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1.
Practice, i.e., as long as the initial conditions cannot be specified exactlty, the outcome of a chaotic dynamical system can only be specified in statistical terms. Evolution equations (e.g., the Fokker-Planck equation) for a distribution of test particles can then be formulated, and as an alternative to analytical, mostly approximate or idealised solutions one may simulate the problem using Monte Carlo techniques. Such simulations are a well-known tool in the study of completely chaotic many-body systems such as star clusters or planetary rings, where the sample of test particles can indeed be taken to represent a random set of true solutions according to Bowen's shadowing lemma. In this sense the Monte Carlo modelling plays a role analogous to that of averaging or mapping in regular dynamics, i.e.: the exact dynamical system is replaced by a model overlooking the details of the short-term motion but yielding a good approximation to the long-term behaviour. By a further discretization of the problem the stochastic system can be modelled as a Markov chain. Both Monte Carlo simulations and Markov models have been used in cometary dynamics, and we review some examples from this work to illustrate the success as well as limitations of these stochastic modelling techniques. Lyapunov characteristic exponents and Kolmogorov entropy appear to be suitable tools for estimating the underlying stochasticity to which Monte Carlo simulations refer.  相似文献   

2.
Hydrogen Lyman α (Lyα) is our primary emission-line window into high-redshift galaxies. Despite an extensive literature, Lyα radiative transfer in the most realistic case of a dusty, multiphase medium has received surprisingly little detailed theoretical attention. We investigate Lyα resonant scattering through an ensemble of dusty, moving, optically thick gas clumps. We treat each clump as a scattering particle and use Monte Carlo simulations of surface scattering to quantify continuum and Lyα surface scattering angles, absorption probabilities, and frequency redistribution, as a function of the gas dust content. This atomistic approach speeds up the simulations by many orders of magnitude, making possible calculations which are otherwise intractable. Our fitting formulae can be readily adapted for fast radiative transfer in numerical simulations. With these surface scattering results, we develop an analytic framework for estimating escape fractions and line widths as a function of gas geometry, motion, and dust content. Our simple analytic model shows good agreement with full Monte Carlo simulations. We show that the key geometric parameter is the average number of surface scatters for escape in the absence of absorption,     , and we provide fitting formulae for several geometries of astrophysical interest. We consider the following two interesting applications. (i) Equivalent widths ( EWs ). Lyα can preferentially escape from a dusty multiphase interstellar medium if most of the dust lies in cold neutral clouds, which Lyα photons cannot penetrate. This might explain the anomalously high EWs sometimes seen in high-redshift/submillimetre sources. (ii) Multiphase galactic outflows . We show the characteristic profile is asymmetric with a broad red tail, and relate the profile features to the outflow speed and gas geometry. Many future applications are envisaged.  相似文献   

3.
We outline the steps needed in order to incorporate the evolution of single and binary stars into a particular Monte Carlo code for the dynamical evolution of a star cluster. We calibrate the results against N -body simulations, and present models for the evolution of the old open cluster M67 (which has been studied thoroughly in the literature with N -body techniques). The calibration is done by choosing appropriate free code parameters. We describe, in particular, the evolution of the binary, white dwarf and blue straggler populations, though not all channels for blue straggler formation are represented yet in our simulations. Calibrated Monte Carlo runs show good agreement with results of N -body simulations not only for global cluster parameters, but also for, for example, binary fraction, luminosity function and surface brightness. Comparison of Monte Carlo simulations with observational data for M67 shows that it is possible to get reasonably good agreement between them. Unfortunately, because of the large statistical fluctuations of the numerical data and uncertainties in the observational data the inferred conclusions about the cluster initial conditions are not firm.  相似文献   

4.
Molecular level Monte Carlo simulations have been performed with various model potentials for the CH4-N2 vapor-liquid equilibrium at conditions prevalent in the atmosphere of Saturn’s moon Titan. With a single potential parameter adjustment to reproduce the vapor-liquid equilibrium at a higher temperature, Monte Carlo simulations are in excellent agreement with available laboratory measurements. The results demonstrate the ability of simple pair potential models to describe phase equilibria with the requisite accuracy for atmospheric modeling, while keeping the number of adjustable parameters at a minimum. This allows for stable extrapolation beyond the range of available laboratory measurements into the supercooled region of the phase diagram, so that Monte Carlo simulations can serve as a reference to validate phenomenological models commonly used in atmospheric modeling. This is most important when the relevant region of the phase diagram lies outside the range of laboratory measurements as in the case of Titan. The present Monte Carlo simulations confirm the validity of phenomenological thermodynamic equations of state specifically designed for application to Titan. The validity extends well into the supercooled region of the phase diagram. The possible range of saturation levels of Titan’s troposphere above altitudes of 7 km is found to be completely determined by the remaining uncertainty of the most recent revision of the Cassini-Huygens data, yielding a saturation of 100 ± 6% with respect to CH4-N2 condensation up to an altitude of about 20 km.  相似文献   

