MC Method Research Articles

Simulation of Collisions of Ions with Atoms by the PIC–MC Method. Comparative Estimates

Monte Carlo models which simulate ion-atom collisions are considered. Efficient models for calculating the time between collisions are proposed which take into account the velocity dependence of the cross sections and also the probability distribution of the velocities of the ions and the probability distribution of the angles after a collision. The simulation results are compared with theoretical values of the drift velocity of the ions.

Изучение состава этанольных экстрактов сапропелей Новосибирской области органического (оз. Качкульня) и органоминерального (оз. Барчин) типов

The extraction of sapropels of organic type (Kachkulnya Lake) and organo-mineral type (Barchin Lake) from Novosibirsk region by ethanol at a variation of process temperature was studied. It was shown that the rising of the temperature from 50 °C to 200 °C results in an increase the yields of extracts by 19,0 and 13,7 times for sapropels organic and organo-mineral - types respectively The composition of obtained extracts was established by IR and GC – MC methods. Products from sapropel organic type contained 68,1 % ethyl esters , mainly of fatty acids with carbon atoms in the molecule are from 18 to 29 numbers. It was established that relative content of ethyl esters in extract of organo-mineral type sapropel was 43,6 %, they have a significant amounts of ethyl esters of hydroxy - and oxyacids. A distinctive feature of the ethanol extract from organo-mineral type sapropel is the presence of carbohydrates and compounds containing a furan ring.

Dose Calculations for Lung Inhomogeneity in High-Energy Photon Beams and Small Beamlets: A Comparison between XiO and TiGRT Treatment Planning Systems and MCNPX Monte Carlo Code

Introduction Radiotherapy with small fields is used widely in newly developed techniques. Additionally, dose calculation accuracy of treatment planning systems in small fields plays a crucial role in treatment outcome. In the present study, dose calculation accuracy of two commercial treatment planning systems was evaluated against Monte Carlo method. Materials and Methods Siemens Once or linear accelerator was simulated, using MCNPX Monte Carlo code, according to manufacturer’s instructions. Three analytical algorithms for dose calculation including full scatter convolution (FSC) in TiGRT, along with convolution and superposition in XiO system were evaluated for a small solid liver tumor. This solid tumor with a diameter of 1.8 cm was evaluated in a thorax phantom, and calculations were performed for different field sizes (1×1, 2×2, 3×3 and4×4 cm2). The results obtained in these treatment planning systems were compared with calculations by MC method (regarded as the most reliable method). Results For FSC and convolution algorithm, comparison with MC calculations indicated dose overestimations of up to 120%and 25% inside the lung and tumor, respectively in 1×1 cm2field size, using an 18 MV photon beam. Regarding superposition, a close agreement was seen with MC simulation in all studied field sizes. Conclusion The obtained results showed that FSC and convolution algorithm significantly overestimated doses of the lung and solid tumor; therefore, significant errors could arise in treatment plans of lung region, thus affecting the treatment outcomes. Therefore, use of MC-based methods and super position is recommended for lung treatments, using small fields and beamlets.

Analysis of photon transport in biological tissue and the subsequent heating effects

Analysis of laser interaction with matter revealed the possibilities of many industrial and therapeutic applications. This research article discusses the theoretical aspects of laser beam interaction with biological tissues. It introduces the numerical analysis of photon distribution and transport in the tissue and its bio-thermal heating effects. The Monte Carlo method has been applied to simulate the variation of photon distribution and photon fluence with the radial distance from the point of interaction as well as laser powers and tissue thickness. For a specific wavelength, the variation of diffuse reflectance with the absorption coefficient was depicted for different values of the anisotropy factor. It has also been used to simulate the bio-heat transfer to obtain the temperature variation with the heating depth. On the other hand, finite difference method (FDM) has been applied to simulate the heating effect resulted from the incident laser beam on the tissue based on Penne's bio-heat equation combined with the obtained photon distribution and transport parameters from the MC method. The heating effect of the laser beam and hence the occurred thermal damage in the tissue was depicted. A linear relationship between the temperature and the rate of thermal damage has been manifested. This result can be used as a threshold reference for various medical applications of lasers.

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

Lattice spin-fermion models are important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the "spins," are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The "traveling cluster approximation" (TCA) is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10(3) sites. In this publication, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. This allows us to solve generic spin-fermion models easily on 10(4) lattice sites and with some effort on 10(5) lattice sites, representing the record lattice sizes studied for this family of models.

