axisymmetric Body)—A method is developed to predict the shock wave-laminar boundary layer interaction on an axisymmetric body spinning in axial flow. The integral scheme of Lees, Reeves and Klineberg is used. The Falkner Skan “type” equations is then established for the boundary layer on spinning cylinder and used to construct the polynomial representation of the integral quantities. The independence of the polynomials with respect to the spinning rate is demonstrated. A cylinder of 200 mm diameter with a flare is built and tested up to 5000 rmp in wind tunnel at M = 2.21. The pressure measurements are in good agreement with the theoretical results. The rotation induces the decreasing of the pressure level and boundary layer separation inside the interaction region.     

Plasma irregularities in unstable outer ionosphere according to the Intercosmos-Bulgaria-1300 satellite data

The results of the satellite low-latitude and mid-latitude measurements of the disturbed plasma concentration, electron temperature, and quasi-stable electric field at heights of ～900 km after sunset are discussed. It is shown that the sharp fronts of changes in the electron temperature and plasma density observed in the experiment onboard the Intercosmos-Bulgaria-1300 satellite in the low-latitude (and equatorial) outer ionosphere can be related to damping of the oscillations of plasma electrons at local decreases of the plasma density (plasma “pits”) and formation of the vortex plasma structures at density and temperature gradients, which promotes conservation of ionosphere irregularities and makes the fronts of concentration variations steeper. Nonmonotonic variations in the plasma conductivity for the ionosphere currents in unstable plasma can be a cause of observed nonmonotonic disturbances of the vertical component of the “constant” electric field.     

Features of coronal mass ejections of minimum size

The coronal mass ejections (CME) with small angular dimensions (d ≤ 10°) have the simplest form, much simpler than large CME. This fact simplifies the problem of analyzing the CME structure and studying their origin. On the basis of the analysis of the LASCO C2 (SOHO) data, we show in this paper that the motion of a CME having small dimensions proceeds within a magnetic tube (a ray with increased brightness) of the streamer belt and leads to an “explosion-like” increase in the angular dimensions (rapid expansion) of the tube. A hypothesis is put forward that a small CME represents a “plasmoid” (a plasma bunch bounded in space, with its own magnetic field) thrown into the base of the magnetic tube and moving along it away from the Sun.     

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.

     

运载火箭摇摆发动机与全箭动力学特性耦合关系研究

针对运载火箭“摆动发动机-伺服回路”负载频率低,可能影响全箭弹性模态稳定性的问题,首先建立了包含“发动机-伺服回路”动力学模型的全箭动力学模型,分析了“发动机－伺服回路”负载频率对伺服机构传递函数和控制系统开环传递函数特性的影响,指出了“发动机－伺服回路”负载频率与箭体弹性模态之间的动力学耦合关系,给出了保证弹性模态稳定的谐振频率判据,最后计算了保证全箭弹性模态稳定的负载频率边界值,并通过仿真算例验证了结果的正确性。研究结果表明,“发动机－伺服回路”局部的负载频率通过惯性负载力矩作用与全箭弹性模态形成耦合,当负载频率位于上、下边界值范围之内时就会导致某些弹性模态不稳定,因此在实际工程中应对负载频率进行限制,以保证运载火箭的飞行安全。
     

On some spacecraft fatigue-crack propagation problems

For thin-gauge sheet structures the effective critical range of stress-intensity factor ΔK_c can be calculated by curve fitting to the results of the crack propagation tests. A new, more exact, coordinate transformation method based on the Forman formula has been developed for this purpose.The method can be extended to cover the determination of the threshold stress-intensity range ΔK_th as well. There are two candidate transportation formulae for this purpose. The correct one of them will be singled out on the base of practical experience.Recent test data may indicate that even pure atmospheric air can exert a corrosion-like influence on the crack-growth rate of certain light-metal alloys. Should this prove to be true, then respective tests will have to be run in the proper environment and/or corrections will have to be applied for the corrosion influence.     

Determination of vibrational CO2 distributions in thermodynamically-nonequilibrated rarefied flows by use of radiational characteristics in the 15 μm band

A method for determination of the vibrational distributions and populations of individual vibrational levels of vibrationally-nonequilibrated carbon dioxide in bend-stretch manifold and asymmetric stretching mode was developed and substantiated. The method is based on the measurements of integrated radiation intensity in the wide spectral intervals of the 15 μm CO₂ band and total emissivities of its appropriate Q-branches. Computations of radiation intensities and emissivities in P and R-branches were performed by using vibrational-rotational band models and in Q-branches by the direct “line-by-line” integration.It was shown that vibrational temperature of CO₂ asymmetric stretching mode may be determined from the measurements of integrated radiation intensity of the 15 μm band. The populations of individual levels of the bend-stretch manifold may be obtained from the measurements of total emissivities of some Q-branches of the 15 μm band.The procedure of the CO₂ lower vibrational levels populations determination under the conditions typical of 18 μm and 9–11 μm CO₂ laser cavities is described.     

