Monte Carlo calculations of lunar Regolith thickness distributions

Regolith thickness distributions associated with crater populations observed on selected maria surfaces have been calculated using a Monte Carlo computer technique. The calculations assume that the crater type produced and the volume of debris ejected and added to the growing regolith depends on the ratio of crater diameter and regolith thickness present at the time and place of formation of each crater. Calculated thickness distributions obtained are in agreement with those estimated using a previously described statistical method based on the morphology of small lunar craters. Additionally, the Monte Carlo calculations accurately predict the size frequency distributions of the same types of small, fresh lunar craters used in the statistical method. The model employed is therefore realistic. Furthermore, the model calculations presented are shown to have value (a) in predicting the thickness of the regolith from crater populations at various lunar sites, (b) relative dating applications in which crater populations are compared, and (c) in interpreting the origin and history of regolith deposits at specific locations.     

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 This problem is understood, and will not occur in a newer version of the model.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.     

Monte Carlo simulation of GCR neutron capture production of cosmogenic nuclides in stony meteorites and lunar surface

Abstract— A purely physical model based on a Monte Carlo simulation of galactic cosmic ray (GCR) particle interaction with meteoroids is used to investigate neutron interactions down to thermal energies. Experimental and/or evaluated excitation functions are used to calculate neutron capture production rates as a function of the size of the meteoroid and the depth below its surface. Presented are the depth profiles of cosmogenic radionuclides ³⁶Cl, ⁴¹Ca, ⁶⁰Co, ⁵⁹Ni, and ¹²⁹I for meteoroid radii from 10 cm up to 500 cm and a 2π irradiation. Effects of bulk chemical composition on n‐capture processes are studied and discussed for various chondritic and lunar compositions. The mean GCR particle flux over the last 300 ka was determined from the comparison of simulations with measured ⁴¹Ca activities in the Apollo 15 drill core. The determined value significantly differs from that obtained using equivalent models of spallation residue production.     

Dynamical evolution of the Oort cloud: I. A Monte Carlo simulation

We have studied the long-time dynamical evolution of a population of comets surrounding the Solar System at a large distance. Orbital changes are caused by random passing stars. We first emphasize the need for a new simulation because of the lack of completeness of previous analytical and numerical studies. Then the solar neighborhood is modeled by a sphere of 1 pc in radius, which stars cross at random in direction and distance. The geometry of the encounters allows us to compute the impulse gained by the star and the Sun, in the context of an impact approximation. Then we determine the change of orbital elements for a population of comets and follow the evolution of the frequency distribution for the five Keplerian elements. Clouds are selected in such a way that we test the two main hypotheses for the origin of the Oort cloud, and also the regions of stability in an aphelion-eccentricity diagram. We show that stellar perturbations randomize the cloud and prevent one from inferring the initial cloud configuration from the current distribution. Clouds are depleted by the diffusion of comets into the planetary regions, where they become planet-influenced comets or are ejected from the Solar System. The diffusion of aphelion toward interstellar regions proves to be the major source of cometary loss. Direct ejection to hyperbolic orbits amounts to 9% of the originally population over the age of the Solar System. Finally the current and original cloud populations are estimated at 1.8 × 10¹² and 2 × 10¹³ comets and we discuss these results.     

Monte Carlo simulation of pair creation using petawatt lasers

Irradiating high-Z targets such as gold with ultra-intense lasers creates electron-positron pairs. In particular, the positron density in the plasma created by this procedure is higher than that obtained via other laboratory-based methods, with theoretical maximum densities exceeding 10¹⁸ cm⁻³. All of the significantly contributing processes are well-known and hence we can study this phenomenon using Monte Carlo simulation. We focus on the latter part of this procedure, the passage of high-energy electrons through the target creating pairs. In particular, we discuss the usefulness of CERN’s GEANT4 Monte Carlo code in simulating this process. Once this code is successfully calibrated, we will use it to perform parameter studies, and design future targets to optimize the positron yield.     

Monte Carlo simulation of temperature fluctuations in interstellar iron grains

The Monte Carlo technique is used to simulate the temperature fluctuations in interstellar iron grains exposed to a particular radiation field. It is found that iron grains attain time-averaged temperatures almost an order of magnitude greater than dielectrics and that their temperatures may fluctuate by as much as 100 K. The effect that this will have on the catalytic formation of molecular hydrogen is examined. It is also found that small metallic grains are unlikely candidates for explaining the extended red emission observed in many reflection nebulae.     

