54 research outputs found
On the velocity-strengthening behavior of dry friction
The onset of frictional instabilities, e.g. earthquakes nucleation, is
intimately related to velocity-weakening friction, in which the frictional
resistance of interfaces decreases with increasing slip velocity. While this
frictional response has been studied extensively, less attention has been given
to steady-state velocity-strengthening friction, in spite of its potential
importance for various aspects of frictional phenomena such as the propagation
speed of interfacial rupture fronts and the amount of stored energy released by
them. In this note we suggest that a crossover from steady-state
velocity-weakening friction at small slip velocities to steady-state
velocity-strengthening friction at higher velocities might be a generic feature
of dry friction. We further argue that while thermally activated rheology
naturally gives rise to logarithmic steady-state velocity-strengthening
friction, a crossover to stronger-than-logarithmic strengthening might take
place at higher slip velocities, possibly accompanied by a change in the
dominant dissipation mechanism. We sketch a few physical mechanisms that may
account for the crossover to stronger-than-logarithmic steady-state
velocity-strengthening and compile a rather extensive set of experimental data
available in the literature, lending support to these ideas.Comment: Updated to published version: 2 Figures and a section adde
Velocity-strengthening friction significantly affects interfacial dynamics, strength and dissipation
Frictional interfaces are abundant in natural and manmade systems and their
dynamics still pose challenges of fundamental and technological importance. A
recent extensive compilation of multiple-source experimental data has revealed
that velocity-strengthening friction, where the steady-state frictional
resistance increases with sliding velocity over some range, is a generic
feature of such interfaces. Moreover, velocity-strengthening friction has very
recently been linked to slow laboratory earthquakes and stick-slip motion. Here
we elucidate the importance of velocity-strengthening friction by theoretically
studying three variants of a realistic rate-and-state friction model. All
variants feature identical logarithmic velocity-weakening friction at small
sliding velocities, but differ in their higher velocity behaviors. By
quantifying energy partition (e.g. radiation and dissipation), the selection of
interfacial rupture fronts and rupture arrest, we show that the presence or
absence of velocity-strengthening friction can significantly affect the global
interfacial resistance and the total energy released during frictional
instabilities ("event magnitude"). Furthermore, we show that different forms of
velocity-strengthening friction (e.g. logarithmic vs. linear) may result in
events of similar magnitude, yet with dramatically different dissipation and
radiation rates. This happens because the events are mediated by interfacial
rupture fronts with vastly different propagation velocities, where stronger
velocity-strengthening friction promotes slower rupture. These theoretical
results may have significant implications on our understanding of frictional
dynamics.Comment: 9 pages, 6 figure
Instabilities at Frictional Interfaces: Creep Patches, Nucleation and Rupture Fronts
The strength and stability of frictional interfaces, ranging from
tribological systems to earthquake faults, are intimately related to the
underlying spatially-extended dynamics. Here we provide a comprehensive
theoretical account, both analytic and numeric, of spatiotemporal interfacial
dynamics in a realistic rate-and-state friction model, featuring both
velocity-weakening and strengthening behaviors. Slowly extending, loading-rate
dependent, creep patches undergo a linear instability at a critical nucleation
size, which is nearly independent of interfacial history, initial stress
conditions and velocity-strengthening friction. Nonlinear propagating rupture
fronts -- the outcome of instability -- depend sensitively on the stress state
and velocity-strengthening friction. Rupture fronts span a wide range of
propagation velocities and are related to steady state fronts solutions.Comment: Typos and figures corrected. Supplementary information at:
http://www.weizmann.ac.il/chemphys/bouchbinder/frictional_instabilities.htm
Excitonic Funneling in Extended Dendrimers with Non-Linear and Random Potentials
The mean first passage time (MFPT) for photoexcitations diffusion in a
funneling potential of artificial tree-like light-harvesting antennae
(phenylacetylene dendrimers with generation-dependent segment lengths) is
computed. Effects of the non-linearity of the realistic funneling potential and
slow random solvent fluctuations considerably slow down the center-bound
diffusion beyond a temperature-dependent optimal size. Diffusion on a
disordered Cayley tree with a linear potential is investigated analytically. At
low temperatures we predict a phase in which the MFPT is dominated by a few
paths.Comment: 4 pages, 4 figures, To be published in Phys. Rev. Let
Disorder and Funneling Effects on Exciton Migration in Tree-Like Dendrimers
The center-bound excitonic diffusion on dendrimers subjected to several types
of non-homogeneous funneling potentials, is considered. We first study the
mean-first passage time (MFPT) for diffusion in a linear potential with
different types of correlated and uncorrelated random perturbations. Increasing
the funneling force, there is a transition from a phase in which the MFPT grows
exponentially with the number of generations , to one in which it does so
linearly. Overall the disorder slows down the diffusion, but the effect is much
more pronounced in the exponential compared to the linear phase. When the
disorder gives rise to uncorrelated random forces there is, in addition, a
transition as the temperature is lowered. This is a transition from a
