161 research outputs found
Slow Crack Propagation in Heterogeneous Materials
Statistics and thermally activated dynamics of crack nucleation and
propagation in a two-dimensional heterogeneous material containing quenched
randomly distributed defects are studied theoretically. Using the generalized
Griffith criterion we derive the equation of motion for the crack tip position
accounting for dissipation, thermal noise and the random forces arising from
the defects. We find that aggregations of defects generating long-range
interaction forces (e.g., clouds of dislocations) lead to anomalously slow
creep of the crack tip or even to its complete arrest. We demonstrate that
heterogeneous materials with frozen defects contain a large number of arrested
microcracks and that their fracture toughness is enhanced to the experimentally
accessible time scales.Comment: 5 pages, 1 figur
Barrier crossing of semiflexible polymers
We consider the motion of semiflexible polymers in double-well potentials. We
calculate shape, energy, and effective diffusion constant of kink excitations,
and in particular their dependence on the bending rigidity of the semiflexible
polymer. For symmetric potentials, the kink motion is purely diffusive whereas
kink motion becomes directed in the presence of a driving force on the polymer.
We determine the average velocity of the semiflexible polymer based on the kink
dynamics. The Kramers escape over the potential barriers proceeds by nucleation
and diffusive motion of kink-antikink pairs, the relaxation to the straight
configuration by annihilation of kink-antikink pairs. Our results apply to the
activated motion of biopolymers such as DNA and actin filaments or synthetic
polyelectrolytes on structured substrates.Comment: 7 pages, 3 figure
Competitive localization of vortex lines and interacting bosons
We present a theory for the localization of three-dimensional vortex lines or
two-dimensional bosons with short-ranged repulsive interaction which are
competing for a single columnar defect or potential well. For two vortices we
use a necklace model approach to find a new kind of delocalization transition
between two different states with a single bound particle. This
exchange-delocalization transition is characterized by the onset of vortex
exchange on the defect for sufficiently weak vortex-vortex repulsion or
sufficiently weak binding energy corresponding to high temperature. We
calculate the transition point and order of the exchange-delocalization
transition. A generalization of this transition to arbitrary vortex number is
proposed.Comment: 5 pages, 2 figure
Stall force of polymerizing microtubules and filament bundles
We investigate stall force and polymerization kinetics of rigid protofilaments in a microtubule or interacting filaments in bundles under an external load force in the framework of a discrete growth model. We introduce the concecpt of polymerization cycles to describe the stochastic growth kinetics, which allows us to derive an exact expression for the stall force. We find that the stall force is independent of ensemble geometry and load distribution. Furthermore, the stall force is proportional to the number of filaments and increases linearly with the strength of lateral filament interactions. These results are corroborated by simulations, which also show a strong influence of ensemble geometry on growth kinetics below the stall force
Critical Motor Number for Fractional Steps of Cytoskeletal Filaments in Gliding Assays
In gliding assays, filaments are pulled by molecular motors that are immobilized on a solid surface. By varying the motor density on the surface, one can control the number N of motors that pull simultaneously on a single filament. Here, such gliding assays are studied theoretically using brownian (or Langevin) dynamics simulations and taking the local force balance between motors and filaments as well as the force-dependent velocity of the motors into account. We focus on the filament stepping dynamics and investigate how single motor properties such as stalk elasticity and step size determine the presence or absence of fractional steps of the filaments. We show that each gliding assay can be characterized by a critical motor number, N(c). Because of thermal fluctuations, fractional filament steps are only detectable as long as N as determined by the surface density (or coverage) of the motors on the substrate surface
Bifurcation of Velocity Distributions in Cooperative Transport of Filaments by Fast and Slow Motors
Several intracellular processes are governed by two different species of molecular motors, fast and slow ones, that both move in the same direction along the filaments but with different velocities. The transport of filaments arising from the cooperative action of these motors has been recently studied by three in vitro experiments, in which the filament velocity was measured for varying fraction of the fast motors adsorbed onto substrate surfaces in a gliding assay. As the fast motor fraction was increased, two experiments found a smooth change whereas the third one observed an abrupt increase of the filament velocity. Here, we show that all of these experimental results reflect the competition between fast and slow motors and can be understood in terms of an underlying saddle-node bifurcation. The comparison between theory and experiment leads to predictions for the detachment forces of the two motor species. Our theoretical study shows the existence of three different motility regimes: 1), fast transport with a single velocity; 2), slow transport with a single velocity; and 3), bistable transport, where the filament velocity stochastically switches between fast and slow transport. We determine the parameter regions for these regimes in terms of motility diagrams as a function of the surface fraction of fast motors and microscopic single-motor parameters. An abrupt increase of the filament velocity for an increasing fraction of fast motors is associated with the occurrence of bistable transport
Elastometry of deflated capsules elastic moduli from shape and wrinkle analysis
Elastic capsules, prepared from droplets or bubbles attached to a capillary (as in a pendant drop tensiometer), can be deflated by suction through the capillary. We study this deflation and show that a combined analysis of the shape and wrinkling characteristics enables us to determine the elastic properties in situ. Shape contours are analyzed and fitted using shape equations derived from nonlinear membrane-shell theory to give the elastic modulus, Poisson ratio and stress distribution of the membrane. We include wrinkles, which generically form upon deflation, within the shape analysis. Measuring the wavelength of wrinkles and using the calculated stress distribution gives the bending stiffness of the membrane. We illustrate this method on two very different capsule materials: polymerized octadecyltrichlorosilane (OTS) capsules and hydrophobin (HFBII) coated bubbles. Our results are in agreement with the available rheological data. For hydrophobin coated bubbles the method reveals an interesting nonlinear behavior consistent with the hydrophobin molecules having\ud
a rigid core surrounded by a softer shell
Theory of plastic vortex creep
We develop a theory for plastic flux creep in a topologically disordered
vortex solid phase in type-II superconductors. We propose a detailed
description of the plastic vortex creep of the dislocated, amorphous vortex
glass in terms of motion of dislocations driven by a transport current . The
{\em plastic barriers} show power-law divergence at
small drives with exponents for single dislocation creep and for creep of dislocation bundles. The suppression of the creep rate is a
hallmark of the transition from the topologically ordered vortex lattice to an
amorphous vortex glass, reflecting a jump in from ,
characterizing creep in the topologically ordered vortex lattice near the
transition, to its plastic values. The lower creep rates explain the observed
increase in apparent critical currents in the dislocated vortex glass.Comment: 4 pages, 1 figur
Coupling of actin hydrolysis and polymerization: Reduced description with two nucleotide states
The polymerization of actin filaments is coupled to the hydrolysis of
adenosine triphosphate (ATP), which involves both the cleavage of ATP and the
release of inorganic phosphate. We describe hydrolysis by a reduced two-state
model with a cooperative cleavage mechanism, where the cleavage rate depends on
the state of the neighboring actin protomer in a filament. We obtain
theoretical predictions of experimentally accessible steady state quantities
such as the size of the ATP-actin cap, the size distribution of ATP-actin
islands, and the cleavage flux for cooperative cleavage mechanisms.Comment: 6 page
Stability of the Bragg glass phase in a layered geometry
We study the stability of the dislocation-free Bragg glass phase in a layered
geometry consisting of coupled parallel planes of d=1+1 vortex lines lying
within each plane, in the presence of impurity disorder. Using renormalization
group, replica variational calculations and physical arguments we show that at
temperatures the 3D Bragg glass phase is always stable for weak
disorder. It undergoes a weakly first order transition into a decoupled 2D
vortex glass upon increase of disorder.Comment: RevTeX. Submitted to EP
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