Illuminance Calculation Using Monte Carlo Method.

Response surface method-based efficient approach for the load and resistance factors calibration of breakwater foundation considering soil spatial variability

Introduction: Previous studies have shown that a Monte Carlo method for the transportations photon beam in medical linear accelerator is a good way. Strip of simulation can be used to measure the dose distribution in phantoms and patients' body. EGSnrc Code is the only code written for use in the field of radiation therapy that has many subset codes that BEAMnrc code is an important one, in which transferred electrons and photons simulation takes place in the head of medical device. DBS technique (Directional Bremsstrahlung Splitting) is a technique that applies a braking radiation in collision. In this study will be discussed to evaluate the effect of this technique on simulation time and particle number of phase-space data and its effect on output spectrum photon beam (6MV) Siemens accelerator Primus model Materials and Methods: : Beginning the geometry of accelerator was stimulated according to its specifications by using the appropriate combination code BEAMnrc. Scoring plane that get phase-space data, in parts of the device such as: target, it was determined the flattening filter by using BEAMDP program to extract their average energy and output spectra in these parts. Also the other side of the research, simulation parameters and output spectra were compared by changing the amount of DBS. Results: Due to the importance of time in fast Mont Carlo, in the simulation with low history of DBS. Considering the time and quality of the spectrum, DBS can be useful. Conclusion: The results show that by changing the number of DBS from 1 to 1000, the amount of simulation time (Elapsed Time) and CPU time and number of particles into phase- space file, respectively have been 7.1, 7 and 36.9 times.

Summary: Monte Carlo method was used to simulate the degradation of porous PLA scaffolds. The simulated volume was assumed to be divided homogeneously between the pore and solid PLA with the ratio equal to the bulk porosity of the scaffold. The volume was divided into surface and bulk elements where the surface elements were in direct contact with the aqueous degradation medium, while the bulk elements were surrounded by the pore and solid PLA. The effect of degradation time on PLA ester groups and carboxylic acid end‐groups for surface and bulk elements, pH, PLA degradation rate and mass loss, and PLA molecular weight distribution was simulated. For surface elements, pH remained constant at 7.4 over the entire time of degradation, while for bulk elements its value decreased significantly to as low as 5.8. The highest drop in pH within the scaffold was observed for the highest porosity of 90%. There was a lag time of at least 7 weeks in the mass loss for surface as well as bulk elements for porosities ranging from 70 to 90%. The mass loss for bulk elements was considerably faster than the surface elements. This difference in the rate of mass loss between the surface and bulk elements could affect the 3D morphology and dimensional stability of the scaffold in vivo as degradation proceeds. The simulation predicts that, due to differences in the rate of bulk and surface degradation, hollow structures could form inside the scaffold after 19, 17, and 15 weeks for initial porosities of 70, 80, and 90%, respectively.A schematic diagram illustrating the degradation of an element on the outer surface of the scaffold (surface element) versus an element within the volume of the scaffold (bulk element).imageA schematic diagram illustrating the degradation of an element on the outer surface of the scaffold (surface element) versus an element within the volume of the scaffold (bulk element).

This study presents a theoretical approach to the dosimetry for small and non-equilibrium radiation fields. We applied the newly developed VMCBC© algorithm to the dosimetry for megavoltage photon beams using Monte Carlo techniques. The approach assumes that a Monte Carlo simulated beam can be calibrated per incident particle at the target in an x-ray tube or in an accelerator head. Since the geometry of the accelerator head and beam defining systems can be modeled in detail, the output of a radiation beam can be accurately related to the number of incident particles through particle transport calculations. The proposed methodology is benchmarked and validated using existing radiosurgery beam commissioning data, which were experimentally measured for narrow beams defined by conical collimators with diameters ranging from 7.5 mm to 30 mm. The Monte Carlo predicted beam outputs agree with the measurement values within the uncertainty of the experiments. The Monte Carlo approach developed and introduced in this study allows the user to perform absolute radiation dosimetry in addition to relative dose distributions at locations where charged-particle equilibrium (CPE) does not exist, such as radiation dose from a narrow stereotactic radiosurgery beam, and where experimental measurements are difficult. The BEAMnrc/DOSXYZnrc code was employed in the Monte Carlo simulations.

