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At least 127 records · Page 7

A Mechanism-Based Reaction–Diffusion Model for Accelerated Discovery of Thermoset Resins Frontally Polymerized by Olefin Metathesis

Frontal ring-opening metathesis polymerization (FROMP) involves a self-perpetuating exothermic reaction, which enables the rapid and energy-efficient manufacturing of thermoset polymers and composites. Current state-of-the-art reaction–diffusion FROMP models rely on a phenomenological description of the olefin metathesis kinetics, limiting their ability to model the governing thermo-chemical FROMP processes. Furthermore, the existing models are unable to predict the variations in FROMP kinetics with changes in the resin composition and as a result are of limited utility toward accelerated discovery of new resin formulations. In this work, we formulate a chemically meaningful model grounded in the established mechanism of ring-opening metathesis polymerization (ROMP). Our study aims to validate the hypothesis that the ROMP mechanism, applicable to monomer-initiator solutions below 100 °C, remains valid under the nonideal conditions encountered in FROMP, including ambient to >200 °C temperatures, sharp temperature gradients, and neat monomer environments. Through extensive simulations, we demonstrate that our mechanism-based model accurately predicts the FROMP behavior across various resin compositions, including polymerization front velocities and thermal characteristics (e.g., T max ). Additionally, we introduce a semi-inverse workflow that predicts FROMP behavior from a single experimental data point. Notably, the physiochemical parameters utilized in our model can be obtained through DFT calculations and minimal experiments, highlighting the model’s potential for rapid screening of new FROMP chemistries in pursuit of thermoset polymers with superior thermo-chemo-mechanical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

D$e^+e^-$ffusion: Capturing the Beam-Beam Physics of $e^+e^-$ Collisions with Diffusion Models

Beam-induced backgrounds at high-luminosity $e^+e^-$ colliders, such as the FCC-ee, are dominated by incoherent pair creation (IPC), and require computationally expensive simulations with dedicated Monte Carlo (MC) event generators. Reliable detector and machine-detector interface studies necessitate event samples that are several orders of magnitude larger than what is practically attainable with existing MC. To alleviate this bottleneck, we present D$e^+e^-$ffusion, a denoising diffusion probabilistic model that operates as a permutation-equivariant, set-valued surrogate for fast IPC simulation. Trained on a small GuineaPig++ sample, D$e^+e^-$ffusion faithfully reproduces the marginal and joint kinematic, angular, and positional distributions of all three IPC production processes. In addition, we assess the fidelity at the detector level by propagating both Geant4 and D$e^+e^-$ffusion events through a Geant4 simulation of the CLD vertex detector and by training a transformer-based two-sample classifier; the classifier achieves an area under the ROC curve of $0.553 \pm 0.016$. The trained model generates events nearly four orders of magnitude faster than Geant4, paving the way for a fast-simulation surrogate for FCC-ee design studies.

Chahine, Antonio [Imperial Coll., London]↗

Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport

We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation. Furthermore, we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders s ∊ [0.5, 1). We also present an application of the advection-diffusion equation to anomalous transport of solutes.

97 MATHEMATICS AND COMPUTING↗

Parameters estimation using the first passage times method in a jump-diffusion model

The main purposes of this paper are two contributions: (1) it presents a new method, which is the first passage time (FPT method) generalized for all passage times (GPT method), in order to estimate the parameters of stochastic Jump-Diffusion process. (2) it compares in a time series model, share price of gold, the empirical results of the estimation and forecasts obtained with the GPT method and those obtained by the moments method and the FPT method applied to the Merton Jump-Diffusion (MJD) model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Diffusion models for Jupiter's radiation belt

Solutions are given for the diffusion of trapped particles in a planetary magnetic field in which the first and second adiabatic invariants are preserved but the third is not, using as boundary conditions a fixed density at the outer boundary (the magnetopause) and a zero density at an inner boundary (the planetary surface). Losses to an orbiting natural satellite are included and an approximate evaluation is made of the effects of the synchrotron radiation on the energy of relativistic electrons. Choosing parameters appropriate to Jupiter, the electrons required to produce the observed synchrotron radiation are explained. If a speculative mechanism in which the diffusion is driven by ionospheric wind is the true explanation of the electrons producing the synchrotron emission it can be concluded that Jupiter's inner magnetosphere is occupied by an energetic proton flux that would be a serious hazard to spacecraft.

