804 research outputs found
A small transitive family of continuous functions on the Cantor set
In this paper we show that, when we iteratively add Sacks reals to a model of
ZFC we have for every two reals in the extension a continuous function defined
in the ground model that maps one of the reals onto the other.Comment: 11 page
Resonant Generation of Topological Modes in Trapped Bose Gases
Trapped Bose atoms cooled down to temperatures below the Bose-Einstein
condensation temperature are considered. Stationary solutions to the
Gross-Pitaevskii equation (GPE) define the topological coherent modes,
representing nonground-state Bose-Einstein condensates. These modes can be
generated by means of alternating fields whose frequencies are in resonance
with the transition frequencies between two collective energy levels
corresponding to two different topological modes. The theory of resonant
generation of these modes is generalized in several aspects: Multiple-mode
formation is described; a shape-conservation criterion is derived, imposing
restrictions on the admissible spatial dependence of resonant fields; evolution
equations for the case of three coherent modes are investigated; the complete
stability analysis is accomplished; the effects of harmonic generation and
parametric conversion for the topological coherent modes are predicted. All
considerations are realized both by employing approximate analytical methods as
well as by numerically solving the GPE. Numerical solutions confirm all
conclusions following from analytical methods.Comment: One reference modifie
Metallo-dielectric diamond and zinc-blende photonic crystals
It is shown that small inclusions of a low absorbing metal can have a
dramatic effect on the photonic band structure. In the case of diamond and
zinc-blende photonic crystals, several complete photonic band gaps (CPBG's) can
open in the spectrum, between the 2nd-3rd, 5th-6th, and 8th-9th bands. Unlike
in the purely dielectric case, in the presence of small inclusions of a low
absorbing metal the largest CPBG for a moderate dielectric constant
(epsilon<=10) turns out to be the 2nd-3rd CPBG. The 2nd-3rd CPBG is the most
important CPBG, because it is the most stable against disorder. For a diamond
and zinc-blende structure of nonoverlapping dielectric and metallo-dielectric
spheres, a CPBG begins to decrease with an increasing dielectric contrast
roughly at the point where another CPBG starts to open--a kind of gap
competition. A CPBG can even shrink to zero when the dielectric contrast
increases further. Metal inclusions have the biggest effect for the dielectric
constant 2<=epsilon<=12, which is a typical dielectric constant at near
infrared and in the visible for many materials, including semiconductors and
polymers. It is shown that one can create a sizeable and robust 2nd-3rd CPBG at
near infrared and visible wavelengths even for a photonic crystal which is
composed of more than 97% low refractive index materials (n<=1.45, i.e., that
of silica glass or a polymer). These findings open the door for any
semiconductor and polymer material to be used as genuine building blocks for
the creation of photonic crystals with a CPBG and significantly increase the
possibilities for experimentalists to realize a sizeable and robust CPBG in the
near infrared and in the visible. One possibility is a construction method
using optical tweezers, which is analyzed here.Comment: 25 pp, 23 figs, RevTex, to appear in Phys Rev B. For more information
look at
http://www.amolf.nl/research/photonic_materials_theory/moroz/moroz.htm
Grain-Boundary Structural Relaxation in Thin-Film Photovoltaics
Grain boundaries play an important role in the efficiency of thin-film photovoltaics, where the absorber layer is invariably polycrystalline. Density-functional-theory simulations have previously identified a “self-healing” mechanism in Sb2Se3 that passivates the grain boundaries. During “self-healing,” extensive structural relaxation at the grain boundary removes the band-gap electronic defect states that give rise to high carrier recombination rates. In this work, lattice imaging in a transmission electron microscope is used to uncover evidence for the theoretically proposed structural relaxation in Sb2Se3. The strain measured along the [010] crystal direction is found to be dependent on the nature of the grain-boundary plane. For a (010) grain boundary, the strain and structural relaxation is minimal, since no covalent bonds are broken by termination of the grain. On the other hand, strains of up to approximately 4% extending approximately 2 nm into the grain interior are observed for a (041) grain boundary, where grain termination results in significant structural relaxation due to the ideal atomic coordination being disrupted. These results are consistent with theory and suggest that Sb2Se3 may have a high level of grain-boundary-defect tolerance
Obesity and Breast Cancer Metastasis across Genomic Subtypes
Background: Obese women have higher risk of aggressive breast tumors and distant metastasis. However, obesity has rarely been assessed in association with metastasis in diverse populations. Methods: In the Carolina Breast Cancer Study Phase 3 (2008–2013), waist-to-hip ratio (WHR), body mass index (BMI), and molecular subtype [PAM50 risk-of-recurrence (ROR) score] were assessed. Obesity measures were evaluated in association with metastasis within five years of diagnosis, overall and stratified by race and ROR score. Absolute risk of metastasis and risk differences between strata were calculated using the Kaplan–Meier estimator, adjusted for age, grade, stage, race, and ER status. Relative frequency of metastatic site and multiplicity were estimated in association with obesity using generalized linear models. Results: High-WHR was associated with higher risk of metastasis (5-year risk difference, RD, 4.3%; 95% confidence interval, 2.2–6.5). It was also associated with multiple metastases and metastases at all sites except brain. The 5-year risk of metastasis differed by race (11.2% and 6.9% in Black and non-Black, respectively) and ROR score (19.5% vs. 6.6% in high vs. low-to-intermediate ROR-PT). Non-Black women and those with low-to-intermediate ROR scores had similar risk in high- and low-WHR strata. However, among Black women and those with high ROR, risk of metastasis was elevated among high-WHR (RDBlack/non-Black = 4.6%, RDHigh/Low-Int = 3.1%). Patterns of metastasis were similar by BMI. Conclusions: WHR is associated with metastatic risk, particularly among Black women and those with high-risk tumors. Impact: Understanding how risk factors for metastasis interact may help in tailoring care plans and surveillance among patients with breast cancer
Homeownership and parenting practices: Evidence from the community advantage panel
This study examines whether there is a significant relationship between homeownership and engaged parenting practices among low- and moderate-income households. Using analytic methods which account for selection effects and clustering, we test whether homeownership can act as a protective factor against parental disengagement from children. Controlling for individual characteristics, analyses demonstrate that homeowners are more likely than renters to demonstrate engaged parenting behaviors such as organizing structured activities for their children. While renters are more likely to read to their children, the children of homeowners spend less time watching television and playing video games. Implications for low-income housing policy are discussed in light of these findings
Substructures in lens galaxies: PG1115+080 and B1555+375, two fold configurations
We study the anomalous flux ratio which is observed in some four-image lens
systems, where the source lies close to a fold caustic. In this case two of the
images are close to the critical curve and their flux ratio should be equal to
unity, instead in several cases the observed value differs significantly. The
most plausible solution is to invoke the presence of substructures, as for
instance predicted by the Cold Dark Matter scenario, located near the two
images. In particular, we analyze the two fold lens systems PG1115+080 and
B1555+375, for which there are not yet satisfactory models which explain the
observed anomalous flux ratios. We add to a smooth lens model, which reproduces
well the positions of the images but not the anomalous fluxes, one or two
substructures described as singular isothermal spheres. For PG1115+080 we
consider a smooth model with the influence of the group of galaxies described
by a SIS and a substructure with mass as well as a
smooth model with an external shear and one substructure with mass . For B1555+375 either a strong external shear or two substructures
with mass reproduce the data quite well.Comment: 26 pages, updated bibliography, Accepted for publication in
Astrophysics & Space Scienc
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