Implications of pressure diffusion for shock waves

The report deals with the possible implications of pressure diffusion for shocks in one dimensional traveling waves in an ideal gas. From this new hypothesis all aspects of such shocks can be calculated except shock thickness. Unlike conventional shock theory, the concept of entropy is not needed or used. Our analysis shows that temperature rises near a shock, which is of course an experimental fact; however, it also predicts that very close to a shock, density increases faster than pressure. In other words, a shock itself is cold

The Structure and Freezing of fluids interacting via the Gay-Berne (n-6) potentials

We have calculated the pair correlation functions of a fluid interacting via the Gay-Berne(n-6) pair potentials using the \PY integral equation theory and have shown how these correlations depend on the value of n which measures the sharpness of the repulsive core of the pair potential. These results have been used in the density-functional theory to locate the freezing transitions of these fluids. We have used two different versions of the theory known as the second-order and the modified weighted density-functional theory and examined the freezing of these fluids for $8 \leq n \leq 30$ and in the reduced temperature range lying between 0.65 and 1.25 into the nematic and the smectic A phases. For none of these cases smectic A phase was found to be stabilized though in some range of temperature for a given $n$ it appeared as a metastable state. We have examined the variation of freezing parameters for the isotropic-nematic transition with temperature and $n$. We have also compared our results with simulation results wherever they are available. While we find that the density-functional theory is good to study the freezing transitions in such fluids the structural parameters found from the \PY theory need to be improved particularly at high temperatures and lower values of $n$.Comment: 21 Pages (in RevTex4), 6 GIF and 4 Postscript format Fig

Enumeration of Linear Transformation Shift Registers

We consider the problem of counting the number of linear transformation shift registers (TSRs) of a given order over a finite field. We derive explicit formulae for the number of irreducible TSRs of order two. An interesting connection between TSRs and self-reciprocal polynomials is outlined. We use this connection and our results on TSRs to deduce a theorem of Carlitz on the number of self-reciprocal irreducible monic polynomials of a given degree over a finite field.Comment: 16 page