Jacques, S. A.↗

A baseline for ensemble-based, time-resolved inflow reconstruction for a single turbine using large-eddy simulations and latent diffusion models

We are interested in reconstructing winds flowing through a turbine on a second-by-second basis over a 10 min window. Previously, we developed a machine learning algorithm that takes in a snapshot of wind speed measurements and generates ensembles of three-dimensional wind field estimates. Here, we use these estimates as initial conditions in large-eddy simulations and reconstruct atmospheric and turbine response dynamic quantities in a synthetic field campaign. In doing so, we establish a baseline for model validation that future time-aware data assimilation techniques will be compared to. In turbine-free case studies, ground truth wind speeds consistently fall within our estimated wind speed distribution for the first 100 s after the simulation start. In simulations with turbines, the wind estimates show a small bias of 0.10 m s 1 and good correlation of 0.80 during the first 100 s. During this window, our estimates of the Blade 1 bending moment and generator power typically span the ground truth, with the estimate of the former performing better overall. In summary, this approach shows promise as a stand-alone technique for reconstructing real-world inflow and turbine dynamics in 1-2 min windows and as a foundation for future time-aware data assimilation techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A generative artificial intelligence framework based on a molecular diffusion model for the design of metal-organic frameworks for carbon capture

Metal-organic frameworks (MOFs) exhibit great promise for CO 2 capture. However, finding the best performing materials poses computational and experimental grand challenges in view of the vast chemical space of potential building blocks. Here, we introduce GHP-MOFassemble, a generative artificial intelligence (AI), high performance framework for the rational and accelerated design of MOFs with high CO 2 adsorption capacity and synthesizable linkers. GHP-MOFassemble generates novel linkers, assembled with one of three pre-selected metal nodes (Cu paddlewheel, Zn paddlewheel, Zn tetramer) into MOFs in a primitive cubic topology. GHP-MOFassemble screens and validates AI-generated MOFs for uniqueness, synthesizability, structural validity, uses molecular dynamics simulations to study their stability and chemical consistency, and crystal graph neural networks and Grand Canonical Monte Carlo simulations to quantify their CO 2 adsorption capacities. We present the top six AI-generated MOFs with CO 2 capacities greater than 2m mol g -1 , i.e., higher than 96.9% of structures in the hypothetical MOF dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Moisture ingress in commercial steel drums: Water content determination, diffusion modelling and predicted permeation rates

Commercial steel drums underpin the global economy, playing a pivotal role in the storage and transportation of critical materials. Transported and stored materials, such as food, chemical and nuclear waste, can be sensitive to ambient conditions, particularly moisture that can enhance negative effects such as corrosion and material degradation. Although international standards and regulations are in place for the qualification of steel drums, there are no current testing requirements, established limits or boundaries for the permeation of moisture into the drums during transportation or storage. This work aims to provide insights into the moisture ingress over time into properly sealed steel drums and provides estimated moisture ingress rates over time through extrapolation. Water vapour transmission rate (WVTR) measurements through the gasket material at 10–40°C were 0.11–2.1 g/m 2 /day resulting in a permeation activation energy of 30.2 kJ/mol. Water sorption measurements and Karl Fischer titration (KFT) on ethylene propylene diene monomer (EPDM) gasket material revealed a decrease in equilibrium moisture saturation with increasing temperature. KFT measurements also revealed the presence of moisture within the adhesive and drum wall after exposure to ambient conditions. KFT and Fourier transform infrared spectroscopy (FTIR) show that moisture will desorb from the EPDM and drum wall after exposure to desiccating conditions, although a minimal amount of moisture will remain present. When sealed to the manufacturer's recommendations, the steel drums are effective in minimizing moisture ingress. In conclusion, in sealed empty drums, moisture ingress rates for 19-L drums were 0.4–1.5 mg/day at 25°C 15% relative humidity (RH) and increased to 7.1–8.8 mg/day at 40°C 90% RH, and moisture ingress rates for 210-L drums were 2.5 and 3.5 mg/day at field deployment conditions of 15.5°C 51.5% RH and 23°C 40% RH, respectively.

