82,597 research outputs found
Index theorems for quantum graphs
In geometric analysis, an index theorem relates the difference of the numbers
of solutions of two differential equations to the topological structure of the
manifold or bundle concerned, sometimes using the heat kernels of two
higher-order differential operators as an intermediary. In this paper, the case
of quantum graphs is addressed. A quantum graph is a graph considered as a
(singular) one-dimensional variety and equipped with a second-order
differential Hamiltonian H (a "Laplacian") with suitable conditions at
vertices. For the case of scale-invariant vertex conditions (i.e., conditions
that do not mix the values of functions and of their derivatives), the constant
term of the heat-kernel expansion is shown to be proportional to the trace of
the internal scattering matrix of the graph. This observation is placed into
the index-theory context by factoring the Laplacian into two first-order
operators, H =A*A, and relating the constant term to the index of A. An
independent consideration provides an index formula for any differential
operator on a finite quantum graph in terms of the vertex conditions. It is
found also that the algebraic multiplicity of 0 as a root of the secular
determinant of H is the sum of the nullities of A and A*.Comment: 19 pages, Institute of Physics LaTe
Patterns of gene expression in schistosomes: localization by whole mount in situ hybridization
rom the identification of genes to the characterization of their functions and interactions. Developmental biologists have long used whole mount in situ hybridization (WISH) to determine gene expression patterns, as a vital tool for formulating and testing hypotheses about function. This paper describes the application of WISH to the study of gene expression in larval and adult schistosomes. Fixed worms were permeablized by proteinase K treatment for hybridization with digoxygenin-labelled RNA probes, with binding being detected by alkaline phosphatase-coupled anti-digoxygenin antibodies, and BM Purple substrate. Discrete staining patterns for the transcripts of the molecules Sm29, cathepsin L, antigen 10.3 and chorion were observed in the tegument cell bodies, gut epithelium, oesophageal gland and vitelline lobules, respectively, of adult worms. Transcripts of the molecules SGTP4, GP18-22 and cathepsin L were localized to tegument cell bodies and embryonic gut, respectively, of lung schistosomula. We also showed that Fast Red TR fluorescent substrate can refine the pattern of localization permitting use of confocal microscopy. We believe that method of WISH will find broad application, in synergy with other emerging post-genomic techniques, such as RNA interference, to studies focused at increasing our molecular understanding of schistosomes
Repulsive Casimir Pistons
Casimir pistons are models in which finite Casimir forces can be calculated
without any suspect renormalizations. It has been suggested that such forces
are always attractive. We present three scenarios in which that is not true.
Two of these depend on mixing two types of boundary conditions. The other,
however, is a simple type of quantum graph in which the sign of the force
depends upon the number of edges.Comment: 4 pages, 2 figures; RevTeX. Minor additions and correction
Reconstruction of Cluster Masses using Particle Based Lensing I: Application to Weak Lensing
We present Particle-Based Lensing (PBL), a new technique for gravitational
lensing mass reconstructions of galaxy clusters. Traditionally, most methods
have employed either a finite inversion or gridding to turn observational
lensed galaxy ellipticities into an estimate of the surface mass density of a
galaxy cluster. We approach the problem from a different perspective, motivated
by the success of multi-scale analysis in smoothed particle hydrodynamics. In
PBL, we treat each of the lensed galaxies as a particle and then reconstruct
the potential by smoothing over a local kernel with variable smoothing scale.
In this way, we can tune a reconstruction to produce constant signal-noise
throughout, and maximally exploit regions of high information density.
PBL is designed to include all lensing observables, including multiple image
positions and fluxes from strong lensing, as well as weak lensing signals
including shear and flexion. In this paper, however, we describe a shear-only
reconstruction, and apply the method to several test cases, including simulated
lensing clusters, as well as the well-studied ``Bullet Cluster'' (1E0657-56).
In the former cases, we show that PBL is better able to identify cusps and
substructures than are grid-based reconstructions, and in the latter case, we
show that PBL is able to identify substructure in the Bullet Cluster without
even exploiting strong lensing measurements. We also make our codes publicly
available.Comment: Accepted for publication in ApJ; Codes available at
http://www.physics.drexel.edu/~deb/PBL.htm ; 12 pages,9 figures, section 3
shortene
Pressure induced effects on the Fermi surface of superconducting 2H-NbSe
The pressure dependence of the critical temperature and upper critical
field has been measured up to 19 GPa in the layered superconducting
material 2H-NbSe. Relating the behavior of to Fermi surface
parameters, we find that the electron phonon coupling of the 2D Nb 4d derived
bands shows a peak at 5 GPa when the charge density wave (CDW) order is
suppressed. On the other hand, shows a bell shaped curve with a
maximum at 10.5 GPa, well above the pressure for the suppression of the CDW
order. Changes in the band structure produce this shift in the maximum of
, demonstrating that 2H-NbSe shows important differences with
respect to other compounds where has a maximum in the temperature-density
phase diagram shaped by the suppression of another, non-superconducting, ground
state.Comment: 5 pages, 4 figures. Small changes in discussion. Typos correcte
High-Accuracy Calculations of the Critical Exponents of Dyson's Hierarchical Model
We calculate the critical exponent gamma of Dyson's hierarchical model by
direct fits of the zero momentum two-point function, calculated with an Ising
and a Landau-Ginzburg measure, and by linearization about the Koch-Wittwer
fixed point. We find gamma= 1.299140730159 plus or minus 10^(-12). We extract
three types of subleading corrections (in other words, a parametrization of the
way the two-point function depends on the cutoff) from the fits and check the
value of the first subleading exponent from the linearized procedure. We
suggest that all the non-universal quantities entering the subleading
corrections can be calculated systematically from the non-linear contributions
about the fixed point and that this procedure would provide an alternative way
to introduce the bare parameters in a field theory model.Comment: 15 pages, 9 figures, uses revte
Exciton condensation driving the periodic lattice distortion of 1T-TiSe2
We address the lattice instability of 1T-TiSe2 in the framework of the
exciton condensate phase. We show that, at low temperature, condensed excitons
influence the lattice through electron-phonon interaction. It is found that at
zero temperature, in the exciton condensate phase of 1T-TiSe2, this exciton
condensate exerts a force on the lattice generating ionic displacements
comparable in amplitude to what is measured in experiment. This is thus the
first quantitative estimation of the amplitude of the periodic lattice
distortion observed in 1T-TiSe2 as a consequence of the exciton condensate
phase.Comment: 5 pages, 3 figures and 1 tabl
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