Complex Bifurcation from Real Paths

A new bifurcation phenomenon, called complex bifurcation, is studied. The basic idea is simply that real solution paths of real analytic problems frequently have complex paths bifurcating from them. It is shown that this phenomenon occurs at fold points, at pitchfork bifurcation points, and at isola centers. It is also shown that perturbed bifurcations can yield two disjoint real solution branches that are connected by complex paths bifurcating from the perturbed solution paths. This may be useful in finding new real solutions. A discussion of how existing codes for computing real solution paths may be trivially modified to compute complex paths is included, and examples of numerically computed complex solution paths for a nonlinear two point boundary value problem, and a problem from fluid mechanics are given

A nonlinear equation for ionic diffusion in a strong binary electrolyte

The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description consists of a diffusion equation for each species augmented by transport due to a self consistent electrostatic field determined by the Poisson equation. This mathematical framework also describes other important problems in physics such as electron and hole diffusion across semi-conductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here we derive a more general theory by exploiting the ratio of Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear integro-differential equation which replaces the classical linear equation for ambipolar diffusion but reduces to it in the appropriate limit. Through numerical integration of the full set of equations it is shown that this nonlinear equation provides a better approximation to the exact solution than the linear equation it replaces.Comment: 4 pages, 1 figur

Multidimensional measurement within adult protective services: design and initial testing of the tool for risk, interventions, and outcomes.

This study describes the development, field utility, reliability, and validity of the multidimensional Tool for Risk, Interventions, and Outcomes (TRIO) for use in Adult Protective Services (APS). The TRIO is designed to facilitate consistent APS practice and collect data related to multiple dimensions of typical interactions with APS clients, including the investigation and assessment of risks, the provision of APS interventions, and associated health and safety outcomes. Initial tests of the TRIO indicated high field utility, social worker "relevance and buy-in," and inter-rater reliability. TRIO concurrent validity was demonstrated via appropriate patterns of TRIO item differentiation based on the type of observed confirmed abuse or neglect; and predictive validity was demonstrated by prediction of the risk of actual APS recurrence. The TRIO is a promising new tool that can help meet the challenges of providing and documenting effective APS practices and identifying those at high risk for future APS recurrence

Experimental Study of the Role of Atomic Interactions on Quantum Transport

We report an experimental study of quantum transport for atoms confined in a periodic potential and compare between thermal and BEC initial conditions. We observe ballistic transport for all values of well depth and initial conditions, and the measured expansion velocity for thermal atoms is in excellent agreement with a single-particle model. For weak wells, the expansion of the BEC is also in excellent agreement with single-particle theory, using an effective temperature. We observe a crossover to a new regime for the BEC case as the well depth is increased, indicating the importance of interactions on quantum transport.Comment: 4 pages, 3 figure

Struggling to a monumental triumph : Re-assessing the final stages of the smallpox eradication program in India, 1960-1980

The global smallpox program is generally presented as the brainchild of a handful of actors from the WHO headquarters in Geneva and at the agency's regional offices. This article attempts to present a more complex description of the drive to eradicate smallpox. Based on the example of India, a major focus of the campaign, it is argued that historians and public health officials should recognize the varying roles played by a much wider range of participants. Highlighting the significance of both Indian and international field officials, the author shows how bureaucrats and politicians at different levels of administration and society managed to strengthen—yet sometimes weaken—important program components. Centrally dictated strategies developed at WHO offices in Geneva and New Delhi, often in association with Indian federal authorities, were reinterpreted by many actors and sometimes changed beyond recognition

Resuscitation-promoting factors possess a lysozyme-like domain

The novel bacterial cytokine family – resuscitation-promoting factors (Rpfs) – share a conserved domain of uncharacterized function. Predicting the structure of this domain suggests that Rpfs possess a lysozyme-like domain. The model highlights the good conservation of residues involved in catalysis and substrate binding. A lysozyme-like function makes sense for this domain in the light of experimental characterization of the biological function of Rpfs

The effect of operations on the ground noise footprints associated with a large multibladed, nonbanging helicopter

In order to expand the data base of helicopter external noise characteristics, a flyover noise measurement program was conducted utilizing the NASA Civil Helicopter Research Aircraft. The remotely operated multiple array acoustics range (ROMAAR) and a 2560-m linear microphone array were utilized for the purpose of documenting the noise characteristics of the test helicopter during flyby and landing operations. By utilizing both ROMAAR concept and the linear array, the data necessary to plot the ground noise footprints and noise radiation patterns were obtained. Examples of the measured noise signature of the test helicopter, the ground noise footprint or contours, and the directivity patterns measured during level flyby and landing operations of a large, multibladed, nonbanging helicopter, the CH-53, are presented