816 citations · 1.2k across the 10 of their papers we have counts for
10 papers
Black and Gray Box Learning of Amplitude Equations: Application to Phase Field Systems
Felix P. Kemeth, Sergio Alonso, Blas Echebarria +3
We present a data-driven approach to learning surrogate models for amplitude equations, and illustrate its application to interfacial dynamics of phase field systems. In particular…
Amplitude equation approach to spatiotemporal dynamics of cardiac alternans
Blas Echebarria, Alain Karma
Amplitude equations are derived that describe the spatiotemporal dynamics of cardiac alternans during periodic pacing of one- and two-dimensional homogeneous tissue and one-dimensi…
Quantitative Phase Field Model of Alloy Solidification
Blas Echebarria, Roger Folch, Alain Karma +1
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 solidif…
Instability and Spatiotemporal Dynamics of Alternans in Paced Cardiac Tissue
Blas Echebarria, Alain Karma
We derive an equation that governs the spatiotemporal dynamics of small amplitude alternans in paced cardiac tissue. We show that a pattern-forming linear instability leads to the…
Sideband Instabilities and Defects of Quasipatterns
Blas Echebarria, Hermann Riecke
Quasipatterns have been found in dissipative systems ranging from Faraday waves in vertically vibrated fluid layers to nonlinear optics. We describe the dynamics of octagonal, deca…
Stability of Oscillating Hexagons in Rotating Convection
Blas Echebarria, Hermann Riecke
Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons. We study the stability of…