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Here, we explore conservation of momentum for variable-mass systems by means of two systems: a stalled boat in a lagoon and the propulsion of a rocket. He manages to throw the stones with a speed of I v i SB 0 sb = 4.0 m/s. The mass of the boat and its original load is I M i = 150 kg. The situation in which the rocket continuously dumps mass corresponds to the limit case I m i SB 0 sb -> 0, while I n i -> to maintain the validity of the condition I nm i SB 0 sb = I M i SB E sb . [Extracted from the article]

An arch bridge is a mainly horizontal deck with an arch as its load-carrying structure. The arch works by transferring the weight and other external vertical loads into a horizontal thrust on the abutments placed at both sides. When the main load on the arch is the homogeneously distributed deck weight, and the arch is properly shaped, the arch rib is subjected to pure compression along its whole extension. Both tensile forces along the arch rib and shear forces transversal to it are absent. Bending moments vanish as well. This has made possible the use of masonry for arch bridges, which uses materials such as stone, brick, and concrete that are strong in compression but very weak to tension and shearing. In the following sections, we determine mathematically this optimal arch shape, which turns out to be a parabola. The novelty is that these well-known results are obtained using just basic algebra and trigonometry, without any mention of infinitesimal calculus, including in the demonstration of the absence of shearing forces. Subsequently, the method is extended to cable suspended bridges. [ABSTRACT FROM AUTHOR]

In this work, we study several closely related problems involving chains, conveyor belts, and rockets, which are described and solved without the application of infinitesimal calculus, or even the concept of mathematical limit. On one hand, the novelty lies not in the problems themselves, but in the method used for their solution, which brings them down from more advanced courses of engineering studies to the ambit of early-stage students. On the other hand, they shed new light on old questions and give teachers the chance to discuss subtle matters on energy conservation that have led to some controversy in the recent past. [ABSTRACT FROM AUTHOR]

In the present work, we revisit the issue of the self-trapping dynamical transition at a nonlinear impurity embedded in an otherwise linear lattice. For our Schrödinger chain example, we present rigorous arguments that establish necessary conditions and corresponding parametric bounds for the transition between linear decay and nonlinear persistence of a defect mode. The proofs combine a contraction mapping approach applied to the fully dynamical problem in the case of a 3D-lattice, together with variational arguments for the derivation of parametric bounds for the creation of stationary states associated with the expected fate of the self-trapping dynamical transition. The results are relevant for both power law nonlinearities and saturable ones. The analytical results are corroborated by numerical computations. The latter are performed for cases of different dimension. [ABSTRACT FROM AUTHOR]

An instrument has been designed and constructed for the simultaneous determination of nitrogen dioxide (NO2) and peroxyacetyl nitrate (PAN) in atmospheric samples. The instrument’s design is based on separation by fast gas chromatography (GC) with a 30 ft capillary column (DB-1) followed by detection by luminol chemiluminescence. The chemiluminescent reaction between NO2 or PAN and luminol takes place at the gas–liquid interface on the surface of a solid support. The chemiluminescent emission at 425 nm is detected with a photon counting module. The instrument is controlled by a 1.8 GHz Notebook computer with a WINDOWS 2000 operating system and a custom software application programmed in LABVIEW. Detection limits are in the low parts per trillion (ppt) with a time resolution of 30 s to 1 min. The instrument was operated during the Mexico City Metropolitan Area/Mexico City Megacity 2003 collaborative air quality study. Results for NO2 from this fast GC method were compared with results from a co-located differential optical absorption spectrometer (DOAS) and a tunable diode laser absorption spectromenter (TDLAS). The results support the application of the new luminol-based instrument for atmospheric measurements. [ABSTRACT FROM AUTHOR]

In order to study surface disordering of ice at temperatures below the bulk melting point as a function of depth into the bulk, Car-Parrinello molecular-dynamics simulations of a periodic model of the hexagonal ice (0001) surface were carried out. Partial disorder in the uppermost bilayer was observed at a simulation temperature of 190 K, which is ∼30 K below the estimated bulk melting point, qualitatively validating earlier classical molecular-dynamics studies of this phenomenon. Over 0.5 ps, the time scale of a simulation, there were three particularly useful (and complementary) measures of disorder: The pair distribution function g(r), the distance of the oxygen atoms from the bottommost bilayer, and the distribution of angles φ and θ formed by the molecular dipole vector and the Cartesian axes. Our results set the stage for future studies addressing the effect of the disordered ice surface on heterogeneous atmospheric chemistry. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Examines the development of an electrostatic ion guide in chemical ionization mass spectrometry (CIMS). Transportation of ions over a distance of ten centimeters; Separation of ion from neutral molecules; Effect of ion separation on CIMS detection sensitivity.