Towards a real-time microscopic emissions model

This article presents a new approach to microscopic road traffic exhaust emission modelling. The model described uses data from the SCOOT demand-responsive traffic control system implemented in over 170 cities across the world. Estimates of vehicle speed and classification are made using data from inductive detector loops located on every SCOOT link. This data feeds into a microscopic traffic model to enable enhanced modelling of the driving modes of vehicles (acceleration, deceleration, idling and cruising). Estimates of carbon monoxide emissions are made by applying emission factors from an extensive literature review. A critical appraisal of the development and validation of the model is given before the model is applied to a study of the impact of high emitting vehicles. The article concludes with a discussion of the requirements for the future development and benefits of the application of such a model

Groups of diffeomorphisms and the solution of the classical Euler equations for a perfect fluid.

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On the motion of incompressible fluids

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The recovery of asteroids after two observations

It is shown that a generalization of the use of 'Vaisala orbits', briefly mentioned at the Asteroids 2 Conference, can be very conveniently accomplished by means of an inversion of the 'GEM' form of the Gauss method. The procedure can also be applied to Apollo objects and to indeterminate cases of normal three-observation orbit computation, and there is also a simple extension to situations involving four or more observations

Comet Halley and history

A history of Halley's Comet is presented. Comets Kohoutek and Ikeya-Seki are discussed

Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media

We analyze frequency conversion and its control among three light waves using a geometric approach that enables the dynamics of the waves to be visualized on a closed surface in three dimensions. It extends the analysis based on the undepleted-pump linearization and provides a simple way to understand the fully nonlinear dynamics. The Poincaré sphere has been used in the same way to visualize polarization dynamics. A geometric understanding of control strategies that enhance energy transfer among interacting waves is introduced, and the quasi-phase-matching strategy that uses microstructured quadratic materials is illustrated in this setting for both type I and II second-harmonic generation and for parametric three-wave interactions

Energy dependent Schrödinger operators and complex Hamiltonian systems on Riemann surfaces

We use so-called energy-dependent Schrödinger operators to establish a link between special classes of solutions on N-component systems of evolution equations and finite dimensional Hamiltonian systems on the moduli spaces of Riemann surfaces. We also investigate the phase-space geometry of these Hamiltonian systems and introduce deformations of the level sets associated to conserved quantities, which results in a new class of solutions with monodromy for N-component systems of PDEs. After constructing a variety of mechanical systems related to the spatial flows of nonlinear evolution equations, we investigate their semiclassical limits. In particular, we obtain semicalssical asymptotics for the Bloch eigenfunctions of the energy dependent Schrödinger operators, which is of importance in investigating zero-dispersion limits of N-component systems of PDEs

Nongravitational forces on comets

Methods are presented and discussed for determining the effects of nongravitational forces on the orbits of comets. These methods are applied to short-period and long-period comets. Results are briefly described

Discrete Routh Reduction

This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical $J_2$ correction, as well as the double spherical pendulum. The $J_2$ problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a nontrivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the noncanonical nature of the symplectic structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added, fixed typo