Related papers: Phase-field crystal model for ordered crystals
In this paper, we present a parallel numerical algorithm for solving the phase field crystal equation. In the algorithm, a semi-implicit finite difference scheme is derived based on the discrete variational derivative method. Theoretical…
A model of phase transitions with coupling between the order parameter and its gradient is proposed. It is shown, that this nonlinear model is suitable for the description of phase transitions accompanied by the formation of spatially…
In this paper we have considered a simple lattice gas model of chemisorbed monolayer which allows for the harmonic fluctuations of the bond length between the adsorbate atom and the surface site. The model also involves a short-ranged…
We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions:…
Results are presented from numerical experiments aiming at the computation of stochastic phase-field models for phase transformations by coarse-graining molecular dynamics. The studied phase transformations occur between a solid crystal and…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
A thermodynamically consistent multiphase phase-field approach for stress and temperature-induced martensitic phase transformation at the nanoscale and under large strains is developed. A total of N independent order parameters are…
We investigate the possibility to control the symmetry of ordered states in phase-field crystal models by tuning nonlinear resonances. In two dimensions, we find that a state of square symmetry as well as coexistence between squares and…
A consistent, small scale description of plastic motion in a crystalline solid is presented based on a phase field description. By allowing for independent mass motion given by the phase field, and lattice distortion, the solid can remain…
In this work we investigate the Blume-Capel model with infinite-range ferromagnetic interactions and under the influence of a quenched disorder - a random crystal field. For a suitable choice of the random crystal field the model displays a…
The ground-state phase diagrams of the three-orbital t2g Hubbard model are studied using a Hartree-Fock approximation. First, a complete set of multipolar order parameters for t2g models defined in terms of the effective total angular…
A novel analysis of homogeneous nucleation of dislocations in sheared two-dimensional crystals described by periodized discrete elasticity models is presented. When the crystal is sheared beyond a critical strain $F=F_{c}$, the strained…
Atomistic simulations generate large volumes of noisy structural data, yet extracting phase labels and continuous order parameters (OPs) in a robust and general manner remains challenging. Existing tools are often specialized to a limited…
We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a…
We study the Blume-Emery-Griffiths model in a random crystal field in two and three dimensions, through a real-space renormalization-group approach and a mean-field approximation, respectively. According to the two-dimensional…
We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of…
We optimize a numerical time-stabilization routine for the phase-field crystal (PFC) models of solidification. By numerical experiments, we showcase that our approach can improve the accuracy of underlying time integration schemes by a few…
In vivo and in vitro systems of cells and extra-cellular matrix (ECM) systems are well known to form ordered patterns of orientationally aligned fibers. Here, we interpret them as active analogs of the (disordered) isotropic to the…