The Relative Lyapunov Indicator: An Efficient Method of Chaos Detection     

Zsolt Sándor  Bálint Érdi  András Széll  Barbara Funk 《Celestial Mechanics and Dynamical Astronomy》2004,90(1-2):127-138

A recently introduced chaos detection method, the relative Lyapunov indicator (RLI) is investigated in the cases of symplectic mappings and of a continuous Hamiltonian system. It is shown that the RLI is an efficient and easy-to-calculate numerical tool in determining the true nature of individual orbits, and in separating ordered and regular regions of the phase space of dynamical systems. An application of the RLI for stability investigations of some recently discovered exoplanetary systems is also presented.  相似文献   

Sedimentary processes in a submarine canyon excavated into a temperate‐carbonate ramp (Granada Basin,southern Spain)     

ÁNGEL PUGA‐BERNABÉU  JOSÉ M. MARTÍN  JUAN C. BRAGA 《Sedimentology》2008,55(5):1449-1466

During the Late Tortonian, shallow‐water temperate carbonates were deposited in a small bay on a gentle ramp linked to a small island (Alhama de Granada area, Granada Basin, southern Spain). A submarine canyon (the ‘Alhama Submarine Canyon’) developed close to the shoreline, cross‐cutting the temperate‐carbonate ramp. The Alhama Submarine Canyon had an irregular profile and steep slopes (10° to 30°). It was excavated in two phases reflected by two major erosion surfaces, the lowermost of which was incised at least 50 m into the ramp. Wedge‐shaped and trough‐shaped, concave‐up beds of calcareous (terrigenous) deposits overlie these erosional surfaces and filled the canyon. A combination of processes connected to sea‐level changes is proposed to explain the evolution of the Alhama Submarine Canyon. During sea‐level fall, part of the carbonate ramp became exposed and a river valley was excavated. As sea‐level rose, river flows continued along the submerged, former river‐channel, eroding and deepening the valley and creating a submarine canyon. At this stage, only some of the transported conglomerates were deposited locally. As sea‐level continued to rise, the river mouth became detached from the canyon head; littoral sediments, transported by longshore and storm currents, were now captured inside the canyon, generating erosive flows that contributed to its excavation. Most of the canyon infilling took place later, during sea‐level highstand. Longshore‐transported well‐sorted calcarenites/fine‐grained calcirudites derived from longshore‐drift sandwaves poured into and fed the canyon from the south. Coarse‐grained, bioclastic calcirudites derived from a poorly sorted, bioclastic ‘factory facies’ cascaded into the canyon from the north during storms.  相似文献   

Aeolian sand sea development along the mid‐Cretaceous western Tethyan margin (Spain): erg sedimentology and palaeoclimate implications     

JUAN PEDRO RODRÍGUEZ‐LÓPEZ  NIEVES MELÉNDEZ  POPPE L. DE BOER  ANA ROSA SORIA 《Sedimentology》2008,55(5):1253-1292

The existence of a mid‐Cretaceous erg system along the western Tethyan margin (Iberian Basin, Spain) was recently demonstrated based on the occurrence of wind‐blown desert sands in coeval shallow marine deposits. Here, the first direct evidence of this mid‐Cretaceous erg in Europe is presented and the palaeoclimate and palaeoceanographic implications are discussed. The aeolian sand sea extended over an area of 4600 km². Compound crescentic dunes, linear draa and complex aeolian dunes, sand sheets, wet, dry and evaporitic interdunes, sabkha deposits and coeval extradune lagoonal deposits form the main architectural elements of this desert system that was located in a sub‐tropical arid belt along the western Tethyan margin. Sub‐critically climbing translatent strata, grain flow and grain fall deposits, pin‐stripe lamination, lee side dune wind ripples, soft‐sediment deformations, vertebrate tracks, biogenic traces, tubes and wood fragments are some of the small‐scale structures and components observed in the aeolian dune sandstones. At the boundary between the aeolian sand sea and the marine realm, intertonguing of aeolian deposits and marine facies occurs. Massive sandstone units were laid down by mass flow events that reworked aeolian dune sands during flooding events. The cyclic occurrence of soft sediment deformation is ascribed to intermittent (marine) flooding of aeolian dunes and associated rise in the water table. The aeolian erg system developed in an active extensional tectonic setting that favoured its preservation. Because of the close proximity of the marine realm, the water table was high and contributed to the preservation of the aeolian facies. A sand‐drift surface marks the onset of aeolian dune construction and accumulation, whereby aeolian deposits cover an earlier succession of coastal coal deposits formed in a more humid period. A prominent aeolian super‐surface forms an angular unconformity that divides the aeolian succession into two erg sequences. This super‐surface formed in response to a major tectonic reactivation in the basin, and also marks the change in style of aeolian sedimentation from compound climbing crescentic dunes to aeolian draas. The location of the mid‐Cretaceous palaeoerg fits well to both the global distribution of other known Cretaceous erg systems and with current palaeoclimate data that suggest a global cooling period and a sea‐level lowstand during early mid‐Cretaceous times. The occurrence of a sub‐tropical coastal erg in the mid‐Cretaceous of Spain correlates with the exposure of carbonate platforms on the Arabian platform during much of the Late Aptian to Middle Albian, and is related to this eustatic sea‐level lowstand.  相似文献   

