1,970 research outputs found
Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes
We consider the following eigenvalue optimization problem: Given a bounded
domain and numbers , ,
find a subset of area for which the first Dirichlet
eigenvalue of the operator is as small as possible.
We prove existence of solutions and investigate their qualitative properties.
For example, we show that for some symmetric domains (thin annuli and dumbbells
with narrow handle) optimal solutions must possess fewer symmetries than
; on the other hand, for convex reflection symmetries are
preserved.
Also, we present numerical results and formulate some conjectures suggested
by them.Comment: 24 pages; 3 figures (as separate files); (shortened previous
version); to appear in Comm. Math. Phy
The plasmonic eigenvalue problem
A plasmon of a bounded domain is a non-trivial
bounded harmonic function on which is
continuous at and whose exterior and interior normal
derivatives at have a constant ratio. We call this ratio a
plasmonic eigenvalue of . Plasmons arise in the description of
electromagnetic waves hitting a metallic particle . We investigate
these eigenvalues and prove that they form a sequence of numbers converging to
one. Also, we prove regularity of plasmons, derive a variational
characterization, and prove a second order perturbation formula. The problem
can be reformulated in terms of Dirichlet-Neumann operators, and as a side
result we derive a formula for the shape derivative of these operators.Comment: 22 pages; replacement 8-March-14: minor corrections; to appear in
Review in Mathematical Physic
Storage-ring measurement of the hyperfine induced 47Ti18+(2s 2p 3P0 -> 2s2 1S0) transition rate
The hyperfine induced 2s 2p 3P0 > 2s2 1S0 transition rate AHFI in
berylliumlike 47Ti18+ was measured. Resonant electron-ion recombination in a
heavy-ion storage ring was employed to monitor the time dependent population of
the 3P0 state. The experimental value AHFI=0.56(3)/s is almost 60% larger than
theoretically predicted.Comment: 4 pages. 3 figures, 1 table, accepted for publication in Physical
Review Letter
Absolute rate coefficients for photorecombination and electron-impact ionization of magnesium-like iron ions from measurements at a heavy-ion storage ring
Rate coefficients for photorecombination (PR) and cross sections for
electron-impact ionization (EII) of Fe forming Fe and
Fe, respectively, have been measured by employing the electron-ion
merged-beams technique at a heavy-ion storage ring. Rate coefficients for PR
and EII of Fe ions in a plasma are derived from the experimental
measurements. Simple parametrizations of the experimentally derived plasma rate
coefficients are provided for use in the modeling of photoionized and
collisionally ionized plasmas. In the temperature ranges where Fe is
expected to form in such plasmas the latest theoretical rate coefficients of
Altun et al. [Astron. Astrophys. 474, 1051 (2007)] for PR and of Dere [Astron.
Astrophys. 466, 771 (2007)] for EII agree with the experimental results to
within the experimental uncertainties. Common features in the PR and EII
resonance structures are identified and discussed.Comment: 12 pages, 6 figures, 3 tables, submitted for publication to Physical
Review
Enhanced dielectronic recombination of lithium-like Ti19+ ions in external ExB fields
Dielectronic recombination(DR) of lithium-like Ti19+(1s2 2s) ions via 2s->2p
core excitations has been measured at the Heidelberg heavy ion storage ring
TSR. We find that not only external electric fields (0 <= Ey <= 280 V/cm) but
also crossed magnetic fields (30 mT <= Bz <= 80 mT) influence the DR via high-n
(2p_j nl)-Rydberg resonances. This result confirms our previous finding for
isoelectronic Cl14+ ions [Bartsch T et al, PRL 82, 3779 (1999)] that
experimentally established the sensitivity of DR to ExB fields. In the present
investigation the larger 2p_{1/2}-2p_{3/2} fine structure splitting of Ti19+
allowed us to study separately the influence of external fields via the two
series of Rydberg DR resonances attached to the 2s -> 2p_{1/2} and 2s ->
2p_{3/2} excitations of the Li-like core, extracting initial slopes and
