Strain localization in a shear transformation zone model for amorphous solids

We model a sheared disordered solid using the theory of Shear Transformation Zones (STZs). In this mean-field continuum model the density of zones is governed by an effective temperature that approaches a steady state value as energy is dissipated. We compare the STZ model to simulations by Shi, et al.(Phys. Rev. Lett. 98 185505 2007), finding that the model generates solutions that fit the data,exhibit strain localization, and capture important features of the localization process. We show that perturbations to the effective temperature grow due to an instability in the transient dynamics, but unstable systems do not always develop shear bands. Nonlinear energy dissipation processes interact with perturbation growth to determine whether a material exhibits strain localization. By estimating the effects of these interactions, we derive a criterion that determines which materials exhibit shear bands based on the initial conditions alone. We also show that the shear band width is not set by an inherent diffusion length scale but instead by a dynamical scale that depends on the imposed strain rate.Comment: 8 figures, references added, typos correcte

Dissipative Visco-plastic Deformation in Dynamic Fracture: Tip Blunting and Velocity Selection

Dynamic fracture in a wide class of materials reveals "fracture energy" $\Gamma$ much larger than the expected nominal surface energy due to the formation of two fresh surfaces. Moreover, the fracture energy depends on the crack velocity, $\Gamma=\Gamma(v)$. We show that a simple dynamical theory of visco-plasticity coupled to asymptotic pure linear-elasticity provides a possible explanation to the above phenomena. The theory predicts tip blunting characterized by a dynamically determined crack tip radius of curvature. In addition, we demonstrate velocity selection for cracks in fixed-grip strip geometry accompanied by the identification of $\Gamma$ and its velocity dependence.Comment: 4 pages, 1 figures; presentation improved, refs. changed, figure omitte

Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids

We use the shear transformation zone (STZ) theory of dynamic plasticity to study the necking instability in a two-dimensional strip of amorphous solid. Our Eulerian description of large-scale deformation allows us to follow the instability far into the nonlinear regime. We find a strong rate dependence; the higher the applied strain rate, the further the strip extends before the onset of instability. The material hardens outside the necking region, but the description of plastic flow within the neck is distinctly different from that of conventional time-independent theories of plasticity.Comment: 4 pages, 3 figures (eps), revtex4, added references, changed and added content, resubmitted to PR

Bounds on the derivatives of the Isgur-Wise function from sum rules in the heavy quark limit of QCD

Using the OPE and the trace formalism, we have obtained a number of sum rules in the heavy quark limit of QCD that include the sum over all excited states for any value $j^P$ of the light cloud. We show that these sum rules imply that the elastic Isgur-Wise function $\xi (w)$ is an alternate series in powers of $(w-1)$. Moreover, we obtain sum rules involving the derivatives of the elastic Isgur-Wise function $\xi (w)$ at zero recoil, that imply that the $n$-th derivative can be bounded by the $(n-1)$-th one. For the curvature $\sigma^2 = \xi''(1)$, this proves the already proposed bound $\sigma^2 \geq {5 \over 4} \rho^2$. Moreover, we obtain the absolute bound for the $n$-th derivative $(-1)^n \xi^{(n)}(1) \geq {(2n+1)!! \over 2^{2n}}$, that generalizes the results $\rho^2 \geq {3 \over 4}$ and $\sigma^2 \geq {15 \over 16}$.Comment: 9 pages, Late

A relativistic chiral quark model for pseudoscalar emission from heavy mesons

The amplitudes for one-pion mediated transitions between heavy meson excited states are obtained in the framework of the relativistic chiral quark model. The effective coupling constants to pions and the decay widths of excited heavy mesons with l<=2 for non-radially excited, and the l=0 radially excited mesons are presented for both charmed and beauty mesons. We also discuss the allowed decays of strange excited heavy mesons by emission of a K-meson.Comment: 20 pages, revte

Rate dependent shear bands in a shear transformation zone model of amorphous solids

We use Shear Transformation Zone (STZ) theory to develop a deformation map for amorphous solids as a function of the imposed shear rate and initial material preparation. The STZ formulation incorporates recent simulation results [Haxton and Liu, PRL 99 195701 (2007)] showing that the steady state effective temperature is rate dependent. The resulting model predicts a wide range of deformation behavior as a function of the initial conditions, including homogeneous deformation, broad shear bands, extremely thin shear bands, and the onset of material failure. In particular, the STZ model predicts homogeneous deformation for shorter quench times and lower strain rates, and inhomogeneous deformation for longer quench times and higher strain rates. The location of the transition between homogeneous and inhomogeneous flow on the deformation map is determined in part by the steady state effective temperature, which is likely material dependent. This model also suggests that material failure occurs due to a runaway feedback between shear heating and the local disorder, and provides an explanation for the thickness of shear bands near the onset of material failure. We find that this model, which resolves dynamics within a sheared material interface, predicts that the stress weakens with strain much more rapidly than a similar model which uses a single state variable to specify internal dynamics on the interface.Comment: 10 pages, 13 figures, corrected typos, added section on rate strengthening vs. rate weakening material

Phenomenological Study of Strong Decays of Heavy Hadrons in Heavy Quark Effective Theory

The application of the tensor formalism of the heavy quark effective theory (HQET) at leading order to strong decays of heavy hadrons is presented. Comparisons between experimental and theoretical predictions of ratios of decay rates for B mesons, D mesons and kaons are given. The application of HQET to strange mesons presents some encouraging results. The spin-flavor symmetry is used to predict some decay rates that have not yet been measured.Comment: 10 page

Magnetic Switching of Phase-Slip Dissipation in NbSe2 Nanobelts

The stability of the superconducting dissipationless and resistive states in single-crystalline NbSe2 nanobelts is characterized by transport measurements in an external magnetic field (H). Current-driven electrical measurements show voltage steps, indicating the nucleation of phase-slip structures. Well below the critical temperature, the position of the voltage steps exhibits a sharp, periodic dependence as a function of H. This phenomenon is discussed in the context of two possible mechanisms: the interference of the order parameter and the periodic rearrangement of the vortex lattice within the nanobelt.Comment: 4 figure

More on Symmetries in Heavy Quark Effective Theory

We present a general classification of all normal and ``chiral" symmetries of heavy quark effective theories. Some peculiarities and conondrums associated with the ``chiral" symmetries are discussed.Comment: 15 pages, preprint UR-1320, ER40685-77