Off-fault tensile cracks: A link between geological fault observations, lab experiments, and dynamic rupture models

We examine the local nature of the dynamic stress field in the vicinity of the tip of a semi-infinite sub-Rayleigh (slower than the Rayleigh wave speed, c_R) mode II crack with a velocity-weakening cohesive zone. We constrain the model using results from dynamic photoelastic experiments, in which shear ruptures were nucleated spontaneously in Homalite-100 plates along a bonded, precut, and inclined interface subject to a far-field uniaxial prestress. During the experiments, tensile cracks grew periodically along one side of the shear rupture interface at a roughly constant angle relative to the shear rupture interface. The occurrence and inclination of the tensile cracks are explained by our analytical model. With slight modifications, the model can be scaled to natural faults, providing diagnostic criteria for interpreting velocity, directivity, and static prestress state associated with past earthquakes on exhumed faults. Indirectly, this method also allows one to constrain the velocity-weakening nature of natural ruptures, providing an important link between field geology, laboratory experiments, and seismology

Highly nonlinear pulse splitting and recombination in a two-dimensional granular network

The propagation of highly nonlinear signals in a branched two-dimensional granular system was investigated experimentally and numerically for a system composed of chains of spherical beads of different materials. The system studied consists of a double Y-shaped guide in which high- and low-modulus/mass chains of spheres are arranged in various geometries. We observed the transformation of a single or a train of solitary pulses crossing the interface between branches. We report fast splitting of the initial pulse, rapid chaotization of the signal and impulse redirection and bending. Pulse and energy trapping was also observed in the branches. Numerical analysis based on Hertzian interaction between the particles and the side walls of the guide was found in agreement with the experimental data, except for nonsymmetric arrangements of particles excited by a large mass striker

On the origin of the unusual behavior in the stretching of single-stranded DNA

Force extension curves (FECs), which quantify the response of a variety of biomolecules subject to mechanical force ($f$), are often quantitatively fit using worm-like chain (WLC) or freely-jointed chain (FJC) models. These models predict that the chain extension, $x$, normalized by the contour length increases linearly at small $f$ and at high forces scale as $x \sim (1 - f^{-\alpha})$ where $\alpha$= 0.5 for WLC and unity for FJC. In contrast, experiments on ssDNA show that over a range of $f$ and ionic concentration, $x$ scales as $x\sim\ln f$, which cannot be explained using WLC or FJC models. Using theory and simulations we show that this unusual behavior in FEC in ssDNA is due to sequence-independent polyelectrolyte effects. We show that the $x\sim \ln f$ arises because in the absence of force the tangent correlation function, quantifying chain persistence, decays algebraically on length scales on the order of the Debye length. Our theory, which is most appropriate for monovalent salts, quantitatively fits the experimental data and further predicts that such a regime is not discernible in double stranded DNA.Comment: Accepted for publication in JC

Kinetics of Loop Formation in Polymer Chains

We investigate the kinetics of loop formation in flexible ideal polymer chains (Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the time scale for cyclization is $\tau_c\sim \tau_0 N^2$ (where $\tau_0$ is a microscopic time scale and $N$ is the number of monomers), provided the coupling between the relaxation dynamics of the end-to-end vector and the looping dynamics is taken into account. The resulting analytic expression fits the simulation results accurately when $a$, the capture radius for contact formation, exceeds $b$, the average distance between two connected beads. Simulations also show that, when $a < b$, $\tau_c\sim N^{\alpha_\tau}$, where $1.5<{\alpha_\tau}\le 2$ in the range $7<N<200$ used in the simulations. By using a diffusion coefficient that is dependent on the length scales $a$ and $b$ (with $a<b$), which captures the two-stage mechanism by which looping occurs when $a < b$, we obtain an analytic expression for $\tau_c$ that fits the simulation results well. The kinetics of contact formation between the ends of the chain are profoundly affected when interactions between monomers are taken into account. Remarkably, for $N < 100$ the values of $\tau_c$ decrease by more than two orders of magnitude when the solvent quality changes from good to poor. Fits of the simulation data for $\tau_c$ to a power law in $N$ ($\tau_c\sim N^{\alpha_\tau}$) show that $\alpha_\tau$ varies from about 2.4 in a good solvent to about 1.0 in poor solvents. Loop formation in poor solvents, in which the polymer adopts dense, compact globular conformations, occurs by a reptation-like mechanism of the ends of the chain.Comment: 30 pages, 9 figures. Revised version includes a new figure (8) and minor changes to the tex

Interaction Quench in Nonequilibrium Luttinger Liquids

We study the relaxation dynamics of a nonequilibrium Luttinger liquid after a sudden interaction switch-on ("quench"), focussing on a double-step initial momentum distribution function. In the framework of the non-equilibrium bosonization, the results are obtained in terms of singular Fredholm determinants that are evaluated numerically and whose asymptotics are found analytically. While the quasi-particle weights decay exponentially with time after the quench, this is not a relaxation into a thermal state, in view of the integrability of the model. The steady-state distribution emerging at infinite times retains two edges which support Luttinger-liquid-like power-law singularities smeared by dephasing. The obtained critical exponents and the dephasing length are found to depend on the initial nonequilibrium state.Comment: 11 pages, 5 figure