45,716 research outputs found
Multiple zero modes of the Dirac operator in three dimensions
One of the key properties of Dirac operators is the possibility of a
degeneracy of zero modes. For the Abelian Dirac operator in three dimensions
the construction of multiple zero modes has been sucessfully carried out only
very recently. Here we generalise these results by discussing a much wider
class of Dirac operators together with their zero modes. Further we show that
those Dirac operators that do admit zero modes may be related to Hopf maps,
where the Hopf index is related to the number of zero modes in a simple way.Comment: Latex file, 20 pages, no figure
Chern-Simons action for zero-mode supporting gauge fields in three dimensions
Recent results on zero modes of the Abelian Dirac operator in three
dimensions support to some degree the conjecture that the Chern-Simons action
admits only certain quantized values for gauge fields that lead to zero modes
of the corresponding Dirac operator. Here we show that this conjecture is wrong
by constructing an explicit counter-example.Comment: version as published in PRD, minor change
Millisecond single-molecule localization microscopy combined with convolution analysis and automated image segmentation to determine protein concentrations in complexly structured, functional cells, one cell at a time
We present a single-molecule tool called the CoPro (Concentration of
Proteins) method that uses millisecond imaging with convolution analysis,
automated image segmentation and super-resolution localization microscopy to
generate robust estimates for protein concentration in different compartments
of single living cells, validated using realistic simulations of complex
multiple compartment cell types. We demonstrates its utility experimentally on
model Escherichia coli bacteria and Saccharomyces cerevisiae budding yeast
cells, and use it to address the biological question of how signals are
transduced in cells. Cells in all domains of life dynamically sense their
environment through signal transduction mechanisms, many involving gene
regulation. The glucose sensing mechanism of S. cerevisiae is a model system
for studying gene regulatory signal transduction. It uses the multi-copy
expression inhibitor of the GAL gene family, Mig1, to repress unwanted genes in
the presence of elevated extracellular glucose concentrations. We fluorescently
labelled Mig1 molecules with green fluorescent protein (GFP) via chromosomal
integration at physiological expression levels in living S. cerevisiae cells,
in addition to the RNA polymerase protein Nrd1 with the fluorescent protein
reporter mCherry. Using CoPro we make quantitative estimates of Mig1 and Nrd1
protein concentrations in the cytoplasm and nucleus compartments on a
cell-by-cell basis under physiological conditions. These estimates indicate a
4-fold shift towards higher values in concentration of diffusive Mig1 in the
nucleus if the external glucose concentration is raised, whereas equivalent
levels in the cytoplasm shift to smaller values with a relative change an order
of magnitude smaller. This compares with Nrd1 which is not involved directly in
glucose sensing, which is almost exclusively localized in the nucleus under
high and..
Radial vibrations of BPS skyrmions
We study radial vibrations of spherically symmetric skyrmions in the BPS
Skyrme model. Concretely, we numerically solve the linearised field equations
for small fluctuations in a skyrmion background, both for linearly stable
oscillations and for (unstable) resonances. This is complemented by numerical
solutions of the full nonlinear system, which confirm all the results of the
linear analysis. In all cases, the resulting fundamental excitation provides a
rather accurate value for the Roper resonance, supporting the hypothesis that
the BPS Skyrme model already gives a reasonable approximate description of this
resonance. Further, for many potentials additional higher resonances appear,
again in agreement with known experimental results.Comment: Latex, 41 pages, 22 pdf figures; v2: minor change
Roper resonances and quasi-normal modes of Skyrmions
Radial vibrations of charge one hedgehog Skyrmions in the full Skyrme model
are analysed. We investigate how the properties of the lowest resonance modes
(quasi normal modes) - their frequencies and widths - depend on the form of the
potential (value of the pion mass as well as the addition of further
potentials) and on the inclusion of the sextic term. Then we consider the
inverse problem, where certain values for the frequencies and widths are
imposed, and the field theoretic Skyrme model potential giving rise to them is
reconstructed. This latter method allows to reproduce the physical Roper
resonances, as well as further physical properties of nucleons, with high
precision.Comment: LaTex, 24 pages, 18 figure
BPS Skyrme neutron stars in generalized gravity
We study the coupling of nuclear matter described by the BPS Skyrme model to
generalized gravity. Concretely, we consider the Starobinsky model which
provides the leading-order correction to the Einstein-Hilbert action. Static
solutions describing neutron stars are found both for the full field theory and
for the mean-field approximation. We always consider the full Starobinsky model
in the nonperturbative approach, using appropriately generalized shooting
methods for the numerical neutron star calculations. Many of our results are
similar to previous investigations of neutron stars for the Starobinsky model
using other models of nuclear matter, but there are some surprizing
discrepancies. The "Newtonian mass" relevant for the surface redshift, e.g.,
results larger than the ADM mass in our model, in contrast to other
investigations. This difference is related to the particularly high stiffness
of nuclear matter described by the BPS Skyrme model and offers an interesting
possibility to distinguish different models of nuclear matter within
generalized gravity.Comment: LaTex, 28 pages, 13 figures; v2: minor change
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