On the persistence properties of the cross-coupled Camassa-Holm system

In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the persistence of compact support for the momenta. For solutions of the system itself, the answer is more convoluted, and we determine when the compactness of the support is lost, replaced instead by an exponential decay rate.Comment: 13 pages, 1 figur

The Outer Limits of Galaxy Clusters: Observations to the Virial Radius with Suzaku, XMM, and Chandra

The outskirts of galaxy clusters, near the virial radius, remain relatively unexplored territory and yet are vital to our understanding of cluster growth, structure, and mass. In this presentation, we show the first results from a program to constrain the state of the outer intracluster medium (ICM) in a large sample of galaxy clusters, exploiting the strengths of three complementary X-ray observatories: Suzaku (low, stable background), XMM-Newton (high sensitivity), and Chandra (good spatial resolution). By carefully combining observations from the cluster core to beyond r_200, we are able to identify and reduce systematic uncertainties that would impede our spatial and spectral analysis using a single telescope. Our sample comprises nine clusters at z ~ 0.1-0.2 fully covered in azimuth to beyond r_200, and our analysis indicates that the ICM is not in hydrostatic equilibrium in the cluster outskirts, where we see clear azimuthal variations in temperature and surface brightness. In one of the clusters, we are able to measure the diffuse X-ray emission well beyond r_200, and we find that the entropy profile and the gas fraction are consistent with expectations from theory and numerical simulations. These results stand in contrast to recent studies which point to gas clumping in the outskirts; the extent to which differences of cluster environment or instrumental effects factor in this difference remains unclear. From a broader perspective, this project will produce a sizeable fiducial data set for detailed comparison with high-resolution numerical simulations.Comment: 8 pages, 6 figures. To appear in the proceedings of the Suzaku 2011 Conference, "Exploring the X-ray Universe: Suzaku and Beyond.

Automated precision alignment of optical components for hydroxide catalysis bonding

We describe an interferometric system that can measure the alignment and separation of a polished face of a optical component and an adjacent polished surface. Accuracies achieved are ∼ 1μrad for the relative angles in two orthogonal directions and ∼ 30μm in separation. We describe the use of this readout system to automate the process of hydroxide catalysis bonding of a fused-silica component to a fused-silica baseplate. The complete alignment and bonding sequence was typically achieved in a timescale of a few minutes, followed by an initial cure of 10 minutes. A series of bonds were performed using two fluids - a simple sodium hydroxide solution and a sodium hydroxide solution with some sodium silicate solution added. In each case we achieved final bonded component angular alignment within 10 μrad and position in the critical direction within 4 μm of the planned targets. The small movements of the component during the initial bonding and curing phases were monitored. The bonds made using the sodium silicate mixture achieved their final bonded alignment over a period of ∼ 15 hours. Bonds using the simple sodium hydroxide solution achieved their final alignment in a much shorter time of a few minutes. The automated system promises to speed the manufacture of precision-aligned assemblies using hydroxide catalysis bonding by more than an order of magnitude over the more manual approach used to build the optical interferometer at the heart of the recent ESA LISA Pathfinder technology demonstrator mission. This novel approach will be key to the time-efficient and low-risk manufacture of the complex optical systems needed for the forthcoming ESA spaceborne gravitational waves observatory mission, provisionally named LISA

Short-term shocks, reversion, and long-term decision-making

Many observers claim that discounted cash-flow methods lead to a neglect of long-term and strategic decision-making. Using modern asset pricing methods, we examine one possible reason for this problem. If the cash-flows being discounted have an increasing dependence on an uncertain variable that tends to revert to a long-term equilibrium path in the face of short-term shocks, and if this reversion is ignored, then the uncertainty in the cash-flows will be overestimated. If this uncertainty causes risk discounting, then the amount of risk discounting that is appropriate will also be overestimated, which will tend to result in a relative undervaluation of long-term alternatives. We examine the implications of such an error for the comparative analysis of decision alternatives, including some involving an initial timing option. We use, as examples, decisions about production projects where the output price is the reverting variable.Where applicable, we look at two measures of what is meant by long-term: the operating duration of the project and the length of an initial timing option. For the projects without options, the analysis is based on the relatively straightforward "risk discounting effect" already mentioned. Reversion tends to decrease long-term uncertainty, and, with it, long-term risk discounting, which increases the relative value of long-term alternatives. Options complicate matters. The long-term decrease in uncertainty due to reversion tends directly to decrease long-term option values. Moreover, in addition to the original risk discounting effect and this "variance effect," there can be direct "future reversion effects" if the options involve a timing component or payoffs generated by cash-flows over a period of time. The overall influence can be a complicated mixture of the three different types of effects.We use this classification scheme to analyze two sets of examples: investment timing options on an instantaneous production project (equivalent to at-the-money American options on the project output price), and "now-or-never" options, as well as investment timing options, on projects that differ in their operating lives. We find that a neglect of reversion leads to an undervaluation of at- or in-the-money options on projects with longer operating lives. This is primarily due to the risk discounting effect. Longer timing options on the same project tend to be relatively overvalued by a neglect of reversion if the operating life of the project is moderately long, and undervalued if the project is instantaneous and currently at the money. The first is primarily due to variance and future-reversion effects. The second is primarily due to risk-discounting and future-reversion effects.Because parts of the economy may be influenced by short-term shocks in the presence of long-term equilibrium, these results suggest a reexamination of those aspects of analyses in the "real options" literature that depend on the use of non-reverting models.Supported by the Natural Science and Engineering Research Council of Canada, Imperial Oil University Research Grants, Interprovincial Pipeline Co., Saskoil, Exxon Corp., and the Social Science and Humanities Research Council of Canada, and by the Central Research Fund, a Nova Faculty Fellowship, the Muir Research Fund and the Institute for Financial Research of the University of Alberta, and by the Finance, Investment and Contracts Program of the MIT Center for Energy and Environmental Policy Research

