Viscoelastic Fracture of Biological Composites

Soft constituent materials endow biological composites, such as bone, dentin and nacre, with viscoelastic properties that may play an important role in their remarkable fracture resistance. In this paper we calculate the scaling properties of the quasi-static energy release rate and the viscoelastic contribution to the fracture energy of various biological composites, using both perturbative and non-perturbative approaches. We consider coarse-grained descriptions of three types of anisotropic structures: (i) Liquid-crystal-like composites (ii) Stratified composites (iii) Staggered composites, for different crack orientations. In addition, we briefly discuss the implications of anisotropy for fracture criteria. Our analysis highlights the dominant lengthscales and scaling properties of viscoelastic fracture of biological composites. It may be useful for evaluating crack velocity toughening effects and structure-dissipation relations in these materials.Comment: 18 pages, 3 figure

Extended Palatini action for general relativity and the natural emergence of the cosmological constant

In the Palatini action of general relativity the connection and the metric are treated as independent dynamical variables. Instead of assuming a relation between these quantities, the desired relation between them is derived through the Euler-Lagrange equations of the Palatini action. In this manuscript we construct an extended Palatini action, where we do not assume any a priori relationship between the connection, the covariant metric tensor, and the contravariant metric tensor. Instead we treat these three quantities as independent dynamical variables. We show that this action reproduces the standard Einstein field equations depending on a single metric tensor. We further show that in this formulation the cosmological constant has an additional theoretical significance. Normally the cosmological constant is added to the Einstein field equations for the purpose of having general relativity be consistent with cosmological observations. In the formulation presented here, the nonvanishing cosmological constant also ensures the self-consistency of the theory.Comment: in the revised version the original scalar matter action is replaced with a general matter actio

Probing Cosmic-Ray Ion Acceleration with Radio-Submm and Gamma-Ray Emission from Interaction-Powered Supernovae

The optical and near-IR emission from some classes of supernovae (SNe), including Type IIn and possibly some super-luminous SNe, is likely powered by a collision between the SN ejecta and dense circumstellar material (CSM). We argue that for a range of CSM masses and their radii, a collisionless shock can form, allowing for efficient cosmic-ray (CR) acceleration. We show that pp collisions between these newly accelerated CRs and the CSM leads to not only gamma rays but also secondary electrons and positrons that radiate synchrotron photons in the high-frequency radio bands. Our estimates imply that various facilities including the Jansky Very Large Array (VLA) and the Atacama Large Millimeter/submillimeter Array (ALMA) may observe such SNe at Gpc distances by followup observations in months-to-years, although the detectability strongly depends on the CSM density as well as observed frequency. Detecting this signal would give us a unique probe of CR acceleration at early times, and even non-detections can put interesting limits on the possibility of CR ion acceleration. Following our previous work, we also show that GeV gamma rays can escape from the system without severe attenuation, encouraging point-source and stacking analyses with Fermi. We provide recipes for diagnosing interaction-powered SN scenario with multi-messenger (neutrino and gamma-ray) observations.Comment: 18 pages, 11 figures, minor revision, accepted for publication in MNRA

Ultrahigh Hot Carrier Transient Photocurrent in Nanocrystal Arrays by Auger Recombination.

In this report, we show that a new mechanism for carrier transport in solution-processed colloidal semiconductor nanocrystal arrays exists at high excitation intensity on ultrafast time scales and allows for facile intrinsic transport between as-prepared nanocrystals over long distances. By combining a high speed photoconductive switch with an ultrafast laser excitation in a sub-40 ps photoconductor, we observed transient photocurrents with peak densities of 3 × 104 - 106 mA/cm2 in self-assembled PbSe nanocrystals capped with long native oleic acid ligands. The ratio between the transient photocurrent peak and the steady-state dark current is 10 orders of magnitude. The transient mobility at the peak current is estimated to range between 0.5-17.5 cm2/(V s) for the various nanocrystal sizes studied, which is 6 to 9 orders of magnitude higher than the dark current steady-state mobility in PbSe, CdSe, and CdTe nanocrystals capped with native ligands. The results are analyzed using a kinetic model which attributes the ultrahigh transient photocurrent to multiple photogenerated excitons undergoing on-particle Auger recombination, followed by rapid tunneling at high energies. This mechanism is demonstrated for a wide range of PbSe nanocrystals sizes (diameters from 2.7 to 7.1 nm) and experimental parameters. Our observations indicate that native ligand-capped nanocrystal arrays are promising for optoelectronics applications wherein multiple carriers are photoinjected to interband states

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

Higher chordality: From graphs to complexes

We generalize the fundamental graph-theoretic notion of chordality for higher dimensional simplicial complexes by putting it into a proper context within homology theory. We generalize some of the classical results of graph chordality to this generality, including the fundamental relation to the Leray property and chordality theorems of Dirac.Comment: 13 pages, revised; to appear in Proc. AM

Autonomy and Singularity in Dynamic Fracture

The recently developed weakly nonlinear theory of dynamic fracture predicts $1/r$ corrections to the standard asymptotic linear elastic $1/\sqrt{r}$ displacement-gradients, where $r$ is measured from the tip of a tensile crack. We show that the $1/r$ singularity does not automatically conform with the notion of autonomy (autonomy means that any crack tip nonlinear solution is uniquely determined by the surrounding linear elastic $1/\sqrt{r}$ fields) and that it does not automatically satisfy the resultant Newton's equation in the crack parallel direction. We show that these two properties are interrelated and that by requiring that the resultant Newton's equation is satisfied, autonomy of the $1/r$ singular solution is retained. We further show that the resultant linear momentum carried by the $1/r$ singular fields vanishes identically. Our results, which reveal the physical and mathematical nature of the new solution, are in favorable agreement with recent near tip measurements.Comment: 4 pages, 2 figures, related papers: arXiv:0902.2121 and arXiv:0807.486

Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation I: Basic Principles

We develop an athermal version of the shear-transformation-zone (STZ) theory of amorphous plasticity in materials where thermal activation of irreversible molecular rearrangements is negligible or nonexistent. In many respects, this theory has broader applicability and yet is simpler than its thermal predecessors. For example, it needs no special effort to assure consistency with the laws of thermodynamics, and the interpretation of yielding as an exchange of dynamic stability between jammed and flowing states is clearer than before. The athermal theory presented here incorporates an explicit distribution of STZ transition thresholds. Although this theory contains no conventional thermal fluctuations, the concept of an effective temperature is essential for understanding how the STZ density is related to the state of disorder of the system.Comment: 7 pages, 2 figures; first of a two-part serie