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At least 433 records · Page 24

DG-IMEX method for a two-moment model for radiation transport in the $\mathscr{O}$($v$/$c$) limit

Here, we consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to $\mathscr{O}$($v$/$c$), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct $\mathscr{O}$($v$/$c$) Eulerian-frame number density and is consistent, to $\mathscr{O}$($v$/$c$), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical uxes; (iii) a realizability-preserving implicit collision update; and(iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a "spectral redistribution" scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

SU-F-T-658: Out-Of-Field Dose Comparison for TrueBeam Low Energy Beams for Extended Distances: Measurement Vs Monte Carlo Simulation

Purpose: Patient dose far from the treatment field is comprised of scatter from within the patient, and treatment head leakage. We quantify the treatment head leakage for TrueBeam linear accelerator for 6X and 6X-FFF beams by comparing measurements to Monte Carlo simulations for a variety of jaw sizes and collimator rotations. This work is conceptually similar to that of Kry et al. (Medical Physics 2006; 33: 4405), who considered a Clinac linear accelerator. Methods: Measurements were made using an EXRADIN A101 ion chamber positioned in the patient plane, at distances up to 100 cm from isocenter. Simulations were done using VirtuaLinac, the GEANT4-based Monte Carlo model of the TrueBeam treatment head, and an in-house (U. Virginia) GEANT4-based code. In-house code modelled an ion chamber with build-up, based on a CT scan of the chamber. VirtuaLinac included a detailed model of the treatment head shielding, and was run on the Amazon Web Services cloud to generate spherical phase space files surrounding the treatment head. These phase space files were imported into the in-house code. Results: Initial comparisons between measurements and simulation showed an excess of dose in the in-plane direction, away from the gantry, in the simulations. This was traced to an incomplete model of the shielding—specifically, the component holding the primary collimator was smaller in the model than in the TrueBeam. Modifications were made to VirtuaLinac to more closely match the engineering drawings. In the in-plane direction, the lowest out of field dose was away from gantry (negative abscissa values) at around 60 cm from isocenter, for fields smaller than 10×10 cm2. Out of field dose decreased with decreasing jaw size. Flattening-filter free beam produced out-of-field doses as low as 65% of those with flattened beam. Conclusion: Doses determined from simulation and measurement were in close agreement. Funding support from the Jefferson Trust Foundation.

60 APPLIED LIFE SCIENCES↗

Canonical quantization of classical mechanics in curvilinear coordinates. Invariant quantization procedure

In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. An explicit form of position and momentum operators as well as their appropriate ordering in arbitrary curvilinear coordinates is demonstrated. Finally, the extension of presented formalism onto non-flat case and related ambiguities of the process of quantization are discussed. -- Highlights: •An invariant quantization procedure of classical mechanics on the phase space over flat configuration space is presented. •The passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. •Explicit form of position and momentum operators and their appropriate ordering in curvilinear coordinates is shown. •The invariant form of Hamiltonian operators quadratic and cubic in momenta is derived. •The extension of presented formalism onto non-flat case and related ambiguities of the quantization process are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Attractor comparisons based on density

Recognizing a chaotic attractor can be seen as a problem in pattern recognition. Some feature vector must be extracted from the attractor and used to compare to other attractors. The field of machine learning has many methods for extracting feature vectors, including clustering methods, decision trees, support vector machines, and many others. In this work, feature vectors are created by representing the attractor as a density in phase space and creating polynomials based on this density. Density is useful in itself because it is a one dimensional function of phase space position, but representing an attractor as a density is also a way to reduce the size of a large data set before analyzing it with graph theory methods, which can be computationally intensive. The density computation in this paper is also fast to execute. In this paper, as a demonstration of the usefulness of density, the density is used directly to construct phase space polynomials for comparing attractors. Comparisons between attractors could be useful for tracking changes in an experiment when the underlying equations are too complicated for vector field modeling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exploring the Nucleon Structure via Deep Electroproduction Processes

