Even Galois Representations and the Fontaine--Mazur conjecture II

We prove, under mild hypotheses, that there are no irreducible two-dimensional_even_ Galois representations of \Gal(\Qbar/\Q) which are de Rham with distinct Hodge--Tate weights. This removes the "ordinary" hypothesis required in previous work of the author. We construct examples of irreducible two-dimensional residual representations that have no characteristic zero geometric (= de Rham) deformations.Comment: Updated to take into account suggestions of the referee; the main theorems remain unchange

Factoring-in agglomeration of carbon nanotubes and nanofibers for better prediction of their toxicity versus asbestos

<p>Abstract</p> <p>Background</p> <p>Carbon nanotubes (CNT) and carbon nanofibers (CNF) are allotropes of carbon featuring fibrous morphology. The dimensions and high aspect ratio of CNT and CNF have prompted the comparison with naturally occurring asbestos fibers which are known to be extremely pathogenic. While the toxicity and hazardous outcomes elicited by airborne exposure to single-walled CNT or asbestos have been widely reported, very limited data are currently available describing adverse effects of respirable CNF.</p> <p>Results</p> <p>Here, we assessed pulmonary inflammation, fibrosis, oxidative stress markers and systemic immune responses to respirable CNF in comparison to single-walled CNT (SWCNT) and asbestos. Pulmonary inflammatory and fibrogenic responses to CNF, SWCNT and asbestos varied depending upon the agglomeration state of the particles/fibers. Foci of granulomatous lesions and collagen deposition were associated with dense particle-like SWCNT agglomerates, while no granuloma formation was found following exposure to fiber-like CNF or asbestos. The average thickness of the alveolar connective tissue - a marker of interstitial fibrosis - was increased 28 days post SWCNT, CNF or asbestos exposure. Exposure to SWCNT, CNF or asbestos resulted in oxidative stress evidenced by accumulations of 4-HNE and carbonylated proteins in the lung tissues. Additionally, local inflammatory and fibrogenic responses were accompanied by modified systemic immunity, as documented by decreased proliferation of splenic T cells <it>ex vivo </it>on day 28 post exposure. The accuracies of assessments of effective surface area for asbestos, SWCNT and CNF (based on geometrical analysis of their agglomeration) versus estimates of mass dose and number of particles were compared as predictors of toxicological outcomes.</p> <p>Conclusions</p> <p>We provide evidence that effective surface area along with mass dose rather than specific surface area or particle number are significantly correlated with toxicological responses to carbonaceous fibrous nanoparticles. Therefore, they could be useful dose metrics for risk assessment and management.</p

First-principles envelope-function theory for lattice-matched semiconductor heterostructures

In this paper a multi-band envelope-function Hamiltonian for lattice-matched semiconductor heterostructures is derived from first-principles norm-conserving pseudopotentials. The theory is applicable to isovalent or heterovalent heterostructures with macroscopically neutral interfaces and no spontaneous bulk polarization. The key assumption -- proved in earlier numerical studies -- is that the heterostructure can be treated as a weak perturbation with respect to some periodic reference crystal, with the nonlinear response small in comparison to the linear response. Quadratic response theory is then used in conjunction with k.p perturbation theory to develop a multi-band effective-mass Hamiltonian (for slowly varying envelope functions) in which all interface band-mixing effects are determined by the linear response. To within terms of the same order as the position dependence of the effective mass, the quadratic response contributes only a bulk band offset term and an interface dipole term, both of which are diagonal in the effective-mass Hamiltonian. Long-range multipole Coulomb fields arise in quantum wires or dots, but have no qualitative effect in two-dimensional systems beyond a dipole contribution to the band offsets.Comment: 25 pages, no figures, RevTeX4; v3: final published versio

Reflection of light and heavy holes from a linear potential barrier

In this paper we study reflection of holes in direct-band semiconductors from the linear potential barrier. It is shown that light-heavy hole transformation matrix is universal. It depends only on a dimensionless product of the light hole longitudinal momentum and the characteristic length determined by the slope of the potential and doesn't depend on the ratio of light and heavy hole masses, provided this ratio is small. It is shown that the transformation coefficient goes to zero both in the limit of small and large longitudinal momenta, however the phase of a reflected hole is different in these limits. An approximate analytical expression for the light-heavy hole transformation coefficient is found.Comment: 6 pages, 2 figure

Tunnelling Studies of Two-Dimensional States in Semiconductors with Inverted Band Structure: Spin-orbit Splitting, Resonant Broadening