Mermin Differential Inverse Inelastic Mean Free Path of Electrons in Polymethylmethacrylate

INTRODUCTION Electrons continually interact with the matter around us. We use electron beams for our purposes, either on the side of production of materials or on that of their characterization. Let us think to the many applications such as the processing of materials with plasma and to the local melting of materials for joining large components. We use electron beams also in the electron lithography, an important technique utilized for the production of the microelectronics devices. Let us consider the importance of the beams of electrons in the characterization of the materials, performed using techniques such as the electron microscopy and all the electron spectroscopies. Electrons interact with the surfaces of the space-crafts. The plasma– wall interaction in the fusion reactors also involves electron–matter interaction. Electrons play a role also in the cancer proton therapy, where cascades of secondary electrons are produced. These electrons of very low energy are toxic for the human body cells, since they produce damage to the biomolecules due to ionizations/excitations and the resulting break of chemical bonds. Also the secondary electrons which have ultra-low energies – and which, for a long time, were thought to be relatively harmless – are dangerous for the biomolecules due to the so-called “dissociative electron attachment.” And, of course, we wish to minimize the effects of the irradiation on the healthy tissues near to the diseased cells. In all the mentioned cases, the modeling of the interaction of the electrons with the matter is very important, as it can be used to provide a solid theoretical interpretation of the experimental evidences. The interpretation of the experimental results is often based on the Monte Carlo method (MC). The doping contrast in secondary-electron emission of pnjunctions was investigated by the use of the MC method (Dapor et al., 2008; Rodenburg et al., 2010). The modeling of electron interaction with polymers, and in particular with the polymethylmethacrylate, has been demonstrated to be very important in nano-metrology. Line-scan of resist materials with given geometrical cross-sections deposited on silicon or silicon dioxide, and the corresponding linewidth measurements, obtained with the secondary electrons in the CriticalDimension Scanning Electron Microscope (CD SEM), require an interpretation that can be performed using MC calculations (Dapor et al., 2010). The MC method, in turn, requires an accurate description of the differential inverse inelastic mean free path (DIIMFP), in order to calculate the inelastic mean free path (IMFP) and the distribution function for inelastic collisions of electrons causing energy losses less than or equal to given values.

PD-0448: Influence of geometry and DNA target composition on the ionization cluster distributions using MC methods

PD-0448: Influence of geometry and DNA target composition on the ionization cluster distributions using MC methods

Frontier Fields: Combining HST, VLT, andSpitzerdata to explore thez~ 8 Universe behind the lensing cluster MACSJ0416.1−2403

(Abridged) The HST Frontier Fields project started at the end of 2013 with the aim of providing extremely deep images of 6 massive galaxy clusters. One of the main goals of this program is to push several telescopes to their limits in order to provide the best current view of the earliest stages of the Universe. We present a detailed analysis of $z$$\sim$8 objects behind the HFFs lensing cluster, MACS0416-2403, combining 0.3-1.6 $\mu$m imaging from HST, ground-based $K_s$ imaging from VLT HAWK-I, and 3.6 $\mu$m and 4.5 $\mu$m Spitzer Space Telescope. We apply the classical Lyman Break technique, combining non-detection criteria and color-selection. In order to avoid contamination by mid-$z$ interlopers, we require a strong break between optical and near infrared data. The luminosity function at $z$$\sim$8 is computed using a MC method taking advantage of the SED-fitting results. A piece of cautionary information is gleaned from new deep optical photometry of a previously identified $z$$\sim$8 galaxy in this cluster, which is now firmly detected as a mid-$z$ interloper with a strong $\approx1.5$ mag Balmer break (between F606W and F125W). Using the SED of this interloper, we estimate the contamination rate of our MACS0416$-$2403 sample, as well as for previous samples in Abell 2744 based on HFF data. Our selection recovers 4 robust objects with m$_{F160W}$ ranging from 26.0 to 27.9 AB and located in modest amplification regions ($\mu<$2.4). Two of the objects display a secondary break between the IRAC 3.6 $\mu$m and 4.5 $\mu$m bands which could be associated to the Balmer break or emission lines at $z$$\sim$8. The candidates generally have star formation rates around $\sim$10 M$_{\odot}$/yr and sizes ranging from 0.2 to 0.5 kpc, in good agreement with previous observations and expectations for objects in the early Universe.

