Well-posedness and stability results for the Gardner equation

In this article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation. We also cover the energy space H^1(R) where global well-posedness follows from the conservation laws of the system. Moreover, we construct solitons of the Gardner equation explicitly and prove that, under certain conditions, this family is orbitally stable in the energy space.Comment: 1 figure. Accepted for publication in Nonlin.Diff Eq.and App

How BAO measurements can fail to detect quintessence

We model the nonlinear growth of cosmic structure in different dark energy models, using large volume N-body simulations. We consider a range of quintessence models which feature both rapidly and slowly varying dark energy equations of state, and compare the growth of structure to that in a universe with a cosmological constant. The adoption of a quintessence model changes the expansion history of the universe, the form of the linear theory power spectrum and can alter key observables, such as the horizon scale and the distance to last scattering. The difference in structure formation can be explained to first order by the difference in growth factor at a given epoch; this scaling also accounts for the nonlinear growth at the 15% level. We find that quintessence models which feature late $(z<2)$, rapid transitions towards $w=-1$ in the equation of state, can have identical baryonic acoustic oscillation (BAO) peak positions to those in $\Lambda$CDM, despite being very different from $\Lambda$CDM both today and at high redshifts $(z \sim 1000)$. We find that a second class of models which feature non-negligible amounts of dark energy at early times cannot be distinguished from $\Lambda$CDM using measurements of the mass function or the BAO. These results highlight the need to accurately model quintessence dark energy in N-body simulations when testing cosmological probes of dynamical dark energy.Comment: 10 pages, 7 figures, to appear in the Invisible Univers International Conference AIP proceedings serie

New Civil Liability for Corporations: The Seventh Circuit Takes a Stand on the Alien Tort Statute

Many Americans may be surprised to learn that because of the Alien Tort Statute (ATS), federal courts are open to foreign plaintiffs who may bring claims against non-immune public officials for violations of international law. Recent litigation in the field has hit a speed bump, however, and the multi-million dollar question is whether the ATS covers corporations. The circuit courts of appeals are split on the issue. The Seventh Circuit ruled in Flomo v. Firestone National Rubber Co. that the ATS does apply to corporations that commit violations of international law. In reaching this conclusion, the Seventh Circuit rejected the district court’s reliance on a recent Second Circuit case, Kiobel v. Royal Dutch Petroleum Corp. In Kiobel, a decision now before the Supreme Court, the Second Circuit expressly held that the ATS does not apply to corporations. This article contends that the Seventh Circuit was correct in rejecting Kiobel for two reasons: first, the fundamental theories of international law provide that domestic nations may determine what remedies they will provide for plaintiffs aggrieved by violations of international norms; second, provisions in newer international treaties show an erosion of resistance to criminal corporate liability and a gradual acceptance of civil corporate liability, even if those attitudes did not exist in the recent past. With Kiobel representing the odd-man out, the Supreme Court now has the opportunity to create uniformity among the circuits by overturning Kiobel and adopting the Seventh Circuit\u27s rationale in Flomo

New Civil Liability for Corporations: The Seventh Circuit Takes a Stand on the Alien Tort Statute

Many Americans may be surprised to learn that because of the Alien Tort Statute (ATS), federal courts are open to foreign plaintiffs who may bring claims against non-immune public officials for violations of international law. Recent litigation in the field has hit a speed bump, however, and the multi-million dollar question is whether the ATS covers corporations. The circuit courts of appeals are split on the issue. The Seventh Circuit ruled in Flomo v. Firestone National Rubber Co. that the ATS does apply to corporations that commit violations of international law. In reaching this conclusion, the Seventh Circuit rejected the district court’s reliance on a recent Second Circuit case, Kiobel v. Royal Dutch Petroleum Corp. In Kiobel, a decision now before the Supreme Court, the Second Circuit expressly held that the ATS does not apply to corporations. This article contends that the Seventh Circuit was correct in rejecting Kiobel for two reasons: first, the fundamental theories of international law provide that domestic nations may determine what remedies they will provide for plaintiffs aggrieved by violations of international norms; second, provisions in newer international treaties show an erosion of resistance to criminal corporate liability and a gradual acceptance of civil corporate liability, even if those attitudes did not exist in the recent past. With Kiobel representing the odd-man out, the Supreme Court now has the opportunity to create uniformity among the circuits by overturning Kiobel and adopting the Seventh Circuit\u27s rationale in Flomo