A technique for estimating the probability of radiation-stimulated failures of integrated microcircuits in low-intensity radiation fields: Application to the Spektr-R spacecraft

In developing radio-electronic devices (RED) of spacecraft operating in the fields of ionizing radiation in space, one of the most important problems is the correct estimation of their radiation tolerance. The “weakest link” in the element base of onboard microelectronic devices under radiation effect is the integrated microcircuits (IMC), especially of large scale (LSI) and very large scale (VLSI) degree of integration. The main characteristic of IMC, which is taken into account when making decisions on using some particular type of IMC in the onboard RED, is the probability of non-failure operation (NFO) at the end of the spacecraft’s lifetime. It should be noted that, until now, the NFO has been calculated only from the reliability characteristics, disregarding the radiation effect. This paper presents the so-called “reliability” approach to determination of radiation tolerance of IMC, which allows one to estimate the probability of non-failure operation of various types of IMC with due account of radiation-stimulated dose failures. The described technique is applied to RED onboard the Spektr-R spacecraft to be launched in 2007.     

On radiative and conductive heat transfer in spacecraft

The “radiative” boundary condition in a heat conduction problem relates the heat flux in a point of the wall to the temperatures in all the other points of the surface system.That is, this condition is of a “functional” type. This “functional” can be solved in discrete terms by using the conventional technique of dividing the body in small discrete elements or “nodes”. This paper instead presents an approach on a continuous scheme, by which the functional is solved in terms of “spacewise harmonics” of the temperature inside the body; the heat conduction problem is thus reduced to an ordinary form differential system whose unknowns are these “harmonics”. An interative linearized procedure to solve this system is also suggested, by which “exact” solutions are obtained. The merits of these solutions, with respect to practical discrete element computations, are in the better spacewise resolution and in the consequent more accurate treatment of both radiation and conduction. The application of the procedure is, however, limited to particular geometries. It is relevant to note that among these possible geometries many are included of practical interest, like hollow cylinders and polygons, cubic boxes etc. A numerical example completes the work.     

Apogee manoeuvre with a restartable liquid bipropellant motor

Unified Propulsion Systems present perceptible advantages for geostationary spacecrafts design: mass savings, as the ergols tanks are the same for the apogee motor and for the Attitude and Orbit Control System, higher performance, as specific impulse of bi-ergols motors is higher than the one of solid propellant motors and higher operational flexibility as the fuel amount can be adapted to the real flight conditions and as biliquid motors are restartable. On the other hand, the use of these propulsion systems for geostationary spacecrafts sets quite new mission analysis problems: the “predictability” of each delivered Delta-V is rather coarse (the corresponding uncertainty is about 4% for the existing motors). Also, only midlevel thrusters (about 400N) are available and so the finite burn losses associated with long burns arcs have to be minimized. This paper surveys the problems resulting from these new operational constraints and deals successively with the following items: optimal splitting up of the apogee manoeuvre, taking into account the possible dispersions on each Delta-V and the on-station longitude acquisition; minimization of the finite burn losses; adaptation of the apogee manoeuvre to the initial orbit parameters corresponding to the first North-South station-keeping cycle. The operation procedures derived from this survey will be used for the future launch of the ARABSAT spacecraft and for the following spacecrafts of the SPACEBUS family.     

Context Affects Scale Selection for Proximity Terms

Abstract

Spatial proximity terms, such as near and far, communicate information regarding the distance in which a “located” object can be found with respect to a “reference” object. The present paper investigates whether people take into account the location of an object extraneous to the located object and reference object pair, when setting the scale for proximity language judgements. Across three experiments participants rated the appropriateness of near and far to describe spatial scenes that included a third (distractor) object positioned the same distance as the located object from the reference object, but at varying distances from the located object. The results show that the presence of other spatial relations affects scale setting, resulting in differences in appropriateness ratings for those spatial terms.     

