A Conceptual Shift to Rectify a Defect in the Lorentz-Dirac Equation

In his analysis of the Classical Theory of Radiating Electrons, Dirac (1938) draws attention to the characteristic instability of solutions to the third order equation of motion. He remarks that changing the sign of the self-force eliminates the runaway solutions and gives `reasonable behaviour'. Dirac rejects such a change and proceeds with an ad hoc modification to the solutions of the initial value problem that is not consistent with the principle of causality. We argue that his reasons for rejecting the change of sign are invalid on both physical and mathematical grounds. The conceptual shift is to treat the physical particle as a composite of the source particle and the energy-momentum that is reversibly generated in its self-field by its motion. The reversibly generated energy in the self-field is interpreted as kinetic energy, and the changes that follow result in Dirac's change of sign. Several exact solutions to the new equation of motion and its linearisation are given. For a particle in orbital motion the self-force enables the applied force to generate radiation and kinetic energy in the self-field that results in an outward spiral motion. The theory is consistent with all well-established principles of physics, including the principle of causality.Comment: 20 page

Fuels for Future Electric Power

OVER THE NEXT FORTY YEARS, THE U.S. WILL EXPERIENCE PROBLEMS BECAUSE OF DWINDLING SUPPLIES OF FOSSIL FUELS AND AN INCREASING DEPENDENCE ON FOREIGN OIL. SEVERAL ALTERNATIVES ARE AVAILABLE, SUCH AS MORE STRINGENT CONSERVATION MEASURES OR ALTERNATIVE SOURCES OF ENERGY. HOWEVER, NO SINGLE ALTERNATIVE WILL BE SUFFICIENT. A STUDY WAS CONDUCTED TO DETERMINE THE MOST EFFICIENT ALLOCATION POSSIBLE OF RESOURCES. THE ANALYSIS WAS CONDUCTED ON THE BASIS OF ASSUMED HAPPENINGS IN THE FUTURE RATHER THAN BY PROJECTING HISTORIC TRENDS INTO THE FUTURE. FOR EXAMPLE, AS ONE SOURCE OF ENERGY SUCH AS OIL BECOMES MORE SCARCE, THE COST WILL GO UP, INDUCING A CHANGE TO ANOTHER SOURCE. SYNTHETIC FUELS FROM COAL AND HYDROGEN FROM ELECTROLYSIS WILL BECOME MORE PRACTICAL BY THE END OF THE CENTURY. COAL AND OIL WILL BE USED. HEAVILY THIS CENTURY WITH NUCLEAR FUEL BECOMING MORE EFFICIENT EARLY IN THE NEXT CENTURY. CHART

Assessment in mathematics: A multimedia resource for preservice teachers

It is commonly accepted that teachers teach the way they were taught and that innovation is difficult to achieve. In this project, the theoretical framework of situated cognition or situated learning has been used to design an interactive multimedia resource that allows preservice teachers to become aware of different assessment strategies in mathematics education, and how to apply them. The resource enables users to encounter the authentic use of a range of assessment strategies and to view their interpretations from multiple perspectives which include the teacher's decision-making processes, the child's thinking, expert opinion and written documentation

Power corrections in models with extra dimensions

We critically revisit the issue of power-law running in models with extra dimensions. The general conclusion is that, in the absence of any additional physical principle, the power-corrections tend to depend strongly on the details of the underlying theory.Comment: Talk given at EPS2003 - Aachen, Germany, July 2003, 3 pages, 1 figur

Computational aspects of the prediction of multidimensional transonic flows in turbomachinery

The analytical prediction and description of transonic flow in turbomachinery is complicated by three fundamental effects: (1) the fluid equations describing the transonic regime are inherently nonlinear, (2) shock waves may be present in the flow, and (3) turbomachine blading is geometrically complex, possessing large amounts of curvature, stagger, and twist. A three-dimensional computation procedure for the study of transonic turbomachine fluid mechanics is described. The fluid differential equations and corresponding difference operators are presented, the boundary conditions for complex blade shapes are described, and the computational implementation and mapping procedures are developed. Illustrative results of a typical unthrottled transonic rotor are also presented

Systematic review and meta-analysis of optimal P2Y₁₂ blockade in dual antiplatelet therapy for patients with diabetes with acute coronary syndrome

Background: Patients with diabetes are at increased risk of acute coronary syndromes (ACS) and their mortality and morbidity outcomes are significantly worse following ACS events, independent of other comorbidities. This systematic review sought to establish the optimum management strategy with focus on P2Y₁₂ blockade in patients with diabetes with ACS. Methods: MEDLINE (1946 to present) and EMBASE (1974 to present) databases, abstracts from major cardiology conferences and previously published systematic reviews were searched to June 2014. Relevant randomised control trials with clinical outcomes for P2Y₁₂ inhibitors in adult patients with diabetes with ACS were scrutinised independently by 2 authors with applicable data was extracted for primary composite end point of cardiovascular death, myocardial infarction (MI) and stroke; enabling calculation of relative risks with 95% CI with subsequent direct and indirect comparison. Results: Four studies studied clopidogrel in patients with diabetes, with two (3122 patients) having primary outcome data showing superiority of clopidogrel against placebo with RR0.84 (95% CI 0.72–0.99). Irrespective of management strategy, the newer agents prasugrel (2 studies) and ticagrelor (1 study) had a lower primary event rate compared with clopidogrel; RR 0.80 (95% CI 0.66 to 0.97) and RR 0.89 (95% CI 0.77 to 1.02), respectively. When ticagrelor was indirectly compared with prasugrel, there was a trend to an improved primary outcome with prasugrel (RR 1.11 (95% CI 0.94 to 1.31)) particularly in those managed with percutaneous coronary intervention (PCI) (RR 1.23 (95% CI 0.95 to 1.59)). Prasugrel demonstrated a statistical superiority with prevention of further MI with RR 1.48 (95% CI 1.11 to 1.97). This was not at the expense of increased major thrombolysis in MI (TIMI) bleeding rates RR 0.94 (95% CI 0.59 to 1.51). Conclusions: This meta-analysis shows the addition of a P2Y₁₂ inhibitor is superior to placebo, with a trend favouring the use of prasugrel in patients with diabetes with ACS, particularly those undergoing PCI

Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces

We develop tools to construct Lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped Euler system under the influence of external and interaction potential forces with respect to the 2-Wasserstein distance. We also discuss the overdamped limit to a nonlocal equation used in the modelling of granular media with respect to the 2-Wasserstein distance, and provide rigorous proofs for particular examples in one spatial dimension