A Multi-Level Dimension Reduction Monte-Carlo Method for Jump-Diffusion Models

This paper develops and analyses convergence properties of a novel multi-level Monte-Carlo (mlMC) method for computing prices and hedging parameters of plain-vanilla European options under a very general $b$-dimensional jump-diffusion model, where $b$ is arbitrary.The model includes stochastic variance and multi-factor Gaussian interest short rate(s). The proposed mlMC method is built upon (i) the powerful dimension and variance reduction approach developed in Dang et. al 2015 for jump-diffusion models, which, for certain jump distributions, reduces the dimensions of the problem from $b$ to $1$, namely the variance factor, and (ii) the highly effective multi-level MC approach of Giles 2008 applied to that factor. As a result, the proposed multi-level approach avoids potential difficulties associated with the standard multi-level approach in effectively handling simultaneously both multi-dimensionality and jumps. Numerical analysis shows that, when a time discretization scheme having first-order strong convergence, such as the Lamperti-Backward-Euler or Milstein schemes, is used in Step (ii), the proposed MC method requires only an overall complexity $\mathcal{O}(\epsilon^{-2})$ to achieve a root-mean-square error of $\epsilon$. Numerical results illustrating the convergence properties and efficiency of the method with jump sizes following normal and double-exponential distributions are presented.

Boundary discretization in the numerical simulation of light propagation in skin tissue: problem and strategy.

To adapt the complex tissue structure, laser propagation in a two-layered skin model is simulated to compare voxel-based Monte Carlo (VMC) and tetrahedron-based MC (TMC) methods with a geometry-based MC (GMC) method. In GMC, the interface is mathematically defined without any discretization. GMC is the most accurate but is not applicable to complicated domains. The implementation of VMC is simple because of its structured voxels. However, unavoidable errors are expected because of the zigzag polygonal interface. Compared with GMC and VMC, TMC provides a balance between accuracy and flexibility by the tetrahedron cells. In the present TMC, the body-fitted tetrahedra are generated in different tissues. No interface tetrahedral cells exist, thereby avoiding the photon reflection error in the interface cells in VMC. By introducing a distance threshold, the error caused by confused optical parameters between neighboring cells when photons are incident along the cell boundary can be avoided. The results show that the energy deposition error by TMC in the interfacial region is one-tenth to one-fourth of that by VMC, yielding more accurate computations of photon reflection, refraction, and energy deposition. The results of multilayered and n-shaped vessels indicate that a laser with a 1064-nm wavelength should be introduced to clean deep-buried vessels.

Conditional and Unconditional Tests (and Sample Size) Based on Multiple Comparisons for Stratified 2 × 2 Tables.

The Mantel-Haenszel test is the most frequent asymptotic test used for analyzing stratified 2 × 2 tables. Its exact alternative is the test of Birch, which has recently been reconsidered by Jung. Both tests have a conditional origin: Pearson's chi-squared test and Fisher's exact test, respectively. But both tests have the same drawback that the result of global test (the stratified test) may not be compatible with the result of individual tests (the test for each stratum). In this paper, we propose to carry out the global test using a multiple comparisons method (MC method) which does not have this disadvantage. By refining the method (MCB method) an alternative to the Mantel-Haenszel and Birch tests may be obtained. The new MC and MCB methods have the advantage that they may be applied from an unconditional view, a methodology which until now has not been applied to this problem. We also propose some sample size calculation methods.

Effective-field and Monte Carlo studies of a kinetic Blume–Capel model

It has been well established that the spin-1 Blume–Capel (BC) model in a time-dependent oscillating external field and a crystal field interaction exhibits a rich variety of topology in nonequilibrium dynamic phase diagrams. Some interesting dynamic behaviors, quite different from the standard Ising model, have been observed. However, there are some disagreements among these theoretical studies. Here we use the effective-field theory (EFT) and the Monte Carlo method (MC) to show that the dissimilarity among the mean-field theory and EFT results is due to the neglect of thermal fluctuations. The effects of thermal fluctuations on the dynamic phase boundary and the dynamic tricritical point are investigated. The MC method is then carried out to confirm if the reentrant phenomenon obtained by the EFT is correct or not. The dynamic phase diagram of the kinetic BC model given by the MC method is also plotted.

