Monte Carlo Tool Research Articles

Prospects for a polarimetric mapping of the Sgr A molecular cloud complex with IXPE

Context. The X-ray polarization degree of the molecular clouds surrounding Sgr A* is expected to be greatly reduced due to the mixing of the polarized reflection emission with the unpolarized thermal emission that pervades the Galactic center region. This makes this type of observation a challenging experiment for the upcoming Imaging X-ray Polarimeter Explorer (IXPE), whose launch is expected in 2021. Aims. We aim to determine the detectability of four molecular clouds of the Sgr A complex (MC2, Bridge B2, Bridge E, and G0.11-0.11) in a realistic IXPE pointing of the Sgr A field of view. We assess the minimum increase in the detectable polarization when a molecular cloud is off-axis. We provide two different strategies for reconstructing the intrinsic cloud polarization once the data is available. Methods. We used the Monte Carlo tool ixpeobssim to simulate IXPE observations of the Sgr A molecular cloud complex. We used Chandra maps and spectra to model the diffuse emission in the Galactic center region along with a realistic model of the instrumental and diffuse background. We created synthetic polarization products of the unpolarized emission and combined them with a test data set obtained from a simulation of a 2 Ms long IXPE observation to retrieve the intrinsic polarization degree of the molecular clouds. Results. We find that for the molecular clouds considered here, the minimum detectable polarization (MDP) increases by ~1–15% with respect to the case in which a cloud is observed on-axis. We successfully retrieve the intrinsic polarization degree in the 4.0–8.0 keV band and line-of-sight distance of one of them taken as an example, namely, G0.11-0.11, by correcting the observed (i.e., for a 2 Ms-long simulation) polarization degree map using either a synthetic dilution map or a Stokes intensity map of the unpolarized emission. With both methods, the position of the cloud along the line-of-sight is derived from the reconstructed polarization degree with an uncertainty of 7 and 4 pc, respectively. Conclusions. We confirm the results of previous studies, finding that G0.11-0.11 is the most promising target. For the Sgr A molecular complex region, we propose an observation strategy that may permit detection up to three clouds in the 4.0–8.0 keV band, depending on their true line-of-sight position. We demonstrate that by using simulated data products of the unpolarized components, it is possible to clean up the observed polarization maps from the environmental contamination. The methods we present here are potentially useful for the analysis of X-ray polarimetric data of any extended source that is affected by environmental dilution of the polarized signal. To accurately measure (i.e, with uncertainties of the order of a few parsec) the distance of the cloud along the line-of-sight, a high-quality spectrum and image of the clouds quasi simultaneous to the IXPE pointing are needed.

Kinetic Monte Carlo Tool for Kinetic Modeling of Linear Step‐Growth Polymerization: Insight into Recycling of Polyurethanes

AbstractA kinetic Monte Carlo model of polyurethane polymerization which explicitly tracks the polymer sequences is developed and shared. This model is benchmarked against theoretical and experimental polyurethane data and used to investigate the effect on oligomer distributions of unequal reactivity of the first and second isocyanate to react. The reverse reactions using thermodynamic consistency are then added to the framework, and analogous to the addition polymerization concept of ceiling temperature, equilibrium chain length distributions at various temperatures are calculated. For a mixture of three monomers AA, BB, and CC, where BB and CC do not react with one another, are present in stoichiometric proportions, and have different enthalpies of reaction with AA, an odd‐even effect emerges. Odd length chains are more likely than even length chains for temperatures at which BB and CC have significantly different equilibrium conversions. The concept of ceiling temperature that is typically cited for addition polymers is extended here to provide a measure of conditions under which depolymerization for recycling is favored.

MicroBooNE experiment, NuMI absorber, and heavy neutral leptons

Motivated by the recent search for a Higgs-Portal Scalar decaying inside the MicroBooNE detector, we demonstrate that the same search can be used to constrain Heavy Neutral Leptons. These are gauge-singlet fermions that interact with the Standard Model by mixing with neutrinos only and could be related to the origin of neutrino masses. By recasting the results of the MicroBooNE Collaboration's analysis, we show that, for a Heavy Neutral Lepton that mixes predominantly with muon-flavored neutrinos, previously unexplored parameter space can be excluded for masses between 30 and 150 MeV. Additionally, we make our Monte Carlo tools publicly available.

Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines

This article deals with symmetrical data that can be modelled based on Gaussian distribution. We consider a class of partially linear additive spatial autoregressive (PLASAR) models for spatial data. We develop a Bayesian free-knot splines approach to approximate the nonparametric functions. It can be performed to facilitate efficient Markov chain Monte Carlo (MCMC) tools to design a Gibbs sampler to explore the full conditional posterior distributions and analyze the PLASAR models. In order to acquire a rapidly-convergent algorithm, a modified Bayesian free-knot splines approach incorporated with powerful MCMC techniques is employed. The Bayesian estimator (BE) method is more computationally efficient than the generalized method of moments estimator (GMME) and thus capable of handling large scales of spatial data. The performance of the PLASAR model and methodology is illustrated by a simulation, and the model is used to analyze a Sydney real estate dataset.

Study of relationship between dose, LET and the risk of brain necrosis after proton therapy for skull base tumors

PurposeWe investigated the relationship between RBE-weighted dose (DRBE) calculated with constant (cRBE) and variable RBE (vRBE), dose-averaged linear energy transfer (LETd) and the risk of radiographic changes in skull base patients treated with protons. MethodsClinical treatment plans of 45 patients were recalculated with Monte Carlo tool FRED. Radiographic changes (i.e. edema and/or necrosis) were identified by MRI. Dosimetric parameters for cRBE and vRBE were computed. Biological margin extension and voxel-based analysis were employed looking for association of DRBE(vRBE) and LETd with brain edema and/or necrosis. ResultsWhen using vRBE, Dmax in the brain was above the highest dose limits for 38% of patients, while such limit was never exceeded assuming cRBE. Similar values of Dmax were observed in necrotic regions, brain and temporal lobes. Most of the brain necrosis was in proximity to the PTV. The voxel-based analysis did not show evidence of an association with high LETd values. ConclusionsWhen looking at standard dosimetric parameters, the higher dose associated with vRBE seems to be responsible for an enhanced risk of radiographic changes. However, as revealed by a voxel-based analysis, the large inter-patient variability hinders the identification of a clear effect for high LETd.

The SPHERE infrared survey for exoplanets (SHINE)

The SpHere INfrared Exoplanet (SHINE) project is a 500-star survey performed with SPHERE on the Very Large Telescope for the purpose of directly detecting new substellar companions and understanding their formation and early evolution. Here we present an initial statistical analysis for a subsample of 150 stars spanning spectral types from B to M that are representative of the full SHINE sample. Our goal is to constrain the frequency of substellar companions with masses between 1 and 75 MJup and semimajor axes between 5 and 300 au. For this purpose, we adopt detection limits as a function of angular separation from the survey data for all stars converted into mass and projected orbital separation using the BEX-COND-hot evolutionary tracks and known distance to each system. Based on the results obtained for each star and on the 13 detections in the sample, we use a Markov chain Monte Carlo tool to compare our observations to two different types of models. The first is a parametric model based on observational constraints, and the second type are numerical models that combine advanced core accretion and gravitational instability planet population synthesis. Using the parametric model, we show that the frequencies of systems with at least one substellar companion are 23.0−9.7+13.5, 5.8−2.8+4.7, and 12.6−7.1+12.9% for BA, FGK, and M stars, respectively. We also demonstrate that a planet-like formation pathway probably dominates the mass range from 1–75 MJup for companions around BA stars, while for M dwarfs, brown dwarf binaries dominate detections. In contrast, a combination of binary star-like and planet-like formation is required to best fit the observations for FGK stars. Using our population model and restricting our sample to FGK stars, we derive a frequency of 5.7−2.8+3.8%, consistent with predictions from the parametric model. More generally, the frequency values that we derive are in excellent agreement with values obtained in previous studies.

Probing small-scale power spectra with pulsar timing arrays

Models of Dark Matter (DM) can leave unique imprints on the Universe’s small scale structure by boosting density perturbations on small scales. We study the capability of Pulsar Timing Arrays to search for, and constrain, subhalos from such models. The models of DM we consider are ordinary adiabatic perturbations in ΛCDM, QCD axion miniclusters, models with early matter domination, and vector DM produced during inflation. We show that ΛCDM, largely due to tidal stripping effects in the Milky Way, is out of reach for PTAs. Axion miniclusters may be within reach, although this depends crucially on whether the axion relic density is dominated by the misalignment or string contribution. Models where there is matter domination with a reheat temperature below 1 GeV may be observed with future PTAs. Lastly, vector DM produced during inflation can be detected if it is lighter than 10−16 GeV. We also make publicly available a Python Monte Carlo tool for generating the PTA time delay signal from any model of DM substructure.

