Monte Carlo Simulation Of Thermal Fluctuations Below The Onset Of Rayleigh-Benard Convection

The density fluctuations below the onset of convection in the Rayleigh-Benard problem are studied with the direct simulation Monte Carlo method. The particle simulation results clearly show the connection between the static correlation functions of fluctuations below the critical Rayleigh number and the flow patterns above the onset of convection for small Knudsen number flows (Kn=0.01 and Kn=0.005). Furthermore, the physical nature for no convection in the Rayleigh-Benard problem under large Knudsen number conditions (Kn>0.028) is explained based on the dynamics of fluctuations.

Numerical Analysis of Chemical Reactions by Monte Carlo Simulation

Добри Данков, Владимир Русинов, Мария Велинова, Жасмина Петрова - Изследвана е химическа реакция чрез два начина за моделиране на вероятността за химическа реакция използвайки Direct Simulation Monte Carlo метод. Изследван е порядъка на разликите при температурите и концентрациите чрез тези начини. Когато активността на химическата реакция намалява, намаляват и разликите между концентрациите и температурите получени по двата начина. Ключови думи: Механика на флуидите, Кинетична теория, Разреден газ, DSMC

Thickness And Component Distributions Of Yttrium-Titanium Alloy Films In Electron-Beam Physical Vapor Deposition

Thickness and component distributions of large-area thin films are an issue of international concern in the field of material processing. The present work employs experiments and direct simulation Monte Carlo (DSMC) method to investigate three-dimensional low-density, non-equilibrium jets of yttrium and titanium vapor atoms in an electron-beams physical vapor deposition (EBPVD) system furnished with two or three electron-beams, and obtains their deposition thickness and component distributions onto 4-inch and 6-inch mono-crystal silicon wafers. The DSMC results are found in excellent agreement with our measurements, such as evaporation rates of yttrium and titanium measured in-situ by quartz crystal resonators, deposited film thickness distribution measured by Rutherford backscattering spectrometer (RBS) and surface profilometer and deposited film molar ratio distribution measured by RBS and inductively coupled plasma atomic emission spectrometer (ICP-AES). This can be taken as an indication that a combination of DSMC method with elaborate measurements may be satisfactory for predicting and designing accurately the transport process of EBPVD at the atomic level.

Rarefied gas dynamics: fundamentals, simulations and micro flows

Transport and Distribution of Hydroxyl Radicals and Oxygen Atoms from H2O Photodissociation in the Inner Coma of Comet 67P/Churyumov-Gerasimenko

With a combination of the Direct Simulation Monte Carlo (DSMC) calculation and test particle computation, the ballistic transport process of the hydroxyl radicals and oxygen atoms produced by photodissociation of water molecules in the coma of comet 67P/Churyumov-Gerasimenko is modelled. We discuss the key elements and essential features of such simulations which results can be compared with the remote-sensing and in situ measurements of cometary gas coma from the Rosetta mission at different orbital phases of this comet.

Examination of the LBM in simulation of microchannel flow in transitional regime

The gas flows in micro-electro-mechanical systems possess relatively large Knudsen number and usually belong to the slip flow and transitional flow regimes. Recently the lattice Boltzmann method (LBM) was proposed by Nie et al. in Journal of Statistical Physics, vol. 107, pp. 279-289, in 2002 to simulate the microchannel and microcavity flows in the transitional flow regime. The present article intends to test the feasibility of doing so. The results of using the lattice Boltzmann method and the direct simulation Monte Carlo method show good agreement between them for small Kn (Kn = 0.0194), poor agreement for Kn = 0.194, and large deviation for Kn = 0.388 in simulating microchannel flows. This suggests that the present version of the lattice Boltzmann method is not feasible to simulate the transitional channel flow.

