Related papers: Scaling theory for two-dimensional single domain g…
In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…
Strains strongly affect the properties of low-dimensional materials, such as graphene. By combining in situ, in operando, reflection high energy electron diffraction experiments with first-principles calculations, we show that large…
The sessile microbial communities known as biofilms exhibit varying architectures as environmental factors are varied, which for immersed biofilms includes the shear rate of the surrounding flow. Here we modify an established agent-based…
We propose a generalized diffusion equation for a flat Euclidean space subjected to a continuous infinitesimal scale transform. For the special cases of an algebraic or exponential expansion/contraction, governed by time-dependent scale…
We investigate numerically the influence of an homogeneous shear flow on the spinodal decomposition of a binary mixture by solving the Cahn-Hilliard equation in a two-dimensional geometry. Several aspects of this much studied problem are…
We consider (a variant of) the external multi-particle diffusion-limited aggregation (MDLA) process of Rosenstock and Marquardt on the plane. Based on the recent findings of [11], [10] in one space dimension it is natural to conjecture that…
We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations…
We investigate the long time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant $D$. We consider two cases: (a) The particle is pulled forward by a small external constant…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
We investigate analytically and computationally the dynamics of 2D needle crystal growth from the melt in a narrow channel. Our analytical theory predicts that, in the low supersaturation limit, the growth velocity $V$ decreases in time $t$…
In this contribution tracking control designs using output feedback are presented for a two-phase Stefan problem arising in the modeling of the Vertical Gradient Freeze process. The two-phase Stefan problem, consisting of two coupled free…
Ferroelectric switching and nanoscale domain dynamics were investigated using atomic force microscopy on monocrystalline Pb(Zr0.2Ti0.8)O3 thin films. Measurements of domain size versus writing time reveal a two-step domain growth mechanism,…
The exceptional properties of the two-dimensional material graphene make it attractive for multiple functional applications, whose large-area samples are typically polycrystalline. Here, we study the mechanical properties of graphene in…
We apply the generic dynamical scaling theory (GDST) to the surfaces of CdTe polycrystalline films grown in glass substrates. The analysed data were obtained with a stylus profiler with an estimated resolution lateral resolution of $l_c=0.3…
We study the dynamics of domain growth when multipole moments of the order parameter are conserved. Following a quench into the ordered phase of the Ising model, the typical size of domains grows with time as $R(t) \sim t^{1/2}$ in the…
To obtain crystalline thin films of alpha-Quartz represents a challenge due to the tendency for the material towards spherulitic growth. Thus, understanding the mechanisms that give rise to spherulitic growth can help regulate the growth…
A theoretical framework is developed to describe experiments on the structure of epitaxial thin films, particularly niobium on sapphire. We extend the hypothesis of dynamical scaling to apply to the structure of thin films from its…
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between the mechanical pressure and the cell density, the model can…
Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…