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We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion…
The problem of eliminating fast-relaxing variables to obtain an effective drift-diffusion process in position is solved in a uniform and straightforward way for models with velocity a function jointly of position and fast variables. A more…
A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation,…
The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward…
The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the…
The paper studies a higher-order diffusion model of Maxwell-Stefan kind. The model is based upon higher-order moment equations of kinetic theory of mixtures, which include viscous dissipation in the model. Governing equations are analyzed…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
Atomic crystals with dislocations deform plastically at low stresses via dislocation glide. Whether dislocation glide occurs in macroscopic frictional granular media has remained unknown. The discrete element method is employed to simulate…
We investigate stellar metallicity distribution functions (MDFs), including Fe and ${\alpha}$-element abundances, in dwarf galaxies from the Feedback in Realistic Environments (FIRE) project. We examine both isolated dwarf galaxies and…
The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of…
Recent advances in diffusion models have shown remarkable potential in the conditional generation of novel molecules. These models can be guided in two ways: (i) explicitly, through additional features representing the condition, or (ii)…
This study addresses the modelling of elastic bodies, particularly when the relaxed configuration is unknown or non-existent. We adopt the theory of initially stressed materials, incorporating the deformation gradient and stress state of…
Grain boundary (GB) diffusion in polycrystalline materials is a physical phenomenon of great fundamental interest and practical significance. Although the accelerated ("short circuit") atomic transport along GBs has been known for decades,…
Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…
We discuss a class of diffusion-type partial differential equations on a bounded interval and discuss the possibility of replacing the boundary conditions by certain linear conditions on the moments of order 0 (the total mass) and of…
Real-world data generation often involves complex inter-dependencies among instances, violating the IID-data hypothesis of standard learning paradigms and posing a challenge for uncovering the geometric structures for learning desired…
Many particle physics datasets like those generated at colliders are described by continuous coordinates (in contrast to grid points like in an image), respect a number of symmetries (like permutation invariance), and have a stochastic…
To simulate the transient enhanced diffusion near the surface or interface, a set of equations describing the impurity diffusion and quasichemical reactions of dopant atoms and point defects in ion-implanted layers is proposed and analyzed.…
We revisit the phenomenon of elements diffusion in the intergalactic medium (IGM) in clusters of galaxies. The diffusion is driven by gravity, concentration and temperature gradients. The latter cause thermal diffusion, which has been so…
Molecule generation, especially generating 3D molecular geometries from scratch (i.e., 3D \textit{de novo} generation), has become a fundamental task in drug designs. Existing diffusion-based 3D molecule generation methods could suffer from…