The development of Monte Carlo techniques for the verification of radiotherapy treatments

Radiotherapy is a cancer treatment modality in which a dose of ionising radiation is delivered to a tumour. The accurate calculation of the dose to the patient is very important in the design of an effective therapeutic strategy. This study aimed to systematically examine the accuracy of the radiotherapy dose calculations performed by clinical treatment planning systems by comparison againstMonte Carlo simulations of the treatment delivery. A suite of software tools known as MCDTK (Monte Carlo DICOM ToolKit) was developed for this purpose, and is capable of: • Importing DICOM-format radiotherapy treatment plans and producing Monte Carlo simulation input files (allowing simple simulation of complex treatments), and calibrating the results; • Analysing the predicted doses of and deviations between the Monte Carlo simulation results and treatment planning system calculations in regions of interest (tumours and organs-at-risk) and generating dose-volume histograms, so that conformity with dose prescriptions can be evaluated. The code has been tested against various treatment planning systems, linear acceleratormodels and treatment complexities. Six clinical head and neck cancer treatments were simulated and the results analysed using this software. The deviations were greatest where the treatment volume encompassed tissues on both sides of an air cavity. This was likely due to the method the planning system used to model low density media.

The development of Monte Carlo techniques for the verification of radiotherapy treatments

Introduction: Recent advances in the planning and delivery of radiotherapy treatments have resulted in improvements in the accuracy and precision with which therapeutic radiation can be administered. As the complexity of the treatments increases it becomes more difficult to predict the dose distribution in the patient accurately. Monte Carlo (MC) methods have the potential to improve the accuracy of the dose calculations and are increasingly being recognised as the ‘gold standard’ for predicting dose deposition in the patient [1]. This project has three main aims: 1. To develop tools that enable the transfer of treatment plan information from the treatment planning system (TPS) to a MC dose calculation engine. 2. To develop tools for comparing the 3D dose distributions calculated by the TPS and the MC dose engine. 3. To investigate the radiobiological significance of any errors between the TPS patient dose distribution and the MC dose distribution in terms of Tumour Control Probability (TCP) and Normal Tissue Complication Probabilities (NTCP). The work presented here addresses the first two aims. Methods: (1a) Plan Importing: A database of commissioned accelerator models (Elekta Precise and Varian 2100CD) has been developed for treatment simulations in the MC system (EGSnrc/BEAMnrc). Beam descriptions can be exported from the TPS using the widespread DICOM framework, and the resultant files are parsed with the assistance of a software library (PixelMed Java DICOM Toolkit). The information in these files (such as the monitor units, the jaw positions and gantry orientation) is used to construct a plan-specific accelerator model which allows an accurate simulation of the patient treatment field. (1b) Dose Simulation: The calculation of a dose distribution requires patient CT images which are prepared for the MC simulation using a tool (CTCREATE) packaged with the system. Beam simulation results are converted to absolute dose per- MU using calibration factors recorded during the commissioning process and treatment simulation. These distributions are combined according to the MU meter settings stored in the exported plan to produce an accurate description of the prescribed dose to the patient. (2) Dose Comparison: TPS dose calculations can be obtained using either a DICOM export or by direct retrieval of binary dose files from the file system. Dose difference, gamma evaluation and normalised dose difference algorithms [2] were employed for the comparison of the TPS dose distribution and the MC dose distribution. These implementations are spatial resolution independent and able to interpolate for comparisons. Results and Discussion: The tools successfully produced Monte Carlo input files for a variety of plans exported from the Eclipse (Varian Medical Systems) and Pinnacle (Philips Medical Systems) planning systems: ranging in complexity from a single uniform square field to a five-field step and shoot IMRT treatment. The simulation of collimated beams has been verified geometrically, and validation of dose distributions in a simple body phantom (QUASAR) will follow. The developed dose comparison algorithms have also been tested with controlled dose distribution changes. Conclusion: The capability of the developed code to independently process treatment plans has been demonstrated. A number of limitations exist: only static fields are currently supported (dynamic wedges and dynamic IMRT will require further development), and the process has not been tested for planning systems other than Eclipse and Pinnacle. The tools will be used to independently assess the accuracy of the current treatment planning system dose calculation algorithms for complex treatment deliveries such as IMRT in treatment sites where patient inhomogeneities are expected to be significant. Acknowledgements: Computational resources and services used in this work were provided by the HPC and Research Support Group, Queensland University of Technology, Brisbane, Australia. Pinnacle dose parsing made possible with the help of Paul Reich, North Coast Cancer Institute, North Coast, New South Wales.

