#### Filter Results:

- Full text PDF available (9)

#### Publication Year

1998

2017

- This year (1)
- Last five years (7)

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

- Alain Karma, Mathis Plapp
- 1998

Spiral surface growth is well understood in the limit where the step motion is controlled by the local supersaturation of adatoms near the spiral ridge. In epitaxial thin-film growth, however, spirals can form in a step-flow regime where desorption of adatoms is negligible and the ridge dynamics is governed by the non-local diffusion field of adatoms on the… (More)

A phase-field model that allows for quantitative simulations of low-speed eutectic and peritectic solidification under typical experimental conditions is developed. Its cornerstone is a smooth free-energy functional, specifically designed so that the stable solutions that connect any two phases are completely free of the third phase. For the simplest choice… (More)

- Blas Echebarria, Roger Folch, Alain Karma, Mathis Plapp
- Physical review. E, Statistical, nonlinear, and…
- 2004

We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect to previous phase-field models is achieved by the addition of a phenomenological "antitrapping" solute current in the… (More)

- Kuo-An Wu, Mathis Plapp, Peter W Voorhees
- Journal of physics. Condensed matter : an…
- 2010

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 the coexistence between squares and hexagons can be easily obtained. In contrast, it is delicate to obtain the coexistence of squares and liquid. We… (More)

Bacillus subtilis swarms rapidly over the surface of a synthetic medium creating remarkable hyperbranched dendritic communities. Models to reproduce such effects have been proposed under the form of parabolic Partial Differential Equations representing the dynamics of the active cells (both motile and multiplying), the passive cells (non-motile and… (More)

During the directional solidification of peritectic alloys, two stable solid phases (parent and peritectic) grow competitively into a metastable liquid phase of larger impurity content than either solid phase. When the parent or both solid phases are morphologically unstable, i.e., for a small temperature gradient/growth rate ratio (G/v(p)), one solid phase… (More)

We present a novel computational method to simulate accurately a wide range of interfacial patterns whose growth is limited by a large-scale diffusion field. To illustrate the computational power of this method, we demonstrate that it can be used to simulate three-dimensional dendritic growth in a previously unreachable range of low undercoolings that is of… (More)

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 integral simulations of eutectic growth show good accuracy for steady-state lamellae, but the results for limit cycles… (More)

- Marc-Olivier Bernard, Mathis Plapp, Jean-François Gouyet
- Physical review. E, Statistical, nonlinear, and…
- 2003

We develop electrochemical mean-field kinetic equations to simulate electrochemical cells. We start from a microscopic lattice-gas model with charged particles, and build mean-field kinetic equations following the lines of earlier work for neutral particles. We include the Poisson equation to account for the influence of the electric field on ion migration,… (More)

- Sebastian Gurevich, Alain Karma, Mathis Plapp, Rohit Trivedi
- Physical review. E, Statistical, nonlinear, and…
- 2010

We use a quantitative phase-field approach to study directional solidification in various three-dimensional geometries for realistic parameters of a transparent binary alloy. The geometries are designed to study the steady-state growth of spatially extended hexagonal arrays, linear arrays in thin samples, and axisymmetric shapes constrained in a tube. As a… (More)