Stability and symmetry-breaking bifurcation for the ground states of a NLS with a δ′\delta^\prime interaction

We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) $\delta^\prime$ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) $\omega$. More precisely, there exists a critical value \om^* of the nonlinear eigenvalue \om, such that: if \om_0 < \om < \om^*, then there is a single ground state and it is an odd function; if \om > \om^* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for \om < \om^*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (\om =\om^*+0), ground states are stable if $\mu$ does not exceed a value $\mu^\star$ that lies between 2 and 2.5, and become unstable for $\mu > \mu^*$. Finally, for $\mu > 2$ and \om \gg \om^*, all ground states are unstable. The branch of odd ground states for \om \om^*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non standard techniques have to be used to establish the needed properties of linearization operators.Comment: 46 pages, 5 figure

Decay of kaonium in a chiral approach

The decay of the K+K- hadronic atom kaonium is investigated non-perturbatively using meson-meson interaction amplitudes taken from leading order chiral perturbation theory in an approach adapted from that proposed by Oller and Oset [18]. The Kudryavtsev-Popov eigenvalue equation is solved numerically for the energy shift and decay width due to strong interactions in the 1s state. These calculations introduce a cutoff ~ 1.4 GeV in O(4) momentum space that is necessary to regulate divergent loop contributions to the meson-meson scattering amplitudes in the strong-interaction sector. One finds lifetimes of 2.2 \pm 0.9 x 10-18s for the ground state of kaonium.Comment: 10 pages, 2 figures. Added new reference to isospin-breaking of scattering lengt

Potential-density pairs for axisymmetric galaxies: the influence of scalar fields

We present a formulation for potential-density pairs to describe axisymmetric galaxies in the Newtonian limit of scalar-tensor theories of gravity. The scalar field is described by a modified Helmholtz equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. The net gravitational force is given by two contributions: the standard Newtonian potential plus a term stemming from massive scalar fields. General solutions have been found for axisymmetric systems and the multipole expansion of the Yukawa potential is given. In particular, we have computed potential-density pairs of galactic disks for an exponential profile and their rotation curves.Comment: 8 pages, no figures, corrected version to the one that will appear in Gen. Relativ. Gravit., where a small typo in eq. (13) is presen

Scaling analysis of electron transport through metal-semiconducting carbon nanotube interfaces: Evolution from the molecular limit to the bulk limit

We present a scaling analysis of electronic and transport properties of metal-semiconducting carbon nanotube interfaces as a function of the nanotube length within the coherent transport regime, which takes fully into account atomic-scale electronic structure and three-dimensional electrostatics of the metal-nanotube interface using a real-space Green's function based self-consistent tight-binding theory. As the first example, we examine devices formed by attaching finite-size single-wall carbon nanotubes (SWNT) to both high- and low- work function metallic electrodes through the dangling bonds at the end. We analyze the nature of Schottky barrier formation at the metal-nanotube interface by examining the electrostatics, the band lineup and the conductance of the metal-SWNT molecule-metal junction as a function of the SWNT molecule length and metal-SWNT coupling strength. We show that the confined cylindrical geometry and the atomistic nature of electronic processes across the metal-SWNT interface leads to a different physical picture of band alignment from that of the planar metal-semiconductor interface. We analyze the temperature and length dependence of the conductance of the SWNT junctions, which shows a transition from tunneling- to thermal activation-dominated transport with increasing nanotube length. The temperature dependence of the conductance is much weaker than that of the planar metal-semiconductor interface due to the finite number of conduction channels within the SWNT junctions. We find that the current-voltage characteristics of the metal-SWNT molecule-metal junctions are sensitive to models of the potential response to the applied source/drain bias voltages.Comment: Minor revision to appear in Phys. Rev. B. Color figures available in the online PRB version or upon request to: [email protected]

Universally Coupled Massive Gravity, II: Densitized Tetrad and Cotetrad Theories

Einstein's equations in a tetrad formulation are derived from a linear theory in flat spacetime with an asymmetric potential using free field gauge invariance, local Lorentz invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. These results are adapted to produce universally coupled massive variants of Einstein's equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The theories derived, upon fixing the local Lorentz gauge freedom, are seen to be a subset of those found by Ogievetsky and Polubarinov some time ago using a spin limitation principle. In view of the stability question for massive gravities, the proven non-necessity of positive energy for stability in applied mathematics in some contexts is recalled. Massive tetrad gravities permit the mass of the spin 0 to be heavier than that of the spin 2, as well as lighter than or equal to it, and so provide phenomenological flexibility that might be of astrophysical or cosmological use.Comment: 2 figures. Forthcoming in General Relativity and Gravitatio

