113 research outputs found
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
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