Evaluation of displacement damage in solids induced by fast positrons: Modeling and effect on vacancy measurement

• The latest theoretical models of radiation damage in solid and numerical results of Mott differential cross section were used; • Displacement cross section by positrons for elements in most commonly used solids was calculated and the difference between positron and electron radiation was emphasized; • Displacement thresholds of kinetic energy for positrons in 30 elemental solids were presented; • Defects spatial distribution was obtained using Monte Carlo modeling. Positron Annihilation Technique is very sensitive to vacancy defects and small vacancy clusters and has been used as supplementary for TEM in radiation damage research. In this paper, we evaluated the displacement damage in solids induced by positrons and its effect on defects measurement, which has not been considered carefully in most PAT application. Displacement damage could only be produced when kinetic energy of positron exceeds a threshold determined by average displacement energy and the mass of atoms. Based on the latest models of displacement damage and numerical Mott elastic differential cross section of positrons interacting with atoms, displacement cross section for fast positron in solids was calculated and compared with that for electrons. In the energy range from 1 MeV to 100 MeV, electrons will produce more displacement defects than positrons do, especially in high-Z materials. Number of total defects depends on the primary displacement cross section and the size of damage cascades. To get distributions of defects and terminating position of positrons in materials, a Monte Carlo tool with full damage model was developed and validated. From the results of Monte Carlo modeling, the defects -generated by mono-energy positron beam have shallower distribution than the stopping position of positrons, indicating separation of defects and positrons and this fact benefits defects measurement because displacement damage produced by fast probing positron beam have little affection on the measurement. But for the positron beams from radioactive sources (such as 22 Na and 64 Cu) with continuous energy spectrum (from 0 to E max ), the depth profile of defects and terminated position of positrons overlap with each other and this fact indicated that defects measurement in materials will be affected by extra defects produced by positrons. The density of defects produced by positron beam is quite low with a typical value of about 0.01–0.1 cm −3 per positron in low-Z materials, which could be comparable with the defect density limitation if enough accumulated positrons are implanted into materials during measurement. For commonly used structural metals (such as Fe, Mn, Cu and metals with Z number higher than 40), using positron from 22 N and 64 Cu directly to measure defects density is quite safe because the energy is smaller than the displacement threshold.

Quasi-Monte Carlo method for calculating X-ray scatter in CT

In this paper we transform the trajectories of X-ray as it interacts with a phantom into a high-dimensional integration problem and give the integral formula for the probability of photons emitted from the X-ray source through the phantom to reach the detector. We propose a superior algorithm called gQMCFRD, which combines GPU-based quasi-Monte Carlo (gQMC) method with forced random detection (FRD) technique to simulate this integral. QMC simulation is deterministic versions of Monte Carlo (MC) simulation, which uses deterministic low discrepancy points (such as Sobol' points) instead of the random points. By using the QMC and FRD technique, the gQMCFRD greatly increases the simulation convergence rate and efficiency. We benchmark gQMCFRD, GPU based MC tool (gMCDRR), which performs conventional simulations, a GPU-based Metropolis MC tool (gMMC), which uses the Metropolis-Hasting algorithm to sample the entire photon path from the X-ray source to the detector and gMCFRD, that uses random points for sampling against PENELOPE subroutines: MC-GPU. The results are in excellent agreement and the Efficiency Improvement Factor range 27 ∼ 37 (or 1.09 ∼ 1.16, or 0.12 ∼ 0.15, or 3.62 ∼ 3.70) by gQMCFRD (or gMCDRR, or gMMC, or gMCFRD) with comparison to MC-GPU in all cases. It shows that gQMCFRD is more effective in these cases.