Orbital evolution of long-period comets I. Trivariate Monte Carlo simulation

The mean orbital evolution of long-period comets for 16 representative initial orbits to short-period comets is calculated by a Monte Carlo method. First, trivariate perturbation distributions of barycentric Kepler energy, total angular momentum, and its z component in single encounters of comets with Jupiter are obtained numerically. Their characteristics are examined in detail and the distributions are found to be simple, symmetric, and easy to handle. Second, utilizing these distributions, we have done trivariate Monte Carlo simulations of the orbital evolution of long-period comets, with special emphasis on high-inclination orbits. About half of the 16 initial orbits are traced up to 5000 returns. For each of these orbits, the mean values of semimajor axis, perihelion distance, and inclination; their standard deviations, survival, and capture rates; as well as time scales of orbital evolution are calculated as functions of return number. Survival rates of the initial orbits with high inclination (～90°) and small perihelion distance (～1–2 AU) have been found to be only two or three times smaller than those of the main-source orbits of short-period comets established quantitatively by Everhart. The time scales of orbitsl evolution of the former, however, are nearly 10 times longer than the latter. There is a general trend that, for smaller perihelion distance, the survival efficiency becomes higher. The results of this paper should be considered a basis for a succeeding paper (Paper II) in which the physical lifetime of comets will be determined, and a comparison with the orbital data will be done.     

A Monte Carlo simulation of the intergalactic absorption and the detectability of the Lyman continuum from distant galaxies

We have made a Monte Carlo simulation of the intergalactic absorption in order to model the Lyman continuum absorption, which is required to estimate the escape fraction of the Lyman continuum from distant galaxies. To input into the simulation, we derive an empirical distribution function of the intergalactic absorbers which reproduces recent observational statistics of the Lyman α forest, Lyman limit systems (LLSs) and damped Lyman α systems (DLAs) simultaneously. In particular, we assume a common functional form of the number evolution along the redshift for all types of absorbers. The Lyman series transmissions in our simulation reproduce the observed redshift evolution of the transmissions excellently, and the Lyman continuum transmission also agrees with an observed estimation which is still quite rare in the literature. The probability distribution of the Lyman α opacity in our simulation is lognormal with a tail towards a large opacity. This tail is produced by DLAs. The probability distribution of the Lyman continuum opacity in our simulation also shows a broad tail towards a large opacity. This tail is produced by LLSs. Because of the rarity of LLSs, we have a chance to have a clean line of sight in the Lyman continuum even for   z ∼ 4  with a probability of about 20 per cent. Our simulation expects a good correlation between the Lyman continuum opacity and the Lyman α opacity, which may be useful to estimate the former from the latter for an individual line of sight.     

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.     

Monte Carlo modelling of cometary dynamics

Monte Carlo simulations can either be viewed as a numerical method for solving evolutionary equations or as a way for statistically modelling the outcome of chaotic dynamical systems. Thus they are well suited for treating many aspects of cometary dynamics. We present a critical review of past applications of Monte Carlo simulations for both long- and short-period comets indicating the strength and weaknesses of the methods with suggestions for future applications.     

The significance of the magnetism observed in lunar rocks

Partial thermal remanence experiments on lunar igneous rocks indicate that the magnetization of lunar rocks is not a normal single component thermoremanent magnetization. The magnetization therefore may not have been acquired at the time of initial cooling of the rock and thus should be used cautiously in making estimates of the intensity of the ancient lunar magnetic field.Contribution No. 201, Geosciences Division, The University of Texas at Dallas.     

Electrical conductivity of lunar surface rocks and chondritic meteorites

The electrical conductivities of several samples from returned Apollo 11 and 12 lunar rocks and from chondritic meteorites were measured from 300 to 1100K. Collectively the lunar samples represent all three of the major NASA classifications of lunar surface rocks. Of general interest is the observation that the conductivities of the lunar samples are much larger than the values which have previously been used in theoretical discussions of lunar phenomena. It is also found that the conductivity at 300K, (300), is extremely sensitive to the thermal history of the sample for both lunar and meteoritic material. Magnetic measurements are presented to help characterize the changes which occur upon heating.Principal Investigator - Apollo Lunar Science Program, Geophysics Research Laboratory, University of Tokyo, Japan.     

Shock melting and vaporization of lunar rocks and minerals

The entropy associated with the thermodynamic states produced by hypervelocity meteoroid impacts at various velocities are calculated for a series of lunar rocks and minerals and compared with the entropy values required for melting and vaporization.Taking into account shock-induced phase changes in the silicates, we calculate that iron meteorites impacting at speeds varying from 4 to 6 km/s will produce shock melting in quartz, plagioclase, olivine, and pyroxene. Although calculated with less certainty, impact speeds required for incipient vaporization vary from ~ 7 to 11 km/s for the range of minerals going from quartz to periclase for aluminum (silicate-like) projectiles. The impact velocities which are required to induce melting in a soil, are calculated to be in the range of 3 to 4 km/s, provided thermal equilibrium is achieved in the shock state.Contribution number 210, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, Calif. 91109, U.S.A.     

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.     

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 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.     

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.     

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.