Monte Carlo simulation for Multi-Mode Elastic Peak Electron Spectroscopy of crystalline materials: Effects of surface structure and excitation

The Multi-Mode Elastic Peak Electron Spectroscopy (MM-EPES) analysis is confined to incoherent electron elastic scattering and the use of variable primary energy. This experimental method is very sensitive to the surface region of the sample. However, for quantitative interpretation, the MM-EPES method needs jointly a Monte Carlo (MC) computer simulation of electron trajectories in the solid. In the present work, we proposed a new approach to calculate the percentage η_e of elastic reflected electrons by the surface of a sample. This simulation takes into account the surface effects (i.e. surface plasmon), and the atoms arrangement in the substrate. The concept of the surface excitation parameter (SEP) is also presented. Computer simulations were performed on the three low index single crystals of Cu, Au, Si and Ag. The results confirm that the distribution of substrate atoms, according to the crystallographic structure, influences the intensity measured by EPES.A simple prediction formula was proposed to calculate η_e for elastic electrons entering in a Retarding Field Analyzer (RFA) spectrometer which is the apparatus giving experimentally numerical values of the percentage η_e.     

Virial-bias Monte Carlo methods

A new sampling technique is proposed for the isothermal-isobaric (T, P, N) ensemble Monte Carlo computer simulation. The new method selects the volume perturbations by using the partial derivative of the volume with respect to the internal energy. Test calculations on the Lennard-Jones fluid show significant improvements over the conventionally used method.     

Auxiliary-field Monte Carlo methods

I discuss Monte Carlo algorithms for quantum many-body systems that employ an auxiliary field to linearize a two-body interaction. These reduce the evaluation of the partition function to sampling many one-body evolutions in a fluctuating field. Fermions and bosons are treated on an equal footing. Applications to potential models and to quantum spin systems are discussed. This work was supported in part by the National Science Foundation, grants PHY82-07332 and PHY85-05682. The potential-model studies were done in collaboration with G. Sugiyama, while A. Khan and T. Troudet were responsible for the work on the quantum spin systems.     

Relativistic calculations using Monte Carlo methods: one-electron systems

Variance minimization and Monte Carlo integration are used to evaluate the four-component Dirac equation for a number of one-electron atomic and diatomic systems. This combination produces accurate energies, is relatively simple to implement, and exhibits few of the problems associated with traditional techniques.     

Shell model Monte Carlo methods

We review quantum Monte Carlo methods for dealing with large shell model problems. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in fluctuating one-body fields; the resultant path integral is evaluated stochastically. We first discuss the motivation, formalism, and implementation of such Shell Model Monte Carlo (SMMC) methods. There then follows a sampler of results and insights obtained from a number of applications. These include the ground state and thermal properties of pf-shell nuclei, the thermal and rotational behavior of rare-earth and γ-soft nuclei, and the calculation of double beta-decay matrix elements. Finally, prospects for further progress in such calculations are discussed.     

Local magnetic moments in crystalline and amorphous alloys

Hyperfine Interactions - Recent57Fe and61Ni Mössbauer spectroscopy studies of Fe and Ni magnetic moments in crystalline and amorphous alloys, as well as X-ray photoelectron spectroscopy...     

Improved Monte Carlo methods for fermions

We describe an improved version of the Kuti-Von Neumann-Ulam algorithm useful for fermion contributions in lattice field theories. This is done by sampling the Neumann series for the propagator, which may be thought of as a sum over a set of weighted paths between two points on the lattice. Rather than selecting paths by a locally determined random walk, we average over sets of paths globally preselected for their importance in evaluating the few needed elements of the inverse. We also describe a method for the calculation of ratios of fermion determinants which is considerably less time consuming than the conventional one.     

Monte Carlo methods for yrast spectroscopy

We discuss the details of the recently proposed Monte Carlo method to evaluate the exact energies of yrast levels. Energy levels are evaluated up to J = 18 with small statistical errors using the Metropolis method for the case of ¹⁶⁶Er using the pairing plus quadrupole model within one major shell. We also discuss the evaluation of the probabilities of the Hartree-Fock-Bogoliubov wave functions in the corresponding yrast eigenstates and they are found to be large. The model displays a too strong backbending behaviour not seen experimentally.Received: 29 September 2003, Published online: 24 August 2004PACS: 21.60.-n Nuclear-structure models and methods - 02.70.Ss Quantum Monte Carlo methods - 21.60.Ka Monte Carlo models - 21.10.Re Collective levels     

Loudness pattern-based speech quality evaluation using bayesian modeling and Markov chain Monte Carlo methods

This work presents a speech quality evaluation method which is based on Moore and Glasberg's loudness model and Bayesian modeling. In the proposed method, the differences between the loudness patterns of the original and processed speech signals are employed as the observed features for representing speech quality, a Bayesian learning model is exploited as the cognitive model which maps the features into quality scores, and Markov chain Monte Carlo methods are used for the Bayesian computation. The performance of the proposed method was demonstrated through comparisons with the state-of-the-art speech quality evaluation standard, ITU-T P.862, using seven ITU subjective quality databases.     

