Monte Carlo Modeling of the Thermal Conductivity of Porous Cometary Ice

The basic structure of comet nuclei is an aggregation of grains, with a size distribution that extends over several orders of magnitude and a similar distribution of pores. Although attempts have been made to assess the effect of porosity on the thermal conductivity, the effect of pore size distribution has been ignored. Modeling a porous structure with a wide size distribution would require a very fine 3-D grid, so as to accommodate the smallest and largest voids. In order to circumvent this difficulty, we adopt a hierarchical procedure. Thus we assume a random and fractal porous structure and use a 3-D Monte Carlo model. The basic configuration is a cube made of unit cells of two types, (ice) filled and void, randomly distributed. Their relative number corresponds to a prescribed porosity. We solve the heat transport equation for this cube until a steady state is obtained, and from this solution the effective thermal conductivity is derived. The calculations are repeated for a range of porosities and temperatures, since the ice conductivity is temperature dependent. The basic cube serves as a unit filled cell in a larger cube, and in this way the hierarchical structure of the medium is built up.We find that the thermal conductivity is lowered by several orders of magnitude at high porosities. The correction factor, obtained as a fit to the results of our calculations, is expressed as a smooth function of the porosity, which tends to zero as the porosity approaches the percolation threshold of the solid. If only the porosity of the medium is known, this correction is not uniquely determined, but rather a range of values is possible. Only if the size distribution of the pores is known does the correction become uniquely determined.     

Sungrazing Comets: Properties of Nuclei and in Situ Detectability of Cometary Ions at 1 AU

A one-dimensional sublimation model for cometary nuclei is used to derive size limits for the nuclei of sungrazing comets and to estimate oxygen ion fluxes at 1 AU from their evaporation. Given that none of the ≈300 sungrazers detected by the SOlar and Heliospheric Observatory (SOHO) was observed after disappearing behind the sun, and that small nuclei with a radius of ≈3.5 m could be observed, it is assumed that all SOHO sungrazers were completely destroyed. For the case that sublimation alone is sufficient for destruction, the model yields an upper size limit as a function of nuclear density ?, albedo A, and perihelion distance q. If the density of the nuclei is that typical of porous ice (600 kg m⁻³), the maximum size is 63 m. These results confirm similar model calculations by Weissman (1983). An analytical expression is derived that approximates the model results well. We discuss possible modifications of our results by different disruption mechanisms. While disruption by thermal stress does not change the upper size limits significantly, they may be somewhat increased by tidal disruption (up to 100 m for a density of 600 kg m⁻³), dependent on the isotropy of the sublimation process and the tensile strength of the comet. Implications for the Kreutz family of sungrazers are discussed.Oxygen ions from the sublimation of sungrazing comets form a tail. Fluxes from this tail are sufficiently high to be measured at 1 AU by particle detectors on spacecraft, but the duration of a tail crossing is only about half an hour. Therefore, the probability of a spacecraft actually encountering a tail of an evaporating sungrazer is only of the order of 2% per year.     

Monte Carlo Simulation of Solar Active-Region Energy

A Monte Carlo approach to solving a stochastic-jump transition model for active-region energy (Wheatland and Glukhov: Astrophys. J. 494, 858, 1998; Wheatland: Astrophys. J. 679, 1621, 2008) is described. The new method numerically solves the stochastic differential equation describing the model, rather than the equivalent master equation. This has the advantages of allowing more efficient numerical solution, the modeling of time-dependent situations, and investigation of details of event statistics. The Monte Carlo approach is illustrated by application to a Gaussian test case and to the class of flare-like models presented in Wheatland (Astrophys. J. 679, 1621, 2008), which are steady-state models with constant rates of energy supply, and power-law distributed jump transition rates. These models have two free parameters: an index (δ), which defines the dependence of the jump transition rates on active-region energy, and a nondimensional ratio ( ) of total flaring rate to rate of energy supply. For the nondimensional mean energy of the active-region satisfies , resulting in a power-law distribution of flare events over many decades of energy. The Monte Carlo method is used to explore the behavior of the waiting-time distributions for the flare-like models. The models with δ≠0 are found to have waiting times that depart significantly from simple Poisson behavior when . The original model from Wheatland and Glukhov (Astrophys. J. 494, 858, 1998), with δ=0 (i.e., no dependence of transition rates on active-region energy), is identified as being most consistent with observed flare statistics.     

