In the original publication [1], there was a mistake in the legend for Figure 2. The spherical variables were misdefined by using latitude and longitude. The correct legend and figure appear below: There was an inconsistency between the spherical variables defined in Figure 2 and Equations (13)–(15). A correction was made to 2. Central Focus Scheme, 2.2. Generation via Coordinate Transformation: (Formula presented.) (Formula presented.) (Formula presented.) The obtained code by means the coordinate transformation, which is shown in Appendix B, was also changed: Some typos were also corrected: In Abstract, “a Gaussian distributions” has been corrected to “a Gaussian distribution”. In Keywords, “discreet energy spectra” has been corrected to “discrete energy spectra”. In Introduction, “azimuth and longitude” has been corrected to “azimuth and zenith”. The authors state that the scientific conclusions are unaffected. These corrections were approved by the Academic Editor. The original publication has also been updated.

In this study, by attempting to resolve the difficulties related to the angular distribution during the particle generation for the muon tomography applications in the GEANT4 simulations, we exhibit an unconventional methodology that is hinged on the direction limitation via the vectorial construction from the generation location to the restriction area rather than using a certain angular distribution or interval. In other words, we favor a momentum direction that is determined by a vector constructed between an initial point randomly chosen on a generative point/plane and a second point arbitrarily selected on a restrictive plane of the same dimensions with the basal cross section of the volume-of-interest (VOI). On account of setting out such a generation scheme, we optimize the particle loss by keeping an angular acceptance that is directly dependent on the VOI geometry as well as the vertical position of the restrictive plane for a tomographic system of a finite size. We demonstrate our strategy for a set of target materials including aluminum, iron, copper, lead, and uranium with a dimension of 40×10×40 cm3 over three restrictive planes of different positions by using a discrete energy spectrum between 0.1 and 8 GeV and we compute the scattering angle, the number of absorption, and the particle loss. Upon our simulation outcomes, we show that the particle generation by means of restrictive planes is an effective strategy that is flexible towards a variety of computational objectives in the GEANT4 simulations.

The structural characterization of the nuclear materials constitutes an indispensable aspect that necessitates a careful transportation, a limited interaction, and under certain circumstances an on-site investigation for the nuclear fields including but not limited to nuclear waste management, nuclear forensics, and nuclear proliferation. To attain this purpose, among the promising non-destructive/non-hazardous techniques that are performed for the interrogation of the nuclear materials is the muon tomography where the target materials are discriminated by the interplay between the atomic number, the material density, and the material thickness on the basis of the scattering angle and the absorption in the course of the muon propagation within the target volume. In this study, we employ the Monte Carlo simulations by using the GEANT4 code to demonstrate the capability of muon tomography based on the dual-parameter analysis in the examination of the nuclear waste barrels. Our current hodoscope setup consists of three top and three bottom plastic scintillators made of polyvinyl toluene with the thickness of 0.4 cm, and the composite target material is a cylindrical nuclear waste drum with the height of 96 cm and the radius of 29.6 cm where the outermost layer is stainless steel with the lateral thickness of 3.2 cm and the filling material is ordinary concrete that encapsulates the nuclear materials of dimensions 20×20×20 cm3. By simulating with a narrow planar muon beam of 1×1 cm2 over the uniform energy interval between 0.1 and 8 GeV, we determine the variation of the average scattering angle together with the standard deviation by utilizing a 0.5-GeV bin length, the counts of the scattering angle by using a 1-mrad step, and the number of the absorption events for the five prevalent nuclear materials starting from cobalt and ending in plutonium. Via the duo-parametric analysis that is founded on the scattering angle as well as the absorption in the present study, we show that the presence of the nuclear materials in the waste barrels is numerically visible in comparison with the concrete-filled waste drum without any nuclear material, and the muon tomography is capable of distinguishing these nuclear materials by coupling the information about the scattering angle and the number of absorption in the cases where one of these two parameters yields strong similarity for certain nuclear materials.