Simulation tool for predicting and optimizing the performance of nanoparticle based strain sensors

In this work a Monte-Carlo tool simulating platinum nanoparticle (NP) based strain-sensors, on flexible substrates, is presented. The tool begins by randomly placing the NPs on the simulation area, with the ability to tune the NP surface coverage. After the calculation of the conductive paths that were generated in the previous step, the whole system is represented with an equivalent circuit; the NPs and the NP clusters act as nodes and the inter-particle gaps as resistances. The effective resistance is then calculated with the use of a Laplacian Matrix, which has proven extremely effective in significantly reducing the overall computational time. The simulation results are then benchmarked with experimental measurements from actual strain-sensing devices. The software is capable of predicting the strain-sensitivity for different NP sizes as well as surface coverages, emerging as a powerful computational tool for design-optimization of NP based devices in polymeric substrates, while it could well be extended to other nanocomposite materials used in flexible or stretchable electronic applications.

Translating Simulated Chain Length and Molar Mass Distributions in Chain‐Growth Polymerization for Experimental Comparison and Mechanistic Insight

AbstractThe molar mass distribution (MMD), which is also known as the molecular weight distribution (MWD), is a key molecular property for a polymerization process, as it determines polymer strength and polymeric material deformation. Several MMD and related chain length distribution (CLD) representations are however used interchangeably, often leading to biased conclusions. Herein it is highlighted how the most interesting simulated CLD/MMD representations, i.e., the number, mass, z‐based, and logarithmic CLD/MMD, can be translated into each other and how they need to be corrected to facilitate comparison with experimental size exclusion chromatography traces. Their relevance is highlighted by including case studies with increasing complexity in polymer products, addressing first linear, then branched, and ultimately crosslinked systems. For illustration purposes, the case studies are restricted to chain‐growth polymerization, including free radical polymerization, cationic ring‐opening polymerization, and free radical‐induced grafting. All model parameters are taken from literature and kinetic Monte Carlo tools are utilized. Guidelines are also provided for both the experimentalist and modeler to maximize the reliability of CLD/MMD reporting in future kinetic studies.

THUBrachy: fast Monte Carlo dose calculation tool accelerated by heterogeneous hardware for high-dose-rate brachytherapy

The Monte Carlo (MC) simulation is regarded as the gold standard for dose calculation in brachytherapy, but it consumes a large amount of computing resources. The development of heterogeneous computing makes it possible to substantially accelerate calculations with hardware accelerators. Accordingly, this study develops a fast MC tool, called THUBrachy, which can be accelerated by several types of hardware accelerators. THUBrachy can simulate photons with energy less than 3 MeV and considers all photon interactions in the energy range. It was benchmarked against the American Association of Physicists in Medicine Task Group No. 43 Report using a water phantom and validated with Geant4 using a clinical case. A performance test was conducted using the clinical case, showing that a multicore central processing unit, Intel Xeon Phi, and graphics processing unit (GPU) can efficiently accelerate the simulation. GPU-accelerated THUBrachy is the fastest version, which is 200 times faster than the serial version and approximately 500 times faster than Geant4. The proposed tool shows great potential for fast and accurate dose calculations in clinical applications.

As-Built Simulation of the High Flux Isotope Reactor

The Oak Ridge National Laboratory High Flux Isotope Reactor (HFIR) is an 85 MWt flux trap-type research reactor that supports key research missions, including isotope production, materials irradiation, and neutron scattering. The core consists of an inner and an outer fuel element containing 171 and 369 involute-shaped plates, respectively. The thin fuel plates consist of a U3O8-Al dispersion fuel (highly enriched), an aluminum-based filler, and aluminum cladding. The fuel meat thickness is varied across the width of the involute plate to reduce thermal flux peaks at the radial edges of the fuel elements. Some deviation from the designed fuel meat shaping is allowed during manufacturing. A homogeneity scan of each fuel plate checks for potential anomalies in the fuel distribution by scanning the surface of the plate and comparing the attenuation of the beam to calibration standards. While typical HFIR simulations use homogenized fuel regions, explicit models of the plates were developed under the Low-Enriched Uranium Conversion Program. These explicit models typically include one inner and one outer fuel plate with nominal fuel distributions, and then the plates are duplicated to fill the space of the corresponding fuel element. Therefore, data extracted from these simulations are limited to azimuthally averaged quantities. To determine the reactivity and physics impacts of an as-built outer fuel element and generate azimuthally dependent data in the element, 369 unique fuel plate models were generated and positioned. This model generates the three-dimensional (i.e., radial–axial–azimuthal) plate power profile, where the azimuthal profile is impacted by features within the adjacent control element region and beryllium reflector. For an as-built model of the outer fuel element, plate-specific homogeneity data, 235U loading, enrichment, and channel thickness measurements were translated into the model, yielding a much more varied azimuthal power profile encompassed by uncertainty factors in analyses. These models were run with the ORNL-TN and Shift Monte Carlo tools, and they contained upwards of 500,000 cells and 100,000 unique tallies.

