Generating Multiphase Fluid Configurations in Fractures using Diffusion Models
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Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models
Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.
36 MATERIALS SCIENCE↗
A Generalization of Threshold-Based and Probability-Based Models of Information Diffusion
Diffusion of information through complex networks is of interest in studies such as propagation prediction and influence maximization, both of which have applications in viral marketing and rumor controlling. There are a variety of information diffusion models, all of which simulate the adoption and spread of information over time. However, there is a lack of understanding of whether, despite their conceptual differences, these models represent the same underlying generative structures. For instance, if two different models utilize different conceptual mechanisms, but generate the same results, does the choice of model matter? A classification of diffusion of information models is developed based on the neighbor knowledge of the model infection requirement and the stochasticity of the model. This classification allows for the identification of models that fall into each respective category. The study involves the analysis of the following agent-based models on directed scale-free networks: (1) a linear absolute threshold model (LATM), (2) a linear fractional threshold model (LTFM), (3) the independent cascade model (ICM), (4) Bass-Rand-Rust model (BRRM) (5) a stochastic linear absolute threshold model (SLATM) (6) a stochastic fractional threshold model (SLFTM), and (7) Dodds–Watts model (DWM). Through the execution of simulations and analysis of the experimental results, the distinctive properties of each model are identified. Our analysis reveals that similarity in conceptual design does not imply similarity in behavior concerning speed, final state of nodes and edges, and sensitivity to parameters. Therefore, we highlight the importance of considering the unique behavioral characteristics of each model when selecting a suitable information diffusion model for a particular application.
97 MATHEMATICS AND COMPUTING↗
Comparison of Experimental Methods for Estimating Matrix Diffusion Coefficients for Contaminant Transport Modeling
Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
A method for modeling oxygen diffusion in an agent-based model with application to host-pathogen infection
This paper describes a method for incorporating a diffusion field modeling oxygen usage and dispersion in a multi-scale model of Mycobacterium tuberculosis (Mtb) infection mediated granuloma formation. We implemented this method over a floating-point field to model oxygen dynamics in host tissue during chronic phase response and Mtb persistence. The method avoids the requirement of satisfying the Courant-Friedrichs-Lewy (CFL) condition, which is necessary in implementing the explicit version of the finite-difference method, but imposes an impractical bound on the time step. Instead, diffusion is modeled by a matrix-based, steady state approximate solution to the diffusion equation. Moreover, presented in figure 1 is the evolution of the diffusion profiles of a containment granuloma over time.
59 BASIC BIOLOGICAL SCIENCES↗
Diffusion Probabilistic Modeling for Video Generation
Denoising diffusion probabilistic models are a promising new class of generative models that mark a milestone in high-quality image generation. This paper showcases their ability to sequentially generate video, surpassing prior methods in perceptual and probabilistic forecasting metrics. We propose an autoregressive, end-to-end optimized video diffusion model inspired by recent advances in neural video compression. The model successively generates future frames by correcting a deterministic next-frame prediction using a stochastic residual generated by an inverse diffusion process. We compare this approach against six baselines on four datasets involving natural and simulation-based videos. We find significant improvements in terms of perceptual quality and probabilistic frame forecasting ability for all datasets.
97 MATHEMATICS AND COMPUTING↗
Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation
We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assuming equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Modeling water diffusion in polybenzimidazole membranes using partial immobilization and free volume theory
Not provided.
Polymer Science↗
Multi-solid and multi-fluid diffuse interface model: Applications to dynamic fracture and fragmentation
We extend the model of diffuse solid–fluid interfaces developed earlier by authors of this paper to the case of arbitrary number of interacting hyperelastic solids. Plastic transformations of solids are taken into account through a Maxwell type model. The specific energy of each solid is given in separable form: it is the sum of a hydrodynamic part of the energy depending only on the density and the entropy, and an elastic part of the energy which is unaffected by the volume change. It allows us to naturally pass to the fluid description in the limit of vanishing shear modulus. In spite of a large number of governing equations, the model has a quite simple mathematical structure: it is a duplication of a single visco-elastic model. The model is well posed both mathematically and thermodynamically: it is hyperbolic and compatible with the second law of thermodynamics. The resulting model can be applied in the situations involving an arbitrary number of fluids and solids. In particular, we show the ability of the model to describe spallation and penetration phenomena occurring during high velocity impacts.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A comparison of probabilistic generative frameworks for molecular simulations
Generative artificial intelligence is now a widely used tool in molecular science. Despite the popularity of probabilistic generative models, numerical experiments benchmarking their performance on molecular data are lacking. Here, in this work, we introduce and explain several classes of generative models, broadly sorted into two categories: flow-based models and diffusion models. We select three representative models: neural spline flows, conditional flow matching, and denoising diffusion probabilistic models, and examine their accuracy, computational cost, and generation speed across datasets with tunable dimensionality, complexity, and modal asymmetry. Our findings are varied, with no one framework being the best for all purposes. In a nutshell, (i) neural spline flows do best at capturing mode asymmetry present in low-dimensional data, (ii) conditional flow matching outperforms other models for high-dimensional data with low complexity, and (iii) denoising diffusion probabilistic models appear the best for low-dimensional data with high complexity. Our datasets include a Gaussian mixture model and the dihedral torsion angle distribution of the Aib9 peptide, generated via a molecular dynamics simulation. We hope our taxonomy of probabilistic generative frameworks and numerical results may guide model selection for a wide range of molecular tasks.