Étude des artefacts en tomodensitométrie par simulation Monte Carlo

En radiothérapie, la tomodensitométrie (CT) fournit l’information anatomique du patient utile au calcul de dose durant la planification de traitement. Afin de considérer la composition hétérogène des tissus, des techniques de calcul telles que la méthode Monte Carlo sont nécessaires pour calculer la dose de manière exacte. L’importation des images CT dans un tel calcul exige que chaque voxel exprimé en unité Hounsfield (HU) soit converti en une valeur physique telle que la densité électronique (ED). Cette conversion est habituellement effectuée à l’aide d’une courbe d’étalonnage HU-ED. Une anomalie ou artefact qui apparaît dans une image CT avant l’étalonnage est susceptible d’assigner un mauvais tissu à un voxel. Ces erreurs peuvent causer une perte cruciale de fiabilité du calcul de dose. Ce travail vise à attribuer une valeur exacte aux voxels d’images CT afin d’assurer la fiabilité des calculs de dose durant la planification de traitement en radiothérapie. Pour y parvenir, une étude est réalisée sur les artefacts qui sont reproduits par simulation Monte Carlo. Pour réduire le temps de calcul, les simulations sont parallélisées et transposées sur un superordinateur. Une étude de sensibilité des nombres HU en présence d’artefacts est ensuite réalisée par une analyse statistique des histogrammes. À l’origine de nombreux artefacts, le durcissement de faisceau est étudié davantage. Une revue sur l’état de l’art en matière de correction du durcissement de faisceau est présentée suivi d’une démonstration explicite d’une correction empirique.

Using the Ferrenberg-Swendsen Monte Carlo method for nonuniversal exponents

We use the method of Monte Carlo evolution in the coupling constant space of Ferrenberg and Swendsen to evaluate the nonuniversal exponent η* associated to a linear defect in a 2d Ising model. © 1989.

More than just Good Luck. How to Explain the Success of Monte Carlo Simulations

Monte Carlo simulation is a powerful method in many natural and social sciences. But what sort of method is it? And where does its power come from? Are Monte Carlo simulations experiments, theories or something else? The aim of this talk is to answer these questions and to explain the power of Monte Carlo simulations. I provide a classification of Monte Carlo techniques and defend the claim that Monte Carlo simulation is a sort of inference.

Relating in situ gas measurements to the surface outgassing properties of cometary nuclei

The sensitivity of the gas flow field to changes in different initial conditions has been studied for the case of a highly simplified cometary nucleus model. The nucleus model simulated a homogeneously outgassing sphere with a more active ring around an axis of symmetry. The varied initial conditions were the number density of the homogeneous region, the surface temperature, and the composition of the flow (varying amounts of H2O and CO2) from the active ring. The sensitivity analysis was performed using the Polynomial Chaos Expansion (PCE) method. Direct Simulation Monte Carlo (DSMC) was used for the flow, thereby allowing strong deviations from local thermal equilibrium. The PCE approach can be used to produce a sensitivity analysis with only four runs per modified input parameter and allows one to study and quantify non-linear responses of measurable parameters to linear changes in the input over a wide range. Hence the PCE allows one to obtain a functional relationship between the flow field properties at every point in the inner coma and the input conditions. It is for example shown that the velocity and the temperature of the background gas are not simply linear functions of the initial number density at the source. As probably expected, the main influence on the resulting flow field parameter is the corresponding initial parameter (i.e. the initial number density determines the background number density, the temperature of the surface determines the flow field temperature, etc.). However, the velocity of the flow field is also influenced by the surface temperature while the number density is not sensitive to the surface temperature at all in our model set-up. Another example is the change in the composition of the flow over the active area. Such changes can be seen in the velocity but again not in the number density. Although this study uses only a simple test case, we suggest that the approach, when applied to a real case in 3D, should assist in identifying the sensitivity of gas parameters measured in situ by, for example, the Rosetta spacecraft to the surface boundary conditions and vice versa.

