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The analysis and design of advection-diffusion based molecular communication (MC) systems in cylindrical environments is of particular interest for applications such as micro-fluidics and targeted drug delivery in blood vessels. Therefore,…
We analyze a coupled system of evolution equations that describes the effect of thermal gradients on the motion and deposition of $N$ populations of colloidal species diffusing and interacting together through Smoluchowski production terms.…
The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…
We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence…
Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational…
Diffusion models have achieved impressive performance on multi-focus image fusion (MFIF). However, a key challenge in applying diffusion models to the ill-posed MFIF problem is that defocus blur can make common symmetric geometric…
A possibility to use an integral operator for establishing the link between physical and structural levels of materials in modeling diffusion processes is considered. We show how to perform the transition from the stochastic description of…
Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the…
Diffusion probabilistic models have made their way into a number of high-profile applications since their inception. In particular, there has been a wave of research into using diffusion models in the prediction and design of biomolecular…
Diffusion models (DMs) have emerged as powerful tools for modeling complex data distributions and generating realistic new samples. Over the years, advanced architectures and sampling methods have been developed to make these models…
Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…
In this paper we develop a model to describe the diffusion process in a porous medium. For the observed decrease in current yield, we propose other causes than difference in diffusivity, which we consider unaltered by the porous medium. The…
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…
Weather forecasting remains a crucial yet challenging domain, where recently developed models based on deep learning (DL) have approached the performance of traditional numerical weather prediction (NWP) models. However, these DL models,…
A folded type model is developed for analyzing compositional data. The proposed model involves an extension of the $\alpha$-transformation for compositional data and provides a new and flexible class of distributions for modeling data…
Recent advances in diffusion models have demonstrated their strong capabilities in generating high-fidelity samples from complex distributions through an iterative refinement process. Despite the empirical success of diffusion models in…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
Probabilistic denoising diffusion models (DDMs) have set a new standard for 2D image generation. Extending DDMs for 3D content creation is an active field of research. Here, we propose TetraDiffusion, a diffusion model that operates on a…