World economics for mankind's frontier

In Acta Astronautica, Vol. 56, No. 5, March 2006, at ISSN0094-5765 there appears the article entitled “Will space actually be the Final Frontier of humankind?” written by Giancarlo Genta, and Michael Rycroft. This Acta Astronautica article requires amplification on the economic side. The writer of this article was personally present at the Apollo 11th launchings for the first landing on the Moon, by Buzz Aldrin and others. The Apollo 11 take off to the Moon, from Cape Carnival, did not leave the situation “so humankind seems forever to be bound to its own planet!” There was nothing pessimistic about the launch of Apollo 11. It is written that there was a lack of vision at that time, which is also not correct. The ‘Final Frontier’ myth was never mentioned on that occasion. At Apollo 11 we did take planet earth's “first faltering step for mankind” on the path towards a space faring civilization, exactly as these two authors later correctly mention. Now with the US Presidential initiatives “Moon, Mars and Beyond,” the authors suggested that it “will depend on social, political and economic issues rather than technological and scientific ones.” This Academy Note respectfully submits that all of these factors social, political and economic issues, plus psychological and scientific ones, instead of, “rather than technical and scientific ones” are going to be the determining factors of the speed of progress of the exploration of the entire universe, and particularly the sun in our Milky Way Galaxy. Russia and Ukraine are now on same, deep-space policy directions. The attention of the readers of this Academy Note is called to the current “Cosmic Collision” excellent presentation at the Hayden Planetarium, located at the Museum of National History in the City of New York. It shows the past, the present and the future of international humankind in exploring space and the creation of the universe, with particular reference to the protons of our sun, for our Milky Way Galaxy.     

Directional Solidification Using a Baffle in Microgravity

Numerical simulations were performed to optimize the conditions and parameters for directional solidification of Te-doped GaSb in reduced gravity ranging from 10⁻³ to 10⁻⁵g₀. Our key goal was to quantify the velocity and concentration fields with and without a baffle present in the melt. The effect of the distance of the baffle from the solid–liquid interface was investigated. When the baffle is placed 0.5 cm from the solid–liquid interface, acceleration of 10⁻³g₀ does not cause significant interference with segregation. Furthermore, the flow between the baffle and the interface (low Reynolds number “creeping” flow) does not depend on fluid properties (viscosity).     

Collisions of stars by oscillating orbits of the second kind

Ordinary estimations of the number of star collisions in our galaxy—by simple kinematic considerations—lead to a very small number of such collisions: about one or even less every millions of years. However star collisions can occur through the following indirect way which has a much higher probability. (a) Binary stars are very common in our galaxy, about 30–50% of the stars. (b) If two binary stars meet a triple system can be formed by an ordinary exchange type motion. (c) A triple system is generally decomposed into the “inner orbit” (i.e. the relative orbit of the two nearest stars) and the “outer orbit” (i.e. the relative orbit of the third star with respect to the center of mass of the two nearest stars). The major axes of these two orbits have generally small perturbations and it is the same for the eccentricity of the outer orbit. On the contrary, if the relative inclination of the two orbits is large, the perturbations of the eccentricity of the inner orbit are important and can even in some cases lead to an eccentricity equal to one, that is to a collision of the two stars of the inner orbit.Such orbits can be called “oscillating orbits of the second kind”, indeed the first oscillating orbits—conceived by Khilmi and described for the first time in an example by Sitnikov—have unbounded mutual distances r_ij, but the system always come back to small sizes, it has an infinite number of very large expansions followed by strong contractions and, in the three-body case, an upper bound of lim inf (r_1.2 + r_1.3 + r_2.3) can be given in terms of the three masses and the integrals of motion. For the oscillating orbits of the second kind the mutual distances r_ij are bounded, but the velocities are unbounded (i.e. lim inf r_ij = 0 for at least one r_ij) and the system goes to a collision if the bodies have non-zero radius even small. The analytical study of the oscillating orbits of the second kind is a part of the general analytical study of the three-body problem, a part which must be valid for large eccentricities and large inclinations. The use of Delaunay's variables and of a Von Zeipel transformation lead to a first order integrable approximation, valid for any eccentricities and any inclinations, and giving the following results: (a) The oscillating orbits of the second kind occur when the angular momentum of the outer orbit has a modulus sufficiently close to the modulus of the total angular momentum of the three-body system. Hence these orbits occur for inclinations in the vicinity of 90°. (b) The oscillating orbits represent a set of positive measure of phase space and the first order study allows to give a rough estimation of the probability of collisions—even for stars of infinitely small radius. This probability, for given initial major axes and eccentricities and for isotropic arbitrary initial orientations, is generally of the order of m₃$\text{R}\text{M}$ (m₃ being the mass of the outer star, M the total mass and R the ratio of the period of the inner orbit to that of outer orbit).One question remains to be solved: how many collisions of stars are due to that phenomenon? That question is difficult because the probability of formation of a triple system by a random meeting of two binaries is very uneasy to estimate. However it seems that, compared to the usual evaluations based on pure kinematic considerations without gravitational effects, the number of collisions must be multiplied by a factor between one thousand and one million.