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    Reply to "Comment(s) on `Preacceleration without radiation: The non-existence of preradiation phenomenon," by J. D. Jackson [Am. J. Phys. 75, 844-845 (2007)] and V. Hnizdo [Am. J. Phys. 75, 845-846 (2007)

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    This paper replies the comments by J. D. Jackson [Am. J. Phys. 75, 844-845 (2007)] and V. Hnizdo [Am. J. Phys. 75, 845-846 (2007)].Comment: 9 pages. See also the related paper: "E. Eriksen and O. Gron, Does preradiation exist? [Phys. Scr. 76, 60-63 (2007)].

    Preacceleration without radiation: the non-existence of preradiation phenomenon

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    An unexpected prediction of classical electrodynamics is that a charge can accelerate before a force is applied. We would expect that a preaccelerated charge would radiate so that there would be spontaneous preradiation, an acausal phenomenon. We reexamine the subtle relation between the Larmor formula for the power radiated by a point charge and the Abraham-Lorentz equation and find that for well-behaved external forces acting for finite times, the charge does not radiate in time intervals where there is preacceleration. That is, for these forces preradiation does not exist even though the charge is preaccelerated. The radiative energy is emitted only in time intervals when the external force acts on the charge.Comment: Equation (37) of the published paper in AJP has been correcte

    Gas-phase and heat-exchange effects on the ignition of high- and low-exothermicity porous solids subject to constant heating

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    This article investigates the ignition of low-exothermicity reactive porous solids exposed to a maintained source of heat (hotspot), without oxygen limitation. The gas flow within the solid, particularly in response to pressure gradients (Darcy’s law), is accounted for. Numerical experiments related to the ignition of low-exothermicity porous materials are presented. Gas and solid products of reaction are included. The first stage of the paper examines the (pseudo-homogeneous) assumption of a single temperature for both phases, amounting to an infinite rate of heat exchange between the two. Isolating the effect of gas production and flow in this manner, the effect of each on the ignition time is studied. In such cases, ignition is conveniently defined by the birth of a self-sustained combustion wave. It is found that gas production decreases the ignition time, compared to equivalent systems in which the gas-dynamic problem is effectively neglected. The reason for this is quite simple; the smaller heat capacity of the gas allows the overall temperature to attain a higher value in a similar time, and so speeds up the ignition process. Next, numerical results using a two-temperature (heterogeneous) model, allowing for local heat exchange between the phases, are presented. The pseudo-homogeneous results are recovered in the limit of infinite heat exchange. For a finite value of heat exchange, the ignition time is lower when compared to the single-temperature limit, decreasing as the rate of heat exchange decreases. However, the decrease is only mild, of the order of a few percent, indicating that the pseudo-homogeneous model is in fact a rather good approximation, at least for a constant heat-exchange rate. The relationships between the ignition time and a number of physico-chemical parameters of the system are also investigated

    Re-introduction of the Mallorcan midwife toad, Mallorca, Spain

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    The Mallorcan midwife toad (Alytes muletensis, Sanchíz & Alcover, 1977) or ferreret was first described in the 1970s as Baleaphryne muletensis from upper Pleistocene fossils, and was considered extinct. The discovery of live tadpoles in 1980 led to further research which confirmed the species as extant and endemic to Mallorca (Mayol & Alcover, 1981). Subfossils suggest that the species was once widespread across the island, but today it is confined to a few gorges within the Serra de Tramuntana mountains in the north-west part of the island. There are currently about 34 populations within the mountains and adjacent areas (16 original wild populations plus 18 re-introductions). These are largely isolated from each other by physiographic barriers, but there is little evidence of any inbreeding depression. Re-introduction of captive bred toads started in 1989 and it is estimated that about 25% of the wild toads stem from captive bred stock. The successful re-introduction program contributed to the downgrading of the species from ‘Critically Endangered’ to ‘Vulnerable’ in the Global Amphibian Assessment of 2004. There is little evidence that wild populations are continuing to decline, but the recent discovery of chytridiomycosis in four populations gives cause for concern

    Correlation inequalities for noninteracting Bose gases

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    For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0 independent of the number of particles we derive the inequalities _N < _{N+1}, _N _N _N for i\neq j, \partial _N/\partial \beta >0 and ^+_N _N. Here N_i is the occupation number of the ith eigenstate of H^0, \beta is the inverse temperature and the superscript + refers to adding an extra level to those of H^0. The results follow from the convexity of the N-particle free energy as a function of N.Comment: a further inequality adde

    Equidistributing grids

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