Artificial intelligence↗
Forecasting residential solar photovoltaic deployment in California
Residential distributed photovoltaic (PV) deployment in the United States has experienced robust growth, and policy changes impacting the value of solar are likely to occur at the federal and state levels. To establish a credible baseline and evaluate impacts of potential new policies, this analysis employs multiple methods to forecast residential PV deployment in California, including a time-series forecasting model, a threshold heterogeneity diffusion model, a Bass diffusion model, and National Renewable Energy Laboratory's dSolar model. As a baseline, the residential PV market in California is modeled to peak in the early 2020s, with a peak annual installation of 1.5-2 GW across models. We then use the baseline results from the dSolar model and the threshold model to gauge the impact of the recent federal investment tax credit (ITC) extension, the newly approved California net energy metering (NEM) policy, and a hypothetical value-of-solar (VOS) compensation scheme. We find that the recent ITC extension may increase annual PV installations by 12%-18% (roughly 500 MW, MW) for the California residential sector in 2019-2020. The new NEM policy only has a negligible effect in California due to the relatively small new charges (< 100 MW in 2019-2020). Moreover, impacts of the VOS compensation scheme (0.12 cents per kilowatt-hour) are larger, reducing annual PV adoption by 32% (or 900-1300 MW) in 2019-2020.
14 SOLAR ENERGY↗
Physically constrained 3D diffusion for inverse design of fiber-reinforced polymer composite materials
Designing fiber-reinforced polymer composites (FRPCs) with a tailored nonlinear stress-strain response is crucial for applications such as energy absorption in crash structures, flexible robotics, and impact-resistant protective gear. However, the inherent complexities of composite materials and the multitude of parameters involved, render traditional design and optimization methods inadequate for achieving effective inverse design of composites. In this paper, we present an AI-based inverse design framework that effectively and efficiently generates FRPCs with targeted nonlinear stress-strain responses. We introduce a physically constrained diffusion model (PC3D_Diffusion) capable of managing the complexities of composite materials and producing detailed, high-quality designs. We propose a loss-guided, learning-free approach to generate physically feasible microstructure designs by explicitly enforcing physical constraints during the generation process. For training purposes, 1.35 million FRPC samples were created, and their corresponding stress-strain curves were computed using established physics-based computational models. The results show that PC3D_Diffusion consistently generates high-quality designs with tailored mechanical behaviors, while guaranteeing compliance with the physical constraints. PC3D_Diffusion advances FRPC inverse design and may facilitate the inverse design of other 3D materials, offering potential applications in industries reliant on materials with custom mechanical properties.
Xu, Pei [Clemson Univ., SC (United States)]↗
A comparison of molecular dynamics and diffuse interface model predictions of Lennard-Jones fluid evaporation
The unsteady evaporation of a thin planar liquid film is studied by molecular dynamics simulations of Lennard-Jones fluid. The obtained results are compared with the predictions of a diffuse interface model in which capillary Korteweg contributions are added to hydrodynamic equations, in order to obtain a unified description of the liquid bulk, liquid-vapor interface and vapor region. Particular care has been taken in constructing a diffuse interface model matching the thermodynamic and transport properties of the Lennard-Jones fluid. The comparison of diffuse interface model and molecular dynamics results shows that, although good agreement is obtained in equilibrium conditions, remarkable deviations of diffuse interface model predictions from the reference molecular dynamics results are observed in the simulation of liquid film evaporation. It is also observed that molecular dynamics results are in good agreement with preliminary results obtained from a composite model which describes the liquid film by a standard hydrodynamic model and the vapor by the Boltzmann equation. The two mathematical model models are connected by kinetic boundary conditions assuming unit evaporation coefficient.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Importance Sampling Model-Based Diffusion for Trajectory Optimization
Trajectory optimization for robotic systems remains a challenging problem. This is especially true for robotic systems featuring nonlinear dynamics and many degrees of freedom. Data-based or model-free diffusion has recently been popularized in the fields of artificial intelligence and trajectory optimization. Model-Based Diffusion provides a data-free method of trajectory optimization, trained at runtime on a system dynamics model, suitable for high-dimensional models. This paper examines how importance sampling can enhance the performance of Model-Based Diffusion for trajectory optimization. Here, we quantify the benefits of importance sampling across three long horizon planning tasks. These results show as much as a 13x improvement in sample efficiency depending on environment and optimization parameters.