A two-method solution to the investment timing option

Within the realm of derivative asset valuation, two types of methods are available for solving the investment timing option, each with a serious limitation for practical projects. Methods that use Monte Carlo simulation of risk-adjusted probability measures allow consideration of the complicated cash flow models typical of real projects, in the face of prespecified operating policies, but they do not provide an adequate way to determine what the optimal policy is. Formulation of the problem as an American option in the vein of Black-Scholes and Merton permits calculation of an optimal start policy, but only in situations with drastically simplified cash flow models. The solution to this dilemma is the development of an approach which applies the two methods in tandem. The rights to explore and develop an oil field are used as an example, and Monte Carlo simulation is used to calculate the value of these rights as a function of start time and contemporaneous oil price. This payoff function is then input to a Black-Scholes-Merton option calculation. The resulting optimal start policy is then reinserted to the Monte Carlo model for further analysis of project and individual cash-flow magnitudes and risks. Also, possible bias because of numerical-analysis errors are checked by direct search of start policies in the vicinity of the calculated optimum.Supported by the Social Science and Humanities Research Council of Canada, the Natural Science and Engineering Research Council of Canada, Imperial Oil and various research funds of the University of Alberta and the M.I.T. Center for Energy Policy Research

Options for Processing Shrimp Landed in South Carolina

Resource /Energy Economics and Policy,

Project evaluation : a practical asset pricing method

This paper presents a practical approach to project evaluation using techniques of modern financial economics, with a sample application to oil development under a complex tax system. The method overcomes shortcomings of conventional DCF methods which are either imprecise about the relation between economic value and uncertainty, or are rigid and unrealistic in the required assumptions about how a project's risks (and therefore its value) are influenced by market conditions, the project physical structure, and tax and contract provisions. It is based on the formulation and estimation of an "information model" which represents the resolution over time of uncertainties underlying a project (oil prices in the examples shown). Oil prices are the underlying uncertainty in the examples shown. The project can then be valued using derivative asset valuation, which replicates the consequences of a complex asset by a traded portfolio of simpler assets (in our case, riskless bonds and future claims on oil). For ease of implementation, the method is designed to resemble current industry practice. The information model can be estimated using analysis and judgment similar to that applied in conventional evaluation. The formulation of decision alternatives, the selection of underlying uncertainties, and the design of a cash-flow model are the same as in standard DCF methods. Simulation and valuation results also can be represented in a familiar format. Restrictions must be placed on the "best" current asset pricing theory to achieve this convenient framework: the expected returns on the basic assets, which comprise the portfolios traded to replicate project cash flows, must be assumed to be known with certainty at the time of an evaluation.Supported by the MIT Center for Energy Policy Research, the Social Science and Humanities Research Council of Canada, the Natural Science and Engineering Research Council of Canada, the Imperial Oil University Research Grants Programme, the Central Research Fund, a Nova Faculty Fellowship, the Muir Research Fund and the Institute for Financial Research of the University of Alberta

A safe method for the retrieval of a dislocated trial head in total hip arthroplasty

Total hip arthroplasty is a life changing procedure providing a significant improvement in the quality of life for those receiving treatment. An 81-year-old male with severe right sided hip osteoarthritis underwent uncemented total hiparthroplasty. Intraoperatively the 32mm trial head dislodged from the trial stem over the anterior rim of the acetabulum relocating to within the pelvic cavity. Time efficient retrieval was performed during primary surgery through a mini-incision at the iliac crest