41,412 research outputs found
Kinetics of Open Circuit Processes in Undischarged Li/SOC12 Cells
The kinetics of the heat producing processes in undischarged Li/SOCl2 cells under open circuit conditions were measured by heat-conduction microcalorimetry. The cells studied, Honeywell type G2666 reserve cells, were activated as needed and the rate of open circuit heat output determined as a function of time since activation and temperature. The results at each temperature can be described by an equation of the form q = Bktx where q is the rate of heat output, B is the heat produced per unit of reaction, k and x are empirical constants, and t is the time since activation. Both x and k are found to be functions of temperature; therefore, accelerated testing at elevated temperatures is probably not valid for these cells until the processes involved are better understood
A compactness lemma and its application to the existence of minimizers for the liquid drop model
The ancient Gamow liquid drop model of nuclear energies has had a renewed
life as an interesting problem in the calculus of variations: Find a set
with given volume A that minimizes the sum of its
surface area and its Coulomb self energy. A ball minimizes the former and
maximizes the latter, but the conjecture is that a ball is always a minimizer
-- when there is a minimizer. Even the existence of minimizers for this
interesting geometric problem has not been shown in general. We prove the
existence of the absolute minimizer (over all ) of the energy divided by
(the binding energy per particle). A second result of our work is a general
method for showing the existence of optimal sets in geometric minimization
problems, which we call the `method of the missing mass'. A third point is the
extension of the pulling back compactness lemma from to .Comment: 16 page
Sharp constants in several inequalities on the Heisenberg group
We derive the sharp constants for the inequalities on the Heisenberg group
H^n whose analogues on Euclidean space R^n are the well known
Hardy-Littlewood-Sobolev inequalities. Only one special case had been known
previously, due to Jerison-Lee more than twenty years ago. From these
inequalities we obtain the sharp constants for their duals, which are the
Sobolev inequalities for the Laplacian and conformally invariant fractional
Laplacians. By considering limiting cases of these inequalities sharp constants
for the analogues of the Onofri and log-Sobolev inequalities on H^n are
obtained. The methodology is completely different from that used to obtain the
R^n inequalities and can be (and has been) used to give a new, rearrangement
free, proof of the HLS inequalities.Comment: 30 pages; addition of Corollary 2.3 and some minor changes; to appear
in Annals of Mathematic
Norms of quantum Gaussian multi-mode channels
We compute the norm of a general Gaussian
gauge-covariant multi-mode channel for any , where is a Schatten space. As a consequence, we verify the Gaussian optimizer
conjecture and the multiplicativity conjecture in these cases.Comment: 9 pages; minor changes; to appear in J. Math. Phy
Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality
We give a new proof of certain cases of the sharp HLS inequality. Instead of
symmetric decreasing rearrangement it uses the reflection positivity of
inversions in spheres. In doing this we extend a characterization of the
minimizing functions due to Li and Zhu.Comment: 15 pages; references added and minor change
Maximizers for the Stein-Tomas inequality
We give a necessary and sufficient condition for the precompactness of all
optimizing sequences for the Stein-Tomas inequality. In particular, if a
well-known conjecture about the optimal constant in the Strichartz inequality
is true, we obtain the existence of an optimizer in the Stein-Tomas inequality.
Our result is valid in any dimension.Comment: 37 page
Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
We show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schrödinger-like operators remain true, with possibly different constants, when the critical Hardy-weight C │x│^(-2) is subtracted from the Laplace operator. We do so by first establishing a Sobolev inequality for such operators. Similar results are true for fractional powers of the Laplacian and the Hardy-weight and, in particular, for relativistic Schrödinger operators. We also allow for the inclusion of magnetic vector potentials. As an application, we extend, for the first time, the proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Zɑ = 2/π, for ɑ less than some critical value
Electron omnidirectional intensity contours in the earth's outer radiation zone at the magnetic equator
Omnidirectional electron intensities in the outer belt at earths magnetic equato
Single molecule photon counting statistics for quantum mechanical chromophore dynamics
We extend the generating function technique for calculation of single
molecule photon emission statistics [Y. Zheng and F. L. H. Brown, Phys. Rev.
Lett., 90,238305 (2003)] to systems governed by multi-level quantum dynamics.
This opens up the possibility to study phenomena that are outside the realm of
purely stochastic and mixed quantum-stochastic models. In particular, the
present methodology allows for calculation of photon statistics that are
spectrally resolved and subject to quantum coherence. Several model
calculations illustrate the generality of the technique and highlight
quantitative and qualitative differences between quantum mechanical models and
related stochastic approximations. Calculations suggest that studying photon
statistics as a function of photon frequency has the potential to reveal more
about system dynamics than the usual broadband detection schemes.Comment: Submitted to the Journal of Physical Chemistr
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