384 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
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
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
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
Mechanics of collective unfolding
Mechanically induced unfolding of passive crosslinkers is a fundamental
biological phenomenon encountered across the scales from individual
macro-molecules to cytoskeletal actin networks. In this paper we study a
conceptual model of athermal load-induced unfolding and use a minimalistic
setting allowing one to emphasize the role of long-range interactions while
maintaining full analytical transparency. Our model can be viewed as a
description of a parallel bundle of N bistable units confined between two
shared rigid backbones that are loaded through a series spring. We show that
the ground states in this model correspond to synchronized, single phase
configurations where all individual units are either folded or unfolded. We
then study the fine structure of the wiggly energy landscape along the reaction
coordinate linking the two coherent states and describing the optimal mechanism
of cooperative unfolding. Quite remarkably, our study shows the fundamental
difference in the size and structure of the folding-unfolding energy barriers
in the hard (fixed displacements) and soft (fixed forces) loading devices which
persists in the continuum limit. We argue that both, the synchronization and
the non-equivalence of the mechanical responses in hard and soft devices, have
their origin in the dominance of long-range interactions. We then apply our
minimal model to skeletal muscles where the power-stroke in acto-myosin
crossbridges can be interpreted as passive folding. A quantitative analysis of
the muscle model shows that the relative rigidity of myosin backbone provides
the long-range interaction mechanism allowing the system to effectively
synchronize the power-stroke in individual crossbridges even in the presence of
thermal fluctuations. In view of the prototypical nature of the proposed model,
our general conclusions pertain to a variety of other biological systems where
elastic interactions are mediated by effective backbones
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