155 research outputs found
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
Action minimizing fronts in general FPU-type chains
We study atomic chains with nonlinear nearest neighbour interactions and
prove the existence of fronts (heteroclinic travelling waves with constant
asymptotic states). Generalizing recent results of Herrmann and Rademacher we
allow for non-convex interaction potentials and find fronts with non-monotone
profile. These fronts minimize an action integral and can only exists if the
asymptotic states fulfil the macroscopic constraints and if the interaction
potential satisfies a geometric graph condition. Finally, we illustrate our
findings by numerical simulations.Comment: 19 pages, several figure
Subsonic phase transition waves in bistable lattice models with small spinodal region
Phase transitions waves in atomic chains with double-well potential play a
fundamental role in materials science, but very little is known about their
mathematical properties. In particular, the only available results about waves
with large amplitudes concern chains with piecewise-quadratic pair potential.
In this paper we consider perturbations of a bi-quadratic potential and prove
that the corresponding three-parameter family of waves persists as long as the
perturbation is small and localised with respect to the strain variable. As a
standard Lyapunov-Schmidt reduction cannot be used due to the presence of an
essential spectrum, we characterise the perturbation of the wave as a fixed
point of a nonlinear and nonlocal operator and show that this operator is
contractive in a small ball in a suitable function space. Moreover, we derive a
uniqueness result for phase transition waves with certain properties and
discuss the kinetic relation.Comment: revised version with extended introduction, improved perturbation
method, and novel uniqueness result; 20 pages, 5 figure
Active gel segment behaving as an active particle
Quantifying the outcomes of cells collisions is a crucial step in building
the foundations of a kinetic theory of living matter. Here, we develop a
mechanical theory of such collisions by first representing individual cells as
extended objects with internal activity and then reducing this description to a
model of size-less active particles characterized by their position and
polarity. We show that, in the presence of an applied force, a cell can either
be dragged along or self-propel against the force, depending on the polarity of
the cell. The co-existence of these regimes offers a self-consistent mechanical
explanation for cell re-polarization upon contact. We rationalize the
experimentally observed collision scenarios within the extended and particle
models and link the various outcomes with measurable biological parameters
Frictionless Motion of Lattice Defects
Energy dissipation by fast crystalline defects takes place mainly through the
resonant interaction of their cores with periodic lattice. We show that the
resultant effective friction can be reduced to zero by appropriately tuned
acoustic sources located on the boundary of the body. To illustrate the general
idea, we consider three prototypical models describing the main types of
strongly discrete defects: dislocations, cracks and domain walls. The obtained
control protocols, ensuring dissipation-free mobility of topological defects,
can be also used in the design of meta-material systems aimed at transmitting
mechanical information
Optimality of contraction-driven crawling
We study a model of cell motility where the condition of optimal trade-off
between performance and metabolic cost can be made precise. In this model a
steadily crawling fragment is represented by a layer of active gel placed on a
frictional surface and driven by contraction only. We find analytically the
distribution of contractile elements (pullers) ensuring that the efficiency of
self-propulsion is maximal. We then show that natural assumptions about
advection and diffusion of pullers produce a distribution that is remarkably
close to the optimal one and is qualitatively similar to the one observed in
experiments on fish keratocytes
Homogeneous nucleation of dislocations as a pattern formation phenomenon
Dislocation nucleation in homogeneous crystals initially unfolds as a linear
symmetry-breaking elastic instability. In the absence of explicit nucleation
centers, such instability develops simultaneously all over the crystal and due
to the dominance of long range elastic interactions it advances into the
nonlinear stage as a collective phenomenon through pattern formation. In this
paper we use a novel mesoscopic tensorial model (MTM) of crystal plasticity to
study the delicate role of crystallographic symmetry in the development of the
dislocation nucleation patterns in defect free crystals loaded in a hard
device. The model is formulated in 2D and we systematically compare lattices
with square and triangular symmetry. To avoid the prevalence of the
conventional plastic mechanisms, we consider the loading paths represented by
pure shears applied on the boundary of the otherwise unloaded body. These
loading protocols can be qualified as exploiting the 'softest' and the
'hardest' directions and we show that the associated dislocation patterns are
strikingly different
Beyond Kinetic Relations
We introduce the concept of kinetic equations representing a natural
extension of the more conventional notion of a kinetic relation. Algebraic
kinetic relations, widely used to model dynamics of dislocations, cracks and
phase boundaries, link the instantaneous value of the velocity of a defect with
an instantaneous value of the driving force. The new approach generalizes
kinetic relations by implying a relation between the velocity and the driving
force which is nonlocal in time. To make this relations explicit one needs to
integrate the system of kinetic equations. We illustrate the difference between
kinetic relation and kinetic equations by working out in full detail a
prototypical model of an overdamped defect in a one-dimensional discrete
lattice. We show that the minimal nonlocal kinetic description containing now
an internal time scale is furnished by a system of two ordinary differential
equations coupling the spatial location of defect with another internal
parameter that describes configuration of the core region.Comment: Revised version, 33 pages, 9 figure
Boiling Crisis as a Critical Phenomenon
We present the first experimental study of intermittency and avalanche distribution during a boiling crisis. To understand the emergence of power law statistics we propose a simple spin model capturing the measured critical exponent. The model suggests that behind the critical heat flux is a percolation phenomenon involving drying-rewetting competition close to the hot surface
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