Stability of the solar system     

Zdeněk Kopal 《Earth, Moon, and Planets》1980,22(1):5-11

If the solar system is considered as a mechanical clockwork consisting of its present members which attract each other as mass-points, the extent of its present approach to secular stability (i.e., the state of minimum potential energy) — manifested by the existence of a number of nearcommensurabilities of the present orbital periods, not only of the planets, but also of their satellites —could not have been attained in a time-span of 4.6×10⁹ yr of its age by gravitational perturbations alone.The existence of such commensurabilities — striking in many instances— could then be understood only on the assumption that either (a) the solar system was actually born with the present 2-, 3- and 4-term couplings between the orbital period of the planets already built-in from the outset (which is improbable on any known grounds); or (b) that these couplings — in particular, the 25 Jupiter-Saturn commensurability — have arisen as a result of tidal interaction between proto-planetary globes of much larger dimensions than these planets possess today. For the present dimensions and mutual distances of these planets, their tidal interaction in 10⁹ yr would exert but negligible effects; and during that time neither their masses, nor the scale of the solar system underwent any essential change.Therefore, a hypothesis is proposed that the situation now obtaining had its origin in the early days of the formation of the solar system, when the planetary globes — in particular, those of Jupiter and Saturn (now in the terminal stage of Kelvin contraction) — were very much larger than they are today; and when, as a result, the tidal coupling between them operated at a much higher rate than at the present time.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.  相似文献   

Vibrational stability of rotating stars     

Zdeněk Kopal 《Astrophysics and Space Science》1981,76(1):187-212

The aim of the present paper will be to detail the explicit form of the equations which govern first-order oscillations of fast-rotating globes of self-gravitating fluids; with due account taken of the effects arising from the centrifugal as well as Coriolis force. As such configurations oscillate in general about distorted figures of equilibrium, the equations governing them can be conveniently expressed in terms of the Clairaut coordinates, associated with distorted spheroidal figures, and introduced in our previous paper (Kopal, 1980) for this purpose.In Section 2 which follows a brief outline of our problem, the equilibrium properties of fast-rotating configurations or arbitrary structure will be formulated. In Section 3 we shall carry out a separation of the variables in the equations of motion, and reduce the partial differential equations of the problem to an equivalent system of ordinary differential equations, by an expansion of expressions for the velocity componentsU, V, W in terms of tesseral harmonicsY _n ^m (, ). The explicit form of such a system, including the effects of all tesseral harmonics of orders up tom=n=4, will be specified in Section 3 for configurations whose equilibrium form is a sphere; while in Section 4 this latter condition will be relaxed to allow for the equilibrium configuration to become a rotational spheroid.In the concluding Section 5 we shall convert the complex form of our equations of motion into real terms, amenable to a solution-analytical or numerical-in terms of real variables; and shall establish the boundary conditions necessary for a specification of the characteristic frequencies of oscillation.  相似文献   

Editorial     

Cornelis De Jager  Zdeněk Švestka 《Solar physics》1978,56(1):3-4

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Fourier analysis of the light curves of eclipsing variables,IX     

Zdeněk Kopal 《Astrophysics and Space Science》1976,45(2):269-281

The aim of the present paper will be to detail the procedure outlined in our previous investigations (Kopal, 1975; Kopalet al., 1976) for a solution of the elements of distorted eclipsing systems by a Fourier analysis of their light changes. This procedure—which constitutes an equivalent, in the frequency-domain, of rectification hitherto practised in the time-domain — should enable us to free the observed momentsA _2m of the light curves from all photometric effects of distortion (between minima as well as within eclipses) — a feat impossible in the time-domain except under very restricted conditions — and thus to make it possible to obtain the geometrical elements of the eclipses which should be free from any obvious source of systematic errors.  相似文献   

Fourier analysis of the light curves of eclipsing variables,II     

Zdeněk Kopal 《Astrophysics and Space Science》1975,35(1):159-170

The aim of the present paper will be to extend the Fourier methods of analysis of the light curves of eclipsing binaries, outlined in our previous communication (Kopal, 1975) in connection with systems whose components would appear as uniformly bright discs, to systems whose components exhibit discs characterized by an arbitrary radially-symmetrical distribution of brightness —i.e., an arbitrary law of darkening towards the limb — be it linear or nonlinear.In Section 2 which follows a few brief introductory remarks, fundamental equations will be set up which govern the light changes arising from the mutual eclipses of limb-darkened stars — be such eclipses total, partial or annular; and Section 3 will contain a closed algebraic solution for the elements of the occulation eclipses terminating in total phase. Such a solution proves to be no more complicated than it turned out to be for uniformly bright discs in our previous paper; and calls for no special functions for the purpose — as will be put in proper perspective in the concluding Section 4.The cases of transit eclipses terminating in an annular phase, of partial eclipses of occulation or transit type, will be similarly dealt with by Fourier methods in the next paper of the present series.  相似文献   

Will the river Irtysh survive the year 2030? Impact of long-term unsuitable land use and water management of the upper stretch of the river catchment (North Kazakhstan)     

