463 research outputs found

    Chebyshev method to solve the time-dependent Maxwell equations

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    Chebyshev method to solve the time-dependent Maxwell equations

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    We present a one-step algorithm to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We compare the results of this algorithm with those obtained from unconditionally stable algorithms and demonstrate that for a range of applications the one-step algorithm may be orders of magnitude more efficient than multiple time-step, finite-difference time-domain algorithms. We discuss both the virtues and limitations of this one-step approach.</p

    Density of Neutral Solitons in Weakly Disordered Peierls Chains

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    We study the effects of weak off-diagonal disorder on Peierls systems with a doubly degenerate ground state. We show that for these systems disorder in the electron hopping amplitudes induces a finite density of solitons in the minimal-energy lattice configuration of a single chain. These disorder-induced dimerization kinks are neutral and have spin 1/2. Using a continuum model for the Peierls chain and treating the lattice classically, we analytically calculate the average free energy and density of kinks. We compare these results to numerical calculations for a discrete model and discuss the implications of the kinks for the optical and magnetic properties of the conjugated polymer trans-polyacetylene.Comment: 28 pages, revtex, 5 Postscript figures, to appear in Phys. Rev.

    Acoustic phonon exchange, attractive interactions, and the Wentzel-Bardeen singularity in single-wall nanotubes

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    We derive the effective low-energy theory for interacting electrons in metallic single-wall carbon nanotubes taking into account acoustic phonon exchange within a continuum elastic description. In many cases, the nanotube can be described as a standard Luttinger liquid with possibly attractive interactions. We predict surprisingly strong attractive interactions for thin nanotubes. Once the tube radius reaches a critical value R03.6±1.4R_0 \approx 3.6\pm 1.4 \AA, the Wentzel-Bardeen singularity is approached, accompanied by strong superconducting fluctuations. The surprisingly large R0R_0 indicates that this singularity could be reached experimentally. We also discuss the conditions for a Peierls transition due to acoustic phonons.Comment: 11 pages, 2 figures, final version to be published in Phys. Rev.

    A Hypothesis for the Evolution of Nuclear-Encoded, Plastid-Targeted Glyceraldehyde-3-Phosphate Dehydrogenase Genes in “Chromalveolate” Members

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    Eukaryotes bearing red alga-derived plastids — photosynthetic alveolates (dinoflagellates plus the apicomplexan Toxoplasma gondii plus the chromerid Chromera velia), photosynthetic stramenopiles, haptophytes, and cryptophytes — possess unique plastid-targeted glyceraldehyde-3-phosphate dehydrogenases (henceforth designated as “GapC1”). Pioneering phylogenetic studies have indicated a single origin of the GapC1 enzymes in eukaryotic evolution, but there are two potential idiosyncrasies in the GapC1 phylogeny: Firstly, the GapC1 tree topology is apparently inconsistent with the organismal relationship among the “GapC1-containing” groups. Secondly, four stramenopile GapC1 homologues are consistently paraphyletic in previously published studies, although these organisms have been widely accepted as monophyletic. For a closer examination of the above issues, in this study GapC1 gene sampling was improved by determining/identifying nine stramenopile and two cryptophyte genes. Phylogenetic analyses of our GapC1 dataset, which is particularly rich in the stramenopile homologues, prompt us to propose a new scenario that assumes multiple, lateral GapC1 gene transfer events to explain the incongruity between the GapC1 phylogeny and the organismal relationships amongst the “GapC1-containing” groups. Under our new scenario, GapC1 genes uniquely found in photosynthetic alveolates, photosynthetic stramenopiles, haptophytes, and cryptopyhytes are not necessarily a character vertically inherited from a common ancestor

    Possible origins of macroscopic left-right asymmetry in organisms

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    I consider the microscopic mechanisms by which a particular left-right (L/R) asymmetry is generated at the organism level from the microscopic handedness of cytoskeletal molecules. In light of a fundamental symmetry principle, the typical pattern-formation mechanisms of diffusion plus regulation cannot implement the "right-hand rule"; at the microscopic level, the cell's cytoskeleton of chiral filaments seems always to be involved, usually in collective states driven by polymerization forces or molecular motors. It seems particularly easy for handedness to emerge in a shear or rotation in the background of an effectively two-dimensional system, such as the cell membrane or a layer of cells, as this requires no pre-existing axis apart from the layer normal. I detail a scenario involving actin/myosin layers in snails and in C. elegans, and also one about the microtubule layer in plant cells. I also survey the other examples that I am aware of, such as the emergence of handedness such as the emergence of handedness in neurons, in eukaryote cell motility, and in non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue. Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec
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