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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 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 it appeared as a metastable
state. We have examined the variation of freezing parameters for the
isotropic-nematic transition with temperature and . 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 .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
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