The Cherenkov Telescope Array (CTA) - an array of several tens of Cherenkov telescopes - is the next generation of ground-based instrument in the field of very high energy gamma-ray astronomy. The CTA observatory is expected to produce a main data stream for permanent storage of the order of 1-to-5 GB/s for about 1000 hours of observation per year, thus producing a total data volume of the order of several PB per year. The CPU time needed to calibrate and process one hour of data taking will be of the order of some thousands CPU hours with current technology. The high data rate of CTA, together with the large computing power requirements for Monte Carlo (MC) simulations, need dedicated computing resources. Massive MC simulations are needed to study the physics of cosmic-ray atmospheric showers as well as telescope response and performance for different detectors and layout configurations. Given these large storage and computing requirements, the Grid approach is well suited, and a vast number of MC simulations are already running on the European Grid Infrastructure (EGI). In order to optimize resource usage and to handle all production and future analysis activities in a coherent way, a high-level framework with advanced functionalities is desirable. For this purpose we have preliminarly evaluated the DIRAC framework for distributed computing and tested it for the CTA workload and data management systems. In this paper we present a possible implementation of a Distributed Computing Infrastructure (DCI) Computing Model for CTA as well as the benchmark test results of DIRAC.

A parallel implementation of the Stokesian Dynamics method applied to the simulation of colloidal suspensions

Rapid estimation of the coseismic fault model for medium-to-large-sized earthquakes is key for disaster response. To estimate the coseismic fault model for large earthquakes, the Geospatial Information Authority of Japan and Tohoku University have jointly developed a real-time GEONET analysis system for rapid deformation monitoring (REGARD). REGARD can estimate the single rectangular fault model and slip distribution along the assumed plate interface. The single rectangular fault model is useful as a first-order approximation of a medium-to-large earthquake. However, in its estimation, it is difficult to obtain accurate results for model parameters due to the strong effect of initial values. To solve this problem, this study proposes a new method to estimate the coseismic fault model and model uncertainties in real time based on the Bayesian inversion approach using the Markov Chain Monte Carlo (MCMC) method. The MCMC approach is computationally expensive and hyperparameters should be defined in advance via trial and error. The sampling efficiency was improved using a parallel tempering method, and an automatic definition method for hyperparameters was developed for real-time use. The calculation time was within 30 s for 1 × 106 samples using a typical single LINUX server, which can implement real-time analysis, similar to REGARD. The reliability of the developed method was evaluated using data from recent earthquakes (2016 Kumamoto and 2019 Yamagata-Oki earthquakes). Simulations of the earthquakes in the Sea of Japan were also conducted exhaustively. The results showed an advantage over the maximum likelihood approach with a priori information, which has initial value dependence in nonlinear problems. In terms of application to data with a small signal-to-noise ratio, the results suggest the possibility of using several conjugate fault models. There is a tradeoff between the fault area and slip amount, especially for offshore earthquakes, which means that quantification of the uncertainty enables us to evaluate the reliability of the fault model estimation results in real time.

Problem statement: The main problem in solving of the Boltzmann equation by statistical methods is its long computational time (CPU time). The problem of decreasing of CPU time usage in statistical solution methods of Boltzmann equation for rarefied vortex flows was studied. Approach: In this study the Boltzmann equation in a rarefied Taylor-Quette flow regime was solved using the new Monte Carlo method which is officially named time Relaxated Mont Carlo method that applied the equilibrium conditions in each time step. Results: The results obtained from time Relaxated Mont Carlo method for the problem at hand were compared with those from the usual Direct Simulation Monte Carlo method. This comparison showed good agreement between the two sets of results. Conclusion: Whereas, the number of collisions and CPU usage time in the suggested method, as compared to the direct simulation Monte Carlo method, showed a significant decrease.

