Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “ERROR FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

SU-E-T-333: Towards Customizable Radiotherapy Enhancement (CuRE) for Prostate Cancer Using Cisplatin Nanoparticles

Purpose: Replacing routinely used brachytherapy spacers with multifunctional ones loaded with cisplatin nanoparticles (CNP), which can be released into the tumor after implantation, could enable customizable radiation boosting to the prostate tumor in addition to chemotherapy effect. This study investigates the feasibility of customizing the intra-tumor biodistribution and corresponding dose enhancement (DEF) over time for the released CNP as a function of nanoparticle size. Methods: Dose enhancement factors (DEF) due to photon-induced emission of photo-/Auger electrons from CNPs were calculated as a function of concentration using previously published analytical calculation method. An experimentally determined diffusion coefficient (D) for 10 nm nanoparticles in mouse tumor model was employed to estimate D for other sizes using the Stoke- Einstein equation. The error function diffusion model in the experimental study was applied to generate the intra-tumor concentration profile for a burst release of CNPs from the spacer over time. The corresponding DEF profiles were then determined for brachytherapy using Pd-103 and I-125 sources. Results: As expected, the generated profiles showed greater DEF over time for smaller CNP sizes at sample distances from the spacer. For example, for a centrally located spacer, clinically significant DEF (> 20%) could be achieved near the tumor periphery (ca. 0.85 cm distance from the spacer for average PCa tumor size) after 20, and 100 days, respectively for CNPs sizes of 2 nm, and 10 nm, using I-125. Meanwhile for Pd-103, clinically significant DEF could be achieved at the same position after 22 and 108 days, respectively, for same size particles. Conclusion: Our preliminary results demonstrate the feasibility of customizing dose enhancement to prostate tumors as a function of spacer location, brachytherapy source type or size of CNPs released from multifunctional spacers. Such an approach could enable customizable radiation boosting to tumor sub-volumes, while minimizing dose to healthy tissues.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Exploring the dependence of gas cooling and heating functions on the incident radiation field with machine learning

ABSTRACT Gas cooling and heating functions play a crucial role in galaxy formation. But, it is computationally expensive to exactly compute these functions in the presence of an incident radiation field. These computations can be greatly sped up by using interpolation tables of pre-computed values, at the expense of making significant and sometimes even unjustified approximations. Here, we explore the capacity of machine learning to approximate cooling and heating functions with a generalized radiation field. Specifically, we use the machine learning algorithm XGBoost to predict cooling and heating functions calculated with the photoionization code cloudy at fixed metallicity, using different combinations of photoionization rates as features. We perform a constrained quadratic fit in metallicity to enable a fair comparison with traditional interpolation methods at arbitrary metallicity. We consider the relative importance of various photoionization rates through both a principal component analysis (PCA) and calculation of SHapley Additive exPlanation (shap) values for our XGBoost models. We use feature importance information to select different subsets of rates to use in model training. Our XGBoost models outperform a traditional interpolation approach at each fixed metallicity, regardless of feature selection. At arbitrary metallicity, we are able to reduce the frequency of the largest cooling and heating function errors compared to an interpolation table. We find that the primary bottleneck to increasing accuracy lies in accurately capturing the metallicity dependence. This study demonstrates the potential of machine learning methods such as XGBoost to capture the non-linear behaviour of cooling and heating functions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A Differentiable Hydrology Approach for Modeling With Time-Varying Parameters

In the analysis of observational data with mathematical models, it is often desirable to let one or more model parameters vary with time to account for changing environmental conditions or to offer more flexibility. A standard approach for dynamic models is to allow for the number of parameters to grow as a function of time, leading to a high-dimensional inference problem for long data records. We propose using Hamiltonian Monte Carlo, a gradient-based Markov chain Monte Carlo (MCMC) method, to perform Bayesian inference for time-varying parameters (TVP) in hydrology models. As derivatives of model error functions with regard to parameters are not available in closed form, we implemented the GR4J rainfall-runoff models in Theano/PyMC3, and Jax/NumPyro, allowing for the application of automatic differentiation techniques. A simulation experiment assessing the viability of these methods for recovering underlying temporal variation in parameters indicates that a discrete Gaussian random walk-based prior appears to be best suited across a range of scenarios while the continuous-time Gaussian process compares relatively poorly. In an analysis of 20 years of daily real-world streamflow records from the Model Parameter Estimation Experiment (MOPEX) hydrology data set with increasing data sparsity and at multiple temporal resolutions, we find that TVP inference with gradient-based MCMC is a flexible and reliable approach for analyzing hydrology models with dynamic parameter sets.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1990

