Chaotic Diffusion And Effective Stability of Jupiter Trojans     

Kleomenis Tsiganis  Harry Varvoglis  Rudolf Dvorak 《Celestial Mechanics and Dynamical Astronomy》2005,92(1-3):71-87

It has recently been shown that Jupiter Trojans may exhibit chaotic behavior, a fact that has put in question their presumed long term stability. Previous numerical results suggest a slow dispersion of the Trojan swarms, but the extent of the ‘effective’ stability region in orbital elements space is still an open problem. In this paper, we tackle this problem by means of extensive numerical integrations. First, a set of 3,200 fictitious objects and 667 numbered Trojans is integrated for 4 Myrs and their Lyapunov time, T_L, is estimated. The ones following chaotic orbits are then integrated for 1 Gyr, or until they escape from the Trojan region. The results of these experiments are presented in the form of maps of T_Land the escape time, T_E, in the space of proper elements. An effective stability region for 1 Gyr is defined on these maps, in which chaotic orbits also exist. The distribution of the numbered Trojans follows closely the T_E=1 Gyr level curve, with 86% of the bodies lying inside and 14% outside the stability region. This result is confirmed by a 4.5 Gyr integration of the 246 chaotic numbered Trojans, which showed that 17% of the numbered Trojans are unstable over the age of the solar system. We show that the size distributions of the stable and unstable populations are nearly identical. Thus, the existence of unstable bodies should not be the result of a size-dependent transport mechanism but, rather, the result of chaotic diffusion. Finally, in the large chaotic region that surrounds the stability zone, a statistical correlation between T_LandT_E is found.  相似文献   

Generalized Lyapunov exponents indicators in Hamiltonian dynamics: An application to a double star system     

E. Lohinger  C. Froeschlé  R. Dvorak 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):315-322

The Lyapunov characteristic numbers (LCNs) which are defined as the mean value of the distribution of the local variations of the tangent vectors to the flow (=ln _k ⁱ ) (see Froeschlé, 1984) have been found to be sensitive indicators of stochasticity. So we computed the distribution of these local variations and determined the moments of higher order for the integrable and stochastic regions in a binary star system with =0.5.  相似文献   

Stability of motion in the Sitnikov 3-body problem     

P. Soulis  T. Bountis  R. Dvorak 《Celestial Mechanics and Dynamical Astronomy》2007,99(2):129-148

We study the stability of motion in the 3-body Sitnikov problem, with the two equal mass primaries (m ₁ = m ₂ = 0.5) rotating in the x, y plane and vary the mass of the third particle, 0 ≤ m ₃ < 10⁻³, placed initially on the z-axis. We begin by finding for the restricted problem (with m ₃ = 0) an apparently infinite sequence of stability intervals on the z-axis, whose width grows and tends to a fixed non-zero value, as we move away from z = 0. We then estimate the extent of “islands” of bounded motion in x, y, z space about these intervals and show that it also increases as |z| grows. Turning to the so-called extended Sitnikov problem, where the third particle moves only along the z-axis, we find that, as m ₃ increases, the domain of allowed motion grows significantly and chaotic regions in phase space appear through a series of saddle-node bifurcations. Finally, we concentrate on the general 3-body problem and demonstrate that, for very small masses, m ₃ ≈ 10⁻⁶, the “islands” of bounded motion about the z-axis stability intervals are larger than the ones for m ₃ = 0. Furthermore, as m ₃ increases, it is the regions of bounded motion closest to z = 0 that disappear first, while the ones further away “disperse” at larger m ₃ values, thus providing further evidence of an increasing stability of the motion away from the plane of the two primaries, as observed in the m ₃ = 0 case.  相似文献   

The dynamical structure of the habitable zone in the HD 38529, HD 168443 and HD 169830 systems     

B. Érdi  R. Dvorak  Zs. Sándor  E. Pilat-Lohinger  B. Funk 《Monthly notices of the Royal Astronomical Society》2004,351(3):1043-1048

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The stability of the terrestrial planets with a more massive 'Earth'     

Áron Süli  Rudolf Dvorak  Florian Freistetter 《Monthly notices of the Royal Astronomical Society》2005,363(1):241-250

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Nekhoroshev stability at L₄ or L₅ in the elliptic-restricted three-body problem – application to Trojan asteroids     

Ch. Lhotka  C. Efthymiopoulos  R. Dvorak 《Monthly notices of the Royal Astronomical Society》2008,384(3):1165-1177

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Geometry of the September 1971 eruptive fissure at Kilauea volcano,Hawaii     

