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Material stress analysis is a critical aspect of material design and performance optimization. Under dynamic loading, the global stress evolution in materials exhibits complex spatiotemporal characteristics, especially in two-phase random…
The existence and the regularity results obtained in [37] for the variational model introduced in [36] to study the optimal shape of crystalline materials in the setting of stress-driven rearrangement instabilities (SDRI) are extended from…
Ultra-lean premixed hydrogen combustion is a possible solution to decarbonize industry, while limiting flame temperatures and thus nitrous oxide emissions. These lean hydrogen/air flames experience strong preferential diffusion effects,…
Diffusion generative models have recently become a powerful technique for creating and modifying high-quality, coherent video content. This survey provides a comprehensive overview of the critical components of diffusion models for video…
Diffusion-based generative modeling has been achieving state-of-the-art results on various generation tasks. Most diffusion models, however, are limited to a single-generation modeling. Can we generalize diffusion models with the ability of…
We introduce and analyze several variants of a system of differential equations which model the dynamics of social outbursts, such as riots. The systems involve the coupling of an explicit variable representing the intensity of rioting…
We study the gradient flow model for the Landau-de Gennes energy functional for nematic liquid crystals at the nematic-isotropic transition temperature on prototype geometries. We study the dynamic model on a three-dimensional droplet and…
We discuss a new phenomenon of turbulent thermal diffusion associated with turbulent transport of aerosols in the atmosphere and in laboratory experiments. The essence of this phenomenon is the appearance of a nondiffusive mean flux of…
Droplet spreading is ubiquitous and plays a significant role in liquid-based energy systems, thermal management devices, and microfluidics. While the spreading of non-volatile droplets is quantitatively understood, the spreading and flow…
Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical,…
Computational atomic-scale methods continue to provide new information about geometry, energetics, and transition states for interstitial elements in crystalline lattices. This data can be used to determine the diffusivity of interstitials…
Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static…
Diffusion models for image generation function by progressively adding noise to an image set and training a model to separate out the signal from the noise. The noise profile used by these models is white noise -- that is, noise based on…
The hydrodynamic equations for a crystals with interstitials, taking into account the dissipative processes of the viscosity, heat conduction and the interstitial diffusion are derived. To achieve that we use the phenomenological approach…
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion…
We investigate the diffusion of an intruder in a granular gas, with both components modeled as smooth hard spheres, both immersed in a low viscosity carrier fluid to form a particle-laden suspension. In this system, dissipative particle…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
Diffusion models have been popular for point cloud generation tasks. Existing works utilize the forward diffusion process to convert the original point distribution into a noise distribution and then learn the reverse diffusion process to…