Linear groups and computation

We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for this class of groups are surveyed. We illustrate the solution of hard mathematical problems by computer experimentation. Possible avenues for further progress are discussed.     

Computing 2-cocyeles for central extensions and relative difference sets

We present an algorithm to compute H ²(G,U) for a finite group G and finite abelian group U (trivial G-module). The algorithm returns a generating set for the second cohomology group in terms of representative 2-cocycles, which are given explicitly. This information may be used to find presentations for corresponding central extensions of U by G. An application of the algorithm to the construction of relative (4t, 2,4t, 2t) -difference sets is given.     

Participation of incident ion internal energy in molecular O+2-Ar charge-transfer collisions

The O⁺₂—Ar charge-transfer reactions have been investigated for both the X²Π_g and a⁴Π_u states of O⁺₂ in the kinetic energy range of 0.7 to 3.0 keV. Exhibited resonant and non-resonant behavior of the cross sections is consistent with theoretical predictions.     

Study of porosity and stiffness measurement of nanoporous aerogel films with wideband ultrasonic surface waves

Nanoporous aerogel films are of great scientific and commercial interest because of their outstanding potential for application to microelectronic interconnect, associated with low dielectric constant. Of the parameters which describe such aerogel films, density/porosity and stiffness are two of the most critical, but are difficult to measure. This paper shows how measurement of the dispersion of laser-generated surface acoustic wavepackets travelling on submicron-thick aerogel films on silicon substrates allows the density and Young's modulus to be extracted reliably. Particular attention is paid to accuracy of measurements and sensitivity to input data; and a method for extracting measurements on very thin films (<300 nm) is presented.