John J Dvorak 《Bulletin of Volcanology》1990,52(7):507-514

A three-dimensional model has been used to estimate the location and dimensions of the eruptive fissure for the 24–29 September 1971 eruption along the southwest rift zone of Kilauea volcano, Hawaii. The model is an inclined rectangular sheet embedded in an elastic half-space with constant displacement on the plane of the sheet. The set of best model parameters suggests that the sheet is vertical, extends from a depth of about 2 km to the surface, and has a length of about 14 km. Because this sheet intersects the surface where eruptive vents and extensive ground cracking formed during the eruption, this sheet probably represents the conduit for erupted lava. The amount of displacement perpendicular to the sheet is about 1.9 m, in the middle range of values measured for the amount of opening across the September 1971 eruptive fissure. The thickness of the eruptive fissure associated with the January 1983 east rift zone eruption was determined in an earlier paper to be 3.6 m, about twice the thickness determined here for the September 1971 eruption. Because the lengths (12 km for 1983 and 14 km for 1971) and heights (about 2 km) of the sheet models derived for the January 1983 and September 1971 rift zone eruptions are nearly identical, the greater thickness for the January 1983 eruptive fissure implies that the magma pressure was about a factor of two greater to form the January 1983 eruptive fissure. Because the September 1971 and January 1983 eruptive fissures extent to depths of only a few kilometers, the region of greatest compressive stress produced along the volcano's flank by either of these eruptive fissures would also be within a few kilometers of the surface. Previous work has shown that rift eruptions and intrusions contribute to the buildup of compressive stress along Kilauea's south flank and that this buildup is released by increased seismicity along the south flank. Because south flank earthquakes occur at significantly greater depths, i.e., from 5 to 13 km, than the vertical extent of the 1971 and 1983 eruptiv fissures, the depth of emplacement of these eruptive fissures cannot be the main factor in controlling the hypocentral depths of south flank earthquakes. Two possible explanations for the occurrence of south flank earthquakes in the depth range of 5–13 km are (1) a deeper pressure source, possibly related to deeper magma storage within the rift zone, and (2) a lowstrength region located between 5 and 13 km beneath Kilauea's south flank, possibly at the interface between oceanic sediments and the base of the Hawaiian volcanics.  相似文献   

History of earthquakes and vertical ground movement in Campi Flegrei caldera, Southern Italy: comparison of precursory events to the A.D. 1538 eruption of Monte Nuovo and of activity since 1968     

John J. Dvorak  Paolo Gasparini 《Journal of Volcanology and Geothermal Research》1991,48(1-2)

The record of felt earthquakes around Naples Bay in southern Italy is probably complete since the mid-15th century. According to this record, intense earthquake swarms originating beneath Campi Flegrei, an explosive caldera located along the north coast of Naples Bay, have occurred only twice: (1) before the only historical eruption in Campi Flegrei in 1538; and (2) from mid-1983 to December 1984. Earthquake activity during the earlier period, which began at least a few years, and possibly as many as 30 years, before the 1538 eruption, damaged many buildings in the city of Pozzuoli, located near the center of Campi Flegrei. Minor seismic activity, which consisted of only a few felt earthquakes, occurred from 1970 to 1971. The second period of intense earthquake swarms lasted from mid-1983 to 1984, again damaging many buildings in Pozzuoli. Two periods of uplift along the shoreline within Campi Flegrei have also been noted since the mid-15th century: (1) during the few decades before the 1538 eruption; and (2) as two distinct episodes since 1968. Uplift of a few meters probably occurred a few decades before the 1538 eruption; uplift of as much as 3.0 m has occurred in Pozzuoli since 1968.These similarities strongly suggest that, for the first time in 440 years, the same process that caused intense local earthquake swarms and uplift in the early 1500's and led to an eruption in 1538, has again occurred beneath Campi Flegrei. Though no major seismicity or uplift has occurred since December 1984, because of the large amount of extensional strain accumulated during the past two decades, if a third episode of seismicity and rapid uplift occurs, it may lead to an eruption within several months after the resumption of activity.  相似文献   

INTERPRETING THE LARGE LIMB ERUPTION OF JULY 9, 1982     

Jordan  Stuart  Garcia  Adriana  Bumba  Vaclav 《Solar physics》1997,173(2):359-376

A time series of K3 spectroheliograms taken at the Coimbra Observatory exhibits an erupting loop on the east limb on July 9, 1982 in active region NOAA 3804. The Goddard SMM Hard X-Ray Burst Spectrometer (HXRBS) observations taken during this period reveal a hard X-ray flare occurring just before the loop eruption is observed, and SMS-GOES soft X-ray observations reveal a strong long-duration event (LDE) following the impulsive phase of the flare. A Solwind coronagram exhibits a powerful coronal mass ejection (CME) associated with the erupting loop. H flare and prominence observations as well as centimeter and decimeter radio observations of the event are also reviewed. A large, north–south-oriented quiescent prominence reported within the upper part of the CME expansion region may play a role in the eruption as well. The spatial and temporal correlations among these observations are examined in the light of two different current models for prominence eruption and CME activation: (1) The CME is triggered by the observed hard X-ray impulsive flare. (2) The CME is not triggered by a flare, and the observed soft X-ray flare is an LDE due to reconnection within the CME bubble. It is concluded that this event is probably of a mixed type that combines characteristics of models (1) and (2). The July 9 event is then compared to three other energetic CME and flare eruptions associated with the same active-region complex, all occurring in the period July 9 through September 4, 1982. It is noted that these four energetic events coincide with the final evolutionary phase of a long-lasting active-region complex, which is discussed in a companion paper (Bumba, Garcia, and Jordan, 1997). The paper concludes by addressing the solar flare myth controversy in the light of this work.  相似文献   

Preface     

R. Dvorak  J. Henrard 《Celestial Mechanics and Dynamical Astronomy》2000,78(1-4):1-1

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