MO‐E‐18C‐02: Hands‐On Monte Carlo Project Assignment as a Method to Teach Radiation Physics

Purpose:To present a hands‐on project on Monte Carlo methods (MC) recently added to the curriculum and to discuss the students' appreciation.Methods:Since 2012, a 1.5 hour lecture dedicated to MC fundamentals follows the detailed presentation of photon and electron interactions. Students also program all sampling steps (interaction length and type, scattering angle, energy deposit) of a MC photon transport code. A handout structured in a step‐by‐step fashion guides student in conducting consistency checks. For extra points, students can code a fully working MC simulation, that simulates a dose distribution for 50 keV photons. A kerma approximation to dose deposition is assumed. A survey was conducted to which 10 out of the 14 attending students responded. It compared MC knowledge prior to and after the project, questioned the usefulness of radiation physics teaching through MC and surveyed possible project improvements.Results:According to the survey, 76% of students had no or a basic knowledge of MC methods before the class and 65% estimate to have a good to very good understanding of MC methods after attending the class. 80% of students feel that the MC project helped them significantly to understand simulations of dose distributions. On average, students dedicated 12.5 hours to the project and appreciated the balance between hand‐holding and questions/implications.Conclusion:A lecture on MC methods with a hands‐on MC programming project requiring about 14 hours was added to the graduate study curriculum since 2012. MC methods produce “gold standard” dose distributions and slowly enter routine clinical work and a fundamental understanding of MC methods should be a requirement for future students. Overall, the lecture and project helped students relate crosssections to dose depositions and presented numerical sampling methods behind the simulation of these dose distributions.Research funding from governments of Canada and Quebec. PP acknowledges partial support by the CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council (Grant number: 432290)

Establishing photon absorption fields in a Photo-CREC Water II Reactor using a CREC-spectroradiometric probe

The scattering mode and the appropriate boundary conditions in a Photo-CREC Water II annular reactor are assessed from experimental data. These data are obtained by using a novel spectroradiometric probe (CREC-SP). This probe is designed to measure irradiation at different radial positions within the concentric channel. Radiation data obtained is analyzed using a calculated Monte Carlo radiation field inside the slurry photoreactor. The effect of the phase function and the boundary conditions, as relevant to the photoreactor walls, are determined. The MC method proposed by Valades-Pelayo et al. (2014, Chem. Eng. Sci., 107, 123–136) is modified in the present study to account for refraction, absorption and reflection at the probe surface. Lamp emission, refraction and reemission as well as wavelength-dependent absorption and scattering are accounted for. Regarding Degussa P25, a Henyey–Greenstein phase function with g=0.68±0.03 is needed. On this basis, a 3D LVRPA field is established. This approach also allows one to independently set boundary conditions, breaking, in this manner, their correlation with scattering parameters. As a result, this study establishes scattering phase functions and radiation absorption fields with improved accuracy. Clarification of these matters is of crucial importance for the design and scale-up of photocatalytic reactors.

A ReaxFF Investigation of Hydride Formation in Palladium Nanoclusters via Monte Carlo and Molecular Dynamics Simulations

Palladium can readily dissociate and absorb hydrogen from the gas phase, making it applicable in hydrogen storage devices, separation membranes, and hydrogenation catalysts. To investigate hydrogen transport properties in Pd on the atomic scale, we derived a ReaxFF interaction potential for Pd/H from an extensive set of quantum data for both bulk and surface properties. Using this potential, we employed a recently developed hybrid grand canonical-Monte Carlo/molecular dynamics (GC-MC/MD) method to derive theoretical hydrogen absorption isotherms in Pd bulk crystals and nanoclusters for hydrogen pressures ranging from 10–1 atm to 10–14 atm, and at temperatures ranging from 300 to 500 K. Analysis of the equilibrated cluster structures reveals the contributing roles of surface, subsurface, and bulk regions during the size-dependent transition between the solid solution α phase and the hydride β phase. Additionally, MD simulations of the dissociative adsorption of hydrogen from the gas phase were conducted to assess size-dependent kinetics of hydride formation in Pd clusters. Hydrogen diffusion coefficients, apparent diffusion barriers, and pre-exponential factors were derived from MD simulations of hydrogen diffusion in bulk Pd. Both the thermodynamic results of the GC-MC/MD method and the kinetic results of the MD simulations are in agreement with experimental values reported in the literature, thus validating the Pd/H interaction potential, and demonstrating the capability of the GC–MC and MD methods for modeling the complex and dynamic phase behavior of hydrogen in Pd bulk and clusters.