The results of tunnelling studies of the energy spectrum of two-dimensional (2D) states in a surface quantum well in a semiconductor with inverted band structure are presented. The energy dependence of quasimomentum of the 2D states over a wide energy range is obtained from the analysis of tunnelling conductivity oscillations in a quantizing magnetic field. The spin-orbit splitting of the energy spectrum of 2D states, due to inversion asymmetry of the surface quantum well, and the broadening of 2D states at the energies, when they are in resonance with the heavy hole valence band, are investigated in structures with different strength of the surface quantum well. A quantitative analysis is carried out within the framework of the Kane model of the energy spectrum. The theoretical results are in good agreement with the tunnelling spectroscopy data.Comment: 29 pages, RevTeX, submitted in Phys.Rev.B. Figures available on request from [email protected]

Elliptic Curves over Real Quadratic Fields are Modular

We prove that all elliptic curves defined over real quadratic fields are modular.Comment: 38 pages. Magma scripts available as ancillary files with this arXiv versio

General boundary conditions for the envelope function in multiband k.p model

We have derived general boundary conditions (BC) for the multiband envelope functions (which do not contain spurious solutions) in semiconductor heterostructures with abrupt heterointerfaces. These BC require the conservation of the probability flux density normal to the interface and guarantee that the multiband Hamiltonian be self--adjoint. The BC are energy independent and are characteristic properties of the interface. Calculations have been performed of the effect of the general BC on the electron energy levels in a potential well with infinite potential barriers using a coupled two band model. The connection with other approaches to determining BC for the envelope function and to the spurious solution problem in the multiband k.p model are discussed.Comment: 15 pages, 2 figures; to be published in Phys. Rev. B 65, March 15 issue 200

Interface electronic states and boundary conditions for envelope functions

The envelope-function method with generalized boundary conditions is applied to the description of localized and resonant interface states. A complete set of phenomenological conditions which restrict the form of connection rules for envelope functions is derived using the Hermiticity and symmetry requirements. Empirical coefficients in the connection rules play role of material parameters which characterize an internal structure of every particular heterointerface. As an illustration we present the derivation of the most general connection rules for the one-band effective mass and 4-band Kane models. The conditions for the existence of Tamm-like localized interface states are established. It is shown that a nontrivial form of the connection rules can also result in the formation of resonant states. The most transparent manifestation of such states is the resonant tunneling through a single-barrier heterostructure.Comment: RevTeX4, 11 pages, 5 eps figures, submitted to Phys.Rev.

Development of an eight-band theory for quantum-dot heterostructures

We derive a nonsymmetrized 8-band effective-mass Hamiltonian for quantum-dot heterostructures (QDHs) in Burt's envelope-function representation. The 8x8 radial Hamiltonian and the boundary conditions for the Schroedinger equation are obtained for spherical QDHs. Boundary conditions for symmetrized and nonsymmetrized radial Hamiltonians are compared with each other and with connection rules that are commonly used to match the wave functions found from the bulk kp Hamiltonians of two adjacent materials. Electron and hole energy spectra in three spherical QDHs: HgS/CdS, InAs/GaAs, and GaAs/AlAs are calculated as a function of the quantum dot radius within the approximate symmetrized and exact nonsymmetrized 8x8 models. The parameters of dissymmetry are shown to influence the energy levels and the wave functions of an electron and a hole and, consequently, the energies of both intraband and interband transitions.Comment: 36 pages, 10 figures, E-mail addresses: [email protected], [email protected]

Phosphatidylserine Targets Single-Walled Carbon Nanotubes to Professional Phagocytes In Vitro and In Vivo

Broad applications of single-walled carbon nanotubes (SWCNT) dictate the necessity to better understand their health effects. Poor recognition of non-functionalized SWCNT by phagocytes is prohibitive towards controlling their biological action. We report that SWCNT coating with a phospholipid “eat-me” signal, phosphatidylserine (PS), makes them recognizable in vitro by different phagocytic cells - murine RAW264.7 macrophages, primary monocyte-derived human macrophages, dendritic cells, and rat brain microglia. Macrophage uptake of PS-coated nanotubes was suppressed by the PS-binding protein, Annexin V, and endocytosis inhibitors, and changed the pattern of pro- and anti-inflammatory cytokine secretion. Loading of PS-coated SWCNT with pro-apoptotic cargo (cytochrome c) allowed for the targeted killing of RAW264.7 macrophages. In vivo aspiration of PS-coated SWCNT stimulated their uptake by lung alveolar macrophages in mice. Thus, PS-coating can be utilized for targeted delivery of SWCNT with specified cargoes into professional phagocytes, hence for therapeutic regulation of specific populations of immune-competent cells