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The irreversible growth of a binary mixture under far-from-equilibrium conditions is studied in three-dimensional confined geometries of size $L_x \times L_y \times L_z$, where $L_z \gg L_x = L_y$ is the growing direction. A competing…

We study new asymptotic invariant of a pair consisting of a group and a subgroup, which we call Commensurizer Growth. We compute the commensurizer growth for several examples, concentrating mainly on the case of a locally compact…

Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of natural and technological processes, including embryonic development and 3D printing. In this paper…

In this paper, we investigate the tumor instability by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented in a prior study by Feng et al 2023. Building upon the…

An analytical model for the evolution of the boundary of the new phase in transformations ruled by nucleation and growth is presented. Both homogeneous and heterogeneous nucleation have been considered: The former includes transformations…

The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process.…

We develop a description of diffusion limited growth in solid-solid transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase…

A phase-field model for diffusion-limited crystal growth is formulated that is capable of handling highly anisotropic interfaces. It uses a Willmore regularization that yields corners of finite size. An asymptotic analysis reveals that…

A crystal surface which is miscut with respect to a high symmetry plane exhibits steps with a characteristic distance. It is argued that the continuum description of growth on such a surface, when desorption can be neglected, is given by…

The Minkowski problem for a class of unbounded closed convex sets is considered. This is equivalent to a Monge-Amp\`ere equation on a bounded convex open domain with possibly non-integrable given data. A complete solution (necessary and…

A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…

An efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic Monte Carlo is presented. The model used is based on a solid-on-solid bond counting formulation in which elastic effects are…

We consider a Markov evolution of lozenge tilings of a quarter-plane and study its asymptotics at large times. One of the boundary rays serves as a reflecting wall. We observe frozen and liquid regions, prove convergence of the local…

At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…

We study the dynamics of an exactly solvable lattice model for inhomogeneous interface growth. The interface grows deterministically with constant velocity except along a defect line where the growth process is random. We obtain exact…

A two-dimensional free boundary model for the growth of multi-layer tumors has been proposed in [S. Cui, J. Escher: ARMA 191 (2009) 173-193] where the authors derive well-posedness in a functional analytic setting, the stationary solutions…

We present a general approach to study a class of random growth models in $n$-dimensional Euclidean space. These models are designed to capture basic growth features which are expected to manifest at the mesoscopic level for several…

We introduce a model of a randomly growing interface in multidimensional Euclidean space. The growth model incorporates a random order model as an ingredient of its graphical construction, in a way that replicates the connection between the…

We give a characterization for asymptotic dimension growth. We apply it to CAT(0) cube complexes of finite dimension, giving an alternative proof of N. Wright's result on their finite asymptotic dimension. We also apply our new…

The three-dimensional shapes of thin lamina such as leaves, flowers, feathers, wings etc, are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric, given on the…