on the relationship between fast lyapunov indicator and periodic orbits for symplectic mappings

The computation on a relatively short time of a quantity, related to the largest Lyapunov Characteristic Exponent, called Fast Lyapunov Indicator allows to discriminate between ordered and weak chaotic motion and also, under certain conditions, between resonant and non resonant regular orbits. The aim of this paper is to study numerically the relationship between the Fast Lyapunov Indicator values and the order of periodic orbits. Using the two-dimensional standard map as a model problem we have found that the Fast Lyapunov Indicator increases as the logarithm of the order of periodic orbits up to a given order. For higher order the Fast Lyapunov Indicator grows linearly with the order of the periodic orbits. We provide a simple model to explain the relationship that we have found between the values of the Fast Lyapunov Indicator, the order of the periodic orbits and also the minimum number of iterations needed to obtain the Fast Lyapunov Indicator values.     

Estimation of the energy used to melt snow in the Tien Shan mountains and Japanese Islands

The heat needed to melt snow over the Tien Shan mountains and Japanese Islands for 10-day period (TDP) was estimated. Melting curves and a map of snowmelt duration were obtained through the long-term data from 79 stations in the Tien Shan mountains and 20 stations in the Japanese Islands. At high elevations in the mountains, about 40% of the snow melts during penultimate 10 days of snow cover. In the Japanese Islands, about 80% of the snow melts during the last 20 days of snow cover. Over the mountains, 0.13×10⁴ MJ m² year⁻¹ is needed to melt snow in the northern and western Tien Shan where maximum snow accumulation occurred. The volume of air cooled 10 °C by snowmelt amounted to 4.4×10⁶ km³ year⁻¹ over the Tien Shan mountains and 3×10⁶ km³ year⁻¹ over the Japanese Islands. The most significant impact of snowmelt on air temperature was observed at an elevation of 2500 m in the western and northern Tien Shan. Air that was cooled 10 °C could reach an elevation of 2.1 km day⁻¹. Over the Japanese Islands, energy losses from snowmelt amounted to 0.26×10¹⁴ MJ year⁻¹ and the maximum occurred over Honshu Island. The heat loss from snowmelt in the Tien Shan mountains and Japanese Islands amounted to about 2/3 of heat loss in the Eurasian continental plains.     

Modeling of opposition effects with ensembles of clusters: Interplay of various scattering mechanisms

Although the opposition phenomena observed in brightness and polarization for various astronomical objects and laboratory samples have been under intense study for many years, their explanation is still far from being complete. The shadow hiding and coherent backscattering effects are mentioned most frequently in this connection. In the present work we first discuss how other coherent scattering mechanisms, in particular interference and interaction between scatterers in the near field, influence brightness and polarization of complex ensembles of particles at small phase angles. Then we demonstrate the contribution of the different mechanisms to the scattering process in a model regolith described as an ensemble of wavelength-sized clusters as constituents. While the clusters are always densely packed, the porosity of the ensemble itself, i.e., the average distances between the clusters within the ensemble, is allowed to vary. The modeling confirms that the phase dependence of intensity and polarization of light scattered by complex structures in the backscattering domain is mainly caused by the interplay of (1) the constructive interference of waves traveling through the particle ensemble along similar paths but in opposite directions and (2) the near-field effect caused by the inhomogeneity of waves in the immediate vicinity of constituent particles. The first mechanism works more effectively in sparse ensembles, while the second one manifests itself in more compact structures of wavelength-sized scatterers at distances comparable to the wavelength. It is difficult to distinguish quantitatively their contributions in models of simple structures and even more in measurements. A number of observations, especially of moderate and low albedo objects, can, however, be explained only by invoking the near-field effect.     

