A simplified model for the process of steady burning of a stationary droplet of fuel in an oxidizing atmosphere has been examined. Explicit expressions have been obtained for the burning rate of the fuel droplet, for the temperature at the flame front, and for the radius of the combustion surface. The principal assumptions on which our analysis is based are: the flame front is established at a spherical surface surrounding the drop; the rates of delivery of fuel and oxygen to this surface are in stoichionletric proportions; the rates of reaction at the flame front are fast compared to the rates of delivery of conlbustible gases. Our analysis is an extension and generalization of the work of G. A. E. Godsave. We are able to delete several of Godsave's restrictive assumptions by use of an efficient lllethod for forlllulating the problelll in which only integrated forms appear for the expressions of conservation of mass and energy. Our theoretical forlllulas provide a satisfactory correlation of Godsave's experilllental results.N OInencla ture radial distance from center of drop temperature standard reference temperature (usually 298.16 K) time density of g-as mixture density of liquid fuel specific heat at constant pressure of gaseous species K specific heat of liquid fuel thermal conductivitv specific latent heat ~f vaporization of fuel binary diffusion coefficient for species K weight fraction of species K in gaseous mixture mass, rate of flow of fuel vapor specific enthalpy of species K at temperaturc '1' rhK/rhF, ratio of mass rate of flow of species K to thc mass, rate of flow of fuel vapor
As a prerequisite for the evaluation of third- and fourth-order perturbation energies of a rotating-vibrating polyatomic molecule, we derive here an appropriate Schroedinger equation and give a preliminary discussion of a useful contact transformation of the Hamiltonian.
Caustics are complex physical phenomena resulting from the projection of light rays being reflected or refracted by a curved surface. In this work, we address the problem of classifying and removing caustics from images and propose a novel solution based on two Convolutional Neural Networks (CNNs): SalienceNet and DeepCaustics. Caustics result in changes in illumination which are continuous in nature, therefore the first network is trained to produce a classification of caustics which is represented as a saliency map of the likelihood of caustics occurring at a pixel. In applications where caustic removal is essential, the second network is trained to generate a caustic-free image. It is extremely hard to generate real ground truth for caustics. We demonstrate how synthetic caustic data can be used for training in such cases, and then transfer the learning to real data. To the best of our knowledge, out of the handful of techniques which have been proposed this is the first time that the complex problem of caustic removal has been reformulated and addressed as a classification and learning problem. This work is motivated by the real-world challenges in underwater archaeology.
The calculations of third- and fourth-order rotation-vibration energies of a general polyatomic molecule are herein continued with a discussion of the zero-, first-, second-, and third-order transformed Hamiltonians.
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