Monte Carlo simulation of photon migration path in turbid media

A new method of Monte Carlo simulation is developed to simulate the photon migration path in a scattering medium after an ultrashort-pulse laser beam comes into the medium.The most probable trajectory of photons at an instant can be obtained with this method.How the photon migration paths are affected by the optical parameters of the scattering medium is analyzed.It is also concluded that the absorption coefficient has no effect on the most probable trajectory of photons.     

Monte Carlo simulation of ion–material interactions in nuclear fusion devices

One of the key aspects regarding the technological development of nuclear fusion reactors is the understanding of the interaction between high-energy ions coming from the confined plasma and the materials that the plasma-facing components are made of. Among the multiple issues important to plasma–wall interactions in fusion devices, physical erosion and composition changes induced by energetic particle bombardment are considered critical due to possible material flaking, changes to surface roughness, impurity transport and the alteration of physicochemical properties of the near surface region due to phenomena such as redeposition or implantation. A Monte Carlo code named MATILDA (Modeling of Atomic Transport in Layered Dynamic Arrays) has been developed over the years to study phenomena related to ion beam bombardment such as erosion rate, composition changes, interphase mixing and material redeposition, which are relevant issues to plasma-aided manufacturing of microelectronics, components on object exposed to intense solar wind, fusion reactor technology and other important industrial fields. In the present work, the code is applied to study three cases of plasma material interactions relevant to fusion devices in order to highlight the code’s capabilities: (1) the Be redeposition process on the ITER divertor, (2) physical erosion enhancement in castellated surfaces and (3) damage to multilayer mirrors used on EUV diagnostics in fusion devices due to particle bombardment.     

Monte Carlo simulation of the néel relaxation of a single-domain particle

The magnetization reversal kinetics in a single-domain particle with uniaxial magnetic anisotropy was simulated using the Monte Carlo method. The algorithm developed here yields good agreement with the analytical estimates for superparamagnetic relaxation and qualitatively describes some features of magnetic behavior of fine-particle systems.     

Correlations and conductivity of interacting fermions in a disordered chain—a Monte Carlo simulation

The interplay between disorder and interaction in a one dimensional system of fermions is investigated by the use of a Monte Carlo simulation. The model considered (Hubbard Anderson Model) is a combination of the Anderson model, for noninteracting fermions in a random potential, and the extended Hubbard model, for interacting fermions in a periodic potential. To study the physics of this model, a (Quantum) Monte Carlo simulation is performed for a finite chain of 120 sites. The simulation is done for different band fillings, and several values of the interaction parameters and the strength of disorder. The low frequency behaviour of the conductivity is calculated as well as the static correlation functions for the charge density and the spin density. From the results for these quantities the competition between disorder-induced effects (Anderson localization) and interaction-induced effects (Mott transition, long range order) is studied.     

Monte Carlo simulation of phosphorus diffusion in α-iron via the vacancy mechanism

Monte Carlo simulations of the vacancy and phosphorus (P) atom diffusion in body centred cubic (bcc) iron are presented. The input parameters for the calculations, namely the activation energies of atomic jumps, have been obtained using a potential set developed recently for a dilute Fe–P alloy using ab initio data. The diffusion coefficients entering equations for the fluxes of vacancies and solute atoms are evaluated. The results show that, in the temperature range of practical importance for P segregation, P atoms move down the vacancy gradient; hence, under irradiation conditions, vacancies should drag P atoms towards sinks of point defects. This is because of the high binding energy between a P atom and a vacancy in the first and second nearest neighbour sites from each other, which allows a vacancy to move around a P atom without loss of bonding and, hence, co-migrate with it.     

Monte Carlo simulation of the dynamic evolution ofbinary lamellar eutectic in directional solidification

The dynamic evolution of the lamellar eutectic of binary alloys in directional solidification is studied in detail using the Monte Carlo technique. The simulated results can be summarized into two aspects: ({1}) the lamellar spacing λ is found to be inversely proportional to the chemical potential difference Δμ, predicting a linear relationship between the kinetic supercooling ΔT_k and total supercooling at the solid/liquid (S/L) interface; (2) as the solidifying velocity R is low, the dynamic product λ^{2}R shows a considerable dependence on temperature gradient G_T in the liquid in front of the S/L interface, although this dependence becomes much weaker at a high R.     

