On the Stability of the Terrestrial Planets as Models for Exosolar Planetary Systems     

R. Dvorak  Á. Süli 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):77-95

All results, achieved up to now, show the long term stability of our planetary system, although, especially the inner solar system is chaotic, due to some specific secular resonances. We study, by means of numerical integrations, the dynamical evolution of the planetary system where we concentrate on the stability of motion of the terrestrial planets Venus, Earth and Mars. Our model consists of a simplified planetary system with the inner planets Venus, Earth and Mars as well as Jupiter and Saturn. A mass factor was introduced to uniformly change the masses of the terrestrial planets; Jupiter and Saturn were involved in the system with their actual masses. We integrated the equations of motion with a Lie-integration method for a time interval of 10⁷ years. It turned out that when 220 < < 245 and > 250 the system became unstable due to the strong interactions between the planets. We discuss the model planetary systems for small mass-factors 0.5 10 and large ones 160 270 with the aid of several different numerical tools. These results can be applied to recently discovered exoplanetary systems, which configuration is comparable to our own.  相似文献   

Association announcements     

Vaclav Nemec 《Mathematical Geosciences》1976,8(2):203-207

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CLIMATE CHANGE HYDROLOGY AND WATER RESOURCES IMPACT AND ADAPTATION FOR SELECTED RIVER BASINS IN THE CZECH REPUBLIC     

Vaclav Dvorak  Josef Hladny  Ladislav Kasparek 《Climatic change》1997,36(1-2):93-106

The Czech Republic has a northern hemisphere Atlantic-continental type of moderate climate. Mean annual temperature ranges between 1.0 and 9.4 °C (between 8.8 and 18.5 °C in summer and between –6.8 and 0.2 °C in winter). Annual precipitation ranges between 450 mm in dry regions and 1300 mm in mountainous regions of the country. With its 2000 m³ per capita fresh water availability, the Czech Republic is slightly below average. Occasional water shortages do not usually result from general unavailability of water resources but rather from time or space variability of water supply/demand and high degree of water resources exploitation. To study potential impacts of climate change on hydrological system and water resources, four river basins have been selected in the territory of the Czech Republic: the Elbe River at Decin (50761.7 km²), the Zelivka River at Soutice (1188.6 km²), the Upa River at Ceska Skalice (460.7 km²) and the Metuje River at Marsov n. M. (93.9 km²). To simulate potential changes in runoff, three hydrological models have been applied using incremental and GCM (GISS, GFDL and CCCM) scenarios: the BILAN water balance model, the SACRAMENTO (SAC-SMA) conceptual model and the CLIRUN water balance model. The paper reviews methods applied in the study, results of the assessments and concludes with suggestions for possible general adaptation policy options where the preference is for nonstructural measures such as water conservation, efficient water demand management and protection of water resources.  相似文献   

Recent uplift and hydrothermal activity at Tangkuban Parahu volcano, west Java, Indonesia     

John Dvorak  Johannes Matahelumual  Arnold T Okamura  Harun Said  Thomas J Casadevall  Dedi Mulyadi 《Bulletin of Volcanology》1991,53(1):20-28

Tangkuban Parahu is an active stratovolcano located 17 km north of the city of Bandung in the province west Java, Indonesia. All historical eruptive activity at this volcano has been confined to a complex of explosive summit craters. About a dozen eruptions-mostly phreatic events- and 15 other periods of unrest, indicated by earthquakes or increased thermal activity, have been noted since 1829. The last magmatic eruption occurred in 1910. In late 1983, several small phreatic explosions originated from one of the summit craters. More recently, increased hydrothermal and earthquake activity occurred from late 1985 through 1986. Tilt measurements, using a spirit-level technique, have been made every few months since February 1981 in the summit region and along the south and east flanks of the volcano. Measurements made in the summit region indicated uplift since the start of these measurements through at least 1986. From 1981 to 1983, the average tilt rate at the edges of the summit craters was 40–50 microradians per year. After the 1983 phreatic activity, the tilt rate decreased by about a factor of five. Trilateration surveys across the summit craters and on the east flank of the volcano were conducted in 1983 and 1986. Most line length changes measured during this three-year period did not exceed the expected uncertainty of the technique (4 ppm). The lack of measurable horizontal strain across the summit craters seems to contradict the several years of tilt measurements. Using a point source of dilation in an elastic half-space to model tilt measurements, the pressure center at Tangkuban Parahu is located about 1.5 km beneath the southern part of the summit craters. This is beneath the epicentral area of an earthquake swarm that occurred in late 1983. The average rate in the volume of uplift from 1981 to 1983 was 3 million m³ per year; from 1983 to 1986 it averaged about 0.4 million m³ per year. Possible causes for this uplift are increased pressure within a very shallow magma body or heating and expansion of a confined aquifier.  相似文献   

Reviews     

D. F. Merriam  Vaclav Nemec 《Mathematical Geosciences》1973,5(2):211-212

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“Stickiness” in mappings and dynamical systems     

