8,647 research outputs found
Nondispersive solutions to the L2-critical half-wave equation
We consider the focusing -critical half-wave equation in one space
dimension where denotes the
first-order fractional derivative. Standard arguments show that there is a
critical threshold such that all solutions with extend globally in time, while solutions with may develop singularities in finite time.
In this paper, we first prove the existence of a family of traveling waves
with subcritical arbitrarily small mass. We then give a second example of
nondispersive dynamics and show the existence of finite-time blowup solutions
with minimal mass . More precisely, we construct a
family of minimal mass blowup solutions that are parametrized by the energy
and the linear momentum . In particular, our main result
(and its proof) can be seen as a model scenario of minimal mass blowup for
-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page
Theory of Coherent Time-dependent Transport in One-dimensional Multiband Semiconductor Superlattices
We present an analytical study of one-dimensional semiconductor superlattices
in external electric fields, which may be time-dependent. A number of general
results for the (quasi)energies and eigenstates are derived. An equation of
motion for the density matrix is obtained for a two-band model, and the
properties of the solutions are analyzed. An expression for the current is
obtained. Finally, Zener-tunneling in a two-band tight-binding model is
considered. The present work gives the background and an extension of the
theoretical framework underlying our recent Letter [J. Rotvig {\it et al.},
Phys. Rev. Lett. {\bf 74}, 1831 (1995)], where a set of numerical simulations
were presented.Comment: 15 pages, Revtex 3.0, uses epsf, 2 ps figures attache
Electron-vibration interaction in single-molecule junctions: from contact to tunneling regime
Point contact spectroscopy on a H2O molecule bridging Pt electrodes reveals a
clear crossover between enhancement and reduction of the conductance due to
electron-vibration interaction. As single channel models predict such a
crossover at transmission probability of t=0.5, we used shot noise measurements
to analyze the transmission and observed at least two channels across the
junction where the dominant channel has t=0.51+/-0.01 transmission probability
at the crossover conductance, which is consistent with the predictions for
single-channel models.Comment: 4 pages, 1 table, 4 figure
Free Versus Constrained Evolution of the 2+1 Equivariant Wave Map
We compare the numerical solutions of the 2+1 equivariant Wave Map problem
computed with the symplectic, constraint respecting Rattle algorithm and the
well known fourth order Runge-Kutta method. We show the advantages of the
Rattle algorithm for constrained system compared to the free evolution with the
Runge-Kutta method. We also present an expression, which represents the energy
loss due to constraint violation. Taking this expression into account we can
achieve energy conservation for the Runge-Kutta scheme, which is better than
with the Rattle method. Using the symplectic scheme with constraint enforcement
we can reproduce previous calculations of the equivariant case without imposing
the symmetry explicitly, thereby confirming that the critical behaviour is
stable.Comment: 16 pages, 8 figures. Formula for the scaling function on p. 13
corrected and two typos eliminated; otherwise agrees with the published pape
The effects of socioeconomic status and indices of physical environment on reduced birth weight and preterm births in Eastern Massachusetts
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0),
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: Air pollution and social characteristics have been shown to affect indicators of health. While use of spatial methods to estimate exposure to air pollution has increased the power to detect effects, questions have been raised about potential for confounding by social factors.Methods: A study of singleton births in Eastern Massachusetts was conducted between 1996 and 2002 to examine the association between indicators of traffic, land use, individual and area-based socioeconomic measures (SEM), and birth outcomes ( birth weight, small for gestational age and preterm births), in a two-level hierarchical model.Results: We found effects of both individual ( education, race, prenatal care index) and area-based ( median household income) SEM with all birth outcomes. The associations for traffic and land use variables were mainly seen with birth weight, with an exception for an effect of cumulative traffic density on small for gestational age. Race/ethnicity of mother was an important predictor of birth outcomes and a strong confounder for both area-based SEM and indices of physical environment. The effects of traffic and land use differed by level of education and median household income.Conclusion: Overall, the findings of the study suggested greater likelihood of reduced birth weight and preterm births among the more socially disadvantaged, and a greater risk of reduced birth weight associated with traffic exposures. Results revealed the importance of controlling simultaneously for SEM and environmental exposures as the way to better understand determinants of health.This work is supported by the Harvard Environmental Protection Agency (EPA) Center,
Grants R827353 and R-832416, and National Institute for Environmental Health Science (NIEHS) ES-0002
Genetic variation and structure in native populations of the fire ant Solenopsis invicta: evolutionary and demographic implications
We studied population genetic variation and structure in the fire ant Solenopsis invicta using nuclear genotypic and mitochondrial DNA (mtDNA) sequence data obtained from samples collected throughout its native range. Geographic populations are strongly differentiated at both genomes, with such structure more pronounced in Brazil than in Argentina. Higher-level regional structure is evident from the occurrence of isolation-by-distance patterns among populations, the recognition of clusters of genetically similar, geographically adjacent populations by ordination analysis, and the detection of an mtDNA discontinuity between Argentina and Brazil coinciding with a previously identified landform of biogeographical relevance. Multiple lines of evidence from both genomes suggest that the ancestors of the ants we studied resembled extant northern Argentine S. invicta, and that existing Brazilian populations were established more recently by serial long-distance colonizations and/or range expansions. The most compelling evidence for this is the corresponding increase in F-K (a measure of divergence from a hypothetical ancestor) and decrease in genetic diversity with distance from the Corrientes population in northern Argentina. Relatively deep sequence divergence among several mtDNA clades, coupled with geographical partitioning of many of them, suggests prolonged occupation of South America by S. invicta in more-or-less isolated regional populations. Such populations appear, in some cases, to have come into secondary contact without regaining the capacity to freely interbreed. We conclude that nominal S. invicta in its native range comprises multiple entities that are sufficiently genetically isolated and diverged to have embarked on independent evolutionary paths
Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy
Treatment with high energy ionizing radiation is one of the main methods in
modern cancer therapy that is in clinical use. During the last decades, two
main approaches to dose calculation were used, Monte Carlo simulations and
semi-empirical models based on Fermi-Eyges theory. A third way to dose
calculation has only recently attracted attention in the medical physics
community. This approach is based on the deterministic kinetic equations of
radiative transfer. Starting from these, we derive a macroscopic partial
differential equation model for electron transport in tissue. This model
involves an angular closure in the phase space. It is exact for the
free-streaming and the isotropic regime. We solve it numerically by a newly
developed HLLC scheme based on [BerCharDub], that exactly preserves key
properties of the analytical solution on the discrete level. Several numerical
results for test cases from the medical physics literature are presented.Comment: 20 pages, 7 figure
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