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- 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)

- Roger Folch, Mathis Plapp
- Physical review. E, Statistical, nonlinear, and…
- 2005

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)

- Mathis Plapp, Alain Karma
- Physical review letters
- 2000

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)

- 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)

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)

- Roger Folch, Mathis Plapp
- Physical review. E, Statistical, nonlinear, and…
- 2003

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)

We present a numerical study of the effect of a free-energy anisotropy of the solidsolid interphase boundaries on the formation of tilted lamellar microstructures during directional solidification of nonfaceted binary eutectic alloys. We used two different methods – phase-field (PF) and dynamic boundary-integral (BI) – to simulate the growth of periodic… (More)

- Mathis Plapp
- Physical review. E, Statistical, nonlinear, and…
- 2011

In the literature, two quite different phase-field formulations for the problem of alloy solidification can be found. In the first, the material in the diffuse interfaces is assumed to be in an intermediate state between solid and liquid, with a unique local composition. In the second, the interface is seen as a mixture of two phases that each retain their… (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)

- Tsan-Hung Lo, Alain Karma, Mathis Plapp
- Physical review. E, Statistical, nonlinear, and…
- 2001

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)