Burst avalanches in solvable models of fibrous materials

We review limiting models for fracture in bundles of fibers, with statistically distributed thresholds for breakdown of individual fibers. During the breakdown process, avalanches consisting of simultaneous rupture of several fibers occur, and the distribution $D(\Delta)$ of the magnitude $\Delta$ of such avalanches is the central characteristics in our analysis. For a bundle of parallel fibers two limiting models of load sharing are studied and contrasted: the global model in which the load carried by a bursting fiber is equally distributed among the surviving members, and the local model in which the nearest surviving neighbors take up the load. For the global model we investigate in particular the conditions on the threshold distribution which would lead to anomalous behavior, i.e. deviations from the asymptotics $D(\Delta) \sim \Delta^{-5/2}$, known to be the generic behavior. For the local model no universal power-law asymptotics exists, but we show for a particular threshold distribution how the avalanche distribution can nevertheless be explicitly calculated in the large-bundle limit.Comment: 28 pages, RevTeX, 3 Postscript figure

Bounds for the time to failure of hierarchical systems of fracture

For years limited Monte Carlo simulations have led to the suspicion that the time to failure of hierarchically organized load-transfer models of fracture is non-zero for sets of infinite size. This fact could have a profound significance in engineering practice and also in geophysics. Here, we develop an exact algebraic iterative method to compute the successive time intervals for individual breaking in systems of height $n$ in terms of the information calculated in the previous height $n-1$. As a byproduct of this method, rigorous lower and higher bounds for the time to failure of very large systems are easily obtained. The asymptotic behavior of the resulting lower bound leads to the evidence that the above mentioned suspicion is actually true.Comment: Final version. To appear in Phys. Rev. E, Feb 199

Parametric coupling between macroscopic quantum resonators

Time-dependent linear coupling between macroscopic quantum resonator modes generates both a parametric amplification also known as a {}"squeezing operation" and a beam splitter operation, analogous to quantum optical systems. These operations, when applied properly, can robustly generate entanglement and squeezing for the quantum resonator modes. Here, we present such coupling schemes between a nanomechanical resonator and a superconducting electrical resonator using applied microwave voltages as well as between two superconducting lumped-element electrical resonators using a r.f. SQUID-mediated tunable coupler. By calculating the logarithmic negativity of the partially transposed density matrix, we quantitatively study the entanglement generated at finite temperatures. We also show that characterization of the nanomechanical resonator state after the quantum operations can be achieved by detecting the electrical resonator only. Thus, one of the electrical resonator modes can act as a probe to measure the entanglement of the coupled systems and the degree of squeezing for the other resonator mode.Comment: 15 pages, 4 figures, submitte

Research Note:<br>Derivation of temperature lapse rates in semi-arid south-eastern Arizona

International audienceEcological and hydrological modelling at the regional scale requires distributed information on weather variables, and temperature is important among these. In an area of basin and range topography with a wide range of elevations, such as south-eastern Arizona, measurements are usually available only at a relatively small number of locations and elevations, and temperatures elsewhere must be estimated from atmospheric lapse rate. This paper derives the lapse rates to estimate maximum, minimum and mean daily temperatures from elevation. Lapse rates were calculated using air temperatures at 2 m collected during 2002 at 18 locations across south-eastern Arizona, with elevations from 779 to 2512 m. The lapse rate predicted for the minimum temperature was lower than the mean environmental lapse rate (MELR), i.e. 6 K km?1, whereas those predicted for the mean and maximum daily temperature were very similar to the MELR. Lapse rates were also derived from radiosonde data at 00 and 12 UTC (5 pm and 5 am local time, respectively). The lapse rates calculated from radiosonde data were greater than those from the 2 m measurements, presumably because the effect of the surface was less. Given temperatures measured at Tucson airport, temperatures at the other sites were predicted using the different estimates of lapse rates. The best predictions of temperatures used the locally predicted lapse rates. In the case of maximum and mean temperature, using the MELR also resulted in accurate predictions. Keywords: near surface lapse rates, semi-arid climate, mean minimum and maximum temperatures, basin and range topograph

Failure Probabilities and Tough-Brittle Crossover of Heterogeneous Materials with Continuous Disorder

The failure probabilities or the strength distributions of heterogeneous 1D systems with continuous local strength distribution and local load sharing have been studied using a simple, exact, recursive method. The fracture behavior depends on the local bond-strength distribution, the system size, and the applied stress, and crossovers occur as system size or stress changes. In the brittle region, systems with continuous disorders have a failure probability of the modified-Gumbel form, similar to that for systems with percolation disorder. The modified-Gumbel form is of special significance in weak-stress situations. This new recursive method has also been generalized to calculate exactly the failure probabilities under various boundary conditions, thereby illustrating the important effect of surfaces in the fracture process.Comment: 9 pages, revtex, 7 figure

Scaling in the time-dependent failure of a fiber bundle with local load sharing

We study the scaling behaviors of a time-dependent fiber-bundle model with local load sharing. Upon approaching the complete failure of the bundle, the breaking rate of fibers diverges according to $r(t)\propto (T_f-t)^{-\xi}$, where $T_f$ is the lifetime of the bundle, and $\xi \approx 1.0$ is a quite universal scaling exponent. The average lifetime of the bundle $$ scales with the system size as $N^{-\delta}$, where $\delta$ depends on the distribution of individual fiber as well as the breakdown rule.Comment: 5 pages, 4 eps figures; to appear in Phys. Rev.

Subharmonic bifurcation cascade of pattern oscillations caused by winding number increasing entrainment

Convection structures in binary fluid mixtures are investigated for positive Soret coupling in the driving regime where solutal and thermal contributions to the buoyancy forces compete. Bifurcation properties of stable and unstable stationary square, roll, and crossroll (CR) structures and the oscillatory competition between rolls and squares are determined numerically as a function of fluid parameters. A novel type of subharmonic bifurcation cascade (SC) where the oscillation period grows in integer steps as $n (2\pi)/(\omega)$ is found and elucidated to be an entrainment process.Comment: 7 pages, 4 figure

Cloning and expression of a mammalian peptide chain release factor with sequence similarity to tryptophanyl-tRNA synthetases

The termination of protein synthesis is encoded by in-frame nonsense (stop) codons. Most organisms use three nonsense codons: UGA, UAG, and UAA. In contrast to sense codons, which are decoded by specific tRNAs, nonsense codons are decoded by proteins called release factors (RFs). Here we report the cloning of a mammalian RF cDNA by the use of monoclonal antibodies specific for rabbit RF. Functional studies showed that, when expressed in Escherichia coli, the protein encoded by this cDNA has in vitro biochemical characteristics similar to those of previously characterized mammalian RFs. DNA sequencing of this eukaryotic RF cDNA revealed a remarkable sequence similarity to bacterial and mitochondrial tryptophanyl-tRNA synthetases, with the greatest similarity confined to the synthetase active site, and no obvious similarity to bacterial RFs

The Wicked Machinery of Government: Malta and the Problems of Continuity under the New Model Administration

This is a study focused on the early years of British rule in Malta (1800-1813). It explores the application to the island of the “new model” of colonial government, one based on direct rule from London mediated by the continuation of existing laws and institutions. Systemic deficiencies are identified. These tended to undermine the effectiveness of direct British rule. This study also reveals, in the context of legal and constitutional continuity, unresolved tensions between modernity and tradition. The political stability of the island was damaged and the possibility of continued British possession was threatened