R. Dvorak  G. Contopoulos  Ch. Efthymiopoulos  N. Voglis 《Planetary and Space Science》1998,46(11-12)

We present results of a study of the so-called “stickiness” regions where orbits in mappings and dynamical systems stay for very long times near an island and then escape to the surrounding chaotic region. First we investigated the standard map in the form x_i+1 = x_i+y_i+1 and y_i+1 = y_i+K/2π · sin(2πx_i) with a stochasticity parameter K = 5, where only two islands of regular motion survive. We checked now many consecutive points—for special initial conditions of the mapping—stay within a certain region around the island. For an orbit on an invariant curve all the points remain forever inside this region, but outside the “last invariant curve” this number changes significantly even for very small changes in the initial conditions. In our study we found out that there exist two regions of “sticky” orbits around the invariant curves: A small region I confined by Cantori with small holes and an extended region II is outside these cantori which has an interesting fractal character. Investigating also the Sitnikov-Problem where two equally massive primary bodies move on elliptical Keplerian orbits, and a third massless body oscillates through the barycentre of the two primaries perpendicularly to the plane of the primaries—a similar behaviour of the stickiness region was found. Although no clearly defined border between the two stickiness regions was found in the latter problem the fractal character of the outer region was confirmed.  相似文献   

Universal properties of escape in dynamical systems     

Christos Siopis  Henry E. Kandrup  G. Contopoulos  Rudolf Dvorak 《Celestial Mechanics and Dynamical Astronomy》1996,65(1-2):57-68

This paper summarizes a numerical study of the escape properties of three two-dimensional, time-independent potentials possessing different symmetries. It was found, for all three cases, that (i) there is a rather abrupt transition in the behaviour of the late-time probability of escape, when the value of a coupling parameter, , exceeds a critical value, 2. For e > e2, it was found that (ii) the escape probability manifests an initial convergence towards a nearly time-independent value, p _o(), which exhibits a simple scaling that may be universal. However, (iii) at later times the escape probability slowly decays to zero as a power-law function of time. Finally, it was found that (iv) in a statistical sense, orbits that escape from the system at late times tend to have short time Lyapounov exponents which are lower than for orbits that escape at early times.  相似文献   

Encounter frequency of Halley-like comets with the planets     

E. Lohinger  R. Dvorak  C. Froeschlé 《Earth, Moon, and Planets》1995,71(3):225-233

We present the results of a numerical study on encounter frequencies of fictitious Halley-like comets with the planets in a dynamical model of the solar system, in which we take into account the gravitational forces of the Sun and the planets Venus through Neptune. The change of the orbital elements during a close approach with a planet was carefully monitored with the aid of a thoroughly tested numerical integration method with automatic step size control. We computed the encounter frequencies of the comets' orbits using two different spheres of influence and compared the results. In both cases, it turned out that the encounter frequency of the fictitious Halley-like comets with Jupiter and Saturn is about a factor 10 to 100 higher than for the other planets. Concerning the changes of the semi-major axes and inclinations our results show that an increase and decrease of these elements is equally probable after an encounter.  相似文献   

Recent uplift and hydrothermal activity at Tangkuban Parahu volcano,west Java,Indonesia     

John Dvorak  Johannes Matahelumual  Arnold T Okamura  Harun Said  Thomas J Casadevall  Dedi Mulyadi 《Bulletin of Volcanology》1990,53(1):20-28

Tangkuban Parahu is an active stratovolcano located 17 km north of the city of Bandung in the province west Java, Indonesia. All historical eruptive activity at this volcano has been confined to a complex of explosive summit craters. About a dozen eruptions-mostly phreatic events- and 15 other periods of unrest, indicated by earthquakes or increased thermal activity, have been noted since 1829. The last magmatic eruption occurred in 1910. In late 1983, several small phreatic explosions originated from one of the summit craters. More recently, increased hydrothermal and earthquake activity occurred from late 1985 through 1986. Tilt measurements, using a spirit-level technique, have been made every few months since February 1981 in the summit region and along the south and east flanks of the volcano. Measurements made in the summit region indicated uplift since the start of these measurements through at least 1986. From 1981 to 1983, the average tilt rate at the edges of the summit craters was 40–50 microradians per year. After the 1983 phreatic activity, the tilt rate decreased by about a factor of five. Trilateration surveys across the summit craters and on the east flank of the volcano were conducted in 1983 and 1986. Most line length changes measured during this three-year period did not exceed the expected uncertainty of the technique (4 ppm). The lack of measurable horizontal strain across the summit craters seems to contradict the several years of tilt measurements. Using a point source of dilation in an elastic half-space to model tilt measurements, the pressure center at Tangkuban Parahu is located about 1.5 km beneath the southern part of the summit craters. This is beneath the epicentral area of an earthquake swarm that occurred in late 1983. The average rate in the volume of uplift from 1981 to 1983 was 3 million m³ per year; from 1983 to 1986 it averaged about 0.4 million m³ per year. Possible causes for this uplift are increased pressure within a very shallow magma body or heating and expansion of a confined aquifier.  相似文献   

Paläomagnetische Komplexuntersuchungen an Eruptiv- und Sedimentgesteinen des Böhmischen Massivs     

Vaclav Bucha  Žofíe Pokorna  Friedrich Frölich  Heiner Vollstädt 《Pure and Applied Geophysics》1965,61(1):101-112

Summary Complex methods, used at Potsdam since 1960 [4, 5, 6]³), nowadays are successfully tried for paleomagnetic studies also. Results in this direction in the following are discussed in detail.  相似文献