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At least 1,765 records · Page 98

Probabilistic safety assessment of the design of a tall buildings under the extreme load

The paper describes some experiences from the deterministic and probabilistic analysis of the safety of the tall building structure. There are presented the methods and requirements of Eurocode EN 1990, standard ISO 2394 and JCSS. The uncertainties of the model and resistance of the structures are considered using the simulation methods. The MONTE CARLO, LHS and RSM probabilistic methods are compared with the deterministic results. On the example of the probability analysis of the safety of the tall buildings is demonstrated the effectiveness of the probability design of structures using Finite Element Methods.

97 MATHEMATICS AND COMPUTING↗

On the time scale associated with Monte Carlo simulations

Uniform-acceptance force-bias Monte Carlo (fbMC) methods have been shown to be a powerful technique to access longer timescales in atomistic simulations allowing, for example, phase transitions and growth. Recently, a new fbMC method, the time-stamped force-bias Monte Carlo (tfMC) method, was derived with inclusion of an estimated effective timescale; this timescale, however, does not seem able to explain some of the successes the method. In this contribution, we therefore explicitly quantify the effective timescale tfMC is able to access for a variety of systems, namely a simple single-particle, one-dimensional model system, the Lennard-Jones liquid, an adatom on the Cu(100) surface, a silicon crystal with point defects and a highly defected graphene sheet, in order to gain new insights into the mechanisms by which tfMC operates. It is found that considerable boosts, up to three orders of magnitude compared to molecular dynamics, can be achieved for solid state systems by lowering of the apparent activation barrier of occurring processes, while not requiring any system-specific input or modifications of the method. We furthermore address the pitfalls of using the method as a replacement or complement of molecular dynamics simulations, its ability to explicitly describe correct dynamics and reaction mechanisms, and the association of timescales to MC simulations in general.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Experimental and Monte Carlo evaluation of Eclipse treatment planning system for effects on dose distribution of the hip prostheses

The present study aimed to investigate the effects of titanium, titanium alloy, and stainless steel hip prostheses on dose distribution based on the Monte Carlo simulation method, as well as the accuracy of the Eclipse treatment planning system (TPS) at 6 and 18 MV photon energies. In the present study the pencil beam convolution (PBC) method implemented in the Eclipse TPS was compared to the Monte Carlo method and ionization chamber measurements. The present findings show that if high-Z material is used in prosthesis, large dose changes can occur due to scattering. The variance in dose observed in the present study was dependent on material type, density, and atomic number, as well as photon energy; as photon energy increased back scattering decreased. The dose perturbation effect of hip prostheses was significant and could not be predicted accurately by the PBC method for hip prostheses. The findings show that for accurate dose calculation the Monte Carlo-based TPS should be used in patients with hip prostheses.

61 RADIATION PROTECTION AND DOSIMETRY↗

TH-E-BRE-06: Challenges in the Dosimetry of Flattening Filter Free Beams

Purpose: In current dosimetry protocols [AAPM TG51, IAEA TRS-389] the beam quality correction factor kQ and the water-to-air restricted mass collision stopping-power ratio SPR are related to beam quality specifiers %dd(10){sub x} respectively TPR{sub 20,10} Determining kQ and SPR using these regular beam quality specifiers for conventional accelerators (WFF) and flattening filter free accelerators (FFF) similarly could lead to systemic bias.The influence of the flattening filter on the relationship between various beam quality specifiers and SPR respectively k{sub Q} was studied using Monte Carlo simulations with realistic beam sources. Methods: All Monte Carlo simulations were performed using the BEAMnrc/EGSnrc code system. Radiation transport through nine linear accelerator heads modeled according to technical drawings given by the manufactures and a {sup 60} Co therapy source was simulated with BEAMnrc and then used as a radiation source for further simulations. FFF beam sources were implemented by removing the fattening filter from the WFF model. SPR was calculated applying the user code SPRRZnrc. The mean photon energy below the accelerator head and the mean energies of photons and electrons at the measuring point within the water phantom were calculated using FLURZnrc. Dose calculations within a small water voxel and the thimble ionization chamber PTW-31010 in a water depth of 10 cm were made using the egs-chamber code. Results: SPR and k{sub Q} as a function of fluence spectra based beam quality specifiers as well as conventional beam quality specifiers differ systematically between FFF and WFF beams. According to the results the specifier %dd(10){sub x} revealed the smallest deviation (max. 0.4%) between FFF and WFF beams. Conclusion: The results show that %dd(10){sub x} is an acceptable beam quality specifier for FFF beams. Nevertheless the results confirm the expected bias between FFF and WFF beams which must by further investigated.

