A test of the hypothesis that impact-induced fractures are preferred sites for later tectonic activity

Impact cratering has been an important process in the solar system. The cratering event is generally accompanied by faulting in adjacent terrain. Impact-induced faults are nearly ubiquitous over large areas on the terrestrial planets. The suggestion is made that these fault systems, particularly those associated with the largest impact features are preferred sites for later deformation in response to lithospheric stresses generated by other processes. The evidence is a perceived clustering of orientations of tectonic features either radial or concentric to the crater or basin in question. An opportunity exists to test this suggestion more directly on Earth. The terrestrial continents contain more than 100 known or probable impact craters, with associated geological structures mapped to varying levels of detail. Prime facie evidence for reactivation of crater-induced faults would be the occurrence of earthquakes on these faults in response to the intraplate stress field. Either an alignment of epicenters with mapped fault traces or fault plane solutions indicating slip on a plane approximately coincident with that inferred for a crater-induced fault would be sufficient to demonstrate such an association

Biological control networks suggest the use of biomimetic sets for combinatorial therapies

Cells are regulated by networks of controllers having many targets, and targets affected by many controllers, but these "many-to-many" combinatorial control systems are poorly understood. Here we analyze distinct cellular networks (transcription factors, microRNAs, and protein kinases) and a drug-target network. Certain network properties seem universal across systems and species, suggesting the existence of common control strategies in biology. The number of controllers is ~8% of targets and the density of links is 2.5% \pm 1.2%. Links per node are predominantly exponentially distributed, implying conservation of the average, which we explain using a mathematical model of robustness in control networks. These findings suggest that optimal pharmacological strategies may benefit from a similar, many-to-many combinatorial structure, and molecular tools are available to test this approach.Comment: 33 page

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

Reply to the comment by Jacobs and Thorpe

Reply to a comment on "Infinite-Cluster geometry in central-force networks", PRL 78 (1997), 1480. A discussion about the order of the rigidity percolation transition.Comment: 1 page revTe

Self-Attracting Walk on Lattices

We have studied a model of self-attracting walk proposed by Sapozhnikov using Monte Carlo method. The mean square displacement $\sim t^{2\nu}$ and the mean number of visited sites $\sim t^{k}$ are calculated for one-, two- and three-dimensional lattice. In one dimension, the walk shows diffusive behaviour with $\nu=k=1/2$. However, in two and three dimension, we observed a non-universal behaviour, i.e., the exponent $\nu$ varies continuously with the strength of the attracting interaction.Comment: 6 pages, latex, 6 postscript figures, Submitted J.Phys.

Extremal statistics in the energetics of domain walls

We study at T=0 the minimum energy of a domain wall and its gap to the first excited state concentrating on two-dimensional random-bond Ising magnets. The average gap scales as $\Delta E_1 \sim L^\theta f(N_z)$, where $f(y) \sim [\ln y]^{-1/2}$, $\theta$ is the energy fluctuation exponent, $L$ length scale, and $N_z$ the number of energy valleys. The logarithmic scaling is due to extremal statistics, which is illustrated by mapping the problem into the Kardar-Parisi-Zhang roughening process. It follows that the susceptibility of domain walls has also a logarithmic dependence on system size.Comment: Accepted for publication in Phys. Rev.

Quasi-static cracks and minimal energy surfaces

We compare the roughness of minimal energy(ME) surfaces and scalar ``quasi-static'' fracture surfaces(SQF). Two dimensional ME and SQF surfaces have the same roughness scaling, w sim L^zeta (L is system size) with zeta = 2/3. The 3-d ME and SQF results at strong disorder are consistent with the random-bond Ising exponent zeta (d >= 3) approx 0.21(5-d) (d is bulk dimension). However 3-d SQF surfaces are rougher than ME ones due to a larger prefactor. ME surfaces undergo a ``weakly rough'' to ``algebraically rough'' transition in 3-d, suggesting a similar behavior in fracture.Comment: 7 pages, aps.sty-latex, 7 figure

Infinite-cluster geometry in central-force networks

We show that the infinite percolating cluster (with density P_inf) of central-force networks is composed of: a fractal stress-bearing backbone (Pb) and; rigid but unstressed ``dangling ends'' which occupy a finite volume-fraction of the lattice (Pd). Near the rigidity threshold pc, there is then a first-order transition in P_inf = Pd + Pb, while Pb is second-order with exponent Beta'. A new mean field theory shows Beta'(mf)=1/2, while simulations of triangular lattices give Beta'_tr = 0.255 +/- 0.03.Comment: 6 pages, 4 figures, uses epsfig. Accepted for publication in Physical Review Letter

Ground state non-universality in the random field Ising model

Two attractive and often used ideas, namely universality and the concept of a zero temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously on the disorder and so are non-universal. However, we also show that at finite temperature the thermal order parameter exponent one half is restored so that temperature is a relevant variable. The broader implications of these results are discussed.Comment: 4 pages 2 figures, corrected prefactors caused by a missing factor of two in Eq. 2., added a paragraph in conclusions for clarit

Random manifolds in non-linear resistor networks: Applications to varistors and superconductors

We show that current localization in polycrystalline varistors occurs on paths which are, usually, in the universality class of the directed polymer in a random medium. We also show that in ceramic superconductors, voltage localizes on a surface which maps to an Ising domain wall. The emergence of these manifolds is explained and their structure is illustrated using direct solution of non-linear resistor networks