saturation fields of the enhancement. We find that for Ey > 80 V/cm the field
induced enhancement is about 1.8 times stronger for the 2p_{3/2} series than
for the 2p_{1/2} series.Comment: 10 pages, 3 figures, to be published in Journal of Physics B, see
also http://www.strz.uni-giessen.de/~k
Absolute rate coefficients for photorecombination of berylliumlike and boronlike silicon ions
We report measured rate coefficients for electron-ion recombination for Si10+
forming Si9+ and for Si9+ forming Si8+, respectively. The measurements were
performed using the electron-ion merged-beams technique at a heavy-ion storage
ring. Electron-ion collision energies ranged from 0 to 50 eV for Si9+ and from
0 to 2000 eV for Si10+, thus, extending previous measurements for Si10+ [Orban
et al. 2010, Astrophys. J. 721, 1603] to much higher energies. Experimentally
derived rate coefficients for the recombination of Si9+ and Si10+ ions in a
plasma are presented along with simple parameterizations. These rate
coefficients are useful for the modeling of the charge balance of silicon in
photoionized plasmas (Si9+ and Si10+) and in collisionally ionized plasmas
(Si10+ only). In the corresponding temperature ranges, the experimentally
derived rate coefficients agree with the latest corresponding theoretical
results within the experimental uncertainties.Comment: 17 pages, 7 figures, 3 tables, 66 references, submitted to the J.
Phys. B special issue on atomic and molecular data for astrophysicist
Tests of relativity using a microwave resonator
The frequencies of a cryogenic sapphire oscillator and a hydrogen maser are
compared to set new constraints on a possible violation of Lorentz invariance.
We determine the variation of the oscillator frequency as a function of its
orientation (Michelson-Morley test) and of its velocity (Kennedy-Thorndike
test) with respect to a preferred frame candidate. We constrain the
corresponding parameters of the Mansouri and Sexl test theory to and which is equivalent to the best previous result for the
former and represents a 30 fold improvement for the latter.Comment: 8 pages, 2 figures, submitted to Physical Review Letters (October 3,
2002
Dielectronic Recombination in Photoionized Gas. II. Laboratory Measurements for Fe XVIII and Fe XIX
In photoionized gases with cosmic abundances, dielectronic recombination (DR)
proceeds primarily via nlj --> nl'j' core excitations (Dn=0 DR). We have
measured the resonance strengths and energies for Fe XVIII to Fe XVII and Fe
XIX to Fe XVIII Dn=0 DR. Using our measurements, we have calculated the Fe
XVIII and Fe XIX Dn=0 DR DR rate coefficients. Significant discrepancies exist
between our inferred rates and those of published calculations. These
calculations overestimate the DR rates by factors of ~2 or underestimate it by
factors of ~2 to orders of magnitude, but none are in good agreement with our
results. Almost all published DR rates for modeling cosmic plasmas are computed
using the same theoretical techniques as the above-mentioned calculations.
Hence, our measurements call into question all theoretical Dn=0 DR rates used
for ionization balance calculations of cosmic plasmas. At temperatures where
the Fe XVIII and Fe XIX fractional abundances are predicted to peak in
photoionized gases of cosmic abundances, the theoretical rates underestimate
the Fe XVIII DR rate by a factor of ~2 and overestimate the Fe XIX DR rate by a
factor of ~1.6. We have carried out new multiconfiguration Dirac-Fock and
multiconfiguration Breit-Pauli calculations which agree with our measured
resonance strengths and rate coefficients to within typically better than
<~30%. We provide a fit to our inferred rate coefficients for use in plasma
modeling. Using our DR measurements, we infer a factor of ~2 error in the Fe XX
through Fe XXIV Dn=0 DR rates. We investigate the effects of this estimated
error for the well-known thermal instability of photoionized gas. We find that
errors in these rates cannot remove the instability, but they do dramatically
affect the range in parameter space over which it forms.Comment: To appear in ApJS, 44 pages with 13 figures, AASTeX with postsript
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