07 ISOTOPE AND RADIATION SOURCES↗

Properties of reactive oxygen species by quantum Monte Carlo

The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of chemistry, biology, and atmospheric science. Nevertheless, the electronic structure of such species is a challenge for ab initio computational approaches because of the difficulties to correctly describe the statical and dynamical correlation effects in presence of one or more unpaired electrons. Only the highest-level quantum chemical approaches can yield reliable characterizations of their molecular properties, such as binding energies, equilibrium structures, molecular vibrations, charge distribution, and polarizabilities. In this work we use the variational Monte Carlo (VMC) and the lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium geometries and molecular properties of oxygen and oxygen reactive species. Quantum Monte Carlo methods are used in combination with the Jastrow Antisymmetrized Geminal Power (JAGP) wave function ansatz, which has been recently shown to effectively describe the statical and dynamical correlation of different molecular systems. In particular, we have studied the oxygen molecule, the superoxide anion, the nitric oxide radical and anion, the hydroxyl and hydroperoxyl radicals and their corresponding anions, and the hydrotrioxyl radical. Overall, the methodology was able to correctly describe the geometrical and electronic properties of these systems, through compact but fully-optimised basis sets and with a computational cost which scales as N{sup 3} − N{sup 4}, where N is the number of electrons. This work is therefore opening the way to the accurate study of the energetics and of the reactivity of large and complex oxygen species by first principles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A probabilistic graphical model approach to stochastic multiscale partial differential equations

We develop a probabilistic graphical model based methodology to efficiently perform uncertainty quantification in the presence of both stochastic input and multiple scales. Both the stochastic input and model responses are treated as random variables in this framework. Their relationships are modeled by graphical models which give explicit factorization of a high-dimensional joint probability distribution. The hyperparameters in the probabilistic model are learned using sequential Monte Carlo (SMC) method, which is superior to standard Markov chain Monte Carlo (MCMC) methods for multi-modal distributions. Finally, we make predictions from the probabilistic graphical model using the belief propagation algorithm. Numerical examples are presented to show the accuracy and efficiency of the predictive capability of the developed graphical model.

97 MATHEMATICS AND COMPUTING↗

Multifidelity methods for uncertainty quantification of a nonlocal model for phase changes in materials

This study is devoted to the construction of a multifidelity Monte Carlo (MFMC) method for the uncertainty quantification of a nonlocal, non-mass-conserving Cahn-Hilliard model for phase transitions with an obstacle potential. Here, we are interested in estimating the expected value of an output of interest (OoI) that depends on the solution of the nonlocal Cahn-Hilliard model. As opposed to its local counterpart, the nonlocal model captures sharp interfaces without the need for significant mesh refinement. However, the computational cost of the nonlocal Cahn-Hilliard model is higher than that of its local counterpart with similar mesh refinement, inhibiting its use for outer-loop applications such as uncertainty quantification. The MFMC method augments the desired high-fidelity, high-cost OoI with a set of lower-fidelity, lower-cost OoIs to alleviate the computational burden associated with nonlocality. Most of the computational budget is allocated to sampling the cheap surrogate models to achieve speedup, whereas the high-fidelity model is sparsely sampled to maintain accuracy. For the non-mass-conserving nonlocal Cahn-Hilliard model, the use of the MFMC method results in, for a given computational budget, about an order of magnitude reduction in the mean-squared error of the expected value of the OoI relative to that of the Monte Carlo method.

97 MATHEMATICS AND COMPUTING↗

Numerical methods for solving the Boltzmann equation (a review)

The methods are reviewed which are utilized in principal attempts to obtain the numerical solution or modeling of the Boltzmann equation over a broad range of Knudsen numbers. The primary methods considered are the Monte Carlo and the discrete velocities methods. The conculsions drawn from the analysis include the following: (1) The Monte Carlo methods are not well suited in the area of small Knudsen numbers. (2) Among the Monte Carlo methods, the Bird method appears to be the most attractive, since it is more directly related to the Boltzmann equation. (3) The deterministic methods, which include the discrete ordinate technique, offer great possibilities but require exceedingly large computer times. (4) The use of approximating equations in combination with the discrete velocities method will possibly improve computation time and reduce the required memory volume.

Limar, Y. F.↗

Study of applied magnetic field magnetoplasmadynamic thrusters with particle-in-cell code with Monte Carlo collision. I. Computation methods and physical processes

A two-dimensional axisymmetric electromagnetic particle-in-cell code with Monte Carlo collision conditions has been developed for an applied-field magnetoplasmadynamic thruster simulation. This theoretical approach establishes a particle acceleration model to investigate the microscopic and macroscopic characteristics of particles. This new simulation code was used to study the physical processes associated with applied magnetic fields. In this paper (I), detail of the computation procedure and results of predictions of local plasma and field properties are presented. The numerical model was applied to the configuration of a NASA Lewis Research Center 100-kW magnetoplasmadynamic thruster which has well documented experimental results. The applied magnetic field strength was varied from 0 to 0.12 T, and the effects on thrust were calculated as a basis for verification of the theoretical approach. With this confirmation, the changes in the distributions of ion density, velocity, and temperature throughout the acceleration region related to the applied magnetic fields were investigated. Using these results, the effects of applied field on physical processes in the thruster discharge region could be represented in detail, and those results are reported.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Excited states in variational Monte Carlo using a penalty method

