An interplanetary diffusion model for the time behavior of intensity in a solar cosmic ray event
Interplanetary diffusion model for time dependency of intensity of solar cosmic ray event
TIME DEPENDENCY↗
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Extension of the PINN diffusion model to k-eigenvalue problems
This paper extends our recent work on the Physics-Informed Neural Networks (PINN) approach for the fixed source diffusion models and applies it to the diffusion theory based k-eigenvalue problems. To make the PINN equitable for the eigenvalue problems, we introduce a novel integral regularization term to the loss function in the framework, and allow the direct inference of the principal eigenvalue and the associated eigenfunction. The regularization term enforces a pre-defined value on the integration of the model predictions, and this value can be directly related to a physical property of the system. We also introduce an additional learnable parameter to approximate the principal eigenvalue. As a proof of principle, we solve the one-group two-dimensional k-eigenvalue neutron diffusion equation in this work. We then provide two numerical examples to demonstrate the applicability of the PINN approach. In each example, we solve the k-eigenvalue diffusion equation in a multi-region configuration constrained with a set of Robin boundary conditions for generality. We use a FEM solution based on the power-iteration method to verify the results of the PINN solution. The results showed relative percentage error in the predicted eigenvalue of about 0.77% and about 1.2% for example 1 and example 2, respectively. The mean absolute error in the predicted flux for example 1 is ∼ 0.002 and for example 2 is ∼ 0.0024. These results indicate some preliminary successes of the PINN application to k-eigenvalue problems. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Manning condensation in ion exchange membranes: A review on ion partitioning and diffusion models
Here, the rational design of ion exchange membranes (IEMs) is becoming more pertinent as their usage becomes broader and as their staple applications (i.e., electrodialysis, flow batteries, and fuel cells) improve in commercial viability. Such efforts would be catalyzed by an improved fundamental understanding of ion transport in IEMs. This review discusses recent progress in modeling ion partitioning and diffusion in IEMs in an effort to relate IEM performance metrics to fundamental membrane properties over which researchers and membrane manufacturers possess direct and sometimes precise control. Central focus is given to the Donnan-Manning model for ion partitioning and the Manning-Meares model for ion diffusion in IEMs. These two frameworks, which are derived from Manning's counter-ion condensation theory for polyelectrolyte solutions, have been widely used within the IEM literature since their recent introduction. To explore this topic, the mathematical derivation of both models is revisited, followed by a survey of experimental and computational discussions of counter-ion condensation in IEMs. Alternative models which fulfill similar roles in predicting IEM transport properties are compared. This review concludes by highlighting the uniquely favorable positions of the Donnan-Manning and Manning-Meares models and discussing their prospects as leading predictors of IEM partitioning and diffusive properties.
25 ENERGY STORAGE↗
Interplanetary diffusion model for the time behavior of intensity in a solar cosmic ray event.