Understanding the internal structure of the nucleon is a fundamental goal of modern physics, which aims at a comprehensive framework describing the internal dynamics of quarks and gluons. Among other structure functions, Generalized Parton Distributions (GPDs) offer a powerful framework for describing the nucleon dynamics by correlating the longitudinal momentum and the transverse position of its internal partons. Such a correlation provides a three-dimensional picture of the nucleon and enables access to fundamental properties, including the internal pressure distributions and the parton’s angular momentum contribution to the nucleon's total spin, thereby playing a central role in resolving the nucleon spin puzzle. At the Thomas Jefferson National Facility (JLab), polarized electron beam experiments allow for probing GPDs through the measurement of hard exclusive processes. Among the cleanest experimental channels, we find the electro-production of a real photon through the Deeply Virtual Compton Scattering (DVCS) mechanism. The first data-taking period of the CLAS12 program, taking place in 2018, allowed for unique DVCS Beam Spin Asymmetry (BSA) measurements in the phase space covered by a 10.6 GeV polarized electron beam impinging on an unpolarized liquid hydrogen target. Although detecting all final-state particles ensures exclusivity of the process, conservation laws indicate that it is not mandatory. I adopt an approach omitting the direct detection of the recoil proton, providing a simplified yet effective event selection strategy that boosts statistics and gives access to a larger phase space sensitive to the underlying GPD dynamics through BSA and cross section measurements. The Double DVCS (DDVCS) process promises a dedicated mapping of GPDs. Contributing to the electro-production of a lepton pair cross-section, the DDVCS reaction extends DVCS by allowing the final-state photon to be virtual, enriching the kinematic phase space and providing unique access to the internal correlations encoded by GPDs. A feasibility study is conducted to assess the potential of future DDVCS measurements at Jefferson Lab and the future Electron-Ion Collider (EIC). While Jefferson Lab will provide DDVCS measurements in the valence region through the SoLID$\mu$ and $\mu$CLAS12 experimental projects, in the long term, the EIC will provide complementary measurements in the sea region, both accessing unprecedented information about GPDs in a phase space region otherwise inaccessible. Taken together, these investigations demonstrate both the current capabilities and future opportunities for probing GPDs through exclusive processes. The experimental analysis of DVCS at CLAS12 provides precise measurements within an established framework, while the phenomenological study of DDVCS opens the door to richer and more comprehensive explorations with future detectors and facilities.

Alvarado, Juan [Université Paris-Saclay: Gif-sur-Y↗

Complete Hamiltonian analysis of cosmological perturbations at all orders II: non-canonical scalar field

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [1] to non-canonical scalar field and obtain an unique expression of speed of sound in terms of phase-space variable. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.

79 ASTRONOMY AND ASTROPHYSICS↗

Dynamical complexity of the Brans-Dicke cosmology

The dynamics of the Brans-Dicke theory with a quadratic scalar field potential function and barotropic matter is investigated. The dynamical system methods are used to reveal complexity of dynamical evolution in homogeneous and isotropic cosmological models. The structure of phase space crucially depends on the parameter of the theory ω{sub BD} as well as barotropic matter index w{sub m}. In our analysis these parameters are treated as bifurcation parameters. We found sets of values of these parameters which lead to generic evolutional scenarios. We show that in isotropic and homogeneous models in the Brans-Dicke theory with a quadratic potential function the de Sitter state appears naturally. Stability conditions of this state are fully investigated. It is shown that these models can explain accelerated expansion of the Universe without the assumption of the substantial form of dark matter and dark energy. The Poincare construction of compactified phase space with a circle at infinity is used to show that phase space trajectories in a physical region can be equipped with a structure of a vector field on nontrivial topological closed space. For ω{sub BD} < −3/2 we show new types of early and late time evolution leading from the anti-de Sitter to the de Sitter state through an asymmetric bounce. In the theory without a ghost we find bouncing solutions and the coexistence of the bounces and the singularity. Following the Peixoto theorem some conclusions about structural stability are drawn.

79 ASTRONOMY AND ASTROPHYSICS↗

Stacking caustic masses from galaxy clusters

Ongoing and future spectroscopic surveys will measure numerous galaxy redshifts within tens of thousands of galaxy clusters. However, the sampling within these clusters will be low, 15 1000 galaxies per ensemble phase space, the escape-velocity edge becomes readily identifiable and the presence of interloping galaxies is minimized. We develop and test an algorithm to trace the projected phase-space surface directly, which results in minimally biased dynamical mass estimates. We then quantify how binning and sampling affect the phase-space-based mass estimates when using an observational proxy that incorporates realistic mass scatter, like richness, and find the added uncertainty in the binning procedure has minimal influence on the resulting bias and scatter of the stacked mass estimates.

