Active chemo-mechanical solitons

TL;DR

The paper investigates how chemically generated activity can drive directional mechanical waves in a soft, elastic continuum and achieve high efficiency through dispersive energy transport. It introduces a minimal 1D model with bending-dominated elasticity and active pre-stress driven by traveling chemical cues, and analyzes both variational and direct formulations to derive governing equations and energy balance. The authors show that in the supersonic regime the system supports discrete compact traveling pulses whose velocities are quantized and independent of the chemical signal amplitude, and that dispersive energy transport can move energy from trailing regions to leading regions, producing effectively lossless propagation for compactons. In the subsonic regime the pulses decay without exchanging energy with infinity, illustrating regimes of autonomous mechanical behavior, and the work highlights potential applications to soft robotics and active materials.

Abstract

In many biological systems localized mechanical information is transmitted by mechanically neutral chemical signals. Typical examples include contraction waves in acto-myosin cortex at cellular scale and peristaltic waves at tissue level. In such systems, chemical activity is transformed into mechanical deformation by distributed motor-type mechanisms represented by continuum degrees of freedom. To elucidate the underlying principles of chemo-mechanical coupling, we here present the simplest example, involving directional motion of a localized solitary wave in a distributed mechanical system, guided by a purely chemical cue. Our main result is that mechanical signals can be driven by chemical activity in a highly efficient manner.

Figures (8)

• Figure 1: Mechanical model of pantograph with integrated active pulling (contractile) elements represented by red arrows. While the underconstrained pantograph structure is not rigid and contains a longitudinal soft mode, the presence of active elements makes it overconstrained.
• Figure 2: Schematic representation of the active loading \ref{['S']} in the pantographic structure shown in Fig. \ref{['fig:12']}. Note that active elements operate only inside the chemically active region.
• Figure 3: Dimensionless displacement field in compactons for different values of $n$. Here $K=1$ and $-2\leq \tilde{z} \leq 2$.
• Figure 4: Dimensionless displacement field in ( nanopterons) obtained for $\beta=0.9 \beta_2$. Here $K=1$ and $-5\leq \tilde{z} \leq 5$.
• Figure 5: Solitary waves with periodic tails (nanopterons shown in black) in the interval of driving velocities between $\tilde{D}_1=2 \pi / K$ and $\tilde{D}_2 = 4 \pi / K$. The corresponding compactons at $\tilde{D}_1$ and $\tilde{D}_1$ are shown in blue. Here $K=1$, $E=0$.