Topics in bifurcation theory

I. Existence and Structure of Bifurcation Branches

The problem of bifurcation is formulated as an operator equation in a Banach space, depending on relevant control parameters, say of the form G(u,λ) = 0. If dimN(G_u(u_O,λ_O)) = m the method of Lyapunov-Schmidt reduces the problem to the solution of m algebraic equations. The possible structure of these equations and the various types of solution behaviour are discussed. The equations are normally derived under the assumption that G^O_λεR(G^O_u). It is shown, however, that if G^O_λεR(G^O_u) then bifurcation still may occur and the local structure of such branches is determined. A new and compact proof of the existence of multiple bifurcation is derived. The linearized stability near simple bifurcation and "normal" limit points is then indicated.

II. Constructive Techniques for the Generation of Solution Branches

A method is described in which the dependence of the solution arc on a naturally occurring parameter is replaced by the dependence on a form of pseudo-arclength. This results in continuation procedures through regular and "normal" limit points. In the neighborhood of bifurcation points, however, the associated linear operator is nearly singular causing difficulty in the convergence of continuation methods. A study of the approach to singularity of this operator yields convergence proofs for an iterative method for determining the solution arc in the neighborhood of a simple bifurcation point. As a result of these considerations, a new constructive proof of bifurcation is determined.

Assessing societal vulnerability of U.S. Pacific Northwest communities to storm induced coastal change

Progressive increases in storm intensities and extreme wave heights have been documented along the U.S. West Coast. Paired with global sea level rise and the potential for an increase in El Niño occurrences, these trends have substantial implications for the vulnerability of coastal communities to natural coastal hazards. Community vulnerability to hazards is characterized by the exposure, sensitivity, and adaptive capacity of human-environmental systems that influence potential impacts. To demonstrate how societal vulnerability to coastal hazards varies with both physical and social factors, we compared community exposure and sensitivity to storm-induced coastal change scenarios in Tillamook (Oregon) and Pacific (Washington) Counties. While both are backed by low-lying coastal dunes, communities in these two counties have experienced different shoreline change histories and have chosen to use the adjacent land in different ways. Therefore, community vulnerability varies significantly between the two counties. Identifying the reasons for this variability can help land-use managers make decisions to increase community resilience and reduce vulnerability in spite of a changing climate. (PDF contains 4 pages)

The South Atlantic Alliance: A southeastern U.S. state Governors initiative to address opportunities and challenges embodied in the region's coastal and ocean domain

The pressures placed on the natural, environmental, economic, and cultural sectors from continued growth, population shifts, weather and climate, and environmental quality are increasing exponentially in the southeastern U.S. region. Our growing understanding of the relationship of humans with the marine environment is leading us to explore new ecosystem-based approaches to coastal management, marine resources planning, and coastal adaptation that engages multiple state jurisdictions. The urgency of the situation calls for coordinated regional actions by the states, in conjunction with supporting partners and leveraging a diversity of resources, to address critical issues in sustaining our coastal and ocean ecosystems and enhancing the quality of life of our citizens. The South Atlantic Alliance (www.southatlanticalliance.org) was formally established on October 19, 2009 to “implement science-based policies and solutions that enhance and protect the value of coastal and ocean resources of the southeastern United States which support the region's culture and economy now and for future generations.” The Alliance, which includes North Carolina, South Carolina, Georgia, and Florida, will provide a regional mechanism for collaborating, coordinating, and sharing information in support of resource sustainability; improved regional alignment; cooperative planning and leveraging of resources; integrated research, observations, and mapping; increased awareness of the challenges facing the South Atlantic region; and inclusiveness and integration at all levels. Although I am preparing and presenting this overview of the South Atlantic Alliance and its current status, there are a host of representatives from agencies within the four states, universities, NGOs, and ongoing southeastern regional ocean and coastal programs that are contributing significant time, expertise, and energy to the success of the Alliance; information presented herein and to be presented in my oral presentation was generated by the collaborative efforts of these professionals. I also wish to acknowledge the wisdom and foresight of the Governors of the four states in establishing this exciting regional ocean partnership. (PDF contains 4 pages)

Panel discussion: U.S. EPA using modeling and ecosystem services to enhance coastal decision making

This panel will discuss the research being conducted, and the models being used in three current coastal EPA studies being conducted on ecosystem services in Tampa Bay, the Chesapeake Bay and the Coastal Carolinas. These studies are intended to provide a broader and more comprehensive approach to policy and decision-making affecting coastal ecosystems as well as provide an account of valued services that have heretofore been largely unrecognized. Interim research products, including updated and integrated spatial data, models and model frameworks, and interactive decision support systems will be demonstrated to engage potential users and to elicit feedback. It is anticipated that the near-term impact of the projects will be to increase the awareness by coastal communities and coastal managers of the implications of their actions and to foster partnerships for ecosystem services research and applications. (PDF contains 4 pages)

Species Profiles: Life Histories and Environmental Requirements of Coastal Fishes and Invertebrates (Pacific Southwest): Amphipods

(PDF contains 24 pages)

Species Profiles: Life Histories and Environmental Requirements of Coastal Fishes and Invertebrates (Mid-Atlantic): Bay anchovy