Calculation of dose kernels for radiotherapy applications using the GEANT 4 Monte Carlo toolkit

Dose kernels may be used to calculate dose distributions in radiotherapy (as described by Ahnesjo et al., 1999). Their calculation requires use of Monte Carlo methods, usually by forcing interactions to occur at a point. The Geant4 Monte Carlo toolkit provides a capability to force interactions to occur in a particular volume. We have modified this capability and created a Geant4 application to calculate dose kernels in cartesian, cylindrical, and spherical scoring systems. The simulation considers monoenergetic photons incident at the origin of a 3 m x 3 x 9 3 m water volume. Photons interact via compton, photo-electric, pair production, and rayleigh scattering. By default, Geant4 models photon interactions by sampling a physical interaction length (PIL) for each process. The process returning the smallest PIL is then considered to occur. In order to force the interaction to occur within a given length, L_FIL, we scale each PIL according to the formula: PIL_forced = L_FIL 9 (1 - exp(-PIL/PILo)) where PILo is a constant. This ensures that the process occurs within L_FIL, whilst correctly modelling the relative probability of each process. Dose kernels were produced for an incident photon energy of 0.1, 1.0, and 10.0 MeV. In order to benchmark the code, dose kernels were also calculated using the EGSnrc Edknrc user code. Identical scoring systems were used; namely, the collapsed cone approach of the Edknrc code. Relative dose difference images were then produced. Preliminary results demonstrate the ability of the Geant4 application to reproduce the shape of the dose kernels; median relative dose differences of 12.6, 5.75, and 12.6 % were found for an incident photon energy of 0.1, 1.0, and 10.0 MeV respectively.

The generalized Onsager model for the secondary flow in a high-speed rotating cylinder

The generalizations of the Onsager model for the radial boundary layer and the Carrier-Maslen model for the end-cap axial boundary layer in a high-speed rotating cylinder are formulated for studying the secondary gas flow due to wall heating and due to insertion of mass, momentum and energy into the cylinder. The generalizations have wider applicability than the original Onsager and Carrier-Maslen models, because they are not restricted to the limit A >> 1, though they are restricted to the limit R e >> 1 and a high-aspect-ratio cylinder whose length/diameter ratio is large. Here, the stratification parameter A = root m Omega(2)R(2)/2k(B)T). This parameter A is the ratio of the peripheral speed, Omega R, to the most probable molecular speed, root 2k(B)T/m, the Reynolds number Re = rho w Omega R(2)/mu, where m is the molecular mass, Omega and R are the rotational speed and radius of the cylinder, k(B) is the Boltzmann constant, T is the gas temperature, rho(w) is the gas density at wall, and mu is the gas viscosity. In the case of wall forcing, analytical solutions are obtained for the sixth-order generalized Onsager equations for the master potential, and for the fourth-order generalized Carrier-Maslen equation for the velocity potential. For the case of mass/momentum/energy insertion into the flow, the separation-of-variables procedure is used, and the appropriate homogeneous boundary conditions are specified so that the linear operators in the axial and radial directions are self-adjoint. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order and second-order in the radial and axial directions for the Onsager equation, and fourth-order and second-order in the axial and radial directions for the Carrier-Maslen equation) are determined. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations. The comparison reveals that the boundary conditions in the simulations and analysis have to be matched with care. The commonly used `diffuse reflection' boundary conditions at solid walls in DSMC simulations result in a non-zero slip velocity as well as a `temperature slip' (gas temperature at the wall is different from wall temperature). These have to be incorporated in the analysis in order to make quantitative predictions. In the case of mass/momentum/energy sources within the flow, it is necessary to ensure that the homogeneous boundary conditions are accurately satisfied in the simulations. When these precautions are taken, there is excellent agreement between analysis and simulations, to within 10 %, even when the stratification parameter is as low as 0.707, the Reynolds number is as low as 100 and the aspect ratio (length/diameter) of the cylinder is as low as 2, and the secondary flow velocity is as high as 0.2 times the maximum base flow velocity. The predictions of the generalized models are also significantly better than those of the original Onsager and Carrier-Maslen models, which are restricted to thin boundary layers in the limit of high stratification parameter.

Vaporization of heated materials into discharge plasmas

The vaporization of condensed materials in contact with high-current discharge plasmas is considered. A kinetic numerical method named direct simulation Monte Carlo (DSMC) and analytical kinetic approaches based on the bimodal distribution function approximation are employed. The solution of the kinetic layer problem depends upon the velocity at the outer boundary of the kinetic layer which varies from very small, corresponding to the high-density plasma near the evaporated surface, up to the sound speed, corresponding to evaporation into vacuum. The heavy particles density and temperature at the kinetic and hydrodynamic layer interface were obtained by the analytical method while DSMC calculation makes it possible to obtain the evolution of the particle distribution function within the kinetic layer and the layer thickness.