Short‐duration contact metamorphism of calcareous sedimentary rocks by Neoproterozoic Franklin gabbro sills and dykes on Victoria Island,Canada     

P. I. NABELEK  J. H. BÉDARD  M. HRYCIUK  B. HAYES 《Journal of Metamorphic Geology》2013,31(2):205-220

This contribution addresses contact metamorphism and fluid flow in calcareous rocks of the Neoproterozoic Shaler Supergroup on Victoria Island, Arctic Canada. These processes occurred due to intrusion of gabbroic sills and dykes at c. 720 Ma during the Franklin magmatic event, which was associated with the break‐up of Rodinia. The intrusive sheets (sills and dykes) are a few metres to ～50 m thick. Metasedimentary rocks were examined in three locations with very good exposures of vertical dykes feeding horizontal sills, the Northern Feeder Dyke (NFD) complex, the Southern Feeder Dyke (SFD) complex and the Uhuk Massif. In the NFD and SFD complexes, protoliths were limestones and dolostones with minor silicates, and at the Uhuk Massif, the protoliths were silty dolostones. At the time of magma emplacement, these locations were at depths of 1–4 km. The widths of contact aureoles are only several decametres wide, commensurate with thicknesses of the dykes and sills. Splays of tremolite mark incipient metamorphism. Highest grade rocks in the NFD and SFD complexes contain the prograde assemblage diopside + phlogopite whereas at Uhuk they contain the assemblage vesuvianite + garnet + diopside. The assemblages are successfully modelled with T–X(CO₂)^fluid pseudosections that suggest achievement of CO₂‐rich fluid compositions due to early decarbonation reactions, followed by influx of aqueous fluids after peak metamorphism. Rapid heating of host rocks and short near‐peak temperature intervals are demonstrated by the prevalent morphology of diopside as radial splays of acicular crystals that appear to pseudomorph tremolite and by incomplete recrystallization of calcite in marbles. Calcsilicates in the roof of one sill at Uhuk experienced metasomatic influx of Fe that is evidenced by nearly pure andradite rims on grossular garnet. Vesuvianite, which overgrew the grossular portions of garnet, also contains ferric iron. Vesuvianite was partially consumed during retrograde growth of serpentine and andradite. The occurrence of serpentine in high‐grade portions of aureoles is consistent with eventual levelling‐off of temperatures between 350 and 400 °C, an inference that is supported by modelled conductive heat transfer from the cooling magma sheets. Focused fluid flow near intrusion‐wall rock contacts is demonstrated by narrow zones of anomalously low δ¹³C and δ¹⁸O values of carbonate minerals. Although the up to 5‰ decrease of both δ¹³C and δ¹⁸O values from sedimentary values is much smaller than is typical for calcsilicate aureoles around large plutons, it is greater than what could have been achieved by decarbonation alone. The decrease in δ¹³C is attributed to fluid‐mediated exchange with organic low‐¹³C carbon that is dispersed through the unmetamorphosed rocks and the decrease in δ¹⁸O is attributed to fluid‐mediated isotopic exchange with the gabbroic intrusive sheets. This study shows that when gabbroic sills and dykes intrude a sedimentary basin, (i) contact aureoles are likely to be narrow, only on the scale of several decametres; (ii) short high‐temperature regimes prevent achievement of equilibrium metamorphic textures; and (iii) T–X(CO₂)^fluid paths in calcareous contact aureoles are likely to be complex, reflecting a transition from prograde decarbonation reactions to influx of aqueous fluids during cooling.  相似文献   

The perturbations of the orbital elements of Trojan asteriods     

Bálint Érdi 《Celestial Mechanics and Dynamical Astronomy》1981,24(4):377-390

An asymptotic solution for the cylindrical coordinates of Trojan asteroids is derived by using a three-variable expansion method in the elliptic restricted three-body problem. The perturbations of the orbital elements are obtained from this solution by applying the formulas of the two-body problem. The main perturbations of the mean motion are studied in detail.  相似文献   