Here, in this article, the authors present a technique using variational Monte Carlo to solve for excited states of electronic systems. This technique is based on enforcing orthogonality to lower energy states, which results in a simple variational principle for the excited states. Energy optimization is then used to solve for the excited states. This technique is applied to the well-characterized benzene molecule, in which ~10 000 parameters are optimized for the first 12 excited states. Agreement within ~0.2 eV is obtained with higher scaling coupled cluster methods; small disagreements with experiment are likely due to vibrational effects.

36 MATERIALS SCIENCE↗

Monte Carlo Tree Search Methods for the Earth-Observing Satellite Scheduling Problem

This work explores on-board planning for the single spacecraft, multiple ground station Earth-observing satellite scheduling problem through artificial neural network function approximation of state–action value estimates generated by Monte Carlo tree search (MCTS). An extensive hyperparameter search is conducted for MCTS on the basis of performance, safety, and downlink opportunity utilization to determine the best hyperparameter combination for data generation. A hyperparameter search is also conducted on neural network architectures. The learned behavior of each network is explored, and each network architecture’s robustness to orbits and epochs outside of the training distributions is investigated. Furthermore, each algorithm is compared with a genetic algorithm, which serves to provide a baseline for optimality. MCTS is shown to compute near-optimal solutions in comparison to the genetic algorithm. The state–action value networks are shown to match or exceed the performance of MCTS in six orders of magnitude less execution time, showing promise for execution on board spacecraft.

Adam P. Herrmann↗

Performance of quantum Monte Carlo for calculating molecular bond lengths

This work investigates the accuracy of real-space quantum Monte Carlo (QMC) methods for calculating molecular geometries. We present the equilibrium bond lengths of a test set of 30 diatomic molecules calculated using variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods. The effect of different trial wavefunctions is investigated using single determinants constructed from Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals with LDA, PBE, and B3LYP functionals, as well as small multi-configurational self-consistent field (MCSCF) multi-determinant expansions. When compared to experimental geometries, all DMC methods exhibit smaller mean-absolute deviations (MADs) than those given by HF, DFT, and MCSCF. The most accurate MAD of 3 ± 2 × 10{sup −3} Å is achieved using DMC with a small multi-determinant expansion. However, the more computationally efficient multi-determinant VMC method has a similar MAD of only 4.0 ± 0.9 × 10{sup −3} Å, suggesting that QMC forces calculated from the relatively simple VMC algorithm may often be sufficient for accurate molecular geometries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interactive Visualization of Multi-Group Cross Sections on High-Fidelity Spatial Meshes

Core simulation tools utilizing Monte Carlo transport methods represent the 'Holy Grail' for nuclear reactor analysis. However, deterministic transport methods pose a number of advantages to Monte Carlo from a computational perspective, which seems likely to make these methods more viable in the near to intermediate term. Deterministic methods almost universally discretize the energy domain in a few to hundreds of energy groups. One of the key challenges for deterministic transport-based methods to be viable is accurate, reactor agnostic multi-group cross section generation. This paper describes tools for data processing and visualization of multigroup cross sections generated on high-fidelity spatial meshes from the OpenMC Monte Carlo code. Next generation deterministic transport reactor core modeling tools will require multi-group cross section (MGXS) generation on high-fidelity spatial meshes. High-fidelity MGXS are necessary for the accurate simulation of neutron physics in nuclear reactors with a high degree of spectral heterogeneity - e.g., large localized neutron flux gradients throughout a reactor core. Although many local (e.g., pin cell) approximations have been developed to model the scalar flux to compute spectral-averaged MGXS, these techniques cannot account for complex intra-pin and intra-assembly spatial self-shielding effects. Monte Carlo presents the most accurate method for reactor agnostic multi-group cross section generation since it does not require the use of local approximations to the flux. Monte Carlo has been proposed as a highly desirable framework for reactor agnostic cross section generation for many years. Monte Carlo methods can effectively embed all of the relevant spectral effects into the MGXS through the random particle tracking and interaction sampling processes. Previous work has applied MCNP and Serpent to compute few-group constants for diffusion calculations, and OpenMC to compute multi-group cross sections for transport-based methods. The primary difficulty with using Monte Carlo for MGXS generation is the tremendous computational resources required to adequately converge multi-group cross sections in each spatial region and energy group. Recent development of the OpenMC Monte Carlo code for high-performance computing platforms has made multigroup cross section generation from Monte Carlo more tractable in the foreseeable future. The recent release of OpenMC v0.7.1 includes a new Python-based module for MGXS generation. The MGXS generation module leverages many of the algorithms and features for 'big data' analysis of large tally datasets on complex spatial meshes. This paper describes the data management workflow and visualization tools which have been developed to explore the plethora of MGXS data generated with OpenMC. It is the authors' hope that the development of the visualization tool described in this paper will ultimately enable the design of machine learning algorithms to accelerate the convergence rate of high-fidelity multi-group cross section generated with Monte Carlo. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Monte Carlo simulation of the terrestrial hydrogen exosphere

