The reversible-irreversible (RI) transition of particle trajectories in athermal colloidal suspensions under cyclic shear deformation is an archetypal nonequilibrium phase transition which attracts much attention recently. In the low-density limit, the RI transition is predicted to belong to a universality class of the absorbing state transitions, whereas at the high densities well above the jamming transition density, ϕJ, the transition is discontinuous and is closely related to the yielding transition. The transition between the two limiting cases is largely unexplored. In this paper, we study the RI transition of athermal frictionless colloidal particles over a wide range of densities, with emphasis on the region below ϕJ, by using oscillatory sheared molecular dynamics simulation. We reveal that the nature of the RI transitions in the intermediate densities is very rich. As demonstrated by the previous work by Schreck et al.[Phys. Rev. E. 88, 052205 (2013)], there exist the point-reversible and the loop-reversible phases depending on the density and the shear strain amplitude. We find that, between the two reversible phases, a quasi-irreversible phase where the particles' trajectories are highly non-affine and diffusive. The averaged number of contacts of particles is found to characterize the phase boundaries. We also find that the system undergoes the yielding transition below but in the vicinity of ϕJ when the strain with a small but finite strain rate is applied. This yielding transition line matches with the RI transition line separating the loop-reversible from the irreversible phases. Surprisingly, the nonlinear rheological response called "softening" has been observed even below ϕJ. These findings imply that geometrical properties encoded in the sheared configurations control the dynamical transitions.

The materials around us usually exist as mixtures of constituents, each constituent with possibly a different elasto-viscoplastic property. How can we describe the material property of such a mixture is the core question of this paper. We propose a nonlinear blending model that can capture intriguing flowing behaviors that can differ from that of the individual constituents (Fig. 1). We used a laboratory device, rheometer , to measure the flowing properties of various fluid-like foods, and found that an elastic Herschel-Bulkley model has nice agreements with the measured data even for the mixtures of these foods. We then constructed a blending model such that it qualitatively agrees with the measurements and is closed in the parameter space of the elastic Herschel-Bulkley model. We provide validations through comparisons between the measured and estimated properties using our model, and comparisons between simulated examples and captured footages. We show the utility of our model for producing interesting behaviors of various mixtures.