Stationary solutions of the one-dimensional nonlinear Schroedinger equation: I. Case of repulsive nonlinearity

All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the attractive case. Our solutions take the form of stationary trains of dark or grey density-notch solitons. Real stationary states are in one-to-one correspondence with those of the linear Schr\"odinger equation. Complex stationary states are uniquely nonlinear, nodeless, and symmetry-breaking. Our solutions apply to many physical contexts, including the Bose-Einstein condensate and optical pulses in fibers.Comment: 11 pages, 7 figures -- revised versio

Truth and Reconciliation: The Ku Klux Klan Hearings of 1871 and the Genesis of Section 1983

Over the course of seven months in 1871, Congress did something extraordinary for the time: It listened to Black people. At hearings in Washington, D.C. and throughout the former Confederate states, Black women and men—who just six years earlier were enslaved and barred from testifying in Southern courts—appeared before Congress to tell their stories. The stories were heartbreaking. After experiencing the joy of Emancipation and the initial hope of Reconstruction, they had been subjected to unspeakable horror at the hands of white terrorists. They had been raped and sexually humiliated. Their children and spouses murdered. They had been savagely beaten and forced to seek refuge in swamps. The terrorists were often state actors or respected members of society who claimed to engage in savagery for self-defense and community protection. And state courts were unable or unwilling to prosecute the crimes. Congress listened and did something else extraordinary. For the first time in American history, Congress interposed federal courts between the states and their citizens as guardians of federal constitutional rights. Through the Ku Klux Klan Act of 1871, which includes what is now codified as 42 U.S.C. § 1983, Congress rejected the proposition that the federal government had no power to intercede when state officials violated the federal constitution. Section 1983 provides a federal remedy for constitutional violations committed by state actors. The text is plain: Any state actor who violates the federal constitutional or statutory rights of any U.S. citizen “shall be liable to the party injured in an action at law.” But the Supreme Court of the United States has refused to enforce the statute as written. The Court instead invented the doctrine of qualified immunity that shields state actors from liability under Section 1983 unless victims can identify prior precedent where a state actor violated federal rights in a nearly identical manner. With the U.S. Supreme Court’s blessing, federal courts have granted qualified immunity to state officials who violate federal rights in increasingly depraved and unreasonable ways. This Article demonstrates that the Supreme Court is permitting the very evil that Section 1983 was designed to end. This Article does so by reviewing the painful narratives of the courageous Black people who testified before Congress in 1871. The Ku Klux Klan Hearings were the United States’ closest attempt at truth and reconciliation in the aftermath of slavery and the terror that followed. The testimony is replete with examples of a particular form of violence—assaults committed by state actors that local governments were unable or unwilling to remedy—which Congress specifically sought to rectify through Section 1983. And it is this precise form of violence that the Supreme Court of the United States permits through its expansive application of qualified immunity

Nonlinear atom optics and bright gap soliton generation in finite optical lattices

We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture for the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due the atom-atom interaction are discussed in detail, such as atom optical limiting and atom optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A new scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded in a controlled way starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties

Hole-Burning Diffusion Measurements in High Magnetic Field Gradients

We describe methods for the measurement of translational diffusion in very large static magnetic field gradients by NMR. The techniques use a "hole-burning" sequence that, with the use of fringe field gradients of 42 T/m, can image diffusion along one dimension on a submicron scale. Two varieties of this method are demonstrated, including a particularly efficient mode called the "hole-comb," in which multiple diffusion times comprising an entire diffusive evolution can be measured within the span of a single detected slice. The advantages and disadvantages of these methods are discussed, as well as their potential for addressing non-Fickian diffusion, diffusion in restricted media, and spatially inhomogeneous diffusion.Comment: 8 pages, 6 figure

180 MeV Proton Scattering from 16-O and 9-Be as Part of a Unified Study of These Nuclei

This work was supported by the National Science Foundation Grant NSF PHY 81-14339 and by Indiana Universit

Matter rogue wave in Bose-Einstein condensates with attractive atomic interaction

We investigate the matter rogue wave in Bose-Einstein Condensates with attractive interatomic interaction analytically and numerically. Our results show that the formation of rogue wave is mainly due to the accumulation of energy and atoms toward to its central part; Rogue wave is unstable and the decay rate of the atomic number can be effectively controlled by modulating the trapping frequency of external potential. The numerical simulation demonstrate that even a small periodic perturbation with small modulation frequency can induce the generation of a near-ideal matter rogue wave. We also give an experimental protocol to observe this phenomenon in Bose-Einstein Condensates

A global research priority agenda to advance public health responses to fatty liver disease

Background & aims An estimated 38% of adults worldwide have non-alcoholic fatty liver disease (NAFLD). From individual impacts to widespread public health and economic consequences, the implications of this disease are profound. This study aimed to develop an aligned, prioritised fatty liver disease research agenda for the global health community. Methods Nine co-chairs drafted initial research priorities, subsequently reviewed by 40 core authors and debated during a three-day in-person meeting. Following a Delphi methodology, over two rounds, a large panel (R1 n = 344, R2 n = 288) reviewed the priorities, via Qualtrics XM, indicating agreement using a four-point Likert-scale and providing written feedback. The core group revised the draft priorities between rounds. In R2, panellists also ranked the priorities within six domains: epidemiology, models of care, treatment and care, education and awareness, patient and community perspectives, and leadership and public health policy. Results The consensus-built fatty liver disease research agenda encompasses 28 priorities. The mean percentage of ‘agree’ responses increased from 78.3 in R1 to 81.1 in R2. Five priorities received unanimous combined agreement (‘agree’ + ‘somewhat agree’); the remaining 23 priorities had >90% combined agreement. While all but one of the priorities exhibited at least a super-majority of agreement (>66.7% ‘agree’), 13 priorities had 90% combined agreement. Conclusions Adopting this multidisciplinary consensus-built research priorities agenda can deliver a step-change in addressing fatty liver disease, mitigating against its individual and societal harms and proactively altering its natural history through prevention, identification, treatment, and care. This agenda should catalyse the global health community’s efforts to advance and accelerate responses to this widespread and fast-growing public health threat. Impact and implications An estimated 38% of adults and 13% of children and adolescents worldwide have fatty liver disease, making it the most prevalent liver disease in history. Despite substantial scientific progress in the past three decades, the burden continues to grow, with an urgent need to advance understanding of how to prevent, manage, and treat the disease. Through a global consensus process, a multidisciplinary group agreed on 28 research priorities covering a broad range of themes, from disease burden, treatment, and health system responses to awareness and policy. The findings have relevance for clinical and non-clinical researchers as well as funders working on fatty liver disease and non-communicable diseases more broadly, setting out a prioritised, ranked research agenda for turning the tide on this fast-growing public health threat