An Algebraic Method to Compute the Critical Points of the Distance Function Between Two Keplerian Orbits

We describe an efficient algorithm to compute all the critical points of the distance function between two Keplerian orbits (either bounded or unbounded) with a common focus. The critical values of this function are important for different purposes, for example to evaluate the risk of collisions of asteroids or comets with the Solar system planets. Our algorithm is based on the algebraic elimination theory: through the computation of the resultant of two bivariate polynomials, we find a 16th degree univariate polynomial whose real roots give us one component of the critical points. We discuss also some degenerate cases and show several examples, involving the orbits of the known asteroids and comets.      

Cometary charge exchange diagnostics in UV and X‐ray

Since the initial discovery of cometary charge exchange emission, more than 20 comets have been observed with a variety of X‐ray and UV observatories. This observational sample offers a broad variety of comets, solar wind environments and observational conditions. It clearly demonstrates that solar wind charge exchange emission provides a wealth of diagnostics, which are visible as spatial, temporal, and spectral emission features. We review the possibilities and limitations of each of those in this contribution (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy and Stress Distributions in Ellipsoids

A closed form solution for a uniform, isotropic, homogenous, rotating, and self-gravitating solid ellipsoid is analyzed as a function of its material properties and angular momentum. This solution recovers the classical results for an incompressible material, namely that Maclaurin and Jacobi ellipsoids minimize the total strain energy of an ellipsoid. As the solid becomes compressible we find that Maclaurin-type spheroids are energetically preferred over all relevant values of angular momentum, although the gradient toward these spheroids is weak, at best. Compressibility allows the weak minima to encompass most observed asteroid shapes.Using this solution, a simple failure criterion of maximum principal stress is examined. Under this failure criterion, an ellipsoid rotating at a sufficiently rapid rate can have positive stress on the periphery and in the polar regions. Contours for this failure theory are compared with estimated asteroid rotation rates and ellipsoidal shape estimates. For compressible materials there is surprisingly good correspondence for such a simple theory and criterion, with the failure curve delimiting a demarcation that few observed asteroids cross.This research has implications for the shapes and distortions of rubble pile asteroids. In particular, the theory gives insight into the internal stress field and the effects of energy dissipation in an asteroid after it has been boosted into a nonminimum energy configuration due to an impact event or a close flyby with a planet. Internally there are double-lobed compressive stress regions reminiscent of the external shape of Kleopatra.     

A Monte Carlo approach to scattering off surfaces of triaxial ellipsoids

We developed a Monte Carlo procedure to calculate the scattering properties of ellipsoidal bodies. Although originally intended for application to Saturn's ring A, the technique can also be applied to surfaces of asteroids modeled as triaxial ellipsoids. A simple coordinate transformation allows the Monte Carlo approach to be quick and efficient. By modifying the well-known acceptance-rejection technique to reflect the dependence of surface albedo on the angle of incidence, we can apply this technique to any surface scattering function. The backscattered brightness and the phase curve at small phase angles can be calculated to a high degree of accuracy in a small amount of computing time. The technique is shown to be accurate for problems that have analytic solutions. Light curve amplitudes of biaxial ellipsoids as a function of the axial ratio are plotted for several scattering laws. The application of this technique to a direct integration approach is also considered.     

More Microwave Observations of Saturn: Modeling the Ring with a Monte Carlo Radiative Transfer Code

We present a second epoch of Very Large Array Saturn observations taken in February 1997 spanning wavelengths 1.3-21 cm. These observations complement earlier observations at Saturn's autumnal equinox in November 1995. In this epoch, however, we generally have better signal-to-noise ratios and the ring inclination of the present observations was −5.0°, whereas the previous observations were made with ring inclination +2.7°.Our observations confirm the latitudinal structure on the saturnian disk as seen at 2.0, 3.6, and 6.1 cm. We also see some latitudinal structure at 1.3 cm for the first time. The details of this structure have changed dramatically from those reported by I. de Pater and J. R. Dickel (1991, Icarus94, 474-492) for the 1980s and are consistent with those seen in F. van der Tak et al. (1999, Icarus142, 125-147). The most prominent features are a pair of brightness enhancements just inside the edges of the Equatorial Zone.The rings do not show the east-west asymmetry seen in our previous epoch, perhaps indicative of a viewing angle effect on the scattering properties of the rings. The radial trend in brightness in the ansae is generally consistent with that expected from optical depth variations and increasing distance from the source of scattered light. In particular the increased optical depth towards the center of the C ring is evident. Azimuthal variation in brightness in the C ring shows the forward scattering expected of Mie scattering. By contrast, the A and B rings show little or no azimuthal variation.We present Monte Carlo simulations of the ring brightness under the assumptions of isotropic and Mie scattering. These are the first synthetic maps of Saturn which can be directly compared to the images we obtained. Neither model fits all the data well. However, a hybrid model combining isotropic and Mie scattering does fit well. We interpret the consistency with isotropic scattering in the outer rings as an indication that near-field effects may be important. This in turn implies geometrically thin rings, as predicted by dynamical simulations of these rings.     