42 ENGINEERING↗

SU-E-T-196: Heat Diffusion Modeling for Digital Holographic Interferometry Dosimetry

Purpose: We have previously demonstrated that with Digital Holographic Interferometry (DHI) 2D spatial calorimetric measurements of high dose rate radiation sources can be obtained. The impact of heat transfer must be considered when undertaking any form of calorimetric measurement, as the radiation induced temperature distributions are subject to degradation due to heat diffusion. Unaccounted for, this limits the accuracy of the approach especially for long delivery times. Methods: 3D modelling of the heat diffusion in water was undertaken, and two different approaches developed to account for this effect. The mathematical framework to describe heat diffusion in 3D was applied, with the differential equations solved numerically using an implicit method. The first approach involved the comparison of the DHI measurements to an independent dose model of the source. The model was forward modeled to account for the heat diffusion during irradiation, allowing a direct comparison to validate the measured results. The second approach involved the correction of the measured data directly, by comparing the temperature distribution of two instances and subtracting the effects of heat diffusion of the first distribution from the second instance. This required the use of the Abel transform to approximate the 3D dose distribution from the 2D DHI results, thus limiting the approach to radiation applications possessing cylindrical symmetry. Results: The first approach resulted in higher accuracy and was more straightforward, but has a major limitation in that the measured results are only able to be utilized in comparison with an independent dose model. The applicability of the second approach is affected by noise in the measurement data and introduces higher uncertainties, but results in higher usability of the final data. Conclusion: Both approaches were implemented, and if used in conjunction would provide the most utility for the interpretation and use of DHI measurements.

07 ISOTOPE AND RADIATION SOURCES↗

A Process for Modelling Diffuse Scattering from Disordered Molecular Crystals, Illustrated by Application to Monoclinic 9-Chloro-10-methylanthracene

Diffuse scattering from a crystal contains valuable information about the two-body correlations (related to the nanoscale order) in the material. Despite years of development, the detailed analysis of single crystal diffuse scattering (SCDS) has yet to become part of the everyday toolbox of the structural scientist. Recent decades have seen the pair distribution function approach to diffuse scattering (in fact, total scattering) from powders become a relatively routine tool. However, analysing the detailed, complex, and often highly anisotropic three-dimensional distribution of SCDS remains valuable yet rare because there is no routine method for undertaking the analysis. At present, analysis requires significant investment of time to develop specialist expertise, which means that the analysis of diffuse scattering, which has much to offer, is not incorporated thorough studies of many compounds even though it has the potential to be a very useful adjunct to existing techniques. This article endeavours to outline in some detail how the diffuse scattering from a molecular crystal can be modelled relatively quickly and largely using existing software tools. It is hoped this will provide a template for other studies. To enable this, the entire simulation is included as deposited material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Diffusion model for lightning radiative transfer

A one-speed Boltzmann transport theory, with diffusion approximations, is applied to study the radiative transfer properties of lightning in optically thick thunderclouds. Near-infrared (lambda = 0.7774 micrometers) photons associated with a prominent oxygen emission triplet in the lightning spectrum are considered. Transient and spatially complex lightning radiation sources are placed inside a rectangular parallelepiped thundercloud geometry and the effects of multiple scattering are studied. The cloud is assumed to be composed of a homogeneous collection of identical spherical water droplets, each droplet a nearly conservative, anisotropic scatterer. Conceptually, we treat the thundercloud like a nuclear reactor, with photons replaced by neutrons, and utilize standard one-speed neutron diffusion techniques common in nuclear reactor analyses. Valid analytic results for the intensity distribution (expanded in spherical harmonics) are obtained for regions sufficiently far from sources. Model estimates of the arrival-time delay and pulse width broadening of lightning signals radiated from within the cloud are determined and the results are in good agreement with both experimental data and previous Monte Carlo estimates. Additional model studies of this kind will be used to study the general information content of cloud top lightning radiation signatures.

Koshak, William J.↗

MODIS Solar Diffuser: Modelled and Actual Performance

The Moderate Resolution Imaging Spectroradiometer (MODIS) instrument's solar diffuser is used in its radiometric calibration for the reflective solar bands (VIS, NTR, and SWIR) ranging from 0.41 to 2.1 micron. The sun illuminates the solar diffuser either directly or through a attenuation screen. The attenuation screen consists of a regular array of pin holes. The attenuated illumination pattern on the solar diffuser is not uniform, but consists of a multitude of pin-hole images of the sun. This non-uniform illumination produces small, but noticeable radiometric effects. A description of the computer model used to simulate the effects of the attenuation screen is given and the predictions of the model are compared with actual, on-orbit, calibration measurements.