Neuromorphic learning of continuous-valued mappings from noise-corrupted data. Application to real-time adaptive control

The ability of feed-forward neural network architectures to learn continuous valued mappings in the presence of noise was demonstrated in relation to parameter identification and real-time adaptive control applications. An error function was introduced to help optimize parameter values such as number of training iterations, observation time, sampling rate, and scaling of the control signal. The learning performance depended essentially on the degree of embodiment of the control law in the training data set and on the degree of uniformity of the probability distribution function of the data that are presented to the net during sequence. When a control law was corrupted by noise, the fluctuations of the training data biased the probability distribution function of the training data sequence. Only if the noise contamination is minimized and the degree of embodiment of the control law is maximized, can a neural net develop a good representation of the mapping and be used as a neurocontroller. A multilayer net was trained with back-error-propagation to control a cart-pole system for linear and nonlinear control laws in the presence of data processing noise and measurement noise. The neurocontroller exhibited noise-filtering properties and was found to operate more smoothly than the teacher in the presence of measurement noise.

Troudet, Terry↗
NASA NTRS1992

A new algorithm for L2 optimal model reduction

In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. Convergence of the proposed algorithm to stationary values of the quadratic cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.

Spanos, J. T.↗
NASA NTRS1995

A finite element propagation model for extracting normal incidence impedance in nonprogressive acoustic wave fields

A propagation model method for extracting the normal incidence impedance of an acoustic material installed as a finite length segment in a wall of a duct carrying a nonprogressive wave field is presented. The method recasts the determination of the unknown impedance as the minimization of the normalized wall pressure error function. A finite element propagation model is combined with a coarse/fine grid impedance plane search technique to extract the impedance of the material. Results are presented for three different materials for which the impedance is known. For each material, the input data required for the prediction scheme was computed from modal theory and then contaminated by random error. The finite element method reproduces the known impedance of each material almost exactly for random errors typical of those found in many measurement environments. Thus, the method developed here provides a means for determining the impedance of materials in a nonprogressirve wave environment such as that usually encountered in a commercial aircraft engine and most laboratory settings.

Watson, Willie R.↗
NASA NTRS1990

Optimal model reduction and frequency-weighted extension

In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. The existence of globally optimal stable solutions to the optimization problem is established, and convergence of the algorithm to stationary values of the cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.

Spanos, J. T.↗
DOE OSTI2014

SU-C-9A-01: Parameter Optimization in Adaptive Region-Growing for Tumor Segmentation in PET

Purpose: To design a reliable method to determine the optimal parameter in the adaptive region-growing (ARG) algorithm for tumor segmentation in PET. Methods: The ARG uses an adaptive similarity criterion m - fσ ≤ I-PET ≤ m + fσ, so that a neighboring voxel is appended to the region based on its similarity to the current region. When increasing the relaxing factor f (f ≥ 0), the resulting volumes monotonically increased with a sharp increase when the region just grew into the background. The optimal f that separates the tumor from the background is defined as the first point with the local maximum curvature on an Error function fitted to the f-volume curve. The ARG was tested on a tumor segmentation Benchmark that includes ten lung cancer patients with 3D pathologic tumor volume as ground truth. For comparison, the widely used 42% and 50% SUVmax thresholding, Otsu optimal thresholding, Active Contours (AC), Geodesic Active Contours (GAC), and Graph Cuts (GC) methods were tested. The dice similarity index (DSI), volume error (VE), and maximum axis length error (MALE) were calculated to evaluate the segmentation accuracy. Results: The ARG provided the highest accuracy among all tested methods. Specifically, the ARG has an average DSI, VE, and MALE of 0.71, 0.29, and 0.16, respectively, better than the absolute 42% thresholding (DSI=0.67, VE= 0.57, and MALE=0.23), the relative 42% thresholding (DSI=0.62, VE= 0.41, and MALE=0.23), the absolute 50% thresholding (DSI=0.62, VE=0.48, and MALE=0.21), the relative 50% thresholding (DSI=0.48, VE=0.54, and MALE=0.26), OTSU (DSI=0.44, VE=0.63, and MALE=0.30), AC (DSI=0.46, VE= 0.85, and MALE=0.47), GAC (DSI=0.40, VE= 0.85, and MALE=0.46) and GC (DSI=0.66, VE= 0.54, and MALE=0.21) methods. Conclusions: The results suggest that the proposed method reliably identified the optimal relaxing factor in ARG for tumor segmentation in PET. This work was supported in part by National Cancer Institute Grant R01 CA172638; The dataset is provided by AAPM TG211.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Study of Plastic Scintillator Properties for Radioactive Sources Dosimetry - Paper 108