Unified interplanetary diffusion model for time behavior of intensity of several solar cosmic ray events, accounting for decay phases
SOLAR COSMIC RAY↗
Chemically reacting Couette flow with hydrogen injection for two diffusion models
Chemically reacting Couette flow with variable transport properties and hydrogen injection for two diffusion models
Graves, R. A., Jr.↗
A diffusion model for the phase delay between thermosphere density and temperature
Two-dimensional time dependent diffusion model for phase delay between thermospheric density and temperature
Mayr, H. G.↗
Study of argon assimilation into the post-disruption runaway electron plateau in DIII-D and comparison with a 1D diffusion model
The assimilation of argon injected into post-disruption runaway electron (RE) plateaus is studied and compared to the vertical loss rate for vertically unstable RE plateaus. A 1D diffusion model is developed to include neutral diffusion and ionization and is used to help in data interpretation. It is found that the radial mixing time scale of argon ions (~0.05 s) is comparable to the vertical loss timescale. Neutral argon becomes the dominant Ar species in the RE plateau for large Ar numbers (> 3 x 10 21 ); at the same time the neutral Ar diffusivity decreases due to plasma cooling, causing a saturation in the assimilation of injected Ar on the vertical loss time scale. Injection of Ar into vertically unstable RE plateaus in DIII-D does increase the vertical loss rate, as predicted by previous modeling of ITER. Furthermore, there is a decreasing trend in RE current at the wall strike as the Ar quantity is turned up or as the Ar is injected earlier, indicating a decrease in RE energy deposited to the wall.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Generative diffusion model surrogates for mechanistic agent-based biological models
Mechanistic, multicellular, agent-based models are commonly used to investigate tissue, organ, and organism-scale biology at single-cell resolution. The Cellular-Potts Model (CPM) is a powerful and popular framework for developing and interrogating these models. CPMs become computationally expensive at large space- and time- scales making application and investigation of developed models difficult. Surrogate models may allow for the accelerated evaluation of CPMs of complex biological systems. However, the stochastic nature of these models means each set of parameters may give rise to different model configurations, complicating surrogate model development. In this work, we leverage denoising diffusion probabilistic models (DDPMs) to train a generative AI surrogate of a CPM used to investigate in vitro vasculogenesis. We describe the use of an image classifier to learn the characteristics that define unique areas of a 2-dimensional parameter space. We then apply this classifier to aid in surrogate model selection and verification. Our CPM model surrogate generates model configurations 20,000 timesteps ahead of a reference configuration and demonstrates approximately a 22x reduction in computational time as compared to native code execution. Our work represents a step towards the implementation of DDPMs to develop digital twins of stochastic biological systems.
97 MATHEMATICS AND COMPUTING↗
Synthetic Scientific Image Generation with VAE, GAN, and Diffusion Model Architectures
Generative AI (genAI) has emerged as a powerful tool for synthesizing diverse and complex image data, offering new possibilities for scientific imaging applications. This review presents a comprehensive comparative analysis of leading generative architectures, ranging from Variational Autoencoders (VAEs) to Generative Adversarial Networks (GANs) on through to Diffusion Models, in the context of scientific image synthesis. We examine each model's foundational principles, recent architectural advancements, and practical trade-offs. Our evaluation, conducted on domain-specific datasets including microCT scans of rocks and composite fibers, as well as high-resolution images of plant roots, integrates both quantitative metrics (SSIM, LPIPS, FID, CLIPScore) and expert-driven qualitative assessments. Results show that GANs, particularly StyleGAN, produce images with high perceptual quality and structural coherence. Diffusion-based models for inpainting and image variation, such as DALL-E 2, delivered high realism and semantic alignment but generally struggled in balancing visual fidelity with scientific accuracy. Importantly, our findings reveal limitations of standard quantitative metrics in capturing scientific relevance, underscoring the need for domain-expert validation. We conclude by discussing key challenges such as model interpretability, computational cost, and verification protocols, and discuss future directions where generative AI can drive innovation in data augmentation, simulation, and hypothesis generation in scientific research.
Generative Adversarial Networks↗
Breakdown of the drift-diffusion model for transverse spin transport in a disordered Pt film
Spin-accumulation and spin-current profiles are calculated for a disordered Pt film subjected to an in-plane electric current within the nonequilibrium Green's function approach. In the bulklike region of the sample, this approach captures the intrinsic spin Hall effect found in other calculations. Near the surfaces, the results reveal qualitative differences with the results of the widely used spin-diffusion model, even when the boundary conditions are modified to try to account for them. One difference is that the effective spin-diffusion length for transverse spin transport is significantly different from its longitudinal counterpart and is instead similar to the mean-free path. Furthermore, this feature may be generic for spin currents generated via the intrinsic spin Hall mechanism because of the differences in transport mechanisms compared to longitudinal spin transport. Orbital accumulation in the Pt film is only significant in the immediate vicinity of the surfaces and has a small component penetrating into the bulk only in the presence of spin-orbit coupling, as a secondary effect induced by the spin accumulation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A time-dependent chloride diffusion model for predicting initial corrosion time of reinforced concrete with slag addition
The effect of granulated blast furnace slag (GBFS) addition on the threshold chloride concentration (TCC) for rebar corrosion was investigated. A modified diffusion model, coupled with a time-dependent effective diffusion coefficient and surface chloride concentration, was proposed to predict the chloride profile. The corrosion initiation time was estimated based on the model predictions and the measured TCC. The results indicate that adding GBFS decreases the TCC by lowering the pH value of the pore solution. The evolution of corrosion potential and current density is found to obey a 3-parameter Weibull distribution. MIP tests show that adding GBFS contributes to refinement of pore structure by decreasing the fraction of large capillary pores. The time-dependent model exhibits good predictive strength and helps understand how GBFS addition delays the corrosion initiation by retarding the chloride diffusion, though a lower TCC is obtained.
