Related papers: Designer Patterns: Flexible Control of Precipitati…
The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to…
Alkane mixtures are model systems where the influence of surface tension gradients during the spreading and the evaporation of wetting drops can be easily studied. The surface tension gradients are mainly induced by concentration gradients,…
Biomolecular condensates are small droplets forming spontaneously in biological cells via phase separation. They play a role in many cellular processes, but it is unclear how cells control them. Cellular regulation often relies on…
These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…
In certain biological contexts, such as the plumage patterns of birds and stripes on certain species of fishes, pattern formation takes place behind a so-called "wave of competency". Currently, the effects of a wave of competency on the…
We introduce a droplet-jumping phenomenon on a superhydrophobic surface driven by the resonant AC electrowetting. The resonant electrical actuation enables a droplet to accumulate sufficient surface energy for jumping, and superhydrophobic…
A two-dimensional small bias model has been developed for a patterned metal current collector $|$ mixed oxygen ion and electronic conductor (MIEC) $|$ patterned metal current collector electrochemical cell in a symmetric gas environment.…
Inference-time controllable generation is essential for real-world applications of unconditional diffusion models. However, most existing techniques focus on individual samples, struggling in applications that require the sample population…
This paper presents adaptive event-triggered formation control strategies for autonomous vehicles (AVs) subject to longitudinal and lateral motion uncertainties. The proposed framework explores various vehicular formations to enable safe…
This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction…
We construct a two-dimensional electric circuit model for creeping discharge. Two types of discharge, surface corona and surface leader, are modeled by a two-step function of conductance. Branched patterns of surface leaders surrounded by…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
Conventional approaches to control and shape the scattering patterns of light generated by different nanostructures are mostly based on engineering of their electric response due to the fact that most metallic nanostructures support…
Diffusion models have emerged as powerful tools for high-quality image generation and editing, but guiding these models to produce specific outputs remains a challenge. Conventional approaches rely on conditioning mechanisms, such as text…
We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed $c\in{I\!\!R}$, we seek a control with minimum cost, which achieves a…
The directed percolation process in the vicinity of non-equilibrium phase transition is studied by the means of field theoretic methods. It will be assumed that percolation takes place in a compressible environment, which will be generated…
This paper presents an improved version of the previously proposed self-consistent drift-diffusion-reaction model correcting for non-physical behavior at longer time scales. To this end a novel boundary condition is employed that takes into…
Wetting of micropatterned surfaces is ubiquitous in nature and key to many technological applications like spray cooling, inkjet printing, and semiconductor processing. Overcoming the intrinsic, chemistry- and topography-governed wetting…
We use molecular dynamics simulations of a simple model to show that dispersions of slightly elongated colloidal particles with long-range dipolar interactions, like ferrofluids, can form a physical (reversible) gel at low volume fractions.…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…