5.
Monte Carlo simulation of space radiation effects induced by protons is important for design of space missions. Geant4 is a well established toolkit for Monte Carlo simulation focused on high energy physics applications. In this work, a set of new validation results versus data for Geant4 electromagnetic and hadronic interaction of protons is presented and discussed. Optimal configuration of Geant4 physics for space applications is proposed.  相似文献   

6.
A revision of Stodoíkiewicz's Monte Carlo code is used to simulate evolution of star clusters. The new method treats each superstar as a single star and follows the evolution and motion of all individual stellar objects. The first calculations for isolated, equal-mass N -body systems with three-body energy generation according to Spitzer's formulae show good agreement with direct N -body calculations for N  = 2000, 4096 and 10 000 particles. The density, velocity, mass distributions, energy generation, number of binaries, etc., follow the N -body results. Only the number of escapers is slightly too high compared with N -body results, and there is no level-off anisotropy for advanced post-collapse evolution of Monte Carlo models as is seen in N -body simulations for N  ≤ 2000. For simulations with N  > 10 000 gravothermal oscillations are clearly visible. The calculations of N   2000, 4096, 10 000, 32 000 and 100 000 models take about 2, 6, 20, 130 and 2500 h, respectively. The Monte Carlo code is at least 105 times faster than the N -body one for N  = 32 768 with special-purpose hardware. Thus it becomes possible to run several different models to improve statistical quality of the data and run individual models with N as large as 100 000. The Monte Carlo scheme can be regarded as a method which lies in the middle between direct N -body and Fokker–Planck models and combines most advantages of both methods.  相似文献   

7.
Validation of global numerical models of planetary atmospheres requires simulating images and spectra from the IR to UV spectral regions in order to compare them with remote observations. This paper describes Rassvet, a 3-D spherical-shell backward Monte Carlo radiative transfer model developed for such simulations. It utilizes a new methodology for calculating atmospheric brightness in scattered sunlight by introducing the concept of an “effective emission source”. This allows for the accumulation of the scattered contribution along the entire path of a ray and the calculation of the atmospheric radiation when both scattered sunlight and thermal emission contribute to the remote measurement - which was not possible in previous models. A “polychromatic” algorithm is extended for applications with the backward Monte Carlo method and implemented in the model. It allows for the calculation of radiative intensity for several wavelengths simultaneously, resulting in improved efficiency. The capabilities of the model are demonstrated by simulating remote measurements from the atmosphere of Io.  相似文献   

8.
The Heitler–Matthews model for hadronic air showers will be extended to all the generations of electromagnetic subshowers in the hadronic cascade. The analysis is outlined in detail for showers initiated by primary protons. For showers initiated by iron primaries the part of the analysis is given for as far as it differs from the analysis for a primary proton. Predictions for shower sizes and the depth of maximum shower size are compared with results of Monte Carlo simulations. The depth of maximum as it follows from the extrapolation of the Heitler–Matthews model restricted to the first generation of electromagnetic subshowers is too small with respect to Monte Carlo predictions. It is shown that the inclusion of all the generations of electromagnetic subshowers leads to smaller predictions for the depth of maximum and to smaller predictions for the elongation rate. The discrepancy between discrete model predictions and Monte Carlo predictions for the depth of maximum can therefore not be explained from the number of generations that is taken into consideration. An alternative explanation will be proposed.  相似文献   

9.
Based on the Monte Carlo simulations we have studied the performance of the HEGRA system of imaging air erenkov telescopes (IACTs) in its present configuration of 4 IACTs as well as in its future final configuration of 5 IACTs. Here we present the results on the basic characteristics of the IACT system which are used in the standard data analysis procedure, i.e., the collection areas, the detection rates, the angular resolution, the energy resolution, and the γ/hadron-separation efficiency. By comparing several key Monte Carlo predictions with experimental results it is possible to check the accuracy of the simulations. The Monte Carlo results concerning hadron-nuclear showers are tested with the recorded cosmic ray events and the results concerning photon-induced showers are tested with a large data sample of γ-rays observed from BL Lac object Mkn 501 during its high flaring activity in 1997. Summarizing the simulations and current observations we give the basic recommendations of using the instrument and the major values of its sensitivity.  相似文献   

10.
There is a very large number of small bodies in the Solar System and their orbits are varied and complicated. Some types of orbits and events are so rare that they occur in numerical simulations only when millions or billions of orbits have been calculated. In order to study these orbits or events an efficient Monte Carlo simulation is useful. Here we describe a new Monte Carlo simulation method and test it against some existing simulations of orbits of small bodies which have been obtained by different methods. We find good agreement with many earlier calculations, and study briefly the possibility of the Oort Cloud capture origin of short period comets. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

11.
We discuss some commonly used methods for determining the significance of peaks in the periodograms of time series. We review methods for constructing the classical significance tests, their corresponding false alarm probability functions and the role played in these by independent random variables and by empirical and theoretical cumulative distribution functions. We discuss the concepts of independent frequencies and oversampling in periodogram analysis. We then compare the results of new Monte Carlo simulations for evenly spaced time series with results obtained previously by other authors, and present the results of Monte Carlo simulations for a specific unevenly spaced time series obtained for V403 Car.  相似文献   