Monte Carlo simulation of the three-dimensional XY model with bilinear–biquadratic exchange interaction

The three-dimensional XY model with bilinear–biquadratic exchange interactions J and J′, respectively, has been studied by Monte Carlo simulations. From the detailed analysis of the thermal variation of various physical quantities, as well as the order parameter and energy histogram analysis, the phase diagram including two different ordered phases has been determined. There is a single phase boundary from a paramagnetic to a dipole–quadrupole ordered phase, which is of second order in a high J/J′ ratio region, changing to a first-order one for 0.35⩽J/J′⩽0.5. Below J/J′=0.35 there are two separate transitions: the first one to the quadrupole long-range order (QLRO) phase at higher temperatures, followed by another one to the dipole–quadrupole long-range order (DLRO) phase at lower temperatures. The finite-size scaling analysis yields values of the critical exponents for both the DLRO and QLRO transitions close to the values for the conventional XY model which includes no biquadratic exchange.     

Multi-step magnetization of the Ising model on a Shastry-Sutherland lattice: a Monte?Carlo simulation

The magnetization behaviors and spin configurations of the classical Ising model on a Shastry-Sutherland lattice are investigated using Monte Carlo simulations, in order to understand the fascinating magnetization plateaus observed in TmB(4) and other rare-earth tetraborides. The simulations reproduce the 1/2 magnetization plateau by taking into account the dipole-dipole interaction. In addition, a narrow 2/3 magnetization step at low temperature is predicted in our simulation. The multi-step magnetization can be understood as the consequence of the competitions among the spin-exchange interaction, the dipole-dipole interaction, and the static magnetic energy.     

Premonitory effects near critical transition temperature in ordering systems – a Monte Carlo simulation

Premonitory effects manifest themselves in an ordering transition of the first kind (order) in the form of anomalously high short-range order (SRO) intensity at temperatures marginally above T _c, the critical transition temperature. This intensity located at the superlattice positions of the long-range ordered (LRO) phase is often attributed to the formation of ‘heterophase fluctuations’ resembling clusters of the LRO phase. Monte Carlo simulations in a hypothetical system showing FCC-to-L1₂ ordering transition have been carried out here to shed some light on this phenomenon and to look into the atomic configurations that make up these fluctuations.     

Decomposition kinetics in Fe–Cu dilute alloys. Monte Carlo simulation using concentration-dependent interactions

A generalization of the statistical (Monte Carlo) simulation technique for determining the structure of alloys is proposed. It takes into account the dependence of effective interactions between the atoms of a dissolved chemical element on their local concentration. Using the ab initio parametrization of the model, the decomposition of the bcc Fe–Cu alloy accompanied by the formation of Cu nanoprecipitates is studied. It is shown that the concentration dependence of effective interactions significantly affects the decomposition kinetics by displacing its onset to longer times in agreement with the experiment.     

A new Monte Carlo code for absorption simulation of laser-skin tissue interaction

In laser clinical applications,the process of photon absorption and thermal energy diffusion in the target tissue and its surrounding tissue during laser irradiation are crucial.Such information allows the selection of proper operating parameters such as laser power,and exposure time for optimal therapeutic.The Monte Carlo method is a useful tool for studying laser-tissue interaction and simulation of energy absorption in tissue during laser irradiation.We use the principles of this technique and write a new code with MATLAB 6.5,and then validate it against Monte Carlo multi layer (MCML) code.The new code is proved to be with good accuracy.It can be used to calculate the total power absorbed in the region of interest.This can be combined for heat modelling with other computerized programs.     

Numerical study of translational nonequilibrium in an He–Xe mixture by direct simulation Monte Carlo

The distributions of pairs of particles over relative velocities at the shock wave front in He with a small Xe additive have been studied. It has turned out that the values of the distributions over relative velocities for an Xe–Xe atomic pair far (up to 10⁹ times) exceed their equilibrium values behind a shock wave within a narrow part of its front at high velocities of the wave and small Mach numbers (M = 2). This feature is lacking in the distributions of He–Xe atomic pairs over relative velocities.     

Neoclassical toroidal viscosity calculations in tokamaks using a δf Monte Carlo simulation and their verifications

Neoclassical toroidal viscosities (NTVs) in tokamaks are investigated using a δf Monte Carlo simulation, and are successfully verified with a combined analytic theory over a wide range of collisionality. A Monte Carlo simulation has been required in the study of NTV since the complexities in guiding-center orbits of particles and their collisions cannot be fully investigated by any means of analytic theories alone. Results yielded the details of the complex NTV dependency on particle precessions and collisions, which were predicted roughly in a combined analytic theory. Both numerical and analytic methods can be utilized and extended based on these successful verifications.     