A Monte Carlo template based analysis for air-Cherenkov arrays

We present a high-performance event reconstruction algorithm: an Image Pixel-wise fit for Atmospheric Cherenkov Telescopes (ImPACT). The reconstruction algorithm is based around the likelihood fitting of camera pixel amplitudes to an expected image template. A maximum likelihood fit is performed to find the best-fit shower parameters. A related reconstruction algorithm has already been shown to provide significant improvements over traditional reconstruction for both the CAT and H.E.S.S. experiments. We demonstrate a significant improvement to the template generation step of the procedure, by the use of a full Monte Carlo air shower simulation in combination with a ray-tracing optics simulation to more accurately model the expected camera images. This reconstruction step is combined with an MVA-based background rejection.Examples are shown of the performance of the ImPACT analysis on both simulated and measured (from a strong VHE source) gamma-ray data from the H.E.S.S. array, demonstrating an improvement in sensitivity of more than a factor two in observation time over traditional image moments-fitting methods, with comparable performance to previous likelihood fitting analyses. ImPACT is a particularly promising approach for future large arrays such as the Cherenkov Telescope Array (CTA) due to its improved high-energy performance and suitability for arrays of mixed telescope types.     

The Diagnosis of Complex Rotation in the Lightcurve of 4179 Toutatis and Potential Applications to Other Asteroids and Bare Cometary Nuclei

The analysis of radar observations of the asteroid 4179 Toutatis by Hudson and Ostro (1995, Science270, 84-86) yielded a complex spin state. We revisit the visible lightcurve data on Toutatis (Spencer et al. 1995, Icarus117, 71-89) to explore the feasibility of using a rotational lightcurve to recover the signature of an excited spin state. For this, we apply Fourier transform and CLEAN algorithm (WindowCLEAN). WindowCLEAN yields clear and precise frequency signatures associated with the precession of the long axis about the total angular momentum vector and a combination of this precession and rotation about the long axis. For a long-axis mode state, our periodicities for Toutatis yield a mean long-axis precession period, P_φ, of 7.38 days and a rotation period around the long axis, P_ψ, of 5.38 days, which compare well with the respective periods of 7.42 and 5.37 days derived by Ostro et al. (1999, Icarus137, 122-139) and represent an independent confirmation of these values. We explain why the dramatic change in the Earth-Toutatis-Sun geometry during the time that the lightcurve was obtained has little effect on the final results obtained. Using the Toutatis example as a guide, we discuss the capabilities as well as the limitations on deriving information about complex spin states from asteroidal lightcurves.     

Catastrophic rupture of lunar rocks: A Monte Carlo simulation

A computer model based on Monte Carlo techniques was developed to simulate the destruction of lunar rocks by catastrophic rupture due to meteoroid impact. Energies necessary to accomplish catastrophic rupture were derived from laboratory experiments. A crater-production rate derived from lunar rocks was utilized to calculate absolute time scales.Calculated median survival times for crystalline lunar rocks are 1.9, 4.6, 10.3, and 22 m.y. for rock masses of 10, 10², 10³, and 10⁴ g respectively. Corresponding times of 6, 14.5, 32, and 68 × 10⁶ yr are required, before the probability of destruction reaches 0.99. These results are consistent with absolute exposure ages measured on returned rocks.Some results also substantiate previous conclusions reached by others: the catastrophic rupture process is significantly more effective in obliterating lunar rocks compared to mass wasting by single particle abrasion. The view is also corroborated that most rocks presently on the lunar surface are either exhumed from the regolith or fragments of much larger boulders, rather than primary ejecta excavated from pristine bedrock.Permanent address: Max-Planck-Institut für Kernphysik, 6900 Heidelberg, F.R.G.     

A new data structure for accelerating kinetic Monte Carlo method

The kinetic Monte Carlo simulation is a rigorous numerical approach to study the chemistry on dust grains in cold dense interstellar clouds. By tracking every single reaction in chemical networks step by step, this approach produces more precise results than other approaches but takes too much computing time. Here we present a method of a new data structure, which is applicable to any physical conditions and chemical networks, to save computing time for the Monte Carlo algorithm. Using the improved structure,the calculating time is reduced by 80 percent compared with the linear structure when applied to the osu-2008 chemical network at 10K. We investigate the effect of the encounter desorption in cold cores using the kinetic Monte Carlo model with an accelerating data structure. We found that the encounter desorption remarkably decreases the abundance of grain-surface H_2 but slightly influences the abundances of other species on the grain.     

