Self-similar slip pulses during rate-and-state earthquake nucleation

For a wide range of conditions, earthquake nucleation zones on rate- and state-dependent faults that obey either of the popular state evolution laws expand as they accelerate. Under the “slip” evolution law, which experiments show to be the more relevant law for nucleation, this expansion takes the form of a unidirectional slip pulse. In numerical simulations these pulses often tend to approach, with varying degrees of robustness, one of a few styles of self-similar behavior. Here we obtain an approximate self-similar solution that accurately describes slip pulses growing into regions initially sliding at steady state. In this solution the length scale over which slip speeds are significant continually decreases, being inversely proportional to the logarithm of the maximum slip speed V_(max), while the total slip remains constant. This slip is close to D_c(1−a/b)^(−1), where D_c is the characteristic slip scale for state evolution and a and b are the parameters that determine the sensitivity of the frictional strength to changes in slip rate and state. The pulse has a “distance to instability” as well as a “time to instability,” with the remaining propagation distance being proportional to (1−a/b)^(−2) [ln(V_(max)Θ_(bg)/D_c)]^(−1), where Θ_(bg) is the background state into which the pulse propagates. This solution provides a reasonable estimate of the total slip for pulses growing into regions that depart modestly from steady state

Sustained eruptions on Enceladus explained by turbulent dissipation in tiger stripes

Spacecraft observations suggest that the plumes of Saturn's moon Enceladus draw water from a subsurface ocean, but the sustainability of conduits linking ocean and surface is not understood. Observations show sustained (though tidally modulated) fissure eruptions throughout each orbit, and since the 2005 discovery of the plumes. Peak plume flux lags peak tidal extension by $\sim$1 radian, suggestive of resonance. Here we show that a model of the tiger stripes as tidally-flexed slots that puncture the ice shell can simultaneously explain the persistence of the eruptions through the tidal cycle, the phase lag, and the total power output of the tiger stripe terrain, while suggesting that the eruptions are maintained over geological timescales. The delay associated with flushing and refilling of \emph{O}(1) m-wide slots with ocean water causes erupted flux to lag tidal forcing and helps to buttress slots against closure, while tidally pumped in-slot flow leads to heating and mechanical disruption that staves off slot freeze-out. Much narrower and much wider slots cannot be sustained. In the presence of long-lived slots, the 10$^6$-yr average power output of the tiger stripes is buffered by a feedback between ice melt-back and subsidence to \emph{O}(10$^{10}$) W, which is similar to the observed power output, suggesting long-term stability. Turbulent dissipation makes testable predictions for the final flybys of Enceladus by the \emph{Cassini} spacecraft. Our model shows how open connections to an ocean can be reconciled with, and sustain, long-lived eruptions. Turbulent dissipation in long-lived slots helps maintain the ocean against freezing, maintains access by future Enceladus missions to ocean materials, and is plausibly the major energy source for tiger stripe activity

Nickel-cadmium cells

A high energy density nickel cadmium cell of aerospace quality was designed. The approach used was to utilize manufacturing techniques which produce highly uniform and controlled starting materials in addition to improvements in the overall design. Parameters controlling the production of plaque and both positive and negative plate were studied. Quantities of these materials were produced and prototype cells were assembled to test the proposed design

On elliptic curves with an isogeny of degree 7

We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of degree 7, then the image of the 7-adic Galois representation attached to $E$ is as large as allowed by the isogeny, except for the curves with complex multiplication by $\mathbf{Q}(\sqrt{-7})$. The analogous result with 7 replaced by a prime $p > 7$ was proved by the first author in [7]. The present case $p = 7$ has additional interesting complications. We show that any exceptions correspond to the rational points on a certain curve of genus 12. We then use the method of Chabauty to show that the exceptions are exactly the curves with complex multiplication. As a by-product of one of the key steps in our proof, we determine exactly when there exist elliptic curves over an arbitrary field $k$ of characteristic not 7 with a $k$-rational isogeny of degree 7 and a specified Galois action on the kernel of the isogeny, and we give a parametric description of such curves.Comment: The revision gives a complete answer to the question considered in Version 1. Version 3 will appear in the American Journal of Mathematic

Magnetic phase diagram of the spin-1 two-dimensional J1-J3 Heisenberg model on a triangular lattice

The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest, $J_1=-(1-p)J,$ $J>0$, and antiferromagnetic third-nearest-neighbor, $J_3=pJ$, exchange interactions is studied in the range of the parameter $0 \leqslant p \leqslant 1$. Mori's projection operator technique is used as a method, which retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature several phase transitions are observed. At $p\approx 0.2$ the ground state is transformed from the ferromagnetic spin structure into a disordered state, which in its turn is changed to an antiferromagnetic long-range ordered state with the incommensurate ordering vector ${\bf Q = Q^\prime} \approx (1.16, 0)$ at $p\approx 0.31$. With the further growth of $p$ the ordering vector moves along the line ${\bf Q^\prime-Q_c}$ to the commensurate point ${\bf Q_c}=(\frac{2\pi}{3}, 0)$, which is reached at $p = 1$. The final state with an antiferromagnetic long-range order can be conceived as four interpenetrating sublattices with the $120^\circ$ spin structure on each of them. Obtained results are used for interpretation of the incommensurate magnetic ordering observed in NiGa$_2$S$_4$.Comment: 18 pages, 6 figures, accepted for publication in Physics Letters

Identifying the Burdens and Opportunities for Tribes and Communities in Federal Facility Cleanup Activities: Environmental Remediation Technology Assessment Matrix For Tribal and Community Decision-Makers

The cleanup of this country's federal facilities can affect a wide range of tribal and community interests and concerns. The technologies now in use, or being proposed by the Department of Energy, Department of Defense and other federal agencies can affect tribal treaty protected fishing, hunting and other rights, affect air and water quality thereby requiring the tribe to bear the burden of increased environmental regulation. The International Institute for Indigenous Resource Management developed a tribal and community decision-maker's Environmental Remediation Technology Assessment Matrix that will permit tribes and communities to array technical information about environmental remediation technologies against a backdrop of tribal and community environmental, health and safety, cultural, religious, treaty and other concerns and interests. Ultimately, the matrix will allow tribes and communities to assess the impact of proposed technologies on the wide range of tribal and community interests and will promote more informed participation in federal facility cleanup activities