Bi-stability resistant to fluctuations

We study a simple micro-mechanical device that does not lose its snap-through behavior in an environment dominated by fluctuations. The main idea is to have several degrees of freedom that can cooperatively resist the de-synchronizing effect of random perturbations. As an inspiration we use the power stroke machinery of skeletal muscles, which ensures at sub-micron scales and finite temperatures a swift recovery of an abruptly applied slack. In addition to hypersensitive response at finite temperatures, our prototypical Brownian snap spring also exhibits criticality at special values of parameters which is another potentially interesting property for micro-scale engineering applications

Printing non-Euclidean solids

Geometrically frustrated solids with non-Euclidean reference metric are ubiquitous in biology and are becoming increasingly relevant in technological applications. Often they acquire a targeted con- figuration of incompatibility through surface accretion of mass as in tree growth or dam construction. We use the mechanics of incompatible surface growth to show that geometrical frustration develop- ing during deposition can be fine-tuned to ensure a particular behavior of the system in physiological (or working) conditions. As an illustration, we obtain an explicit 3D printing protocol for arteries, which guarantees stress uniformity under inhomogeneous loading, and for explosive plants, allowing a complete release of residual elastic energy with a single cut. Interestingly, in both cases reaching the physiological target requires the incompatibility to have a topological (global) component.Comment: 5 pages, 4 figure

Normality condition in elasticity

Strong local minimizers with surfaces of gradient discontinuity appear in variational problems when the energy density function is not rank-one convex. In this paper we show that stability of such surfaces is related to stability outside the surface via a single jump relation that can be regarded as interchange stability condition. Although this relation appears in the setting of equilibrium elasticity theory, it is remarkably similar to the well known normality condition which plays a central role in the classical plasticity theory

Mechanics of motility initiation and motility arrest in crawling cells

Motility initiation in crawling cells requires transformation of a symmetric state into a polarized state. In contrast, motility arrest is associated with re-symmetrization of the internal configuration of a cell. Experiments on keratocytes suggest that polarization is triggered by the increased contractility of motor proteins but the conditions of re-symmetrization remain unknown. In this paper we show that if adhesion with the extra-cellular substrate is sufficiently low, the progressive intensification of motor-induced contraction may be responsible for both transitions: from static (symmetric) to motile (polarized) at a lower contractility threshold and from motile (polarized) back to static (symmetric) at a higher contractility threshold. Our model of lamellipodial cell motility is based on a 1D projection of the complex intra-cellular dynamics on the direction of locomotion. In the interest of analytical transparency we also neglect active protrusion and view adhesion as passive. Despite the unavoidable oversimplifications associated with these assumptions, the model reproduces quantitatively the motility initiation pattern in fish keratocytes and reveals a crucial role played in cell motility by the nonlocal feedback between the mechanics and the transport of active agents. A prediction of the model that a crawling cell can stop and re-symmetrize when contractility increases sufficiently far beyond the motility initiation threshold still awaits experimental verification

Muscle as a meta-material operating near a critical point

Passive mechanical response of skeletal muscles at fast time scales is dominated by long range interactions inducing cooperative behavior without breaking the detailed balance. This leads to such unusual "material properties" as negative equilibrium stiffness and different behavior in force and displacement controlled loading conditions. Our fitting of experimental data suggests that "muscle material" is finely tuned to perform close to a critical point which explains large fluctuations observed in muscles close to the stall force.Comment: Accepted for publication in Physical Review Letter