Long‐term trends in the distribution, abundance and impact of native “injurious” weeds

Questions: How can we quantify changes in the distribution and abundance of injurious weed species (Senecio jacobaea, Cirsium vulgare, Cirsium arvense, Rumex obtusifolius, Rumex crispus and Urtica dioica), over long time periods at wide geographical scales? What impact do these species have on plant communities? To what extent are changes driven by anthropogenically induced drivers such as disturbance, eutrophication and management? Location: Great Britain. Methods: Data from national surveys were used to assess changes in the frequency and abundance of selected weed species between 1978 and 2007. This involved novel method development to create indices of change, and to relate changes in distribution and abundance of these species to plant community diversity and inferred changes in resource availability, disturbance and management. Results: Three of the six weed species became more widespread in GB over this period and all of them increased in abundance (in grasslands, arable habitats, roadsides and streamsides). Patterns were complex and varied by landscape context and habitat type. For most of the species, there were negative relationships between abundance, total plant species richness, grassland, wetland and woodland indicators. Each individual species responds to a different combination of anthropogenic drivers but disturbance, fertility and livestock management significantly influenced most species. Conclusions: The increase in frequency and abundance of weeds over decades has implications for landscape‐scale plant diversity, fodder yield and livestock health. This includes reductions in plant species richness, loss of valuable habitat specialists and homogenisation of vegetation communities. Increasing land‐use intensity, excessive nutrient input, overgrazing, sward damage, poaching and bare ground in fields and undermanagement or too frequent cutting on linear features may have led to increases in weeds. These weeds do have conservation value so we are not advocating eradication, rather co‐existence, without dominance. Land management policy needs to adapt to benefit biodiversity and agricultural productivity

Association between Nephrotoxic Drug Combinations and Acute Kidney Injury in the Neonatal Intensive Care Unit

Objective: To determine the incidence of acute kidney injury (AKI) in infants exposed to nephrotoxic drug combinations admitted to 268 neonatal intensive care units managed by the Pediatrix Medical Group. Study design: We included infants born at 22-36 weeks gestational age, ≤120 days postnatal age, exposed to nephrotoxic drug combinations, with serum creatinine measurements available, and discharged between 2007 and 2016. To identify risk factors associated with a serum creatinine definition of AKI based on the Kidney Disease: Improving Global Outcomes criteria, we performed multivariable logistic and Cox regression adjusting for gestational age, sex, birth weight, postnatal age, race/ethnicity, sepsis, respiratory distress syndrome, baseline serum creatinine, and duration of combination drug exposure. The adjusted odds of AKI were determined relative to gentamicin + indomethacin for the following nephrotoxic drug combinations: chlorothiazide + ibuprofen; chlorothiazide + indomethacin; furosemide + gentamicin; furosemide + ibuprofen; furosemide + tobramycin; ibuprofen + spironolactone; and vancomycin + piperacillin-tazobactam. Results: Among 8286 included infants, 1384 (17%) experienced AKI. On multivariable analysis, sepsis, lower baseline creatinine, and duration of combination therapy were associated with increased odds of AKI. Furosemide + tobramycin and vancomycin + piperacillin-tazobactam were associated with a decreased risk of AKI relative to gentamicin + indomethacin in both the multivariable and Cox regression models. Conclusions: In this cohort, infants receiving longer durations of nephrotoxic combination therapy had an increased odds of developing AKI

Differential cross sections, charge production asymmetry, and spin-density matrix elements for D*(2010) produced in 500 GeV/c pi^- nucleon interactions

We report differential cross sections for the production of D*(2010) produced in 500 GeV/c pi^- nucleon interactions from experiment E791 at Fermilab, as functions of Feynman-x (x_F) and transverse momentum squared (p_T^2). We also report the D* +/- charge asymmetry and spin-density matrix elements as functions of these variables. Investigation of the spin-density matrix elements shows no evidence of polarization. The average values of the spin alignment are \eta= 0.01 +- 0.02 and -0.01 +- 0.02 for leading and non-leading particles, respectively.Comment: LaTeX2e (elsart.cls). 13 pages, 6 figures (eps files). Submitted to Physics Letters

Light propagation in statistically homogeneous and isotropic universes with general matter content

We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular diameter distance and two typos. No change in result