Justice for Dogs

This Essay summarizes the Fourth Amendment’s protection of dogs. The Fourth Amendment protects people from unreasonable seizures. And nearly every circuit has held that it is unreasonable (and therefore unconstitutional) for an officer to shoot (seize) a dog without a very good reason. Killing a nonthreatening family pet is one of the most egregious forms of police misconduct. The courts rightfully recognize that the unjustified harming of a dog violates the Fourth Amendment

Gutting Bivens: How the Supreme Court Shielded Federal Officials from Constitutional Litigation

“No man in this country is so high that he is above the law. . . . All officers of the government, from the highest to the lowest, are creatures of the law, and are bound to obey it. . . . [And the] Courts of justice are established, not only to decide upon the controverted rights of the citizens as against each other, but also upon rights in controversy between them and the government.” —United States v. Lee (1882

Large-area uniform graphene-like thin films grown by chemical vapor deposition directly on silicon nitride

Large-area uniform carbon films with graphene-like properties are synthesized by chemical vapor deposition directly on Si3N4/Si at 1000 degrees C without metal catalysts. The as deposited films are atomically thin and wrinkle- and pinhole-free. The film thickness can be controlled by modifying the growth conditions. Raman spectroscopy confirms the sp(2) graphitic structures. The films show ohmic behavior with a sheet resistance of similar to 2.3-10.5 k Omega/square at room temperature. An electric field effect of similar to 2-10% (V-G=-20 V) is observed. The growth is explained by the self-assembly of carbon clusters from hydrocarbon pyrolysis. The scalable and transfer-free technique favors the application of graphene as transparent electrodes

Surface ruptures on cross-faults in the 24 November 1987 Superstition Hills, California, earthquake sequence

Left-lateral slip occurred on individual surface breaks along northeast-trending faults associated with the 24 November 1987 earthquake sequence in the Superstition Hills, Imperial Valley, California. This sequence included the M_s = 6.2 event on a left-lateral, northeast-trending “cross-fault” between the Superstition Hills fault (SHF) and Brawley seismic zone, which was spatially associated with the left-lateral surface breaks. Six distinct subparallel cross-faults broke at the surface, with rupture lengths ranging from about Formula to 10 km and maximum displacements ranging from 30 to 130 mm. About half a day after the M_s = 6.2 event, an M_s = 6.6 earthquake nucleated near the intersection of the cross-faults with the SHF, and rupture propagated southeast along the SHF. Whereas right-lateral slip on the SHF occurred dominantly on a single trace in a narrow zone, the cross-fault surface slip was distributed over several stands across a 10-km-wide zone. Also, whereas afterslip accounted for a large proportion of total slip on the SHF, there is no evidence for afterslip on the cross-faults. We present documentation of these surface ruptures. A simple mechanical model of faulting illustrates how the foreshock sequence may have triggered the main rupture. Displacement on other cross-faults could trigger an event on the southern San Andreas fault by a similar mechanism in the future

Locally Perturbed Random Walks with Unbounded Jumps

In \cite{SzT}, D. Sz\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \ge 2$. The extension of their result to finite range random walks is straightforward. Here, however, we are interested in the situation when the random walk has unbounded range. Concretely we generalize the statement of \cite{SzT} to unbounded random walks whose jump distribution belongs to the domain of attraction of the normal law. We do this first: for diffusively scaled random walks on $\mathbf Z^d$ $(d \ge 2)$ having finite variance; and second: for random walks with distribution belonging to the non-normal domain of attraction of the normal law. This result can be applied to random walks with tail behavior analogous to that of the infinite horizon Lorentz-process; these, in particular, have infinite variance, and convergence to Brownian motion holds with the superdiffusive $\sqrt{n \log n}$ scaling.Comment: 16 page

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work. For the shape consisting of $n=\omega_d r^d$ sites, where $\omega_d$ is the volume of the unit ball in $\R^d$, we show that the inradius of the set of occupied sites is at least $r-O(\log r)$, while the outradius is at most $r+O(r^\alpha)$ for any $\alpha > 1-1/d$. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with $n=\pi r^2$ particles, we show that the inradius is at least $r/\sqrt{3}$, and the outradius is at most $(r+o(r))/\sqrt{2}$. This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions.Comment: [v3] Added Theorem 4.1, which generalizes Theorem 1.4 for the abelian sandpile. [v4] Added references and improved exposition in sections 2 and 4. [v5] Final version, to appear in Potential Analysi