Hysteresis, Laning, and Negative Drag in Binary Systems with Opposite and Perpendicular Driving

TL;DR

The paper examines how binary mixtures of repulsively interacting particles organize into laned structures and exhibit hysteresis when driven in opposite or perpendicular directions. Using 2D overdamped simulations with long-range repulsion and Lekner summation, the authors map dynamical phases as the drive is swept up and down, revealing jammed, disordered, and laned states for opposite driving, and locked, 1D, disordered, and tilted-lane states for perpendicular driving, all accompanied by strong hysteresis and, in some regimes, negative drag. They further explore fixed longitudinal and varying perpendicular drives, as well as varied longitudinal drives, uncovering a sequence of coupling–decoupling transitions and a rich set of tilted lane configurations whose tilt angles track the net drive direction. The results highlight how driving geometry and density shape dynamic phase behavior, laning stability, defect formation, and transport in binary driven systems, with potential implications for colloidal, pedestrian, and active-matter contexts. Overall, the work broadens understanding of non-equilibrium ordering and transport control via driving orientation and history dependence.

Abstract

We consider a binary system of particles with repulsive interactions that move in opposite or perpendicular directions to each other under an applied external drive. For opposite driving, at higher drives a phase-separated laned state forms that has strong hysteresis in the velocity-force curve and the fraction of topological defects as the drive is cycled up and down from zero. The amount of hysteresis depends on the drive value at which the drive changes from increasing to decreasing. For perpendicular driving, we find a jammed state that transitions into a disordered state or a tilted lane state, both of which also show strong hysteresis effects. Additionally, a negative drag effect can appear in which one species moves in the direction opposite to the other species due to a tilting of the lanes by the perpendicular drive. When a constant drive is applied along one direction while the drive in the perpendicular direction is increased, we observe a series of drops and jumps in the velocity as the system forms locked and tilted laned states. For weakly interacting particles, the jammed system can show co-tilted stripe-forming states.

Figures (28)

• Figure 1: (a) The average $x$ velocity $\langle V^A_x \rangle$ vs drive force $F_D$ for particles driven in opposite directions at a density of $\rho = 0.441$. The black curve represents the ramp-up phase, and the red curve represents the ramp-down phase. (b) The fraction of particles with six neighbors, $P_6$, vs $F_D$ during ramp-up (black) and ramp-down (red). We find three distinct states: a jammed state, a disordered state, and a laned state at high driving. There is strong hysteresis across the laning transition.
• Figure 2: Particle positions for the $\rho=0.441$ oppositely driven system from Fig. \ref{['fig:1']}. Species A (blue) is driven along $+x$, and species B (red) is driven along $-x$. (a) The initial jammed state at $F_D = 0.25$, where the system forms a triangular lattice. (b) The unjammed disordered state at $F_D = 0.5$, where the triangular order is lost. (c) The laned state at $F_D = 2.0$. (d) The $F_D = 0.0$ jammed state after the ramp-down is completed.
• Figure 3: (a) $\langle V_x^A \rangle$ vs $F_D$ for oppositely driven particles at $\rho = 0.208$. (b) The corresponding $P_{6}$ vs $F_{D}$. (c) $\langle V_x^A \rangle$ vs $F_{D}$ for oppositely driven particles at $\rho = 0.93$. (d) The corresponding $P_{6}$ vs $F_{D}$. Black curves are for ramp-up and red curves are for ramp-down. For both densities, the response is strongly hysteretic.
• Figure 4: Particle positions for an oppositely driven system where species A (blue) is driven along $+x$ and species B (red) is driven along $-x$. (a,b) A system with $\rho=0.208$. (a) The laned state at $F_D=1.0$. (b) The jammed state at $F_D=0.0$ after the ramp-down. (c,d) A system with $\rho=0.93$. (c) The laned state at $F_D=2.0$. (d) The jammed state at $F_D=0.0$ after the ramp-down.
• Figure 5: A perpendicularly driven system with species A driven along $+x$ and species B driven along $+y$ at $\rho=0.441$. Black curves are for ramp-up and red curves are for ramp-down. (a) $\langle V^A_x \rangle$ vs $F_D$. (b) $\langle V^A_y \rangle$ vs $F_D$. The brown dashed line is drawn at zero velocity to indicate the point at which the $y$ velocity goes negative. (c) $P_6$ vs $F_D$. There are four phases: a locked phase, a one-dimensional (1D) decoupled phase, a disordered flow phase, and a high-drive tilted lane state.