A total of 57 parabolic‐shaped and 9 approximately circular extended, impact crater related features have been found in Magellan synthetic aperture radar (SAR) and thermal emissivity data covering 92% of the surface of Venus. The parabolic features are, with seven exceptions, oriented E‐W with the apex to the east and the impact crater located just west of the apex. They were first identified in the surface emissivity data derived from Magellan radiometry measurements, but the great majority are only clearly visible in the SAR imagery. The overall sizes of both the parabolic and circular features range from several hundred to about two thousand kilometers and are loosely correlated with the diameters of the “parent” craters. The floors of almost all these craters have high specific radar backscatter cross sections (i.e., they are bright in the SAR imagery) relative to their surroundings and tend to have low emissivities. Approximately one‐third of the impact craters with diameters ≥15 km appear to have bright floors and about half of these have an associated parabolic feature which can be observed in the SAR or emissivity data. No features have been found which overlie the parabolic features, indicating that they are among the youngest features on the surface of the planet. This suggests that radar‐bright floors characterize the freshest impact craters and that modification processes subsequently darken their radar signature. A model for the formation of the parabolic features is developed based on the injection of small particles into the upper atmosphere at the time of impact and their transport to the west by the E‐W zonal winds. Fitting of a small perturbation scattering model to the measured average scattering law for the parabolic features placed an upper limit of about 0.6 cm on the wavelength scale (12.6 cm) surface roughness and, hence, of 1 to 2 cm on the largest particle sizes of interest. Fallout times from 50 km in the Venus atmosphere for particles of this size are about 2 hours, allowing westerly drifts of several hundred kilometers for zonal winds of 50 to 100 m s−1. Measurements of the change in backscatter cross section of features overlaid by these extended ejecta deposits, are consistent with deposit depths of a few centimeters to 1 or 2m.

SUMMARY The anelastic deformation of solids is often treated using continuum damage mechanics. An alternative approach to the brittle failure of a solid is provided by the discrete fibre‐bundle model. Here we show that the continuum damage model can give exactly the same solution for material failure as the fibre‐bundle model. We compare both models with laboratory experiments on the time‐dependent failure of chipboard and fibreglass. The power‐law scaling obtained in both models and in the experiments is consistent with the power‐law seismic activation observed prior to some earthquakes.

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Fiber bundle models, where fibers have random lifetimes depending on their load histories, are useful tools in explaining time-dependent failure in heterogeneous materials. Such models shed light on diverse phenomena such as fatigue in structural materials and earthquakes in geophysical settings. Various asymptotic and approximate theories have been developed for bundles with various geometries and fiber load-sharing mechanisms, but numerical verification has been hampered by severe computational demands in larger bundles. To gain insight at large size scales, interest has returned to idealized fiber bundle models in 1D. Such simplified models typically assume either equal load sharing (ELS) among survivors, or local load sharing (LLS) where a failed fiber redistributes its load onto its two nearest flanking survivors. Such models can often be solved exactly or asymptotically in increasing bundle size, N, yet still capture the essence of failure in real materials. The present work focuses on 1D bundles under LLS. As in previous works, a fiber has failure rate following a power law in its load level with breakdown exponent rho. Surviving fibers under fixed loads have remaining lifetimes that are independent and exponentially distributed. We develop both new asymptotic theories and new computational algorithms that greatly increase the bundle sizes that can be treated in large replications (e.g., one million fibers in thousands of realizations). In particular we develop an algorithm that adapts several concepts and methods that are well-known among computer scientists, but relatively unknown among physicists, to dramatically increase the computational speed with no attendant loss of accuracy. We consider various regimes of rho that yield drastically different behavior as N increases. For 1/2< or =rho< or =1, ELS and LLS have remarkably similar behavior (they have identical lifetime distributions at rho=1) with approximate Gaussian bundle lifetime statistics and a finite limiting mean. For rho>1 this Gaussian behavior also applies to ELS, whereas LLS behavior diverges sharply showing brittle, weakest volume behavior in terms of characteristic elements derived from critical cluster formation. For 0