79 ASTRONOMY AND ASTROPHYSICS↗

Influence of Wetting on Viscous Fingering Via 2D Lattice Boltzmann Simulations

We present simulations of two-phase flow using the Rothman and Keller colour gradient Lattice Boltzmann method to study viscous fingering when a “red fluid” invades a porous model initially filled with a “blue” fluid with different viscosity. We conducted eleven suites of 81 numerical experiments totalling 891 simulations, where each suite had a different random realization of the porous model and spanned viscosity ratios in the range $$M\in [0.01,100]$$ M ϵ [ 0.01 , 100 ] and wetting angles in the range $$\theta _w\in [180^\circ ,0^\circ ]$$ θ w ϵ [ 180 ° , 0 ° ] to allow us to study the effect of these parameters on the fluid-displacement morphology and saturation at breakthrough (sweep). Although sweep often increased with wettability, this was not always so and the sweep phase space landscape, defined as the difference in saturation at a given wetting angle relative to saturation for the non-wetting case, had hills, ridges and valleys. At low viscosity ratios, flow at breakthrough is localized through narrow fingers that span the model. After breakthrough, the flow field continues to evolve and the saturation continues to increase albeit at a reduced rate, and eventually exceeds 90% for both non-wetting and wetting cases. The existence of a complicated sweep phase space at breakthrough, and continued post-breakthrough evolution suggests the hydrodynamics and sweep is a complicated function of wetting angle, viscosity ratio and time, which has major potential implications to Enhanced Oil Recovery by water flooding, and hence, on estimates of global oil reserves. Validation of these results via experiments is required to ensure they translate to field studies.

Engineering↗

SU-E-T-561: Monte Carlo-Based Organ Dose Reconstruction Using Pre-Contoured Human Model for Hodgkins Lymphoma Patients Treated by Cobalt-60 External Beam Therapy

Purpose: Organ doses for the Hodgkin’s lymphoma patients treated with cobalt-60 radiation were estimated using an anthropomorphic model and Monte Carlo modeling. Methods: A cobalt-60 treatment unit modeled in the BEAMnrc Monte Carlo code was used to produce phase space data. The Monte Carlo simulation was verified with percent depth dose measurement in water at various field sizes. Radiation transport through the lung blocks were modeled by adjusting the weights of phase space data. We imported a precontoured adult female hybrid model and generated a treatment plan. The adjusted phase space data and the human model were imported to the XVMC Monte Carlo code for dose calculation. The organ mean doses were estimated and dose volume histograms were plotted. Results: The percent depth dose agreement between measurement and calculation in water phantom was within 2% for all field sizes. The mean organ doses of heart, left breast, right breast, and spleen for the selected case were 44.3, 24.1, 14.6 and 3.4 Gy, respectively with the midline prescription dose of 40.0 Gy. Conclusion: Organ doses were estimated for the patient group whose threedimensional images are not available. This development may open the door to more accurate dose reconstruction and estimates of uncertainties in secondary cancer risk for Hodgkin’s lymphoma patients. This work was partially supported by the intramural research program of the National Institutes of Health, National Cancer Institute, Division of Cancer Epidemiology and Genetics.

61 RADIATION PROTECTION AND DOSIMETRY↗

A Bunch Compression Method for Free Electron Lasers that Avoids Parasitic Compressions

Virtually all existing high energy (>few MeV) linac-driven FELs compress the electron bunch length though the use of off-crest acceleration on the rising side of the RF waveform followed by transport through a magnetic chicane. This approach has at least three flaws: 1) it is difficult to correct aberrations--particularly RF curvature, 2) rising side acceleration exacerbates space charge-induced distortion of the longitudinal phase space, and 3) all achromatic "negative compaction" compressors create parasitic compression during the final compression process, increasing the CSR-induced emittance growth. One can avoid these deficiencies by using acceleration on the falling side of the RF waveform and a compressor with M 56 >0. This approach offers multiple advantages: 1) It is readily achieved in beam lines supporting simple schemes for aberration compensation, 2) Longitudinal space charge (LSC)-induced phase space distortion tends, on the falling side of the RF waveform, to enhance the chirp, and 3) Compressors with M 56 >0 can be configured to avoid spurious over-compression. We will discuss this bunch compression scheme in detail and give results of a successful beam test in April 2012 using the JLab UV Demo FEL