Golembeski, Seth [Georgia Institute of Technology,↗
Contributions to Loss Across the Magnetopause During an Electron Dropout Event
Abstract Dropout events are dramatic decreases in radiation belt electron populations that can occur in as little as 30 minutes. Loss to magnetopause due to a combination of magnetopause shadowing and outward radial transport plays a significant role in these events. We examine the dropout of relativistic electron populations during the October 2012 geomagnetic storm using simulated electron phase space density, evaluating the contribution of different processes to losses across the magnetopause. We compare loss contribution from outward transport calculated using a standard empirical radial diffusion model that assumes a dipolar geomagnetic field to an event‐specific radial diffusion model evaluated with a non‐dipolar geomagnetic field. We additionally evaluate the contribution of Shabansky type 1 particles, which bounce along magnetic field lines with local equatorial maxima, to the loss calculated during this event. We find that the empirical radial diffusion model with a dipolar background field underestimates the contribution of radial diffusion to this dropout event by up to 10% when compared to the event‐specific, non‐dipolar radial diffusion model. We additionally find that including Shabansky type 1 particles in the initial electron phase space density, that is, allowing some magnetic field lines distorted from the typical single‐minima configuration in drift shell construction, increases the calculated loss by an average of 0.75%. This shows that the treatment of the geomagnetic field significantly impacts the calculation of electron losses to the magnetopause during dropout events, with the non‐dipolar treatment of radial diffusion being essential to accurately quantify the loss of outer radiation belt populations.
79 ASTRONOMY AND ASTROPHYSICS↗
Integration and validation of some modules for modelling of high-speed chemically reactive flows in two-phase gas-droplet mixtures
Three modules are integrated into the built-in OpenFOAM rhoCentralFoam solver towards accurate and efficient modelling of high-speed chemically reactive flows in two-phase gas-droplet mixtures within the OpenFOAM 10.0 framework. The first module is the mixture-averaged diffusion model. The second module is the built-in OpenFOAM Lagrangian solver coupled with optimised droplet drag coefficient and convective heat transfer coefficient sub-models. The last module is a sparse stiff chemistry solver based on dynamic adaptive hybrid integration (AHI-S). The optimised droplet sub-models are first verified in correct implementation for subsequent simulations in this work. Further, they show good accuracy against experimental and analytical data in the modelling of ammonia droplet acceleration and cooling in the flowing and/or low-temperature air. The accuracy and efficiency gains related to the mixture-averaged diffusion model and the AHI-S chemistry solver are examined by simulating 1-D detonation propagation in ammonia droplet-free/laden ammoniaoxygen mixtures. Numerical results of detonation propagation speed, gaseous temperature, density, and species distributions around the induction zone show good agreement with experimental data and analytical solutions. Compared to the built-in OpenFOAM diffusion model, the mixture-averaged diffusion model provides different numerical predictions of pulsating instabilities in detonation propagation. It shows better accuracy in depicting the detonation structure within the droplet-free section attributed to improved multi-component diffusion modelling. Compared to the built-in OpenFOAM solver EulerImplicit (backward Euler), the AHI-S chemistry solver reduces the computational cost by around 50%. It achieves satisfactory accuracy in calculating detonation propagation speed within the droplet-free section with the optimal efficiency when the safety factor, β, equals 0.5.
42 ENGINEERING↗
Monte Carlo Modeling of Diffuse Scattering from Single Crystals: The Program ZMC
Diffuse scattering probes the local ordering in a crystal, whereas Bragg peaks are descriptive of the average long-range ordering. The population of local configurations can be explored by modeling the three-dimensional distribution of diffuse scattering. Local configurations are not constrained by the average crystallographic symmetry, so one way of modeling diffuse scattering is by modeling a disordered (short-range-ordered) structure and then calculating its diffuse scattering. The structure must contain enough unit cells to give a statistically valid model of the populations of local configurations, and so requirements for a program to model this ordering are very different from programs that model average crystal structures (used to fit the Bragg diffraction). ZMC is a program that has been developed to model diffuse scattering, particularly from molecular crystals. The strategies used to tackle the problem and the way in which they are implemented will be discussed.
36 MATERIALS SCIENCE↗