Plastic scintillator is a simple material which has the density close to that of human soft tissue (1.06 g/cm{sup 3}). Its energy response is close to that of human soft tissue and it is relatively energy independent. This prospect provide a desired characteristics in measuring dose by plastic scintillator either for radiation monitoring or personal dosimeter. Generally the energy calibration of organic scintillator will be done by using gamma ray sources. The positions of Compton edge in pulse height spectra, which have known energy values will be identified. However the Compton edge normally is very broad and difficult to determine the point corresponding to that particular Compton electron energies. Many researchers used several fitting functions and Monte Carlo simulations to determine the position of Compton edge. For example, Proctor and Wellman (2012) used a straight line fit to the linear part of Compton edge and extrapolated to zero count. While L. Swiderski et al. used a method based on a back-scattered coincidence measurement to measure in a wide energy range the position of Compton edge in organic scintillators. For a simple and quick approach of calibration, we used a Gauss-error function to fit the Compton edge region of interest by assumed that the location of maximum energy of Compton electrons is half-height of the Compton maximum (CM). The reasons is because the CM position could be determined easily from the spectra throughout wide energy range. Interpreting gamma dose rates from accumulated plastic scintillation detector spectra is often a complex task because the probability of a full energy deposition event in the detector is often negligible. Despite no full energy peaks in plastic scintillator spectra, several attempts have been made by the other researchers to obtain the dose from the energy distribution spectra of gamma radiation. For example, Proctor and Wellman used the modified spectrum dose index (SDI) to calculate the exposure rates by multiplying the energy corresponding to its channel and all products are summed before multiply by a calibration constant to yield an exposure rate. While Lobdell and Hertel calculated dose using a response matrix based on spectral unfolding technique. From these points of view, we have made an attempt to correlate the counts obtained in scintillator with absorbed dose or ambient dose equivalent. We aimed to calibrate the plastic scintillator energy deposition for dose, by correlate the counts obtained with a particular value of dose. By designed the scintillator to measure at 1 cm tissue depth might be helpful to be used as radiation monitoring or personal dosimeter since the energy response of plastic scintillator is relatively energy independent compared to that of inorganic scintillators. The energy calibration proposed from simple fitting approach had been verified with calculated spectra. This might be considered as a practical approach for technician or radiation workers with sufficient accuracy. The linear behavior of counts per absorbed dose give promising to calibrate scintillator energy deposition to read dose (equivalent dose or absorbed dose) for photons. Thus the scintillator could provide both the energy and dose response simultaneously, which may important in some radiation field of measurements. Currently the scintillator is able to give dose rate value for gamma sources of Cs-137 and Mn-54. The number of counts per unit absorbed dose would likely to vary somewhat with photon energy, although the plastic scintillator should have a tissue dose response that is relatively energy independent. Further analysis will be done on conversion factor parameters so that it could be used in such situations where the radiation field is complex or unknown. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1977

Neutrally stable atmospheric flow over a two-dimensional rectangular block

The phenomena of atmospheric flow over a two dimensional surface obstruction such as a building modeled as a rectangular block are analyzed by an approach using the Navier-Stokes equations with a two equation model of turbulence. The partial differential equations for the vorticity, stream function, turbulence kinetic energy, and turbulence length scale are solved by a finite difference technique. The predicted results are in agreement with the limited experimental data available. Current computed results show that the separation bubble originates from the upper front corner of the block and extends approximately 11.5 block heights behind the block. The decay of the mean velocity along the wake center line coincides almost perfectly with the experimental data. The vertical profiles of the mean velocity defect are also in reasonable agreement with wind tunnel results. Velocity profiles in the mixing region are shown to agree with the error function profile typically found in the shear layer. Details of the behavior of the turbulence kinetic energy and the turbulence length scale are also discussed.

