Similarity solutions of Reaction-Diffusion equation with space- and time-dependent diffusion and reaction terms

We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction-diffusion systems. Several representative examples of exactly solvable reaction-diffusion equations are presented.Comment: 11 pages, 4 figure

Apparatus for production of ultrapure amorphous metals utilizing acoustic cooling

Amorphous metals are produced by forming a molten unit of metal and deploying the unit into a bidirectional acoustical levitating field or by dropping the unit through a spheroidizing zone, a slow quenching zone, and a fast quenching zone in which the sphere is rapidly cooled by a bidirectional jet stream created in the standing acoustic wave field produced between a half cylindrical acoustic driver and a focal reflector or a curved driver and a reflector. The cooling rate can be further augmented first by a cryogenic liquid collar and secondly by a cryogenic liquid jacket surrounding a drop tower. The molten unit is quenched to an amorphous solid which can survive impact in a unit collector or is retrieved by a vacuum chuck

Superradiant effects on pulse propagation in resonant media

Adopting the so-called genealogical construction, the eigenstates of collective operators can be expressed corresponding to a specified mode for an N-atom system in terms of those for an (N-1)-atom system. Matrix element of a collective operator of an arbitrary mode is presented which can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME was obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups was then introduced. This gave a simple and systematic way of calculating the RME. Results show explicitly the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes and clears up the chief difficulty encounted in the problem of N two-level atoms, spread over large regions, interacting with a multimode radiation field

Xantusia henshawi

Number of Pages: 2Integrative BiologyGeological Science

Contactless pellet fabrication

A small object is coated by holding it in the pressure well of an acoustic standing wave pattern, and then applying a mist of liquid coating material at low velocity into the pressure well. The pressure gradient within the well forces the mist particles to be pushed against the object. A lower frequency acoustic wave also can be applied to the coated object, to vibrate it so as to evenly distribute the coated material. The same lower frequency vibrations can be applied to an object in the shape of a hollow sphere, to center the inner and outer surfaces of the sphere while it remains suspended