High-resolution observations of solar radio bursts with multi-element compound interferometers at 3.75 and 9.4 GHz     

Shinzo Énomé  Takakiyo Kakinuma  Haruo Tanaka 《Solar physics》1969,6(3):428-441

High-resolution observations of solar radio bursts made simultaneously with multi-element compound interferometers at 3.75 and 9.4 GHz are presented.Preliminary results are: (1) The burst of December 16, 1967 showed a change in polarization distribution in the radio source, which suggests a magnetic field change in the source. (2) The existence of the multi-source burst is also confirmed at 3.75 GHz. (3) The source size of the impulsive burst is estimated to be 0.'5. (4) Among the GRF bursts there seem to be two kinds; one has a large angular size and the other has a small one.A brief discussion is given of the burst of December 16, 1967.  相似文献   

Critical inclination of Trojan asteroids     

Bálint Érdi 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):435-441

The author's earlier solution for Trojan asteroids is developed further. It is shown that depending on the amplitude of libration around the Lagrangian point L₄, there is a critical inclination which determines the sign of the variation of the ascending node. If the orbital inclination of a Trojan is smaller than the critical one, then the ascending node decreases and otherwise it increases. The variation of the eccentricity and of the longitude of the perihelion has also a dependence on the critical inclination.  相似文献   

Granulometric investigations of loess profiles in Hungary     

Éva Kis 《GeoJournal》1995,36(2-3):151-156

The granulometric analysis of loess varieties is meant to contribute to the subdivision of loess sequences, to the reconstruction of the environments of loess formation (identifying areas of loess origin [from where the dust derives], geographical obstacles to transport, contemporary wind directions [through drawing isokatharoses lines connecting points with identical FG values] and even wind velocities) and subsequent changes in climatic and geographical conditions. It was investigated whether loesses and loess-like deposits can be described by a generalised grain size parameter (fineness grade, FG) or to what extent other granulometric indices can lead to a more differentiated picture of grain size variation. Fineness grade was used to denominate sediments and to identify finer and coarser sections in the series;K _d index indicates the lithostratigraphical positions of cold stages (maximum values) and warm stages (minimum values); finesorting (S _o) points to eolian accumulation, while fluvial deposits (bedload, saltated and suspended load) are poorly sorted;kurtosis (K) allows conclusions for the reworking of the deposit andasymmetry (S_k) indicates the factor active in the accumulation of the deposit.The paper concentrates primarily on the study of variation in the vertical profile of deposits. Along with other indices, fineness grade was found useful in distinguishing between loess varieties and other sediments and could even replace the function of the conventional index median value (M_d).  相似文献   

A fourth-order solution of the ideal resonance problem     

Bálint Érdi  József Kovács 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):221-230

The second-order solution of the Ideal Resonance Problem, obtained by Henrard and Wauthier (1988), is developed further to fourth order applying the same method. The solutions for the critical argument and the momentum are expressed in terms of elementary functions depending on the time variable of the pendulum as independent variable. This variable is related to the original time variable through a Kepler-equation. An explicit solution is given for this equation in terms of elliptic integrals and functions. The fourth-order formal solution is compared with numerical solutions obtained from direct numerical integrations of the equations of motion for two specific Hamiltonians.  相似文献   

Pre-permian depositional environments around the brabant massif in Belgium,The Netherlands and Germany     

M.J.M. Bless  J. Bouckaert  R. Conil  E. Groessens  W. Kasig  E. Paproth  E. Poty  M. Van Steenwinkel  M. Streel  R. Walter 《Sedimentary Geology》1980,27(1):1-81

Pre-Permian sedimentation in northwestern Europe has been controlled by the structural evolution of this area. Cambro-Silurian deposition has been influenced by partly synsedimentary movements (among others Ordovician-Silurian uplift south of the Brabant/Condroz zone, such as the Stavelot-Venn Massif).Presence, respectively absence of important late Caledonian deformation has subdivided northwestern Europe into three major sedimentary environments during the Devono-Carboniferous: the Caledonian fold belt and the Cornwall-Rhenish Basin which are separated by the Belgo-Dutch platform.Subsequently, the Hercynian or Variscan orogenies have gradually reduced the sedimentary area and produced the overall withdrawal of the marine environment. Eventually, large-scale overthrusts - such as the Dinant Nappe - masked parts of the original sedimentary basins.  相似文献