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In this review we summarize our recent efforts in trying to understand the role of heterogeneity in cancer progression by using neural networks to characterise different aspects of the mapping from a cancer cells genotype and environment to…
A model for phase transitions initiated on grain boundaries is proposed and tested against numerical simulations: this approach based on a grain explicit model (GEM) allows to consider the granular structure, yielding accurate predictions…
During the processes of nucleation and growth of a precipitate cluster from a supersaturated solution, the diffusion flux between the cluster and the solution changes the solute concentration near the cluster-solution interface from its…
The shape phase structure and its transition of the nucleus in the transitional region between the U(5) and SU(3) symmetries is restudied within the framework of coherent-state theory with angular momentum projection in IBM-1. The certain…
The morphology transition from the thermodynamically favorable to the unfavorable phase during growth of free-standing copper nanoclusters is studied by molecular dynamics simulations. We give a detailed description of the kinetics and…
The spatio-temporal aspects of the transition to turbulence are considered in the case of a boundary layer flow developing above a flat plate exposed to free-stream turbulence. Combining results on the receptivity to free-stream turbulence…
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 construct a diffuse-interface model of two-phase solidification that quantitatively reproduces the classic free boundary problem on solid-liquid interfaces in the thin-interface limit. Convergence tests and comparisons with boundary…
We investigate the evolution of a two-phase viscoelastic material at finite strains. The phase evolution is assumed to be irreversible: One phase accretes in time in its normal direction, at the expense of the other. Mechanical response…
Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the…
The nucleation of crystals from the liquid melt is often characterized by a competition between different crystalline structures or polymorphs, and can result in nuclei with heterogeneous compositions. These mixed-phase nuclei can display…
We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the…
The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as…
Heterogeneous nucleation is studied by Monte Carlo simulations and phenomenological theory, using the two-dimensional lattice gas model with suitable boundary fields. A chemical inhomogeneity of length b at one boundary favors the liquid…
We develop a phase-field model of eutectic growth that uses three phase fields, admits strictly binary interfaces as stable solutions, and has a smooth free energy functional. We use this model to simulate oscillatory limit cycles in…
A theoretical study of cell evolution is presented here. By using a toolbox containing an intracellular catalytic reaction network model and a mutation-selection process, four distinct phases of self-organization were unveiled. First, the…
Complex tumor-host interactions can significantly affect the growth dynamics and morphologies of progressing neoplasms. The growth of a confined solid tumor induces mechanical pressure and deformation of the surrounding microenvironment,…
The FeRh alloy is an attractive material for studies of magnetic first-order phase transitions. The phase transition in FeRh from an antiferromagnetic to the ferromagnetic state is accompanied by the nucleation, growth, and merging of…
Few years ago, Boltzmann neutrino transport led to a new and reliable generation of spherically symmetric models of stellar core collapse and postbounce evolution. After the failure to prove the principles of the supernova explosion…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…