Sorption and permeation of gaseous molecules in amorphous and crystalline PPX C membranes: molecular dynamics and grand canonical Monte Carlo simulation studies

Amorphous and crystalline poly (chloro-p-xylylene) (PPX C) membranes are constructed by using a novel computational technique, that is, a combined method of NVT+NPT-molecular dynamics (MD) and gradually reducing the size (GRS) methods. The related free volumes are defined as homology clusters. Then the sorption and the permeation of gases in PPX C polymers are studied using grand canonical Monte Carlo (GCMC) and NVT-MD methods. The results show that the crystalline PPX C membranes provide smaller free volumes for absorbing or transferring gases relative to the amorphous PPX C area. The gas sorption in PPX C membranes mainly belongs to the physical one, and H bonds can appear obviously in the amorphous area. By cluster analyzing on the mean square displacement of gases, we find that gases walk along the x axis in the crystalline area and walk randomly in the amorphous area. The calculated permeability coefficients are close to the experimental data.     

Monte Carlo methods in radiative transfer and electron-beam processing

Monte Carlo methods (MCMs) are the most versatile approaches in solving the integro-differential equations. They are statistical in nature and can be easily adapted for simulation of the propagation of ensembles of quantum particles within absorbing, emitting, and scattering media. In this paper, we use MCM for the solution of the Boltzmann transport equation, which is the governing equation for both radiative transfer and electron-beam processing. We briefly outline the methodology for the solution of MCMs, and discuss the similarities and differences between the two different application areas. The focus of this paper is primarily on the treatment of different scattering phase functions.     

Guidelines for choosing the transition matrix in Monte Carlo methods using Markov chains

The sampling method proposed by Metropolis et al. (J. Chem. Phys. 21 (1953), 1087) requires the simulation of a Markov chain with a specified π as its stationary distribution. Hastings (Biometrika 57 (1970). 97) outlined a general procedure for constructing and simulating such a Markov chain. The matrix P = {p_ij} of transition probabilities is constructed using a defined symmetric function s and an arbitrary transition matrix Q. With respect to asymptotic variance reduction, Peskun (Biometrika 60 (1973), 607) determined, for a given Q, the optimum choice for s_ij. Here, guidelines are given for choosing Q so that the resulting Markov chain sampling method is as precise as is practically possible. Examples illustrating the use of the guidelines, including potential applications to problems in statistical mechanics and to the problem of estimating the probability of an simple event by “hit-ormiss” Monte Carlo in conjunction with Markov chain sampling, are discussed.     

Monte Carlo simulation of grain growth in polycrystalline materials

Understanding the kinetics of grain growth, under the influence of second phase (such as impurities, voids and bubbles) is fundamental to advances in the control of microstructural evolution. As a precursor to this objective, we have investigated the grain growth kinetics in a polycrystalline material using a standard Q-state Potts’ model under Monte Carlo settings. Based on physical reasoning, new modifications are suggested to circumvent some of the disadvantages in the basic Potts model. The efficacy of these modifications vis-à-vis the basic model is verified. The influence of second phase particles on the impurity loaded grain boundaries is investigated for the study of grain growth kinetics.     

Hierarchical Monte Carlo methods for fractal random fields

Two hierarchical Monte Carlo methods for the generation of self-similar fractal random fields are compared and contrasted. The first technique, successive random addition (SRA), is currently popular in the physics community. Despite the intuitive appeal of SRA, rigorous mathematical reasoning reveals that SRA cannot be consistent with any stationary power-law Gaussian random field for any Hurst exponent; furthermore, there is an inherent ratio of largest to smallest putative scaling constant necessarily exceeding a factor of 2 for a wide range of Hurst exponentsH, with 0.30<H<0.85. Thus, SRA is inconsistent with a stationary power-law fractal random field and would not be useful for problems that do not utilize additional spatial averaging of the velocity field. The second hierarchical method for fractal random fields has recently been introduced by two of the authors and relies on a suitable explicit multiwavelet expansion (MWE) with high-moment cancellation. This method is described briefly, including a demonstration that, unlike SRA, MWE is consistent with a stationary power-law random field over many decades of scaling and has low variance.     

Photoemission and band structure of crystalline and amorphous iron phosphoborides

The electronic structure of some crystalline and amorphous iron phosphobirdes is investigated by the photoemission technique : XPS and UPS. For the crystalline compounds the experimental results, compared to those of pure iron, show a rearrangement of iron d states ; such results can be interpreted in a qualitative model where the low energy levels are related to the iron-metalloid bondïng levels meanwhile the upper levels are related to d iron states. For the amorphous alloys our results suggest that the electronic structure is similar to that of crystalline counterpart ; from U.V. spectra there is some hint that the slight variation of the electronic structure from crystalline Fe₃B to Fe₃P is reproduced in the amorphous alloys when the relative phosphorus concentration is increased. However, in the amorphous state the Fermi edge can be sharper and the effect of the structural disorder seems to be a broadening of the low lying states of the valence band.