11,957 research outputs found
A note on the Penrose junction conditions
Impulsive pp-waves are commonly described either by a distributional
spacetime metric or, alternatively, by a continuous one. The transformation
relating these forms clearly has to be discontinuous, which causes two basic
problems: First, it changes the manifold structure and second, the pullback of
the distributional form of the metric under is not well defined within
classical distribution theory. Nevertheless, from a physical point of view both
pictures are equivalent. In this work, after calculating als well as the
''Rosen''-form of the metric in the general case of a pp-wave with arbitrary
wave profile we give a precise meaning to the term ``physically equivalent'' by
interpreting as the distributional limit of a suitably regularized sequence
of diffeomorphisms. Moreover, it is shown that provides an example of a
generalized coordinate transformation in the sense of Colombeau's generalized
functions.Comment: 9 pages, RevTeX, no figures, final version (typos corrected,
references updated
Orthogonal free quantum group factors are strongly 1-bounded
We prove that the orthogonal free quantum group factors
are strongly -bounded in the sense of Jung. In
particular, they are not isomorphic to free group factors. This result is
obtained by establishing a spectral regularity result for the edge reversing
operator on the quantum Cayley tree associated to , and
combining this result with a recent free entropy dimension rank theorem of Jung
and Shlyakhtenko.Comment: v3: accepted versio
Boundary Stabilization of Quasilinear Maxwell Equations
We investigate an initial-boundary value problem for a quasilinear
nonhomogeneous, anisotropic Maxwell system subject to an absorbing boundary
condition of Silver & M\"uller type in a smooth, bounded, strictly star-shaped
domain of . Imposing usual smallness assumptions in addition to
standard regularity and compatibility conditions, a nonlinear stabilizability
inequality is obtained by showing nonlinear dissipativity and
observability-like estimates enhanced by an intricate regularity analysis. With
the stabilizability inequality at hand, the classic nonlinear barrier method is
employed to prove that small initial data admit unique classical solutions that
exist globally and decay to zero at an exponential rate. Our approach is based
on a recently established local well-posedness theory in a class of
-valued functions.Comment: 22 page
Anisotropic Hydrodynamic Mean-Field Theory for Semiflexible Polymers under Tension
We introduce an anisotropic mean-field approach for the dynamics of
semiflexible polymers under intermediate tension, the force range where a chain
is partially extended but not in the asymptotic regime of a nearly straight
contour. The theory is designed to exactly reproduce the lowest order
equilibrium averages of a stretched polymer, and treats the full complexity of
the problem: the resulting dynamics include the coupled effects of long-range
hydrodynamic interactions, backbone stiffness, and large-scale polymer contour
fluctuations. Validated by Brownian hydrodynamics simulations and comparison to
optical tweezer measurements on stretched DNA, the theory is highly accurate in
the intermediate tension regime over a broad dynamical range, without the need
for additional dynamic fitting parameters.Comment: 22 pages, 9 figures; revised version with additional calculations and
experimental comparison; accepted for publication in Macromolecule
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