Zbyněk Hrkal  Alain Gadalia  Pierre Rigaudiere 《Environmental Geology》2006,50(5):717-723

The Irtysh river basin all the way from river spring in China across Kazakhstan as far as the Russian part of Siberia is among the most ecologically endangered and affected regions on our planet. The study provides a summary of the historical reasons for anthropological interventions in this area, which began with the construction of plants of the military—industrial complexes in the forties of the last century during World War II. These plants have a major share in extreme high concentrations of heavy metals in surface as well in groundwaters locally. The Semipalatinsk nuclear polygon plays a specific role as a source of contamination of local waters. The release of top secret data enabled us to gain knowledge about serious problems related to high radioactivity of groundwaters, which should spread uncontrollably through a system of secondary fissures activated by nuclear blasts. Another serious problem in this region is the quantitative aspect of contamination. Model simulations of water balance indicate that large industrial development in the spring area in China and continuously increasing water consumption in Kazakhstan may lead to desiccation of the lower stretch of this large river in Siberia during the summer months of 2030.  相似文献   

Remote sensing detection of atmospheric pollutants by differential absorption LIDAR 510M/SODAR PA2 mobile system     

J. Keder  M. Střižík  P. Berger  A. Černý  P. Engst  I. Němcová 《Meteorology and Atmospheric Physics》2004,85(1-3):155-164

Summary Air pollution problem in the Czech Republic is very complex due to large number of factors as turbulent dispersion and chemical reactions concurring in the status of the PBL. For this 3D distribution of pollutants is a key information that cannot be given by conventional monitoring stations. Combined use of DIAL lidar and sodar can give access to such information. Case studies of air pollutants transport are presented using 3D concentration fields of NO₂ and ozone measured by lidar and meteorological conditions monitored by Doppler Sodar.  相似文献   

Shear and objective stress rates in hypoplasticity by D. Kolymbas and I. Herle. Author's Reply to Discussion by A. Beghini and Z. P. Bazant,R. Chambon and A. Niemunis of ‘Shear and objective stress rates in hypoplasticity’     

Alessandro Beghini  Zdeněk P. Bažant  R. Chambon  D. Kolymbas  I. Herle 《国际地质力学数值与分析法杂志》2004,28(4):365-372

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Forecasting rock slope failure: how reliable and effective are warning systems?     

Martina?S?tteleEmail author  Michael?Krautblatter  Michael?Bründl  Daniel?Straub 《Landslides》2016,13(4):737-750

Warning systems are increasingly applied to reduce damage caused by different magnitudes of rockslides and rockfalls. In an integrated risk-management approach, the optimal risk mitigation strategy is identified by comparing the achieved effectiveness and cost; estimating the reliability of the warning system is the basis for such considerations. Here, we calculate the reliability and effectiveness of the warning system installed in Preonzo prior to a major rockfall in May 2012. “Reliability” is defined as the ability of the warning system to forecast the hazard event and to prevent damage. To be cost-effective, the warning system should forecast an event with a limited number of false alarms to avoid unnecessary costs for intervention measures. The analysis shows that to be reliable, warning systems should be designed as fail-safe constructions. They should incorporate components with low failure probabilities, high redundancy, have low warning thresholds, and additional control systems. In addition, the experts operating the warning system should have limited risk tolerance. In an additional hypothetical probabilistic analysis, we investigate the effect of the risk attitude of the decision makers and of the number of sensors on the probability of detecting the event and initiating a timely evacuation, as well as on the related intervention cost. The analysis demonstrates that quantitative assessments can support the identification of optimal warning system designs and decision criteria.  相似文献   

Geoarchaeological evidence on a Late Bronze Age earthquake,Ohrid Basin (North Macedonia)     

J. Hošek  M. Verčík  P. Pokorný  J. Beneš  V. Komárková  T. Radoměřský  N. Atanasoska  V. Todoroska  P. Ardjanliev 《第四纪科学杂志》2021,36(6):1003-1012

Geoarchaeological investigations on the northeastern shore of Lake Ohrid revealed 3.5 m thick deepwater lacustrine sediments overlying terrestrial vegetation macrofossils, worked wood and abundant potsherds dated to the Late Bronze Age (LBA). Distinct contact of deepwater sediment with the sub-aerial weathered limestone bedrock point to a sudden increase in lake level. According to radiocarbon data, catastrophic flooding occurred shortly after 1214 yr bc. Because the area is located in a highly active seismic zone, we propose that this event was caused by tectonically induced, metre-scale coseismic subsidence related to faults bordering the Ohrid alluvial plain. Moreover, this event coincides well with a dramatic switch in the habitation and settlement strategy in the region. More important, however, is the finding that the age of the proposed massive tectonic event and change in habitation lies within the interval of the proposed ‘earthquake storm’ in the eastern Mediterranean dated to 1225–1175 bc. As the Ohrid-Korça zone belongs to the same tectonic province, a relationship between the abovementioned earthquakes and the proposed event can be expected. This research therefore might provide the first direct evidence of a large-scale earthquake event linkable to the LBA collapse of Europe's first urban civilisation in the Aegean.  相似文献