Modeling the effect of oxygen on the chemical stage of water radiolysis using GPU-based microscopic Monte Carlo simulations, with an application in FLASH radiotherapy

Oxygen plays a critical role in determining the initial DNA damages induced by ionizing radiation. It is important to mechanistically model the oxygen effect in the water radiolysis process. However, due to the computational costs from the many body interaction problem, oxygen is often ignored or treated as a constant continuum radiolysis-scavenger background in the simulations using common microscopic Monte Carlo tools. In this work, we reported our recent progress on the modeling of the chemical stage of the water radiolysis with an explicit consideration of the oxygen effect, based upon our initial development of an open-source graphical processing unit (GPU)-based MC simulation tool, gMicroMC. The inclusion of oxygen mainly reduces the yields of and chemical radicals, turning them into highly toxic and species. To demonstrate the practical value of gMicroMC in large scale simulation problems, we applied the oxygen-simulation-enabled gMicroMC to compute the yields of chemical radicals under a high instantaneous dose rate to study the oxygen depletion hypothesis in FLASH radiotherapy. A decreased oxygen consumption rate (OCR) was found associated with a reduced initial oxygen concentration level due to reduced probabilities of reactions. With respect to dose rate, for the oxygen concentration of 21% and electron energy of 4.5 , OCR remained approximately constant (∼0.22 ) for ’s of , and reduced to 0.19 at , because the increased dose rate improved the mutual reaction frequencies among radicals, hence reducing their reactions with oxygen. We computed the time evolution of oxygen concentration under the FLASH irradiation setups. At the dose rate of and initial oxygen concentrations from 0.01% to 21%, the oxygen is unlikely to be fully depleted with an accumulative dose of 30 Gy, which is a typical dose used in FLASH experiments. The computational efficiency of gMicroMC when considering oxygen molecules in the chemical stage was evaluated through benchmark work to GEANT4-DNA with simulating an equivalent number of radicals. With an initial oxygen concentration of 3% (∼105 molecules), a speedup factor of 1228 was achieved for gMicroMC on a single GPU card when comparing with GEANT4-DNA on a single CPU.

Distribution Changes during Thermal Degradation of Poly(styrene peroxide) by Pairing Tree-Based Kinetic Monte Carlo and Artificial Intelligence Tools

A tree-based kinetic Monte Carlo (kMC) model is presented that differentiates between 38 end-group pairs for isothermal degradation of poly(styrene peroxide) (PSP). The binary trees allow for fast and accurate calculation of reaction probabilities, with mass-weighted binary trees for the accurate sampling of peroxide bond fissions and hydrogen abstractions along chains. The kinetic parameters are tuned via artificial neural networks (ANNs) to successfully predict literature experimental data, among other lumped product yields. ANNs are also utilized for sensitivity analysis to unravel the effects of individual reactions on the time evolution of experimental responses and other simulation outputs, including the variations of the chain length distributions of the macrospecies. PSP degradation is characterized by three stages of degradation considering both instantaneous and time-averaged concentrations. The first stage features rapid unzipping and results in the fast production of major products benzaldehyde and formaldehyde, the second stage features the most significant level of hydrogen abstractions involving PSP and other macrospecies types, and the third stage exhibits the consumption of the remaining peroxide bonds toward oligomeric species in a wide time frame until the degradation process is finalized by the depletion of peroxide bonds. This proof-of-concept study based on unprecedentedly detailed analyses of the chemistry via kinetic Monte Carlo paves the way to further improve our understanding of chemical recycling of solid plastic waste.

