Abstract
Motivated by recent findings from simulation of a driven lattice gas under shifted periodic boundary conditions, we study within the context of a continuum model the interfacial stability of driven diffusive systems. In this model, an external driving field maintains the system away from equilibrium. Well below criticality, steady-state solutions of the associated bulk kinetic equation are obtained. Our results successfully account for the novel features found in simulation. In particular, the solution describing a pair of interfaces tilted with respect to the driving field under periodic boundary conditions shows a tilt-dependent bulk density (and internal energy), and boundary layers near one of the interfaces. Focusing on the interface dynamics, one finds that such an interface exhibits a characteristic Mullins-Sekerka instability. This is argued to be responsible for the onset of the single- to multistrip transformation observed in simulation.
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Leung, K.t. Theory on Morphological Instability in Driven Systems. J Stat Phys 61, 345–364 (1990). https://doi.org/10.1007/BF01013969
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DOI: https://doi.org/10.1007/BF01013969