Shieh, C. F.↗
DOE OSTI2014

The zero-multipole summation method for estimating electrostatic interactions in molecular dynamics: Analysis of the accuracy and application to liquid systems

In the preceding paper [I. Fukuda, J. Chem. Phys. 139, 174107 (2013)], the zero-multipole (ZM) summation method was proposed for efficiently evaluating the electrostatic Coulombic interactions of a classical point charge system. The summation takes a simple pairwise form, but prevents the electrically non-neutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large energetic noises and significant artifacts. The purpose of this paper is to judge the ability of the ZM method by investigating the accuracy, parameter dependencies, and stability in applications to liquid systems. To conduct this, first, the energy-functional error was divided into three terms and each term was analyzed by a theoretical error-bound estimation. This estimation gave us a clear basis of the discussions on the numerical investigations. It also gave a new viewpoint between the excess energy error and the damping effect by the damping parameter. Second, with the aid of these analyses, the ZM method was evaluated based on molecular dynamics (MD) simulations of two fundamental liquid systems, a molten sodium-chlorine ion system and a pure water molecule system. In the ion system, the energy accuracy, compared with the Ewald summation, was better for a larger value of multipole moment l currently induced until l ≲ 3 on average. This accuracy improvement with increasing l is due to the enhancement of the excess-energy accuracy. However, this improvement is wholly effective in the total accuracy if the theoretical moment l is smaller than or equal to a system intrinsic moment L. The simulation results thus indicate L ∼ 3 in this system, and we observed less accuracy in l = 4. We demonstrated the origins of parameter dependencies appearing in the crossing behavior and the oscillations of the energy error curves. With raising the moment l we observed, smaller values of the damping parameter provided more accurate results and smoother behaviors with respect to cutoff length were obtained. These features can be explained, on the basis of the theoretical error analyses, such that the excess energy accuracy is improved with increasing l and that the total accuracy improvement within l ⩽ L is facilitated by a small damping parameter. Although the accuracy was fundamentally similar to the ion system, the bulk water system exhibited distinguishable quantitative behaviors. A smaller damping parameter was effective in all the practical cutoff distance, and this fact can be interpreted by the reduction of the excess subset. A lower moment was advantageous in the energy accuracy, where l = 1 was slightly superior to l = 2 in this system. However, the method with l = 2 (viz., the zero-quadrupole sum) gave accurate results for the radial distribution function. We confirmed the stability in the numerical integration for MD simulations employing the ZM scheme. This result is supported by the sufficient smoothness of the energy function. Along with the smoothness, the pairwise feature and the allowance of the atom-based cutoff mode on the energy formula lead to the exact zero total-force, ensuring the total-momentum conservations for typical MD equations of motion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Model-based optimization of near-field binary-pixelated beam shapers

The optimization of components that rely on spatially dithered distributions of transparent or opaque pixels and an imaging system with far-field filtering for transmission control is demonstrated. The binary-pixel distribution can be iteratively optimized to lower an error function that takes into account the design transmission and the characteristics of the required far-field filter. Simulations using a design transmission chosen in the context of high-energy lasers show that the beam-fluence modulation at an image plane can be reduced by a factor of 2, leading to performance similar to using a non-optimized spatial-dithering algorithm with pixels of size reduced by a factor of 2 without the additional fabrication complexity or cost. The optimization process preserves the pixel distribution statistical properties. Analysis shows that the optimized pixel distribution starting from a high-noise distribution defined by a random-draw algorithm should be more resilient to fabrication errors than the optimized pixel distributions starting from a low-noise, error-diffusion algorithm, while leading to similar beamshaping performance. Furthermore, this is confirmed by experimental results obtained with various pixel distributions and induced fabrication errors.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Concurrent Precipitation of Nb(C,N) and Metastable M 23 C 6 in Alloy 347H at 700°C and 750°C: Computer Simulations and Comparison to Experiment

Here, we present our results for the concurrent precipitation of metastable M 23 C 6 , Nb(C,N) secondary precipitates, and the Nb(C,N) primary crystals in 347H austenitic stainless steel. For precipitation modeling, we have accounted for the elastic contribution to interfacial energy, and for the Fe-spin-polarization for NbC/Fe and M 23 C 6 /Fe interfacial energy values: for NbC/Fe ~ 0.63 J/m 2 . For M 23 C 6 precipitates, an error function was used to describe the interfacial energy growth with particle size. In precipitation simulations, the average size of the primary Nb(C,N) particles remained ~ 1 μm at 700°C and ~ 0.3 μm at 750°C. The M 23 C 6 precipitates at 750°C dissolved after 120 h (our simulations) compared to 300 h (experiments). The Nb(C,N)/Fe interfacial energy was not affected by the nitrogen additions. With these modifications, reasonable agreement with the available experimental data was obtained, which allows using them in the development of the 2nd-phase particle-informed creep theory.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Learning viscoelasticity models from indirect data using deep neural networks

