Preparing Science Teachers in an Era of Reform: Practitioners' Perspectives of Methods Courses

With recent national calls for the reform of science education have come standards that delineate not only science content but also assessment, pedagogy, and teachers’ professional development. If teachers must teach science differently, then teacher preparation must change. This study asked 31 inservice secondary science teachers to complete a survey about topics for inclusion in a secondary science methods course. Respondents ranked a list of prespecified topics and had an opportunity to suggest other topics for inclusion in the course. Results showed that the majority of prespecified potential topics were judged important enough by these teachers to warrant inclusion in a methods course, though no individual added topic appeared on more than two surveys. Results demonstrate that these teachers believe teaching many of the traditional topics in science methods courses is still needed. In addition, they advocated the inclusion of several topics that either represent recent technological and theoretical advances, or longstanding ideas that have recently received considerable attention.     

On the shepherding of Uranian epsilon ring

To explain the long-term existence of Uranian narrow rings, we study the dynamical evolution of Uranian epsilon ring under the influence of its two shepherding satellites: Cordelia and Ophelia. The model of planar-elliptic restricted three-body problem is employed, in which the three bodies are Uranus, a satellite and a test particle. Dissipations due to interparticle collisions are also taken into consideration. A mapping system has been obtained based on the differential equation system. Numerical results show that only those particles originally lying in the libration region of the resonance can be shepherded. The size of the libration region depends mainly on the orbital eccentricity and mass of the shepherd satellite. For the outer shepherd Ophelia with larger orbital eccentricity, if its mass is a third of the nominal mass 2.5 × 10¹⁹ g, most of the orbits are regular and the outer edge of the ring can be shepherded, but more fuzzy than the inner edge. Thus we infer that Ophelia has a smaller mass.     

Solitary wave interactions in lattice systems with pure higher-order nonlinearity

In this paper, we investigate in detail the interactions of solitary waves in lattice systems with interaction potential V(q)=qⁿ/n, where n is 4,6,8…, through their all possible collision types, and establish a quantitative connection between the scattering property of solitary waves and the chaotic dynamics of the systems. Kink and antikink are excited in such lattice systems and the variation of their scattering effect with n is concerned. After a kink-antikink collision, the dominant interaction in the systems, if n is small, is that solitary waves pass through each other and the scattering effect increases with n; if n is large, solitary waves reflect back sometimes due to the influence of phase and this leads to a decrease of the scattering effect with n. The largest Lyapunov exponents of systems at fixed energy density first increase and then decrease with n, which is consistent with a variation of the scattering effect. The application of the special scattering behaviors between kink and antikink in information propagation is also discussed.     

Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension

In this paper, we study an economic model, where internal habits play a role. Their formation is described by a more general functional form than is usually assumed in the literature, because a finite memory effect is allowed. Indeed, the problem becomes the optimal control of a standard ordinary differential equation, with the past of the control entering both the objective function and an inequality constraint. Therefore, the problem is intrinsically infinite dimensional. To solve this model, we apply the dynamic programming approach and we find an explicit solution for the associated Hamilton–Jacobi–Bellman equation, which lets us write the optimal strategies in feedback form. Therefore, we contribute to the existing literature in two ways. Firstly, we fully develop the dynamic programming approach to a type of problem not studied in previous contributions. Secondly, we use this result to unveil the global dynamics of an economy characterized by generic internal habits.     

The eigenvalue-matching renormalization group

The eigenvalue-matching renormalization-group method is extended to the computation of the universal rescaling factors in addition to the universal bifurcation rate. Both the one-dimensional quadratic map and the two-dimensional area-preserving Hénon map are studied. The computation has been carried to very high orders: eleventh in the one-dimensional case and eighth in the two-dimensional case. The accuracy is so high and the algorithm so efficient that it may be used as an alternative to the direct numerical procedure.     

A simple derivation of the stochastic eigenvalue equation in the transition from quasiperiodicity to chaos

A simple derivation of the stochastic eigenvalue equation, previously obtained by irrational decimation of functional integrals, is given to show the universal scaling behavior of external noise in the transition from quasiperiodicity to chaos in dissipative systems.     

A Note on Black Hole Information Paradox in de Sitter Spacetimes

The possibility of stable or quasi-stable Planck mass black hole remnants as solution to the black hole information paradox is commonly believed phenomenologically unacceptable. Since we need a black hole remnant for every possible initial state,the number of remnants is expected to be infinite and that would lead to remnant pair production in any physical process with a total available energy roughly exceeding the Planck mass. In this note I point out that a positive cosmological constant of the Universe would naturally lead to an upper bound on the numberof possible remnants.     

A Note on Black Hole Information Paradox in de Sitter Spacetimes

The possibility of stable or quasi-stable Planck mass black hole remnants as solution to the black hole information paradox is commonly believed phenomenologically unacceptable. Since we need a black hole remnant for every possible initial state, the number of remnants is expected to be infinite and that would lead to remnant pair production in any physical process with a total available energy roughly exceeding the Planck mass. In this note I point out that a positive cosmological constant of the Universe would naturally lead to an upper bound on the number of possible remnants.     

A novel ultrasound instrument for investigation of arterial mechanics

The study of arterial mechanics concerns functional characteristics depending on wall elasticity and flow profile. Wall elasticity can be investigated through the estimation of parameters like the arterial distensibility, which is of high clinical interest because of its known correlation not only with the advanced atherosclerotic disease, but also with aging and major risk factors for cardiovascular disease. The flow velocity profile is also clinically relevant, because it modulates endothelial function and can be responsible for the development and distribution of atherosclerotic plaques. A clinically relevant variable extracted from the blood velocity profile is the wall shear rate (WSR), which represents the spatial velocity gradient near the vessel wall. This paper describes an integrated ultrasound system, capable of detecting both the velocity profile and the wall movements in human arteries. It basically consists of a PC add-on board including a single high-speed digital signal processor. This is dedicated to the analysis of echo-signals backscattered from 128 range cells located along the axis of the interrogating ultrasound (US) beam. Echoes generated from the walls (characterized by high amplitudes and low Doppler frequencies) and from red blood cells (characterized by low amplitudes and relatively high Doppler frequencies) are independently processed in real-time. Wall velocity is detected through the autocorrelation algorithm, while blood velocity is investigated through a complete spectral analysis of all signals backscattered by erythrocytes and WSR is extracted from the estimated velocity profile. Preliminary applications of the new system, including the simultaneous analysis of blood flow and arterial wall movement in healthy volunteers and in a diseased patient, are discussed, and first results are presented.