Instabilities of one-dimensional stationary solutions of the cubic nonlinear Schrodinger equation

The two-dimensional cubic nonlinear Schrodinger equation admits a large family of one-dimensional bounded traveling-wave solutions. All such solutions may be written in terms of an amplitude and a phase. Solutions with piecewise constant phase have been well studied previously. Some of these solutions were found to be stable with respect to one-dimensional perturbations. No such solutions are stable with respect to two-dimensional perturbations. Here we consider stability of the larger class of solutions whose phase is dependent on the spatial dimension of the one-dimensional wave form. We study the spectral stability of such nontrivial-phase solutions numerically, using Hill's method. We present evidence which suggests that all such nontrivial-phase solutions are unstable with respect to both one- and two-dimensional perturbations. Instability occurs in all cases: for both the elliptic and hyperbolic nonlinear Schrodinger equations, and in the focusing and defocusing case.Comment: Submitted: 13 pages, 3 figure

Measurement of the Neutron Radius of 208Pb Through Parity-Violation in Electron Scattering

We report the first measurement of the parity-violating asymmetry A_PV in the elastic scattering of polarized electrons from 208Pb. A_PV is sensitive to the radius of the neutron distribution (Rn). The result A_PV = 0.656 \pm 0.060 (stat) \pm 0.014 (syst) ppm corresponds to a difference between the radii of the neutron and proton distributions Rn - Rp = 0.33 +0.16 -0.18 fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.Comment: 6 pages, 1 figur

New Measurements of the Transverse Beam Asymmetry for Elastic Electron Scattering from Selected Nuclei

5 pages, 3 figures, accepted by PRL. v3: fixed one author name and affiliation, otherwise no changeWe have measured the beam-normal single-spin asymmetry $A_n$ in the elastic scattering of 1-3 GeV transversely polarized electrons from $^1$H and for the first time from $^4$He, $^{12}$C, and $^{208}$Pb. For $^1$H, $^4$He and $^{12}$C, the measurements are in agreement with calculations that relate $A_n$ to the imaginary part of the two-photon exchange amplitude including inelastic intermediate states. Surprisingly, the $^{208}$Pb result is significantly smaller than the corresponding prediction using the same formalism. These results suggest that a systematic set of new $A_n$ measurements might emerge as a new and sensitive probe of the structure of heavy nuclei

Towards regulatory endorsement of drug development tools to promote the application of model-informed drug development in Duchenne muscular dystrophy

Drug development for rare diseases is challenged by small populations and limited data. This makes development of clinical trial protocols difficult and contributes to the uncertainty around whether or not a potential therapy is efficacious. The use of data standards to aggregate data from multiple sources, and the use of such integrated databases to develop statistical models can inform protocol development and reduce the risks in developing new therapies. Achieving regulatory endorsement of such models through defined pathways at the US Food and Drug Administration and European Medicines Authority allows such tools to be used by the drug development community for defined contexts of use without further need for discussion of the underlying model(s). The Duchenne Regulatory Science Consortium (D-RSC) has brought together multiple stakeholders to develop a clinical trial simulation tool for Duchenne muscular dystrophy using such an approach. Here we describe the work of D-RSC as an example of how such an approach may be effective at reducing uncertainty in drug development for rare diseases, and thus bringing effective therapies to patients faster