On the Role of the Precision Monte Carlo Generators in Future Electron Colliders

In this note, we argue that in the future electron–positron colliders with up to two orders higher event rates, the role of the Standard Model precision calculations in the data analysis performed using Monte Carlo (MC) event generators will be dominant, much more important than in the past LEP era experiments. This will require designing, constructing and testing an entirely new class of the precision Monte Carlo event generators for all important processes such as production and decay of the Z and Higgs boson, W pairs and the Bhabha process. We are going to outline challenges on the way to construction of these new MC tools and foresee possible lines of technical developments which will be necessary.

FANSY 2.0: a Monte Carlo tool for study of superhigh-energy cosmic-ray interactions: meson–proton interactions

FANSY 2.0: a Monte Carlo tool for study of superhigh-energy cosmic-ray interactions: meson–proton interactions

Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the Galactic centre

We provide an updated assessment of the power of the Cherenkov Telescope Array (CTA) to search for thermally produced dark matter at the TeV scale, via the associated gamma-ray signal from pair-annihilating dark matter particles in the region around the Galactic centre. We find that CTA will open a new window of discovery potential, significantly extending the range of robustly testable models given a standard cuspy profile of the dark matter density distribution. Importantly, even for a cored profile, the projected sensitivity of CTA will be sufficient to probe various well-motivated models of thermally produced dark matter at the TeV scale. This is due to CTA's unprecedented sensitivity, angular and energy resolutions, and the planned observational strategy. The survey of the inner Galaxy will cover a much larger region than corresponding previous observational campaigns with imaging atmospheric Cherenkov telescopes. CTA will map with unprecedented precision the large-scale diffuse emission in high-energy gamma rays, constituting a background for dark matter searches for which we adopt state-of-the-art models based on current data. Throughout our analysis, we use up-to-date event reconstruction Monte Carlo tools developed by the CTA consortium, and pay special attention to quantifying the level of instrumental systematic uncertainties, as well as background template systematic errors, required to probe thermally produced dark matter at these energies.

Nearly Consistent Finite Particle Estimates in Streaming Importance Sampling

In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of {available data} and prior information. When the distribution of random variables is {intractable}, Monte Carlo (MC) sampling is usually required. {Importance sampling is a standard MC tool that approximates this unavailable distribution with a set of weighted samples.} This procedure is asymptotically consistent as the number of MC samples (particles) go to infinity. However, retaining infinitely many particles is intractable. Thus, we propose a way to only keep a \emph{finite representative subset} of particles and their augmented importance weights that is \emph{nearly consistent}\blue{, i.e., they converge to a close neighborhood of their population ground truth in the large sample limit.} To do so in {an online manner}, we (1) embed the posterior density estimate in a reproducing kernel Hilbert space (RKHS) through its kernel mean embedding; and (2) sequentially project this RKHS element onto a lower-dimensional subspace in RKHS using the maximum mean discrepancy, an integral probability metric. Theoretically, we establish that this scheme results in a bias determined by a compression parameter, which yields a tunable tradeoff between consistency and memory. In experiments, we observe the compressed estimates achieve comparable performance to the dense ones with substantial reductions in representational complexity.

Influence of a 3D electric field enhancement model on the Monte Carlo calculation of the dark current in pixel arrays

A new three-dimensional (3D) electric field enhanced generation model has been developed to describe the electric field effects on the thermal electron–hole pair generation rate. The originality of this model lies in the full three-dimensional description of the synergetic mechanism between the Poole–Frenkel barrier lowering and the phonon-assisted tunneling mechanism. To do this, a classical one-dimensional (1D) model has been integrated over all possible directions of emission of the carriers. The 3D model has been implemented in a Monte Carlo tool devoted to the simulation of the dark current increase induced by radiations in image sensors. Our three-dimensional simulation has been compared to one-dimensional electric field effects’ simulations and experimental data found in the literature in the context of gold contamination. The consequence of using a three-dimensional electric field enhanced generation (EFEG) model is the reduction of the dispersive effect on the dark current distribution of the electric field; hence, each dark current peak is narrower and shows a higher peak's amplitude. The three-dimensional model needs to slightly change the cross-sectional parameters used for a 1D EFEG case to keep a realistic description of each dark current peak of the histogram. In the rest of the paper, we extended our work on constraints relative to space applications. The histograms of the simulated dark current taking into account one- and three-dimensional electric field enhancement effects have been estimated and compared to experimental data acquired after a proton irradiation at room temperature. The use of a three-dimensional model tends to give a more realistic prediction of the dark current non-uniformity in an irradiated pixel array.