36 MATERIALS SCIENCE↗
Cooling rates for lunar samples determined with a diffusion model for phosphide exsolution
A numerical model for diffusion-controlled phase growth has been applied to the exsolution of phosphide lamellae in lunar metal grains. Computer simulations reproduce observed composition profiles, and reveal the influence of cooling rate on dimensional and compositional parameters of phosphide and metal. At lower cooling rates, phosphide lamellae are larger and the concentration of P in the metal host close to the interface is lower. Cooling rates inferred for Apollo 16 samples, based on compositions and dimensions of the phosphide-metal grains, are mostly in the range 1-100 C/day. These rates correspond to burial depths of 5-0.5 m for melt rocks and 3-0.3 m for breccias. This is in good agreement with thicknesses of lunar cooling units determined by other techniques.
Hewins, R. H.↗
Further observational support for the lossy radial diffusion model of the inner Jovian magnetosphere
A mathematical model describing radial diffusion, with violation of the third adiabatic invariant and with local losses, is applied to the Pioneer 10 and 11 observations of omnidirectional integral intensities of electrons with energy exceeding 21 MeV. Local losses outside L = 3 are much stronger than synchrotron losses but weaker than the losses one would expect for strong pitch angle diffusion. If radial diffusion is driven by ionospheric winds, as was suggested by Brice and McDonough (1973), it is found that the theoretical solution which best fits the data requires that the radial diffusion coefficient equals 3 x 10 to the -9th L-cubed/s and the lifetime against local losses is approximately a few million seconds.
Goertz, C. K.↗
Spectroscopy-guided discovery of three-dimensional structures of disordered materials with diffusion models
Spectroscopy techniques such as x-ray absorption near edge structure (XANES) provide valuable insights into the atomic structures of materials, yet the inverse prediction of precise structures from spectroscopic data remains a formidable challenge. In this study, we introduce a framework that combines generative artificial intelligence models with XANES spectroscopy to predict three-dimensional atomic structures of disordered systems, using amorphous carbon (a-C) as a model system. In this work, we introduce a new framework based on the diffusion model, a recent generative machine learning method, to predict 3D structures of disordered materials from a target property. For demonstration, we apply the model to identify the atomic structures of a-C as a representative material system from the target XANES spectra. We show that conditional generation guided by XANES spectra reproduces key features of the target structures. Furthermore, we show that our model can steer the generative process to tailor atomic arrangements for a specific XANES spectrum. Finally, our generative model exhibits a remarkable scale-agnostic property, thereby enabling generation of realistic, large-scale structures through learning from a small-scale dataset (i.e. with small unit cells). Our work represents a significant stride in bridging the gap between materials characterization and atomic structure determination; in addition, it can be leveraged for materials discovery in exploring various material properties as targeted.