Methods for Monte Carlo simulation of planetary exospheres have evolved from early work on the lunar atmosphere, where the regolith surface provides a well defined exobase. A major limitation of the successor simulations of the exospheres of Earth and Venus is the use of an exobase surface as an artifice to separate the collisional processes of the thermosphere from a collisionles exosphere. In this paper a new generalized approach to exosphere simulation is described, wherein the exobase is replaced by a barometric depletion of the major constitents of the thermosphere. Exospheric atoms in the thermosphere-exosphere transition region, and in the outer exosphere as well, travel in ballistic trajectories that are interrupted by collisons with the background gas, and by charge exchange interactions with ionospheric particles. The modified simulator has been applied to the terrestrial hydrogen exosphere problem, using velocity dependent differential cross sections to provide statistically correct collisional scattering in H-O and H-H(+) interactions. Global models are presented for both solstice and equinox over the effective solar cycle range of the F(sub 10.7) index (80 to 230). Simulation results show significant differences with previous terrestrial exosphere models, as well as with the H distributions of the MSIS-86 thermosphere model.

Hodges, R. Richard, Jr.↗

SU-F-T-122: 4Dand 5D Proton Dose Evaluation with Monte Carlo

Purpose: We evaluated uncertainties in therapeutic proton doses of a lung treatment, taking into account intra-fractional geometry changes, such as breathing, and inter-fractional changes, such as tumor shrinkage and weight loss. Methods: A Monte Carlo study was performed using four dimensional CT image sets (4DCTs) and weekly repeat imaging (5DCTs) to compute fixed RBE (1.1) and variable RBE weighted dose in an actual lung treatment geometry. The MC2 Monte Carlo system was employed to simulate proton energy deposition and LET distributions according to a thoracic cancer treatment plan developed with a 3D-CT in a commercial treatment planning system, as well as in each of the phases of 4DCT sets which were recorded weekly throughout the course of the treatment. A cumulative dose distribution in relevant structures was computed and compared to the predictions of the treatment planning system. Results: Using the Monte Carlo method, dose deposition estimates with the lowest possible uncertainties were produced. Comparison with treatment planning predictions indicates that significant uncertainties may be associated with therapeutic lung dose prediction from treatment planning systems, depending on the magnitude of inter- and intra-fractional geometry changes. Conclusion: As this is just a case study, a more systematic investigation accounting for a cohort of patients is warranted; however, this is less practical because Monte Carlo simulations of such cases require enormous computational resources. Hence our study and any future case studies may serve as validation/benchmarking data for faster dose prediction engines, such as the track repeating algorithm, FDC.

60 APPLIED LIFE SCIENCES↗

Monte Carlo-Based Method for Parallelizing Quasi-Static Time-Series Power System Simulations: Preprint

Both commercial and open source power system simulators run quasi-static time-series (QSTS) simulations sequentially. For yearlong high-resolution load profiles this sequential execution of load flows incurs long computation times. Parallelizing QSTS simulations on multiple processors is one possible way to reduce the computation time. Parallelization however introduces errors in the simulation results as the initial state of the system at the beginning of each parallelized time period is not known. In this work a Monte Carlo-based approach has been proposed to estimate the initial state of the system for each parallel simulation run to mitigate the errors in the final results. Classical sequential QSTS simulation is the chosen base case against which all other methods have been compared. Results presented in this paper show that the proposed method improves the simulation results considerably. This paper also discusses possible sensitivities of the proposed method to a number of tunable parameters. Additionally, sensitivity analysis results for a number of parameters have also been presented in the results section.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Derivation and verification of the direct-sampling method for simulating Monte Carlo flight paths in tetrahedral meshes with linear finite-element cross sections

This paper provides a derivation of a direct-sampling approach for modeling continuously varying cross sections in tetrahedral-mesh-based Monte Carlo codes. Specifically, cross sections are spatially approximated using linear nodal finite elements. A linearization strategy is provided for non-linearly varying cross sections. The method is verified against seven analytical pure-absorber test problems. These test problems also highlight the benefit of using linear finite elements over element-wise-constant cross sections.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