Waluschka, Eugene↗

Discovering a reaction–diffusion model for Alzheimer’s disease by combining PINNs with symbolic regression

Misfolded tau proteins play a critical role in the progression and pathology of Alzheimer's disease. Recent studies suggest that the spatio-temporal pattern of misfolded tau follows a reaction-diffusion type equation. However, the precise mathematical model and parameters that characterize the progression of misfolded protein across the brain remain incompletely understood. Here, we use deep learning and artificial intelligence to discover a mathematical model for the progression of Alzheimer's disease using longitudinal tau positron emission tomography from the Alzheimer's Disease Neuroimaging Initiative database. Specifically, we integrate physics informed neural networks (PINNs) and symbolic regression to discover a reaction-diffusion type partial differential equation for tau protein misfolding and spreading. First, we demonstrate the potential of our model and parameter discovery on synthetic data. Then, we apply our method to discover the best model and parameters to explain tau imaging data from 46 individuals who are likely to develop Alzheimer's disease and 30 healthy controls. Our symbolic regression discovers different misfolding models f(c) for two groups, with a faster misfolding for the Alzheimer's group, f(c) = 0.23c 3 – 1.34c 2 + 1.11c, than for the healthy control group, f(c) = –c 3 + 0.62c 2 + 0.39c. Our results suggest that PINNs, supplemented by symbolic regression, can discover a reaction-diffusion type model to explain misfolded tau protein concentrations in Alzheimer's disease. Furthermore, we expect our study to be the starting point for a more holistic analysis to provide image-based technologies for early diagnosis, and ideally early treatment of neurodegeneration in Alzheimer's disease and possibly other misfolding-protein based neurodegenerative disorders.

60 APPLIED LIFE SCIENCES↗

Reaction–drift–diffusion models from master equations: application to material defects

We present a general method to produce well-conditioned continuum reaction–drift–diffusion equations directly from master equations on a discrete, periodic state space. We assume the underlying data to be kinetic Monte Carlo models (i.e. continuous-time Markov chains) produced from atomic sampling of point defects in locally periodic environments, such as perfect lattices, ordered surface structures or dislocation cores, possibly under the influence of a slowly varying external field. Our approach also applies to any discrete, periodic Markov chain. Here, the analysis identifies a previously omitted non-equilibrium drift term, present even in the absence of external forces, which can compete in magnitude with the reaction rates, thus being essential to correctly capture the kinetics. To remove fast modes which hinder time integration, we use a generalized Bloch relation to efficiently calculate the eigenspectrum of the master equation. A well conditioned continuum equation then emerges by searching for spectral gaps in the long wavelength limit, using an established kinetic clustering algorithm to define a proper reduced, Markovian state space.

36 MATERIALS SCIENCE↗

Enabling fast charging of lithium-ion batteries through secondary- /dual- pore network: Part I - Analytical diffusion model

Battery performance is strongly correlated with electrode microstructural properties. Enabling fast charging of lithium-ion batteries requires improved through-plane ionic diffusion that can be achieved through, among other strategies, structured electrodes with a secondary- or dual-pore network (SPN). In this work, an analytical model investigates the impact of such an SPN on ionic diffusion with a composite electrode, considering various pore-channel geometries and comparing to standard electrodes with identical gravimetric- and volumetric-specific theoretical capacities. Relevant SPN design parameters and tortuosity coefficients are identified according to three optimization objectives that aim to balance the improved overall through-plane diffusion, thanks to the coarse aligned channels, and degraded in-plane diffusion because of the porous matrix densification required to maintain gravimetric- and volumetric-specific theoretical capacities. The model indicates that a relatively low amount of SPN is required and that electrodes with high through-plane tortuosity and low in-plane tortuosity benefit most from such architecture.

25 ENERGY STORAGE↗

Perona Malik anisotropic diffusion model using Peaceman Rachford scheme on digital radiographic image

In image processing, it is important to remove noise without affecting the image structure as well as preserving all the edges. Perona Malik Anisotropic Diffusion (PMAD) is a PDE-based model which is suitable for image denoising and edge detection problems. In this paper, the Peaceman Rachford scheme is applied on PMAD to remove unwanted noise as the scheme is efficient and unconditionally stable. The capability of the scheme to remove noise is evaluated on several digital radiography weld defect images computed using MATLAB R2009a. Experimental results obtained show that the Peaceman Rachford scheme improves the image quality substantially well based on the Peak Signal to Noise Ratio (PSNR). The Peaceman Rachford scheme used in solving the PMAD model successfully removes unwanted noise in digital radiographic image.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