Context. A rocky planet is formed out of the agglomeration of around 1040 cosmic dust particles. As dust aggregates grow by coagulation, their number decreases. But until they have grown to hundreds of kilometres, their number still remains well above the number of particles a computer model can handle directly. The growth from micrometres to planetesimal-sized objects therefore has to be modelled using statistical methods, often using size distribution functions or Monte Carlo methods. However, when the particles reach planetary masses, they must be treated individually. This can be done by defining two classes of objects: a class of many small bodies or dust particles treated in a statistical way, and a class of individual bodies such as one or more planets. This introduces a separation between small and big objects, but it leaves open how to transition from small to big objects, and how to treat objects of intermediate sizes. Aims. We aim to improve the Representative Particle Monte Carlo (RPMC) method, which is often used for the study of dust coagulation, to be able to smoothly transition from the many-particle limit into the single-particle limit. Results. Our new version of the RPMC method allows for variable swarm masses, making it possible to refine the mass resolution where needed. It allows swarms to consist of few numbers of particles, and it includes a treatment of the transition from swarm to individual particles. The correctness of the method for a simplified two-component test case is validated with an analytical argument. The method is found to retain statistical balance and to accurately describe runaway growth, as is confirmed with the standard constant kernel, linear kernel, and product kernel tests as well as by comparison with a fiducial non-representative Monte Carlo simulation.

The problem of estimating an illumination distribution from images is called inverse lighting. For inverse lighting, three approaches have been developed based on specular reflection components, diffuse reflection components, and cast shadows. The present study provides theoretical insights as to why the approach based on cast shadows works in a reliable manner, and discusses what kind of basis functions are appropriate to be used for recovering illumination from cast shadows. First, we formalize the approach based on cast shadows by using spherical harmonics. Then, we analyze the approach in the frequency domain and show the advantages and the limitations of the approach. Second, motivated by the observations in the frequency domain, we propose an efficient method using Haar wavelets that provide compact supports and sparsity of coefficients. Finally, we report the results of experiments that compared the method using spherical harmonics and the method using Haar wavelets.

This thesis demonstrates the feasibility of basing dose calculations for electrons in radiotherapy on first-principles single scatter physics, in a calculation time that is comparable to or better than current electron Monte Carlo methods. The macro response Monte Carlo (MRMC) method achieves run times that have potential to be much faster than conventional electron transport methods such as condensed history. The problem is broken down into two separate transport calculations. The first stage is a local, single scatter calculation, which generates probability distribution functions (PDFs) to describe the electron's energy, position, and trajectory after leaving the local geometry, a small sphere or “kugel.” A number of local kugel calculations were run for calcium and carbon, creating a library of kugel data sets over a range of incident energies (0.25–8 MeV) and sizes (0.025 to 0.1 cm in radius). The second transport stage is a global calculation, in which steps that conform to the size of the kugels in the library are taken through the geometry of a phantom. For each step, the appropriate PDFs from the MRMC library are sampled to determine the electron's new energy, position, and trajectory. The electron is immediately advanced to the end of the step and then another kugel is sampled. The process continues in this manner until transport is completed. The MRMC global stepping code was benchmarked as a series of subroutines inside of the Peregrine Monte Carlo code against EGS4 and MCNP for depth dose in simple phantoms having density inhomogeneities. The energy deposition algorithms for spreading dose across 5–10 transport zones per kugel were tested. Most resulting depth dose calculations were within 2%–3% of well-benchmarked Monte Carlo codes.