Approximate solution to vector radiative transfer in gradient-index medium

Within a gradient-index medium, the radiative rays propagate in curved paths, which makes polarized states change continuously and the solution to the radiative transfer be thus more complex and difficult. In this paper, an arbitrary multilayer model is developed to approximately simulate vector (polarized) radiative transfer in a gradient-index plane-parallel medium. The gradient-index medium is divided into an arbitrary number of sublayers, and each sublayer has a uniform refractive index and two virtual Fresnel's interfaces where only transmission (refraction) is considered. Thus the polarization caused by the curved propagation of lights is approximated by that resulting from refraction on the interfaces. Radiative transfer with consideration of polarization caused by particle scattering and refraction (reflection) on the interfaces (surfaces) in the multilayer model is solved by the MC method. The grid independence of results obtained by the multilayer model for vector radiative transfer in gradient-index medium shows that the convergent solution of Stokes vector will be achieved provided that the sublayer number is large enough. The results for apparent emissivity of gradient-index medium and Stokes vector for two-layer medium are compared well with those in published literatures. Finally, we investigate polarized behaviors of radiative transfer in Rayleigh scattering slabs with linear and sinusoidal gradient indexes and present angular distributions of Stokes vector. Results show that total reflection inside the gradient-index medium resulting from the curved paths traveled by the photons affects greatly the angular distribution characteristics of Stokes vector.

Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities

Multilevel Monte Carlo finite element methods (MLMC-FEMs) for the solution of stochastic elliptic variational inequalities are introduced, analyzed, and numerically investigated. Under suitable assumptions on the random diffusion coefficient, the random forcing function, and the deterministic obstacle, we prove existence and uniqueness of solutions of “pathwise” weak formulations. Suitable regularity results for deterministic, elliptic obstacle problems lead to uniform pathwise error bounds, providing optimal-order error estimates of the statistical error and upper bounds for the corresponding computational cost for the classical MC method and novel MLMC-FEMs. Utilizing suitable multigrid solvers for the occurring sample problems, in two space dimensions MLMC-FEMs then provide numerical approximations of the expectation of the random solution with the same order of efficiency as for a corresponding deterministic problem, up to logarithmic terms. Our theoretical findings are illustrated by numerical experiments.

Research on the Near-Infrared (NIR) Photon Migration in the Knee

To study the phenomena of photon migration in the knee joint is very important in the field of non-invasive near-infrared optical early diagnosis of osteoarthritis of the knee (KOA). In this paper, a photon propagation model of the knee layered structure based on Monte Carlo method is proposed. The migration trace and distribution rule of the photons in knee layered structure are simulated by the Monte Carlo modeling. The proportion of photons which collide with bone tissue then migrate out of the muscle tissue and photons directly migrate out of muscle tissue is calculated and analyzed. The conclusion is that the MC method provided in this study is useful to analyze the photon migration in knee layered structure and to place the detector in a suitable position.

Development of kinetic Monte Carlo and Bin-Monte Carlo schemes for simulation of mixtures – vapor–liquid equilibria & adsorption

We describe algorithms for the recently developed Bin-Monte Carlo (Bin-MC) method (Fan et al., 2012) and kinetic Monte Carlo (kMC) (Ustinov and Do, 2012) to simulate binary liquid mixtures, and compare them with simulations of vapour–liquid equilibria from the canonical and Gibbs MC methods. We have found that in kMC, the rule to choose a molecule to move rests purely on the mobility, irrespective of molecular weight. In the Bin-MC, the choice of a molecule to move from one bin to another bin depends on the selection of a component with equal probability. Our simulations show that the Bin-MC and kMC schemes are very effective for the purpose of describing thermodynamic properties and density profiles across the vapour–liquid interface, and show that the Lorentz–Berthelot (LB) mixing rule works well for subcritical systems, and to improve the description of systems having one component under supercritical condition the cross collision diameter and the cross well depth have to be modified from the LB mixing rules, which is in agreement with previous studies (for example, (Wu and Sadus, 2000)). The benefits of the kMC scheme for the direct determination of chemical potential were also demonstrated with a study of adsorption of an argon–krypton mixture on graphite.

VSR Mechanism Based on MC Algorithm Simulation of Grain Growth Behavior of Sustainable Materials

Established a dynamic model of recrystallization dislocation, proposed MC algorithm simulation describing grain growth behaviors that can explain VSR eliminate component residual stress mechanism from the micro, which can provide an intuitive visualization. Used MATLAB programming grain growth of the grain in the different MC steps simulate images, to discuss the grain size distribution and the energy change in different MC steps, while compared the simulation results with the existing sample dislocation configuration electron microscopy photos around the VSR. It reflects the same trend, which can show that the MC method in numerical simulation of grain growth can fully reflect component microstructure evolution around VSR. Micro explains the VSR mechanism of residual stress relief member which provides intuitive visual basis.