Emergence of spatiotemporal dislocation chains in drifting patterns

Abstract

One-dimensional patterns subjected to counter-propagative flows or speed jumps exhibit a rich and complex spatiotemporal dynamics, which is characterized by the perpetual emergence of spatiotemporal dislocation chains. Using a universal amplitude equation of drifting patterns, we show that this behavior is a result of a combination of a phase instability and an advection process caused by an inhomogeneous drift force. The emergence of spatiotemporal dislocation chains is verified in numerical simulations on an optical feedback system with a non-uniform intensity pump. Experimentally this phenomenon is also observed in a tilted quasi-one-dimensional fluidized shallow granular bed mechanically driven by a harmonic vertical vibration.