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To show that steadily propagating nonlinear waves in active matter can be driven internally, we develop a prototypical model of a topological kink moving with a constant supersonic speed. We use a model of a bi-stable mass-spring (FPU) chain capable of generating active stress. In contrast to subsonic kinks in passive bi-stable chains, that are necessarily dissipative, the obtained supersonic solutions are purely anti-dissipative. Our numerical experiments point towards stability of the obtained kink-type solutions and the possibility of propagating kink-anti-kink bundles reminiscent of solitons. We show that even the simplest quasi-continuum approximation of the discrete model captures the most important features of the predicted active phenomena., Comment: The supplementary materials contain a video: https://youtu.be/nVWyGNLbLWc

This paper deals with the theoretical and numerical analysis of dynamic fracture of dissimilar chain consisting of masses lined by springs. Such a structure exhibits quite different dynamic properties in comparison with a symmetrical uniform structure when dynamic properties are in question. Among other to stay in a balance, the external force applied to the system should not be the same but depend on the seed of the crack propagating as the result of the force action. Moreover, in the supersonic regime there is a bang gap in the velocity where the crack of that speed cannot propagate at all. However, having such theoretical prediction, a question still remains where and how those dynamical regimes can be achieved in real structure. We answering on this question by providing tailored numerical simulations demonstrating that various predicted steady-state regimes can be reached after rather short transient states. Among other, we analise how position of applied loading influence the result.

Most of the research concerting crack propagation in discrete media is concerned with specific types of external loading: displacements on the boundaries, or constant energy fluxes or feeding waves originating from infinity. In this paper the action of a moving load is analysed on the simplest lattice model: a thin strip, where the fault propagating in its middle portion as the result of the moving force acting on the destroyed part of the structure. We study both analytically and numerically how the load amplitude and its velocity influence the possible solution, and specifically the way the fracture process reaches its steady-state regime. We present the relation between the possible steady-state crack speed and the loading parameters, as well as the energy release rate. In particular, we show that there exists a class of loading regime corresponding to each point on the energy-speed diagram (and thus determine the same limiting steady-state regime). The phenomenon of the forbidden regimes is discussed in detail, from both the points of view of force and energy. For a sufficiently anisotropic structure, we find a stable steady-state propagation corresponding to the slow crack. Numerical simulations reveal various ways by which the process approaches - or fails to approach - the steady-state regime. The results extend our understanding of fracture processes in discrete structures, and reveal some new questions that should be addressed.