Related papers: On the diffuse interface models for high codimensi…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
The novel concept of spectral diffusivity is introduced to analyse the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is…
Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…
The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and…
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…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
We present a new phase-field formulation for the non-equilibrium interface kinetics. The diffuse interface is considered an integral of numerous representative volume elements (RVEs), in which there is a two-phase mixture with two conserved…
Diffusion probabilistic models have quickly become a major approach for generative modeling of images, 3D geometry, video and other domains. However, to adapt diffusion generative modeling to these domains the denoising network needs to be…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
We minimized the interface diffuseness in the phase-field models by introducing the parabolic double-well potential and localizing the solute redistribution (or latent heat release) into a narrow region within the phase-field interface. In…
We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
A new formulation of the Phase Field Crystal model is presented that is consistent with the necessary microscopic independence between the phase field, reflecting the broken symmetry of the phase, and both mass density and elastic…
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,…
The seven-equation model is a compressible multiphase formulation that allows for phasic velocity and pressure disequilibrium. These equations are solved using a diffused interface method that models resolved multiphase flows. Novel…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
We present a continuum phase-field model of crack propagation. It includes a phase-field that is proportional to the mass density and a displacement field that is governed by linear elastic theory. Generic macroscopic crack growth laws…
An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large…
Stochastic models for the development of cracks in 1 and 2 dimensional objects are presented. In one dimension, we focus on particular scenarios for interacting and non-interacting fragments during the breakup process. For two dimensional…