43 PARTICLE ACCELERATORS↗

On the utility of non thermal plasmas

Nonthermal plasmas have properties which can differ substantially even from thermal plasmas of the same density and energy. In practical applications, many of these differences have utility that can be exploited, often with waves. The goal of this thesis is to explore three such applications of nonthermal plasma for the purposes of wave amplification and, ultimately, controlled nuclear fusion. First, we discuss the outstanding potential for a shaped plasma technology that relies on ionizing a beam of aerosol particles. This ionization results in a Coulomb explosion, yielding a highly nonthermal distribution for the plasma in the target volume. Homogeneous, high aspect ratio plasma couplers such as these could be used in a Raman amplification scheme to attain the next generation of laser intensities. Such a powerful laser could be used to study radiation reaction and vacuum pair production, among many other applications. We describe the conditions under which sufficiently dense aerosol beams can be prepared and provide some experimental validation of these claims. Second, we survey the prospects for controlled p-11B fusion in both magnetic and inertial confinement schemes. Whereas most studies have focused on mitigating the bremsstrahlung loss channel, we focus on nonthermal manipulations of the bulk plasma which could improve the reactivity. In particular, we present upper bounds on the p-11B reactivity using alpha channeling to efficiently heat the proton distribution in both schemes. Finally, we place a sharp limit on the energy that can be extracted from a non-thermal particle distribution using waves. In the quasilinear regime of wave-particle interaction, waves rearrange the densities of states in phase space in a diffusive fashion. A salient consequence is that only certain, generally nonthermal, plasma states can be reached. We characterize this restricted state space and thereby reduce the problem of maximizing energy extraction to linear programming. Varying the connectedness of the phase space so that e.g. particles may only be diffused to parts of phase space close in energy, we describe the implications for the state space and the solution of the optimization problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Parton distribution functions from scalar light-front parton gas model

Here, we propose an application of a microcanonical ensemble with light-front kinematics to model the phase-space distribution of relativistic constituents of a bound state. These constituents denoted by partons are treated as classical spin-zero particles confined inside the bound state with inter-parton collisions as their only interaction. The microcanonical molecular dynamics ensemble is applied to obtain the phase-space distribution of such a thermodynamic system. We sample this phase-space distribution using Monte Carlo algorithms to obtain the parton distribution functions (PDFs) in scenarios with 3, 4, and 5 identical partons. In addition PDFs when a selected number of massless partons are mixed with 3 massive partons are also presented.

Microcanonical ensemble↗

Magnetic and dielectric behavior in YMn{sub 1−x}Fe{sub x}O{sub 3} (x ≤ 0.5)

The role of doping Fe on the structural, magnetic, and dielectric properties of frustrated antiferromagnet YMn{sub 1−x}Fe{sub x}O{sub 3} (x ≤ 0.5) has been investigated. The neutron diffraction analysis shows that the structure of these polycrystalline samples changes from hexagonal phase (space group P6{sub 3}cm) to orthorhombic phase (space group Pnma) for x > 0.2. The frustration parameter decreases with Fe substitution. All the compounds are antiferromagnetic, and the magnetic structure is described as a mixture of Γ3 and Γ4 irreducible representation (IR) in the hexagonal phase, and the ratio of these two IRs is found to vary with Fe doping (x ≤ 0.2). A continuous spin reorientation as a function of temperature is observed in these samples. The magnetic ground state in the orthorhombic phase of the higher doped samples (x ≥ 0.3) is explained by taking Γ1 (G{sub x}C{sub y}A{sub z}) representation of Pnma setting. In YMnO{sub 3} suppression of dielectric constant ε′ is observed below T{sub N} indicative of magnetoelectric coupling. This anomalous behavior reduces in Fe doped samples. The dielectric constant is found to be correlated with the magnetic moment (M) obtained from neutron diffraction experiments and follows a M{sup 2} behavior close to T{sub N} in agreement with Landau theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Semiclassical theory and the Koopman-van Hove equation *

