9,427 research outputs found
Boundary Harnack estimates in slit domains and applications to thin free boundary problems
We provide a higher order boundary Harnack inequality for harmonic functions
in slit domains. As a corollary we obtain the regularity of the free
boundary in the Signorini problem near non-degenerate points
The two membranes problem for different operators
We study the two membranes problem for different operators, possibly
nonlocal. We prove a general result about the H\"older continuity of the
solutions and we develop a viscosity solution approach to this problem. Then we
obtain regularity of the solutions provided that the orders of
the two operators are different. In the special case when one operator
coincides with the fractional Laplacian, we obtain the optimal regularity and a
characterization of the free boundary
Is H3+ cooling ever important in primordial gas?
Studies of the formation of metal-free Population III stars usually focus
primarily on the role played by H2 cooling, on account of its large chemical
abundance relative to other possible molecular or ionic coolants. However,
while H2 is generally the most important coolant at low gas densities, it is
not an effective coolant at high gas densities, owing to the low critical
density at which it reaches local thermodynamic equilibrium (LTE) and to the
large opacities that develop in its emission lines. It is therefore possible
that emission from other chemical species may play an important role in cooling
high density primordial gas. A particularly interesting candidate is the H3+
molecular ion. This ion has an LTE cooling rate that is roughly a billion times
larger than that of H2, and unlike other primordial molecular ions such as H2+
or HeH+, it is not easily removed from the gas by collisions with H or H2. It
is already known to be an important coolant in at least one astrophysical
context -- the upper atmospheres of gas giants -- but its role in the cooling
of primordial gas has received little previous study. In this paper, we
investigate the potential importance of H3+ cooling in primordial gas using a
newly-developed H3+ cooling function and the most detailed model of primordial
chemistry published to date. We show that although H3+ is, in most
circumstances, the third most important coolant in dense primordial gas (after
H2 and HD), it is nevertheless unimportant, as it contributes no more than a
few percent of the total cooling. We also show that in gas irradiated by a
sufficiently strong flux of cosmic rays or X-rays, H3+ can become the dominant
coolant in the gas, although the size of the flux required renders this
scenario unlikely to occur.Comment: 60 pages, 22 figures. Submitted to MNRA
Statistics of conductance and shot-noise power for chaotic cavities
We report on an analytical study of the statistics of conductance, , and
shot-noise power, , for a chaotic cavity with arbitrary numbers of
channels in two leads and symmetry parameter . With the theory
of Selberg's integral the first four cumulants of and first two cumulants
of are calculated explicitly. We give analytical expressions for the
conductance and shot-noise distributions and determine their exact asymptotics
near the edges up to linear order in distances from the edges. For a
power law for the conductance distribution is exact. All results are also
consistent with numerical simulations.Comment: 7 pages, 3 figures. Proc. of the 3rd Workshop on Quantum Chaos and
Localisation Phenomena, Warsaw, Poland, May 25-27, 200
Lie algebra and invariant tensor technology for g2
Proceeding in analogy with su(n) work on lambda matrices and f- and
d-tensors, this paper develops the technology of the Lie algebra g2, its seven
dimensional defining representation gamma and the full set of invariant tensors
that arise in relation thereto. A comprehensive listing of identities involving
these tensors is given. This includes identities that depend on use of
characteristic equations, especially for gamma, and a good body of results
involving the quadratic, sextic and (the non-primitivity of) other Casimir
operators of g2.Comment: 29 pages, LaTe
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