Mixed polyvalent-monovalent metal coating for carbon-graphite fibers

An improved coating of gasification catalyst for carbon-graphite fibers is provided comprising a mixture of a polyvalent metal such as calcium and a monovalent metal such as lithium. The addition of lithium provides a lighter coating and a more flexible coating when applied to a coating of a carboxyl containing resin such as polyacrylic acid since it reduces the crosslink density. Furthermore, the presence of lithium provides a glass-like substance during combustion which holds the fiber together resulting in slow, even combustion with much reduced evolution of conductive fragments. The coated fibers are utilized as fiber reinforcement for composites

A Bubble Rising in Viscous Fluid: Lagrange's Equations For Motion at a High Reynolds Number

A gas bubble rising steadily in a pure liquid otherwise at rest at a moderate Weber number is, to a good approximation, of oblate spheroidal shape. Previous analytical calculations of that shape at high Reynolds numbers have ignored viscosity. This paper shows that if one includes viscosity by incorporating Rayleigh's dissipation integral in Lagrange's equations, then the speed of rise is that given by Moore, and the shape is that found for inviscid flow by El Sawi using the virial integral and by Benjamin using Hamiltonian theory

What Really is a Continuous Function?

There are surprisingly many essentially different definitions of continuity even of a real function of one real variable. This paper shows that the definitions in various textbooks published from 1893 to 1992 have some very different consequences, and that one error that was noticed and corrected in 1904 reappeared in a 1907 book

Bubble Rise in a Liquid With a Surfactant Gas, in Particular Carbon Dioxide

When a gas bubble rises in a surfactant solution, the velocity field and the distribution of surfactant affect each other. This paper gives the theory for small Reynolds and internal Peclet numbers if the surfactant is gaseous or volatile, if its mass flux across the bubble and around its surface dominates its mass flux through the bulk liquid, and if slowness of both adsorption and convective diffusion must be allowed for. The theory is tested on the experiments of Kelsall et al. (J. Chem. Soc. Faraday Trans., vol. 92, 1996, p. 3879). Their bubbles rose as expected in a pure liquid until the apparatus was opened to the atmosphere. That significantly slowed the bubbles down. The effect is so sensitive to small concentrations of slowly adsorbing or reacting surfactants that atmospheric carbon dioxide could have caused it, even though it alters the equilibrium surface tension by less than four parts per million in pure air

The Axisymmetric Prandtl-Batchelor Eddy Behind a Circular Disc in a Uniform Stream

Analytical support is given to Fornberg's numerical evidence that the steady axially symmetric flow of a uniform stream past a bluff body has a wake eddy which tends towards a large Hill's spherical vortex as the Reynolds number tends to infinity. The viscous boundary layer around the eddy resembles that around a liquid drop rising in a liquid, especially if the body is a circular disc, so that the boundary layer on it does not separate. This makes it possible to show that if the first-order perturbation of the eddy shape from a sphere is small then the eddy diameter is of order R1/5 times the disc diameter, where R is the Reynolds number based on the disc diameter. Previous authors had suggested R1/3 and ln R, but they appear to have made unjustified assumptions

Fortran 95 for Fortran 77 Users

For 50 years Fortran has been a computer language used mainly by engineers and scientists (but by few computer scientists), mainly for numerical work. Five versions were standardised and are commonly referred to as f66, f77, f90, f95 and f2003 to indicate the year. F95 has superseded f90, and no f2003 compilers exist yet. These notes concentrate on f77 and f95. They are written to show f77 users a number of the f95 features that I found so useful that I gave up f77 except when writing a program for someone with no f95 compiler. Some new features make programming easier, some allow the machine to detect bugs that f77 compilers cannot, and some make programs easier to read

Reducing Parabolic Partial Differential Equations to Canonical Form

A simple method of reducing a parabolic partial differential equation to canonical form if it has only one term involving second derivatives is the following: find the general solution of the first-order equation obtained by ignoring that term and then seek a solution of the original equation which is a function of one more independent variable. Special cases of the method have been given before, but are not well known. Applications occur in fluid mechanics and the theory of finance, where the Black-Scholes equation yields to the method, and where the variable corresponding to time appears to run backwards, but there is an information-theoretic reason why it should

The Axisymmetric Prandtl-Batchelor Eddy Behind a Circular Disc in a Uniform Stream

Analytical support is given to Fornberg's numerical evidence that the steady axially symmetric flow of a uniform stream past a bluff body has a wake eddy which tends towards a large Hill's spherical vortex as the Reynolds number tends to infinity. The viscous boundary layer around the eddy resembles that around a liquid drop rising in a liquid, especially if the body is a circular disc, so that the boundary layer on it does not separate. This makes it possible to show that if the first-order perturbation of the eddy shape from a sphere is small then the eddy diameter is of order R1/5 times the disc diameter, where R is the Reynolds number based on the disc diameter. Previous authors had suggested R1/3 and ln R, but they appear to have made unjustified assumptions

Propagation of the First Flames in Type Ia Supernovae

We consider the competition of the different physical processes that can affect the evolution of a flame bubble in a Type Ia supernovae -- burning, turbulence and buoyancy. Even in the vigorously turbulent conditions of a convecting white dwarf, thermonuclear burning that begins at a point near the center (within 100 km) of the star is dominated by the spherical laminar expansion of the flame, until the burning region reaches kilometers in size. Consequently flames that ignite in the inner ~20 km promptly burn through the center, and flame bubbles anywhere must grow quite large--indeed, resolvable by large-scale simulations of the global system--for significant motion or deformation occur. As a result, any hot-spot that successfully ignites into a flame can burn a significant amount of white dwarf material. This potentially increases the stochastic nature of the explosion compared to a scenario where a simmering progenitor can have small early hot-spots float harmlessly away. Further, the size where the laminar flame speed dominates other relevant velocities sets a characteristic scale for fragmentation of larger flame structures, as nothing--by definition--can easily break the burning region into smaller volumes. This makes possible the development of semi-analytic descriptions of the earliest phase of the propagation of burning in a Type Ia supernovae, which we present here. Our analysis is supported by fully resolved numerical simulations of flame bubbles.Comment: 33 pages, 14 figures, accepted for publication in Ap

The MMT API: A Generic MKM System

The MMT language has been developed as a scalable representation and interchange language for formal mathematical knowledge. It permits natural representations of the syntax and semantics of virtually all declarative languages while making MMT-based MKM services easy to implement. It is foundationally unconstrained and can be instantiated with specific formal languages. The MMT API implements the MMT language along with multiple backends for persistent storage and frontends for machine and user access. Moreover, it implements a wide variety of MMT-based knowledge management services. The API and all services are generic and can be applied to any language represented in MMT. A plugin interface permits injecting syntactic and semantic idiosyncrasies of individual formal languages.Comment: Conferences on Intelligent Computer Mathematics (CICM) 2013 The final publication is available at http://link.springer.com