Preliminary Monte Carlo Results for the Three-Dimensional Holstein Model

Monte Carlo simulations are used to study the three-dimensional Holstein model. The relationship between the band filling and the chemical potential is obtained for various phonon frequencies and temperatures. The energy of a single electron or a hole is also calculated as a function of the lattice momenta.     

Monte Carlo tuning for the BESⅢ time-of-flight system

Using experimental data, Monte Carlo tuning is implemented for performance parameters associated with the scintillation counters and readout electronics of the BESⅢ time-of-flight (TOF) system, as part of the full simulation model. The implementation of the tuning is described for simulations designed to reproduce the performance of a number of TOF system parameters, including pulse height, hit efficiency, time resolution, dead channels and background. In addition, comparisons with experimental data are presented.     

Monte Carlo tuning for the BESⅢ time-of-flight system

Using experimental data, Monte Carlo tuning is implemented for performance parameters associated with the scintillation counters and readout electronics of the BESⅢ time-of-flight(TOF) system, as part of the full simulation model. The implementation of the tuning is described for simulations designed to reproduce the performance of a number of TOF system parameters, including pulse height, hit efficiency, time resolution, dead channels and background. In addition, comparisons with experimental data are presented.     

Dynamic Monte Carlo simulation of film–substrate interface mixing in the deposition of Co on Cu (001)

Dynamic Monte Carlo simulations are performed to investigate the interface mixing of Co atoms deposited on a Cu (001) substrate. A tight-binding potential was used to determine the input parameters (jump probabilities and energy barriers) for the Dynamic Monte Carlo model. The results show that more Co adatoms penetrate into the substrate as the temperature rises and/or as the deposition rate decreases, and that the intermixing between the layers becomes concomitantly more pronounced. Cu atoms migrating into the Co layer via exchange processes during the growth of consecutive Co layers are proposed to be responsible for the intermixing. Furthermore, an initial Co clustering followed by a layer-by-layer growth mode was observed in the simulations, with the surface concentration of Cu atoms depending on the fraction of migrating Cu atoms and decaying into the Co film following a power law. The fraction of Cu atoms migrating into the Co layer can be adjusted by varying the deposition rate and the substrate temperature.     

Self-diffusion and ‘order–order’ kinetics in B2-ordering AB binary systems with a tendency for triple-defect formation: Monte Carlo simulation

Self-diffusion of component atoms and ‘order–order’ relaxations in a B2-ordering binary system AB showing a tendency for triple-defect formation were consistently simulated by means of two Monte Carlo techniques. In view of a strict correlation between antisite-defect and vacancy concentrations the Kinetic Monte Carlo (KMC) simulations were implemented with a temperature-dependent vacancy concentration determined by means of Semi-Grand Canonical Monte Carlo (SGCMC) simulations. The Ising model of the system was completed with local-configuration-dependent saddle-point energy parameters related to vacancy mediated atomic jumps. The simulations elucidated the atomistic origin of the experimentally observed low rate of ‘order–order’ relaxations in NiAl, as well as reproduced the experimental relation between the activation energies for ‘order–order’ kinetics and Ni self-diffusion in NiAl. Higher value of the deduced activation energy for atomic migration with respect to the effective energy barriers related to individual atomic jumps indicated their high correlation.     

Nanocrystallization behaviour of a ternary amorphous alloy during isothermal annealing： a Monte Carlo simulation

The nanocrystallization behaviour of Zr70Cu20Ni10 metallic glass during isothermal annealing is studied by employing a Monte Carlo simulation incorporating with a modified Ising model and a Q-state Potts model. Based on the simulated microstructure and differential scanning calorimetry curves, we find that the low crystal-amorphous interface energy of Ni plays an important role in the nanocrystallization of primary Zr2Ni. It is found that when T〈T1max （where T1max is the temperature with maximum nucleation rate）, the increase of temperature results in a larger growth rate and a much finer mierostrueture for the primary Zr2Ni, which accords with the microstructure evolution in ＂flash annealing＂. Finally, the Zr2Ni/Zr2Cu interface energy σG contributes to the pinning effect of the primary nano-sized Zr2Ni grains in the later formed normal Zr2Cu grains.