12.
Spacecraft and their subsystem components are subject to a very hazardous radiation environment in both near-Earth and deep space orbits. Knowledge of the effects of this high energy particle and electromagnetic radiation is essential in designing sensors, electronic circuits and living habitats for humans in near Earth orbit, en route to and on the Moon and Mars. This paper discusses the use of Monte Carlo simulations to optimize system design, radiation source modeling, and determination of background in sensors due to galactic cosmic rays and radiation from the Moon. The results demonstrate the use of Monte Carlo particle transport toolkits to predict secondary production, determine dose rates in space and design required shielding geometry.  相似文献   

13.
A statistical analysis of possible clumping (not periodicity) of emission line redshifts of QSO's shows the available data to be compatible with random fluctuations of a smooth, nonclumped distribution. This result is demonstrated with Monte Carlo simulations as well as with the Kolmogorov-Smirnov test. It is in complete disagreement with the analysis by Varshni, which is shown to be incorrect.  相似文献   

14.
We perform numerical simulations of the molecular hydrogen production on the surface of interstellar dust grains and its dissociation by the ultraviolet background in conditions typical for the interstellar medium. The kinetic version of the Monte Carlo method is used for the modeling of the catalytic chemical reactions on the surface of the dust fraction and in the surrounding medium. Our simulations show the importance of the interstellar dust particles for hydrogen chemistry in diffuse molecular clouds.  相似文献   

15.
《Astroparticle Physics》2011,35(5):266-276
In this paper we introduce the concept of Lateral Trigger Probability (LTP) function, i.e., the probability for an Extensive Air Shower (EAS) to trigger an individual detector of a ground based array as a function of distance to the shower axis, taking into account energy, mass and direction of the primary cosmic ray. We apply this concept to the surface array of the Pierre Auger Observatory consisting of a 1.5 km spaced grid of about 1600 water Cherenkov stations. Using Monte Carlo simulations of ultra-high energy showers the LTP functions are derived for energies in the range between 1017 and 1019 eV and zenith angles up to 65°. A parametrization combining a step function with an exponential is found to reproduce them very well in the considered range of energies and zenith angles. The LTP functions can also be obtained from data using events simultaneously observed by the fluorescence and the surface detector of the Pierre Auger Observatory (hybrid events). We validate the Monte Carlo results showing how LTP functions from data are in good agreement with simulations.  相似文献   

16.
A. Woronow 《Icarus》1978,34(2):324-330
The observed abundances of doublet craters do not necessarily indicate a nonrandom process. Previous studies maintained that planetary surfaces have more doublet craters than would result from randomly located impacts. A new probabilistic calculation and more realistic Monte Carlo simulations demonstrate that the expected and observed number of doublet craters do not differ significantly.  相似文献   

17.
We undertake a quantitative investigation, using Monte Carlo simulations, of the amount by which quasars are expected to exceed radio galaxies in optical luminosity in the context of the 'receding torus' model. We compare these simulations with the known behaviour of the [O  III ] λ5007 and [O  II ] λ3727 emission lines and conclude that [O  III ] is the better indicator of the strength of the underlying non-stellar continuum.  相似文献   

18.
We address the problem of assessing the statistical significance of candidate periodicities found using the so-called 'multiharmonic' periodogram, which is being used for detection of non-sinusoidal signals and is based on the least-squares fitting of truncated Fourier series. The recent author's investigation made for the Lomb–Scargle periodogram is extended to the more general multiharmonic periodogram. As a result, closed and efficient analytic approximations to the false alarm probability, associated with multiharmonic periodogram peaks, are obtained. The resulting analytic approximations are tested under various conditions using Monte Carlo simulations. The simulations showed a nice precision and robustness of these approximations.  相似文献   

19.
J. Matthews   《Astroparticle Physics》2005,22(5-6):387-397
A simple, semi-empirical model is used to develop the hadronic portion of air showers in a manner analogous to the well-known Heitler splitting approximation of electromagnetic cascades. Various characteristics of EAS are plainly exhibited with numerical predictions in good accord with detailed Monte Carlo simulations and with data. Results for energy reconstruction, muon and electron sizes, the elongation rate, and for the effects of the atomic number of the primary are discussed.  相似文献   

20.
We present a new framework for radiation hydrodynamics simulations. Gas dynamics is modelled by smoothed particle hydrodynamics (SPH), whereas radiation transfer is simulated via a time-dependent Monte Carlo approach that traces photon packets. As a first step in the development of the method, in this paper we consider the momentum transfer between radiation field and gas, which is important for systems where radiation pressure is high. There is no fundamental limitation on the number of radiation sources, the geometry or the optical depth of the problems that can be studied with the method. However, as expected for any Monte Carlo transfer scheme, stochastic noise presents a serious limitation. We present a number of tests that show that the errors of the method can be estimated accurately by considering Poisson noise fluctuations in the number of photon packets that SPH particles interact with per dynamical time. It is found that, for a reasonable accuracy, the momentum carried by photon packets must be much smaller than the typical momentum of SPH particles. We discuss numerical limitations of the code, and future steps that can be taken to improve performance and applicability of the method.  相似文献   

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