In this study, we propose a novel approach to model viscoelasticity materials, where rate-dependent and non-linear constitutive relationships are approximated with deep neural networks. We assume that inputs and outputs of the neural networks are not directly observable, and therefore common training techniques with input–output pairs for the neural networks are inapplicable. To that end, we develop a novel computational approach to both calibrate parametric and learn neural-network-based constitutive relations of viscoelasticity materials from indirect displacement data in the context of multiple-physics systems. We show that limited displacement data holds sufficient information to quantify the viscoelasticity behavior. We formulate the inverse computation – modeling viscoelasticity properties from observed displacement data – as a PDE-constrained optimization problem and minimize the error functional using a gradient-based optimization method. The gradients are computed by a combination of automatic differentiation and implicit function differentiation rules. The effectiveness of our method is demonstrated through numerous benchmark problems in geomechanics and porous media transport.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Improvements on the minimax algorithm for the Laplace transformation of orbital energy denominators

We present a robust and non-heuristic algorithm that finds all extremum points of the error distribution function of numerically Laplace-transformed orbital energy denominators. The extremum point search is one of the two key steps for finding the minimax approximation. If pre-tabulation of initial guesses is supposed to be avoided, strategies for a sufficiently robust algorithm have not been discussed so far. We compare our non-heuristic approach with a bracketing and bisection algorithm and demonstrate that 3 times less function evaluations are required altogether when applying it to typical non-relativistic and relativistic quantum chemical systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

($\mathrm{INVITED}$)Counter-ion effect on the diffusion behavior of $\mathrm{Y}$b, $\mathrm{L}$u, and $\mathrm{N}$d ions in $\mathrm{YAG}$ transparent ceramics

The ability to fabricate additively manufactured laser waveguides with sharp dopant concentration interfaces is limited by diffusion of the dopants at the temperatures required to fully densify the material. Compositional analysis of bilayer samples, where each layer was either undoped YAG or YAG doped with Yb, Lu, or Nd, were fabricated such that all combinations were available for testing. Samples were fabricated at both 1750°C and 1850°C to determine the diffusion behavior of each dopant alone and also in the presence of a second dopant. It was found that the experimental concentration profiles exhibited both intragranular (bulk) and grain boundary contributions, and thus fitting to a complementary error function equation required the use of two diffusion coefficients. Nd always diffused further along grain boundaries than the other dopants, due in part to its small segregation coefficient in YAG. It is shown that the presence of Nd as a counter dopant inhibits intragranular diffusion of other dopants while enhancing their grain boundary diffusion. All the observed trends were attributed to a combination of intragranular lattice strain due to: dopant ions replacing yttrium substitutionally, the relative driving forces for the segregation of dopant ions to grain boundaries, and the ability of one dopant to affect the diffusion of a different dopant in the other direction to maintain charge neutrality.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order of $1000g_{0}$ , where $g_{0}$ is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duff et al. ( Phys. Fluids , vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar ( Proc. Camb. Phil. Soc. , vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duff et al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a $1/k^{2}$ decay in growth rates as $k\rightarrow \infty$ for large-wavenumber perturbations.

42 ENGINEERING↗
DOE OSTI2020

Resolving atomic transport through iron oxide under irradiation using isotopic tracers

Structural materials in nuclear environments are exposed to complex and harsh conditions, including high temperatures, corrosive solutions, and irradiation. Material stability and likewise degradation are fundamentally controlled by atomic transport mechanisms. Here, we investigate the influence of radiation-induced, non-equilibrium point defect populations on mass transport within model oxide systems using isotopic tracers and atom probe tomography. An isotopically labelled hematite (a-Fe2O3) film was synthesized with 16O- and 18O-rich layers (>30nm and 10 nm, respectively) sequentially deposited via molecular beam epitaxy. One region of the film was proton irradiated to ~0.1 dpa at 450°C, and regions outside the beam spot provided a non-irradiated control of thermal annealing only. 3D APT was used to directly visualize the elemental and O-isotopic redistribution following both thermal and combined thermal and irradiation conditions. Complementary scanning transmission electron microscopy (STEM) was also employed to study the microstructural evolution. Error function fits of the 18O-concentration profiles enabled quantification of diffusion coefficients.

isotopic tracers, diffusion, proton irradiation, h↗