Related papers: Continuum Limit of Dendritic Deposition
Using the formalism of differential equations, we introduce a new method to continuously deform the $s$-embeddings associated with a family of Ising models as their coupling constants vary. This provides a geometric interpretation of the…
Particle systems interacting with a soft repulsion, at thermal equilibrium and under some circumstances, are known to form cluster crystals, i.e. periodic arrangements of particle aggregates. We study here how these states are modified by…
We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner…
The rotational Brownian motion of colloidal spheres in dense suspensions reflects local hydrodynamics and friction, both key to non-linear rheological phenomena such as shear-thickening and jamming, and transport in crowded environments,…
We explore numerically the morphological patterns of thermo-diffusive instabilities in combustion fronts with a continuum fuel source, within a range of Lewis numbers and ignition temperatures, focusing on the cellular regime. For this…
The formation mechanism of planetesimals in protoplanetary discs is hotly debated. Currently, the favoured model involves the accumulation of meter-sized objects within a turbulent disc, followed by a phase of gravitational instability. At…
We study the surface growth generated by the random deposition of particles of different sizes. A model is proposed where the particles are aggregated on an initially flat surface, giving rise to a rough interface and a porous bulk. By…
We consider a system of interacting Brownian particles in R^d with a pairwise potential, which is radially symmetric, of finite range and attains a unique minimum when the distance of two particles becomes a>0. The asymptotic behavior of…
An active Brownian particle is a minimal model for a self-propelled colloid in a dissipative environment. Experiments and simulations show that, in the presence of boundaries and obstacles, active Brownian particle systems approach…
A probabilistic discrete model for 2D protein crystal growth is presented. This model takes into account the available space and can describe growing processes of different nature due to the versatility of its parameters which gives the…
Two basic routes for planetesimal formation have been proposed over the last few decades. One is a classical "slow-growth" scenario. Another one is particle concentration models, in which small pebbles are concentrated locally and then…
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion…
Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the…
Although the dynamics of colloids in the vicinity of a solid interface has been widely characterized in the past, experimental studies of Brownian diffusion close to an air-water interface are rare and limited to particle-interface gap…
In this work a phenomenological stochastic differential equation is proposed to model the time evolution of the radius of a pre-critical molecular cluster during nucleation (the classical order parameter). Such a stochastic differential…
A thin-interface phase-field model of electrochemical interfaces is developed based on Marcus kinetics for concentrated solutions, and used to simulate dendrite growth during electrodeposition of metals. The model is derived in the grand…
Depletion forces play a role in the compaction and de-compation of chromosomal material in simple cells but it remains debatable whether they are sufficient to account for chromosomal collapse. We present coarse-grained molecular dynamics…
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…
In recent years, researchers have increasingly sought batteries as an efficient and cost-effective solution for energy storage and supply, owing to their high energy density, low cost, and environmental resilience. However, the issue of…