Analysis of the Chaotic Behaviour of Orbits Diffusing along the Arnold Web

In a previous work [Guzzo et al. DCDS B 5, 687–698 (2005)] we have provided numerical evidence of global diffusion occurring in slightly perturbed integrable Hamiltonian systems and symplectic maps. We have shown that even if a system is sufficiently close to be integrable, global diffusion occurs on a set with peculiar topology, the so-called Arnold web, and is qualitatively different from Chirikov diffusion, occurring in more perturbed systems. In the present work we study in more detail the chaotic behaviour of a set of 90 orbits which diffuse on the Arnold web. We find that the largest Lyapunov exponent does not seem to converge for the individual orbits while the mean Lyapunov exponent on the set of 90 orbits does converge. In other words, a kind of average mixing characterizes the diffusion. Moreover, the Local Lyapunov Characteristic Numbers (LLCNs), on individual orbits appear to reflect the different zones of the Arnold web revealed by the Fast Lyapunov Indicator. Finally, using the LLCNs we study the ergodicity of the chaotic part of the Arnold web.     

The suevite of drill hole Yucatàn 6 in the Chicxulub impact crater

Abstract— The suevite breccia of the Chicxulub impact crater, Yucatàn, Mexico, is more variable and complex in terms of composition and stratigraphy than suevites observed at other craters. Detailed studies (microscope, electron microprobe, SEM, XRF) have been carried out on a noncontinuous set of samples from the drill hole Yucatàn 6 (Y6) located 50 km SW from the center of the impact structure. Three subunits can be distinguished in the suevite: the upper unit is a fine‐grained carbonate‐rich suevite breccia with few shocked basement clasts, mostly altered melt fragments, and formerly melted carbonate material; the middle suevite is a coarse‐grained suevite with shocked basement clasts and altered silicate melt fragments; the lower suevite unit is composed of shocked basement and melt fragments and large evaporite clasts. The matrix of the suevite is not clastic but recrystallized and composed mainly of feldspar and pyroxene. The composition of the upper members of the suevite is dominated by the sedimentary cover of the Yucatàn target rock. With depth in well Y6, the amount of carbonate decreases and the proportion of evaporite and silicate basement rocks increases significantly. Even at the thin section scale, melt phases of different chemistry can be identified, showing that no widespread homogenization of the melt took place. The melt compositions also reflect the heterogeneity of the deep Yucatàn basement. Calcite with characteristic feathery texture indicates the existence of formerly pure carbonate melt. The proportion of carbonate to evaporite clasts is less than 5:1, except in the lower suevite where large evaporite clasts are present. This proportion constrains the amount of CO₂ and SO_X released by the impact event.     

Afterglow light curves, viewing angle and the jet structure of γ-ray bursts

Gamma-ray bursts are often modelled as jet-like outflows directed towards the observer; the cone angle of the jet is then commonly inferred from the time at which there is a steepening in the power-law decay of the afterglow. We consider an alternative model in which the jet has a beam pattern where the luminosity per unit solid angle (and perhaps also the initial Lorentz factor) decreases smoothly away from the axis, rather than having a well-defined cone angle within which the flow is uniform. We show that the break in the afterglow light curve then occurs at a time that depends on the viewing angle. Instead of implying a range of intrinsically different jets – some very narrow, and others with a similar power spread over a wider cone – the data on afterglow breaks could be consistent with a standardized jet, viewed from different angles. We discuss the implication of this model for the luminosity function.     

Multi-Wavelength Analysis of the 29 September 2002 M2.6/2N Flare

Using TRACE EUV 171 Å line, Hα line, Zürich radio, RHESSI, and HXRS observations the 29 September 2002 flare (M2.6), which occurred in AR NOAA 0134, was analyzed. Flaring structures were compared with a potential magnetic field model (field lines and quasi-separatrix layers) made from SOHO/MDI full-disk magnetogram. Series of high-resolution SOHO/MDI magnetograms and TRACE white-light images were used to find changes in the active region at the photosphere during the flare. The flare began with a rising of a small dark loop followed by the flare brightening observed in 171 Å with TRACE and Hα lines. In radio wavelengths, first type III bursts were observed 5 min prior to the start of hard X-ray emission, indicating a pre-flare coronal activity. The main hard X-ray emission peak (at 06:36 UT) was associated with the second type III burst activity and several slowly negatively drifting features, all starting from one point on the radio spectrum (probably a shock propagating through structures with different plasma parameters). After this time a huge loop formed and three minutes later it became visible in absorption both in Hα and 171 Å EUV lines. The phase of huge dark loop formation was characterized by long-lasting, slowly negatively drifting pulsations and drifting continuum. Finally, considering this huge loop as a surge an evolution of the event under study is discussed.