Abstract The phase space Koopman-van Hove (KvH) equation can be derived from the asymptotic semiclassical analysis of partial differential equations. Semiclassical theory yields the Hamilton–Jacobi equation for the complex phase factor and the transport equation for the amplitude. These two equations can be combined to form a nonlinear semiclassical version of the KvH equation in configuration space. There is a natural injection of configuration space solutions into phase space and a natural projection of phase space solutions onto configuration space. Hence, every solution of the configuration space KvH equation satisfies both the semiclassical phase space KvH equation and the Hamilton–Jacobi constraint. For configuration space solutions, this constraint resolves the paradox that there are two different conserved densities in phase space. For integrable systems, the KvH spectrum is the Cartesian product of a classical and a semiclassical spectrum. If the classical spectrum is eliminated, then, with the correct choice of Jeffreys–Wentzel–Kramers–Brillouin (JWKB) matching conditions, the semiclassical spectrum satisfies the Einstein–Brillouin–Keller quantization conditions which include the correction due to the Maslov index. However, semiclassical analysis uses different choices for boundary conditions, continuity requirements, and the domain of definition. For example, use of the complex JWKB method allows for the treatment of tunneling through the complexification of phase space. Finally, although KvH wavefunctions include the possibility of interference effects, interference is not observable when all observables are approximated as local operators on phase space. Observing interference effects requires consideration of nonlocal operations, e.g. through higher orders in the asymptotic theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exploring the SDSS Data Set with Linked Scatter Plots. I. EMP, CEMP, and CV Stars

We present the results of a search for extremely metal-poor (EMP), carbon-enhanced metal-poor (CEMP), and cataclysmic variable (CV) stars using a new exploration tool based on linked scatter plots (LSPs). Our approach is especially designed to work with very large spectrum data sets such as the SDSS, LAMOST, RAVE, and Gaia data sets, and it can be applied to stellar, galaxy, and quasar spectra. As a demonstration, we conduct our search using the SDSS DR10 data set. We first created a 3326-dimensional phase space containing nearly 2 billion measures of the strengths of over 1600 spectral features in 569,738 SDSS stars. These measures capture essentially all the stellar atomic and molecular species visible at the resolution of SDSS spectra. We show how LSPs can be used to quickly isolate and examine interesting portions of this phase space. To illustrate, we use LSPs coupled with cuts in selected portions of phase space to extract EMP stars, CEMP stars, and CV stars. We present identifications for 59 previously unrecognized candidate EMP stars and 11 previously unrecognized candidate CEMP stars. We also call attention to 2 candidate He ii emission CV stars found by the LSP approach that have not yet been discussed in the literature.

79 ASTRONOMY AND ASTROPHYSICS↗

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables

The typically rugged nature of molecular free energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for data-driven discovery of CVs parameterizing the important large scale motions of the system. A challenge to CV discovery is learning CVs invariant to symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multi-molecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate Permutation Invariant Vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation, and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand sampling of configurational phase space and obtain converged CVs and free energy landscapes. Here, we demonstrate the Permutationally Invariant Network for Enhanced Sampling (PINES) approach in applications to the self-assembly of a 13-atom Argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C 45 H 92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

WE-A-17A-04: Development of An Ultra-Fast Monte Carlo Dose Engine for High Dose Rate Brachytherapy

Purpose: Current clinical brachytherapy dose calculations are based on AAPM TG43 guidelines, which approximate the patient geometry as a large water phantom. This ignores heterogeneities and tends to overestimate skin dose. Although Monte Carlo (MC) dose calculations have been recognized as the most accurate method, its associated long computational time is a major bottleneck for routine clinical applications. This work aims to develop a GPU-based ultra-fast MC dose engine (gBMC) for HDR brachytherapy to provide clinical users with accurate sub-minute dose calculations. Methods: Standard photon transport with discrete events including: Compton scattering, Rayleigh scattering and Photoelectric effect, was implemented. Secondary electrons were transported under the continuous slowing down approximation. To reduce the GPU thread divergence, photons and electrons were separately transported. Transport of photons was grouped according to energy. The source model in gBMC can be either a phase-space file generated using Geant4 or a parameterized source model. This dose engine was validated against TG43 in a water phantom and against Geant4 calculations in heterogeneous patient geometries. Results: A phase space file was generated for the Varian VS2000 Ir-192 source. In a water phantom, the calculated radial dose function was within 0.6% of the TG43 calculations for radial distances from 1 cm to 20 cm. The anisotropy functions were within 1% for radial distances from 1 cm to 20 cm except for polar angles larger than 173°. Local point-dose differences were within 2%. In a Mammosite breast cancer case with 22 dwell locations, gBMC and Geant4 isodose lines compared well. The computation time was about 28 seconds using the phase-space file source and 20 seconds using the parameterized source to simulate 1 billion particles, yielding less than 1% statistical uncertainty. Conclusion: The gBMC dose engine makes it possible to use fast and accurate MC dose calculations for clinical work.

60 APPLIED LIFE SCIENCES↗