The simulation of muon tomography requires a multi-directional particle source that traverses a number of horizontal detectors of limited angular acceptance that are used to track cosmic-ray muons. In this study, we describe a simple strategy that can use GEANT4 simulations to produce a hemispherical particle source. We initially generate random points on a spherical surface of practical radius by using a Gaussian distribution for the three components of the Cartesian coordinates, thereby obtaining a generating surface for the initial position of the particles to be tracked. Since we do not require the bottom half of the sphere, we take the absolute value of the vertical coordinate, resulting in a hemisphere. Next, we direct the generated particles into the target body by selectively favoring the momentum direction along the vector constructed between a random point on the hemispherical surface and the origin of the target, thereby minimizing particle loss through source biasing. We also discuss a second scheme where the coordinate transformation is performed between the spherical and Cartesian coordinates, and the above-source biasing procedure is applied to orient the generated muons towards the target. Finally, a recipe based on restrictive planes from our previous study is discussed. We implement our strategies by using G4ParticleGun in the GEANT4 code. While we apply these techniques to simulations for muon tomography via scattering, these source schemes can be applied to similar studies for atmospheric sciences, space engineering, and astrophysics where a 3D particle source is a necessity.

In the tomographic configurations based on the muon scattering, the angular variation with respect to the kinetic energy indirectly brings forth the ability to coarsely predict the kinetic energy by using the deflection angle owing to the detector layers. Nevertheless, the angular deviation due to the detector components is expected to be minuscule in addition to a relatively high uncertainty in the case of the plastic scintillators. In the present study, we contrast our current tomographic prototype, which consists of the detector layers manufactured from polyvinyl toluene besides a detector accuracy of 1 mrad, with an alternative hodoscope scheme containing stainless steel layers by aiming to investigate the three-group energy structure. Initially, we determine the average deflection angles together with the corresponding standard deviations for our present setup as well as for the alternative scheme by means of the GEANT4 simulations. In the second place, we express a brace of misclassification probabilities founded on the standard deviations where the first procedure assumes a linear finite approximation, whereas the latter approach rests on a positively defined modified Gaussian distribution. Upon our simulation results, we demonstrate that the introduced stainless steel layers in the proposed hodoscope setup do not only serve to augment the average deflection angles, but they also diminish the misclassification probabilities, therewith reducing the classification uncertainty apart from an improved detection performance.

In muon scattering tomography, the investigated materials are discriminated according to the scattering angle that mainly depends on the atomic number, the density, and the thickness of the medium at a given energy value. The scattering angles at different initial energies also provide the opportunity to classify the incoming muons into a number of energy groups. In this study, by employing the GEANT4 code, we show that the deflection angle exponentially decays as a function of energy, and the numerical values for the current configuration are below the detector accuracy except the initial energy bins owing to the low-Z, low density, and low thickness of the current plastic scintillators. This implies the necessity of additional components that provoke the muon scattering. Therefore, we introduce stainless steel surfaces into the top and bottom sections in order to amplify the deflection angle as well as to reduce the uncertainty, thereby improving the detector performance.

Dimension reduction procedure is the recipe to represent defects in two dimensional dislocation dynamics according to the changes in the geometrical properties of the defects triggered by different conditions such as radiation, high temperature, or pressure. In the present study, this procedure is extended to incorporate further features related to the presence of defects with a special focus on face-centered cubic/body-centered cubic alloys used for diverse engineering purposes. In order to reflect the microstructural state of the alloy on the computational cell of two dimensional dislocation dynamics, the distribution of the multi-type defects over slip lines is implemented by using corresponding strength and line spacing for each type of defect. Additionally, a simple recursive incremental relation is set to count the loop accumulation on the precipitates. In the case of continuous resistance against the motion of edge dislocations on the slip lines, an expression of friction is introduced to see its contribution on the yield strength. Each new property is applied independently on a different material by using experimental information about defect properties and grain sizes under the condition of plain strain deformation: both constant and dynamically increasing obstacle strength for precipitate coarsening in prime-aged and heat-treated copper-chromium-zirconium, internal friction in tantalum-2.5tungsten, and mixed hardening due to the presence of precipitates and prismatic loops in irradiated oxide dispersion strengthened EUROFER with 0.3% yttria.

In this study, a dimension reduction procedure of defect properties is proposed together with a two dimensional dislocation dynamics framework in order to simulate tensile response of the materials at different levels of external conditions such as radiation. This procedure delivers ordered pairs of strength and line density according to the changes in the geometrical properties of the defects. Plain strain deformation of irradiated oxygen-free high conductivity copper is investigated by using experimental information about the evolution of stacking-fault tetrahedra at the irradiation doses of 0-0.2 dpa. © 2014 Elsevier B.V. All rights reserved.