Related papers: Nucleation and growth of lattice crystals
We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…
Classical theories of crystal nucleation and growth from the liquid assume activated processes that are interface limited, with the atoms individually joining the growing interface by jumps that occur at a rate that is determined by the…
A general theory of nucleation for colloids and macromolecules in solution is formulated within the context of fluctuating hydrodynamics. A formalism for the determination of nucleation pathways is developed and stochastic differential…
We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
When a system is brought to a metastable state, nuclei of the equilibrium phase form and grow. This is the well-known nucleation and growth of first-order phase transitions. Near a critical point of a continuous phase transition, critical…
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…
We propose a novel approach to continuum modelling of dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
The rate of curvature-driven grain growth in polycrystalline materials is well-known to be limited by interface dissipation. We show analytically and by simulations that, for systems forming modulated phases or non-equilibrium patterns with…
Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by…
We consider the evolution by crystalline curvature of a planar set in a stratified medium, modeled by a periodic forcing term. We characterize the limit evolution law as the period of the oscillations tends to zero. Even if the model is…
Nucleation is an activated process in which the system has to overcome a free energy barrier in order for a first-order phase transition between the metastable and the stable phases to take place. In the liquid-to-solid transition the…
According to classical nucleation theory, a crystal grows from a small nucleus that already bears the symmetry of its end phase - but experiments with colloids now reveal that, from an amorphous precursor, crystallites with different…
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…
The nucleation and/or growth of cracks in elastic-brittle solids has been recently described in [14] in terms of a special class of measures and with a variational technique requiring the minimization of a certain energy over classes of…
Recent advances in classical density functional theory are combined with stochastic process theory and rare event techniques to formulate a theoretical description of nucleation, including crystallization, that can predict nonclassical…
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…
We investigate nuclear pasta structures at high temperatures in the framework of relativistic mean field model with Thomas-Fermi approximation. Typical pasta structures (droplet, rod, slab, tube, and bubble) are obtained, which form various…
A mathematical model to describe the growth of an arbitrarily large number of nanocrystals from solution is presented. First, the model for a single particle is developed. By non-dimensionalising the system we are able to determine the…
Several aspects of the theory of epitaxial crystal growth from atomic or molecular beams are developed from the perspective of statistical physics. Lectures are devoted to the rate equation theory of two-dimensional nucleation and its…
Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually proceeds by nucleation and growth. In…