The bay anchovy occurs along the Atlantic and Gulf of Mexico coasts, from Cape Cod, Massachusetts, to Yucatan, Mexico (Hildebrand 1963), except for the Florida Keys where it is apparently absent (Daly 1970). (PDF contains 22 pages)

Species Profiles: Life Histories and Environmental Requirements of Coastal Fishes and Invertebrates (Gulf of Mexico): Bay anchovy and Striped Anchovy

(PDF contains 24 pages)

An examination of strategic opportunities provided by the conference committee procedure in the U.S. Congress

Deference to committees in Congress has been a much studied phenomena for close to 100 years. This deference can be characterized as the unwillingness of a potentially winning coalition on the House floor to impose its will on a small minority, a standing committee. The congressional scholar is then faced with two problems: observing such deference to committees, and explaining it. Shepsle and Weingast have proposed the existence of an ex-post veto for standing committees as an explanation of committee deference. They claim that as conference reports in the House and Senate are considered under a rule that does not allow amendments, the conferees enjoy agenda-setting power. In this paper I describe a test of such a hypothesis (along with competing hypotheses regarding the effects of the conference procedure). A random-utility model is utilized to estimate legislators' ideal points on appropriations bills from 1973 through 1980. I prove two things: 1) that committee deference can not be said to be a result of the conference procedure; and moreover 2) that committee deference does not appear to exist at all.

Parents aspiration and youth perception to sustainable fisheries development in Kainji Lake basin

Artisanal fisheries development in Nigeria, like in any other developing country of the world is characterized by subsistence level of operation using dugout canoe and paddle. This implies that parents and children constituted the labour in use since they only struggle for the upkeep of the family. A total of 240 questionnaires were used to solicit information from the respondents. This total was divided into 120 each for both parents and the youths respectively. Simple descriptive statistics such as frequency distribution and percentages were used to analyze their responses. Parents have strong aspiration for their children to succeed them hence, 78.3% of the parents expressed their aspiration for succession by the younger ones while 83.3% of parents tend to support their aspiration with persuasive strategies such as allowing their children to partake in fishing activities at will. On the part of the youth over 70% of them perceived fishing as a viable business where they can succeed their parents provided government can come to their aid in form of active involvement in the development of rural fisheries. It is therefore believed that fisheries development could achieve rapid improvement if the aspiration of the parents is balanced with perception of the youth and the government meets their expectation

The Determinants of Energy Efficiency Investments in the U.S.

31 p.

Origin of Th/U variations in chondritic meteorites

Isotope dilution thorium and uranium analyses of the Harleton chondrite show a larger scatter than previously observed in equilibrated ordinary chondrites (EOC). The linear correlation of Th/U with 1/U in Harleton (and all EOC data) is produced by variation in the chlorapatite to merrillite mixing ratio. Apatite variations control the U concentrations. Phosphorus variations are compensated by inverse variations in U to preserve the Th/U vs. 1/U correlation. Because the Th/U variations reflect phosphate ampling, a weighted Th/U average should converge to an improved solar system Th/U. We obtain Th/U=3.53 (1_-mean=0.10), significantly lower and more precise than previous estimates.

To test whether apatite also produces Th/U variation in CI and CM chondrites, we performed P analyses on the solutions from leaching experiments of Orgueil and Murchison meteorites.

A linear Th/U vs. 1/U correlation in CI can be explained by redistribution of hexavalent U by aqueous fluids into carbonates and sulfates.

Unlike CI and EOC, whole rock Th/U variations in CMs are mostly due to Th variations. A Th/U vs. 1/U linear correlation suggested by previous data for CMs is not real. We distinguish 4 components responsible for the whole rock Th/U variations: (1) P and actinide-depleted matrix containing small amounts of U-rich carbonate/sulfate phases (similar to CIs); (2) CAIs and (3) chondrules are major reservoirs for actinides, (4) an easily leachable phase of high Th/U. likely carbonate produced by CAI alteration. Phosphates play a minor role as actinide and P carrier phases in CM chondrites.

Using our Th/U and minimum galactic ages from halo globular clusters, we calculate relative supernovae production rates for ²³²Th/²³⁸U and ²³⁵U/²³⁸U for different models of r-process nucleosynthesis. For uniform galactic production, the beginning of the r-process nucleosynthesis must be less than 13 Gyr. Exponentially decreasing production is also consistent with a 13 Gyr age, but very slow decay times are required (less than 35 Gyr), approaching the uniform production. The 15 Gyr Galaxy requires either a fast initial production growth (infall time constant less than 0.5 Gyr) followed by very low decrease (decay time constant greater than 100 Gyr), or the fastest possible decrease (≈8 Gyr) preceded by slow in fall (≈7.5 Gyr).

基于U形塑料光纤的氧气传感器

报道了一种基于荧光猝灭原理的光纤氧气传感器.采用塑料光纤作为传感和传光元件进行氧气传感,传感头制成U形.以邻菲咯啉钌作为荧光标记物,用溶胶-凝胶法制备敏感材料.采用相移法来实现对荧光寿命的测定.测量了不同弯曲半径传感头对氧气传感的灵敏度,发现当U形光纤的弯曲半径较小时系统的灵敏度较高.对荧光寿命和氧气浓度的关系进行了测量,发现二者呈亚线性关系,提出双荧光体模型解释这一实验现象.