36 MATERIALS SCIENCE↗
Water dynamics in C–S–H and M-S-H cement pastes: A revised jump-diffusion and rotation-diffusion model
The Quasi-Elastic Neutron Scattering (QENS) spectra from four cement pastes are re-analyzed by a new revised jump-diffusion and rotation-diffusion model (rJRM). From the QENS fit, it can be seen that the rJRM is an improved model to fit QENS spectra within the whole detected neutron energy transfer and scattering vector. By the rJRM fitting, the structure parameters extracted from QENS spectra show that both the additives aluminum-silicate nanotubes (ASN) and carboxyl group functionalized ASN (ASN-COOH) can improve magnesium-silicate-hydrate (M-S-H) toward calcium-silicate-hydrate (C–S–H) direction in mechanical properties, but the improvement is weakened with decreasing temperatures. The extracted dynamical parameters show that there is a dynamic anomaly near 230 K in not only translational but also rotational diffusion of water confined in all the investigated samples. In conclusion, the anomaly in rotational diffusion is new compared with those results obtained by the QENS fit using other models.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Point cloud-based diffusion models for the Electron-Ion Collider
At high-energy collider experiments, generative models can be used for a wide range of tasks, including fast detector simulations, unfolding, searches of physics beyond the Standard Model, and inference tasks. In particular, it has been demonstrated that score-based diffusion models can generate high-fidelity and accurate samples of jets or collider events. This work expands on previous generative models in three distinct ways. First, our model is trained to generate entire collider events, including all particle species with complete kinematic information. We quantify how well the model learns event-wide constraints such as the conservation of momentum and discrete quantum numbers. We focus on the events at the future Electron-Ion Collider, but we expect that our results can be extended to proton-proton and heavy-ion collisions. Second, previous generative models often relied on image-based techniques. The sparsity of the data can negatively affect the fidelity and sampling time of the model. We address these issues using point clouds and a novel architecture combining edge creation with transformer modules called Point Edge Transformers. Third, we adapt the foundation model OmniLearn, to generate full collider events. This approach may indicate a transition toward adapting and fine-tuning foundation models for downstream tasks instead of training new models from scratch.
Araz, Jack Y. [Stony Brook Univ., NY (United State↗
Parametric studies with an atmospheric diffusion model that assesses toxic fuel hazards due to the ground clouds generated by rocket launches
Parametric studies were made with a multilayer atmospheric diffusion model to place quantitative limits on the uncertainty of predicting ground-level toxic rocket-fuel concentrations. Exhaust distributions in the ground cloud, cloud stabilized geometry, atmospheric coefficients, the effects of exhaust plume afterburning of carbon monoxide CO, assumed surface mixing-layer division in the model, and model sensitivity to different meteorological regimes were studied. Large-scale differences in ground-level predictions are quantitatively described. Cloud alongwind growth for several meteorological conditions is shown to be in error because of incorrect application of previous diffusion theory. In addition, rocket-plume calculations indicate that almost all of the rocket-motor carbon monoxide is afterburned to carbon dioxide CO2, thus reducing toxic hazards due to CO. The afterburning is also shown to have a significant effect on cloud stabilization height and on ground-level concentrations of exhaust products.
Stewart, R. B.↗
Simulation of Ultra-Small MOSFETs Using a 2-D Quantum-Corrected Drift-Diffusion Model
We describe an electronic transport model and an implementation approach that respond to the challenges of device modeling for gigascale integration. We use the density-gradient (DG) transport model, which adds tunneling and quantum smoothing of carrier density profiles to the drift-diffusion model. We present the current implementation of the DG model in PROPHET, a partial differential equation solver developed by Lucent Technologies. This implementation approach permits rapid development and enhancement of models, as well as run-time modifications and model switching. We show that even in typical bulk transport devices such as P-N diodes and BJTs, DG quantum effects can significantly modify the I-V characteristics. Quantum effects are shown to be even more significant in small, surface transport devices, such as sub-0.1 micron MOSFETs. In thin-oxide MOS capacitors, we find that quantum effects may reduce gate capacitance by 25% or more. The inclusion of quantum effects in simulations dramatically improves the match between C-V simulations and measurements. Significant quantum corrections also occur in the I-V characteristics of short-channel MOSFETs due to the gate capacitance correction.
Biegel, Bryan A.↗