Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

Naive asymptotic expansion of the water wave generated by a slowly moving body

It is pointed out that the naive asymptotic expansion does not satisfy all the body boundary condition. A nonhomogeneous body boundary condition is obtained from this expansion. It is this condition that the additional wave term must satisfy. Moreover, because of this condition, the wave term must appear. It is pointed out that the zeroth approximation in the naive asymptotic expansion has weak singularity and the singularities become still stronger in the subsequent approximations.

An asymptotic solution of hydrodynamic equations at the mid-plane of a plume in the earths mantle

From the partial differential equations of hydrodynamics governing the movements in the Earth's mantle of a Newtonian fluid with a pressure- and temperature-dependent viscosity, considering the bilateral symmetry of velocity and temperature distributions at the mid-plane of the plume, an analytical solution of the governing equations near the mid-plane of the plume was found by the method of asymptotic analysis. The vertical distribution of the upward velocity, viscosity and temperature at the mid-plane, and the temperature excess at the centre of the plume above the ambient mantle temperature were then calculated for two sets of Newtonian rheological parameters. The results obtained show that the temperature at the mid-plane and the temperature excess are nearly independent of the rheological parameters. The upward velocity at the mid-plane, however, is strongly dependent on the rheological parameters.

The asymptotic near-tip solution for mode-iii crack in steady growth in power hardening media

Two local solutions, one perpendicular and one parallel to the direction of solar gravitational field, are discussed. The influence of gravity on the gas-dynamical process driven by the piston is discussed in terms of characteristic theory, and the flow field is given quantitatively. For a typical piston trajectory similar to the one for an eruptive prominence, the velocity of the shock front which locates ahead the transient front is nearly constant or slightly accelerated, and the width of the compressed flow region may be kept nearly constant or increased linearly, depending on the velocity distribution of the piston. Based on these results, the major features of the transient may be explained. Some of the fine structure of the transient is also shown, which may be compared in detail with observations.

On the strategic equivalence of multiple-choice test scoring rules

A disadvantage of multiple-choice tests is that students have incentives to guess. To discourage guessing, it is common to use scoring rules that either penalize wrong answers or reward omissions. These scoring rules are considered equivalent in psychometrics, although experimental evidence has not always been consistent with this claim. We model students' decisions and show, first, that equivalence holds only under risk neutrality and, second, that the two rules can be modified so that they become equivalent even under risk aversion. This paper presents the results of a field experiment in which we analyze the decisions of subjects taking multiple-choice exams. The evidence suggests that differences between scoring rules are due to risk aversion as theory predicts. We also find that the number of omitted items depends on the scoring rule, knowledge, gender and other covariates.

A Non-Parametric Dimension Test of the Term Structure

Published as an article in: Studies in Nonlinear Dynamics & Econometrics, 2004, vol. 8, issue 3, article 6.

Test well exploration in the Myakka River Basin area, Florida

In recent years, difficulties encountered in obtaining ground-water supplies with acceptable chemical characteristics in the Myakka River basin area led to the implementation of a test drilling program. Under this program, well drilling and data collection were executed in such a manner that all water-producing zones of the local aquifers, together with the quality and quantity of the water available, were effectively identified. A step-drilling method was utilized which allowed the collection of formation cuttings, water samples, and water-level data, from isolated zones in the well as drilling proceeded. The step drilling procedure is described. The driller's logs, geophysical logs, and chemical quality of water tables are presented.(Document has 66 pages.)

Using network mesures to test evolved NK-landscapes

In this paper we empirically investigate which are the structural characteristics that can help to predict the complexity of NK-landscape instances for estimation of distribution algorithms. To this end, we evolve instances that maximize the estimation of distribution algorithm complexity in terms of its success rate. Similarly, instances that minimize the algorithm complexity are evolved. We then identify network measures, computed from the structures of the NK-landscape instances, that have a statistically significant difference between the set of easy and hard instances. The features identified are consistently significant for different values of N and K.

Can the change in the composition of the US GDP explain the Great Moderation? A test via oil price shocks

The paper investigates whether the growing GDP share of the services sector can contribute to explain the great moderation in the US. We identify and analyze three oil price shocks and use a SVAR analysis to measure their economic impact on the US economy at both the aggregate and the sectoral level. We find mixed support for the explanation of the great moderation in terms of shrinking oil shock volatilities and observe that increases (decreases) in oil shock volatilities are contrasted by a weakening (strengthening) in their transmission mechanism. Across sectors, services are the least affected by any oil shock. As the contribution of services to the GDP volatility increases over time, we conclude that a composition effect contributed to moderate the conditional volatility to oil shocks of the US GDP.

A Method for siting and prioritizing the removal of derelict vessels in Florida Coastal Waters: test applications in the Florida Keys

Increased boating activities and new waterfront developments have contributed an estimated 3,000 dismantled, abandoned, junked, wrecked, derelict vessels to Florida coastal waters. This report outlines a method of siting and prioritizing derelict vessel removal using the Florida Keys as a test area. The data base was information on 240 vessels, obtained from Florida Marine Patrol files. Vessel location was plotted on 1:250,000 regional and 1:5,000 and 1:12,000 site maps. Type of vessel, length, hull material, engine, fuel tanks, overall condition, afloat and submerged characteristics, and accessibility, were used to derive parametric site indices of removal priority and removal difficulty. Results indicate 59 top priority cases which should be the focus of immediate clean up efforts in the Florida Keys. Half of these cases are rated low to moderate in removal difficulty; the remainder are difficult to remove. Removal difficulty is a surrogate for removal cost: low difficulty -low cost, high difficulty - high cost. The rating scheme offers coastal planners options of focusing removal operations either on (1) specific areas with clusters of high priority derelict vessels or on (2) selected targeted derelicts at various, specific locations. (PDF has 59 pages.)