41,007 research outputs found
Parabolic bundles and representations of the fundamental group
Let X be as smooth complex projective variety with Neron-Severi group
isomorphic to Z, and D an irreducible divisor with normal crossing
singularities. Assume r is equal to 2 or 3. We prove that if the fundamental
group of X doesn't have irreducible PU(r) representations, then the fundamental
group of X-D doesn't have irreducible U(r) representations. The proof uses the
non-existence of certain stable parabolic bundles. We also obtain a similar
result for GL(2) when D is smooth and X is a complex surface.Comment: 13 pages, 1 figure, LaTeX2
Test of the fluctuation theorem for stochastic entropy production in a nonequilibrium steady state
We derive a simple closed analytical expression for the total entropy
production along a single stochastic trajectory of a Brownian particle
diffusing on a periodic potential under an external constant force. By
numerical simulations we compute the probability distribution functions of the
entropy and satisfactorily test many of the predictions based on Seifert's
integral fluctuation theorem. The results presented for this simple model
clearly illustrate the practical features and implications derived from such a
result of nonequilibrium statistical mechanics.Comment: Accepted in Phys. Rev.
Ill-posedness in the Einstein equations
It is shown that the formulation of the Einstein equations widely in use in
numerical relativity, namely, the standard ADM form, as well as some of its
variations (including the most recent conformally-decomposed version), suffers
from a certain but standard type of ill-posedness. Specifically, the norm of
the solution is not bounded by the norm of the initial data irrespective of the
data. A long-running numerical experiment is performed as well, showing that
the type of ill-posedness observed may not be serious in specific practical
applications, as is known from many numerical simulations.Comment: 13 pages, 3 figures, accepted for publication in Journal of
Mathematical Physics (to appear August 2000
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