原子钟噪声的蒙特卡络模拟方法

讨论了原子钟噪声的蒙特卡络模拟方法．具体过程是：先产生模拟所需的正态分布随机数，从实际钟的阿仑方差估算出噪声电平，然后用１组递点函数产生高质量的模拟钟时差的随机序列．在对１台商品铯钟进行具体模拟后，给出了真实数据与模拟值的阿仑方差之问的相符程度，最后对实际问题进行了分析．     

A Monte Carlo study of polarization structures in the Thomson-scattered line radiation

Thomson scattering is often invoked to explain broad wing features that are seen in various objects including active galactic nuclei and symbiotic stars. Despite the wavelength-independent scattering cross-section of Thomson scattering, the line flux may exhibit wavelength-dependent linear degree of polarization, because various parts of emission wings are contributed by photons with different scattering numbers. Specifically, more scattered and hence more weakly polarized photons tend to fill the farther wing parts from the line centre, while the neighbourhood of the line centre is dominated by less-scattered photons with higher degree of polarization. Using a Monte Carlo technique, we investigate the polarization structure of Thomson-scattered line radiation. A detailed analysis of polarization structure formation is conducted by investigating the dependence of the polarization and profile width on the scattering number for various finite electron scattering slabs. Significantly varying degree of polarization is obtained when the scattering medium has Thomson optical depth  τ_Th≥ 1  . We present our high-resolution spectrum of the symbiotic star V1016 Cyg obtained with the Bohyunsan Optical Echelle Spectrograph (BOES) in order to fit the broad profile around Hα by electron scattering wings adopting an oblate spheroidal geometry with Thomson optical depth  τ_Th= 0.5  and electron temperature   T _e= 6.2 × 10⁴  K  . Local maxima in the linear degree of polarization of Thomson-scattered line radiation are expected to appear in the spectral regions characterized by the average scattering number ≃1.     

General relativistic magnetohydrodynamic and Monte Carlo Modeling of sagittarius A*

Using the tunneling method we derive the Hawking temperature of the nonextremal rotating charged black hole in the Gödel universe of five-dimensional minimal supergravity theory found by Wu. We successfully recovered the tunneling probability of charged Dirac particles and the expected Hawking temperature of the black hole, which is exactly consistent with that obtained by other methods.     

A Monte Carlo model for the gardening of the lunar regolith

The processes of movement and turnover of the lunar regolith are described by a Monte Carlo model, which includes the effects of collisions by particles from 10^?7 g to 10¹⁰ g. The movement of material by the direct cratering process is the dominant mode, but slumping is also included for angles exceeding the static angle of repose. Using a group of interrelated computer programs a large number of properties are calculated, including topography, formation of layers, depth of the disturbed layer, nuclear track distributions, cosmogenic nuclides and others. In the most complex program, the history of a 36 point square array is followed for times up to 4 × 10⁸ yr. As expected the histories generated are complex and exhibit great variety. Because a crater covers much less area than its ejecta blanket, there is a tendency for the height change at a test point to exhibit the ‘gambler's ruin’ phenomenon: periods of slow accumulation followed by sudden excavation. In general the agreement with experiment and observation seems good. Two areas of disagreement stand out. First, the calculated surface is rougher than that observed. This problem is understood, and will not occur in a newer version of the model. Second, the observed bombardment ages, of the order of 4 × 10⁸ yr, are shorter than expected (by perhaps a factor of 5). We cannot accept Fireman's (1974) explanation; this remains an important puzzle.     

A Monte Carlo investigation of Jovian perturbations on short-period comet orbits

We present statistical distributions of Jovian perturbations on short-period comet orbits resulting from accurate numerical integrations. Our sample of 60, 000 cometary orbits with low inclinations and random orientations is characterized by perihelia between 0 and 7 AU and aphelia between 4 and 13 AU. The perturbations considered are those experienced because of Jupiter's gravitation per orbital revolution by the comets. Regularization and accurate step-length control in the numerical integration gives statistical results appreciably different from those computed by Rickman and Vaghi (1978). Their use of a crude method of integration led to erroneous results for close encounters. Strong asymmetries of the $\text{δ(}\text{1}\text{a}\text{)}$ distributions, in particular for the extreme tails, are observed for perihelion- or aphelion-tangent orbits. These orbits are also shown to experience the strongest energy perturbations on the average. Some results concerning the perturbations of Tisserand parameters are indicated. The perturbation distributions for the angular elements are described and discussed. The role of the minimum distance from Jupiter as an indicator of perturbations is investigated.