Objective:Mimicking state-of-the-art patient radiotherapy with high-precision irradiators for small animals is expected to advance the understanding of dose–effect relationships and radiobiology in general. We work on the implementation of intensity-modulated radiotherapy-like irradiation schemes for small animals. As a first step, we present a fast analytical dose calculation algorithm for keV photon beams.Methods:We follow a superposition–convolution approach adapted to kV X-rays, based on previous work for microbeam therapy. We assume local energy deposition at the photon interaction point due to the short electron ranges in tissue. This allows us to separate the dose calculation into locally absorbed primary dose and the scatter contribution, calculated in a point kernel approach. We validate our dose model against Geant4 Monte Carlo (MC) simulations and compare the results to Muriplan (XStrahl Ltd, Camberley, UK).Results:For field sizes of (1 mm)2 to (1 cm)2 in water, the depth dose curves show a mean disagreement of 1.7% to MC simulations, with the largest deviations in the entrance region (4%) and at large depths (5% at 7 cm). Larger discrepancies are observed at water-to-bone boundaries, in bone and at the beam edges in slab phantoms and a mouse brain. Calculation times are in the order of 5 s for a single beam.Conclusion:The algorithm shows good agreement with MC simulations in an initial validation. It has the potential to become an alternative to full MC dose calculation.Advances in knowledge:The presented algorithm demonstrates the potential of kernel-based dose calculation for kV photon beams. It will be valuable in intensity-modulated radiotherapy and inverse treatment planning for high precision small-animal radiotherapy.

Influence of polydispersity and breakage on stochastic simulations of spray fluidized bed agglomeration

Monte Carlo (MC) methods are recognized as the gold-standard for dose calculation, however they have not replaced analytical methods up to now due to their lengthy calculation times. GPU-based applications allow MC dose calculations to be performed on time scales comparable to conventional analytical algorithms. This study focuses on validating our GPU-based MC code for proton dose calculation (gPMC) using an experimentally validated multi-purpose MC code (TOPAS) and compare their performance for clinical patient cases. Clinical cases from five treatment sites were selected covering the full range from very homogeneous patient geometries (liver) to patients with high geometrical complexity (air cavities and density heterogeneities in head-and-neck and lung patients) and from short beam range (breast) to large beam range (prostate). Both gPMC and TOPAS were used to calculate 3D dose distributions for all patients. Comparisons were performed based on target coverage indices (mean dose, V95, D98, D50, D02) and gamma index distributions. Dosimetric indices differed less than 2% between TOPAS and gPMC dose distributions for most cases. Gamma index analysis with 1%/1 mm criterion resulted in a passing rate of more than 94% of all patient voxels receiving more than 10% of the mean target dose, for all patients except for prostate cases. Although clinically insignificant, gPMC resulted in systematic underestimation of target dose for prostate cases by 1–2% compared to TOPAS. Correspondingly the gamma index analysis with 1%/1 mm criterion failed for most beams for this site, while for 2%/1 mm criterion passing rates of more than 94.6% of all patient voxels were observed. For the same initial number of simulated particles, calculation time for a single beam for a typical head and neck patient plan decreased from 4 CPU hours per million particles (2.8–2.9 GHz Intel X5600) for TOPAS to 2.4 s per million particles (NVIDIA TESLA C2075) for gPMC. Excellent agreement was demonstrated between our fast GPU-based MC code (gPMC) and a previously extensively validated multi-purpose MC code (TOPAS) for a comprehensive set of clinical patient cases. This shows that MC dose calculations in proton therapy can be performed on time scales comparable to analytical algorithms with accuracy comparable to state-of-the-art CPU-based MC codes.

Algorithms for approximate Bayesian inference, such as those based on sampling (i.e., Monte Carlo methods), provide a natural source of models of how people may deal with uncertainty with limited cognitive resources. Here, we consider the idea that individual differences in working memory capacity (WMC) may be usefully modeled in terms of the number of samples, or "particles," available to perform inference. To test this idea, we focus on two recent experiments that report positive associations between WMC and two distinct aspects of categorization performance: the ability to learn novel categories, and the ability to switch between different categorization strategies ("knowledge restructuring"). In favor of the idea of modeling WMC as a number of particles, we show that a single model can reproduce both experimental results by varying the number of particles-increasing the number of particles leads to both faster category learning and improved strategy-switching. Furthermore, when we fit the model to individual participants, we found a positive association between WMC and best-fit number of particles for strategy switching. However, no association between WMC and best-fit number of particles was found for category learning. These results are discussed in the context of the general challenge of disentangling the contributions of different potential sources of behavioral variability.