high- regime in which all paths contribute to the MFPT to a low- regime
in which only a few of them do. We further explore the funneling within a
realistic non-linear potential for extended dendrimers in which the dependence
of the lowest excitonic energy level on the segment length was derived using
the Time-Dependent Hatree-Fock approximation. Under this potential the MFPT
grows initially linearly with but crosses-over, beyond a molecular-specific
and -dependent optimal size, to an exponential increase. Finally we consider
geometrical disorder in the form of a small concentration of long connections
as in the {\it small world} model. Beyond a critical concentration of
connections the MFPT decreases significantly and it changes to a power-law or
to a logarithmic scaling with , depending on the strength of the funneling
force.Comment: 13 pages, 9 figure
Slow rupture of frictional interfaces
The failure of frictional interfaces and the spatiotemporal structures that
accompany it are central to a wide range of geophysical, physical and
engineering systems. Recent geophysical and laboratory observations indicated
that interfacial failure can be mediated by slow slip rupture phenomena which
are distinct from ordinary, earthquake-like, fast rupture. These discoveries
have influenced the way we think about frictional motion, yet the nature and
properties of slow rupture are not completely understood. We show that slow
rupture is an intrinsic and robust property of simple non-monotonic
rate-and-state friction laws. It is associated with a new velocity scale
, determined by the friction law, below which steady state rupture
cannot propagate. We further show that rupture can occur in a continuum of
states, spanning a wide range of velocities from to elastic
wave-speeds, and predict different properties for slow rupture and ordinary
fast rupture. Our results are qualitatively consistent with recent
high-resolution laboratory experiments and may provide a theoretical framework
for understanding slow rupture phenomena along frictional interfaces.Comment: 6 pages, 4 figures, 1 table (Supplementary material: 5 pages, 2
figures
Survival and residence times in disordered chains with bias
We present a unified framework for first-passage time and residence time of
random walks in finite one-dimensional disordered biased systems. The
derivation is based on exact expansion of the backward master equation in
cumulants. The dependence on initial condition, system size, and bias strength
is explicitly studied for models with weak and strong disorder. Application to
thermally activated processes is also developed.Comment: 13 pages with 2 figures, RevTeX4; v2:minor grammatical changes, typos
correcte
Single Molecule Statistics and the Polynucleotide Unzipping Transition
We present an extensive theoretical investigation of the mechanical unzipping
of double-stranded DNA under the influence of an applied force. In the limit of
long polymers, there is a thermodynamic unzipping transition at a critical
force value of order 10 pN, with different critical behavior for homopolymers
and for random heteropolymers. We extend results on the disorder-averaged
behavior of DNA's with random sequences to the more experimentally accessible
problem of unzipping a single DNA molecule. As the applied force approaches the
critical value, the double-stranded DNA unravels in a series of discrete,
sequence-dependent steps that allow it to reach successively deeper energy
minima. Plots of extension versus force thus take the striking form of a series
of plateaus separated by sharp jumps. Similar qualitative features should
reappear in micromanipulation experiments on proteins and on folded RNA
molecules. Despite their unusual form, the extension versus force curves for
single molecules still reveal remnants of the disorder-averaged critical
behavior. Above the transition, the dynamics of the unzipping fork is related
to that of a particle diffusing in a random force field; anomalous,
disorder-dominated behavior is expected until the applied force exceeds the
critical value for unzipping by roughly 5 pN.Comment: 40 pages, 18 figure
Mechanical Stress Induces Remodeling of Vascular Networks in Growing Leaves
International audienceDifferentiation into well-defined patterns and tissue growth are recognized as key processes in organismal development. However, it is unclear whether patterns are passively, homogeneously dilated by growth or whether they remodel during tissue expansion. Leaf vascu-lar networks are well-fitted to investigate this issue, since leaves are approximately two-dimensional and grow manyfold in size. Here we study experimentally and computationally how vein patterns affect growth. We first model the growing vasculature as a network of viscoelastic rods and consider its response to external mechanical stress. We use the so-called texture tensor to quantify the local network geometry and reveal that growth is heterogeneous , resembling non-affine deformations in composite materials. We then apply mechanical forces to growing leaves after veins have differentiated, which respond by anisotropic growth and reorientation of the network in the direction of external stress. External mechanical stress appears to make growth more homogeneous, in contrast with the model with viscoelastic rods. However, we reconcile the model with experimental data by incorporating randomness in rod thickness and a threshold in the rod growth law, making the rods viscoelastoplastic. Altogether, we show that the higher stiffness of veins leads to their reorientation along external forces, along with a reduction in growth heterogeneity. This process may lead to the reinforcement of leaves against mechanical stress. More generally , our work contributes to a framework whereby growth and patterns are coordinated through the differences in mechanical properties between cell types
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