10,325 research outputs found
Fay-like identities of the Toda Lattice Hierarchy and its dispersionless limit
In this paper, we derive the Fay-like identities of tau function for the Toda
lattice hierarchy from the bilinear identity. We prove that the Fay-like
identities are equivalent to the hierarchy. We also show that the
dispersionless limit of the Fay-like identities are the dispersionless Hirota
equations of the dispersionless Toda hierarchy.Comment: 20 page
Non-degenerate solutions of universal Whitham hierarchy
The notion of non-degenerate solutions for the dispersionless Toda hierarchy
is generalized to the universal Whitham hierarchy of genus zero with
marked points. These solutions are characterized by a Riemann-Hilbert problem
(generalized string equations) with respect to two-dimensional canonical
transformations, and may be thought of as a kind of general solutions of the
hierarchy. The Riemann-Hilbert problem contains arbitrary functions
, , which play the role of generating functions of
two-dimensional canonical transformations. The solution of the Riemann-Hilbert
problem is described by period maps on the space of -tuples
of conformal maps from disks of the
Riemann sphere and their complements to the Riemann sphere. The period maps are
defined by an infinite number of contour integrals that generalize the notion
of harmonic moments. The -function (free energy) of these solutions is also
shown to have a contour integral representation.Comment: latex2e, using amsmath, amssym and amsthm packages, 32 pages, no
figur
Casimir effect of electromagnetic field in Randall-Sundrum spacetime
We study the finite temperature Casimir effect on a pair of parallel
perfectly conducting plates in Randall-Sundrum model without using scalar field
analogy. Two different ways of interpreting perfectly conducting conditions are
discussed. The conventional way that uses perfectly conducting condition
induced from 5D leads to three discrete mode corrections. This is very
different from the result obtained from imposing 4D perfectly conducting
conditions on the 4D massless and massive vector fields obtained by decomposing
the 5D electromagnetic field. The latter only contains two discrete mode
corrections, but it has a continuum mode correction that depends on the
thicknesses of the plates. It is shown that under both boundary conditions, the
corrections to the Casimir force make the Casimir force more attractive. The
correction under 4D perfectly conducting condition is always smaller than the
correction under the 5D induced perfectly conducting condition. These
statements are true at any temperature.Comment: 20 pages, 4 figure
Majorana Fermions and Non-Abelian Statistics in Three Dimensions
We show that three dimensional superconductors, described within a Bogoliubov
de Gennes framework can have zero energy bound states associated with pointlike
topological defects. The Majorana fermions associated with these modes have
non-Abelian exchange statistics, despite the fact that the braid group is
trivial in three dimensions. This can occur because the defects are associated
with an orientation that can undergo topologically nontrivial rotations. A new
feature of three dimensional systems is that there are "braidless" operations
in which it is possible to manipulate the groundstate associated with a set of
defects without moving or measuring them. To illustrate these effects we
analyze specific architectures involving topological insulators and
superconductors.Comment: 4 pages, 2 figures, published versio
Transcriptional factor PU.1 regulates decidual C1q expression in early pregnancy in human
"Copyright: © 2015 Madhukaran, Kishore, Jamil, Teo, Choolani and Lu. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms."C1q is the first recognition subcomponent of the complement classical pathway, which in addition to being synthesized in the liver, is also expressed by macrophages and dendritic cells (DCs). Trophoblast invasion during early placentation results in accumulation of debris that triggers the complement system. Hence, both early and late components of the classical pathway are widely distributed in the placenta and decidua. In addition, C1q has recently been shown to significantly contribute to feto-maternal tolerance, trophoblast migration, and spiral artery remodeling, although the exact mechanism remains unknown. Pregnancy in mice, genetically deficient in C1q, mirrors symptoms similar to that of human preeclampsia. Thus, regulated complement activation has been proposed as an essential requirement for normal successful pregnancy. Little is known about the molecular pathways that regulate C1q expression in pregnancy. PU.1, an Ets-family transcription factor, is required for the development of hematopoietic myeloid lineage immune cells, and its expression is tissue-specific. Recently, PU.1 has been shown to regulate C1q gene expression in DCs and macrophages. Here, we have examined if PU.1 transcription factor regulates decidual C1q expression. We used immune-histochemical analysis, PCR, and immunostaining to localize and study the gene expression of PU.1 transcription factor in early human decidua. PU.1 was highly expressed at gene and protein level in early human decidual cells including trophoblast and stromal cells. Surprisingly, nuclear as well as cytoplasmic PU.1 expression was observed. Decidual cells with predominantly nuclear PU.1 expression had higher C1q expression. It is likely that nuclear and cytoplasmic PU.1 localization has a role to play in early pregnancy via regulating C1q expression in the decidua during implantation
The Multicomponent KP Hierarchy: Differential Fay Identities and Lax Equations
In this article, we show that four sets of differential Fay identities of an
-component KP hierarchy derived from the bilinear relation satisfied by the
tau function of the hierarchy are sufficient to derive the auxiliary linear
equations for the wave functions. From this, we derive the Lax representation
for the -component KP hierarchy, which are equations satisfied by some
pseudodifferential operators with matrix coefficients. Besides the Lax
equations with respect to the time variables proposed in \cite{2}, we also
obtain a set of equations relating different charge sectors, which can be
considered as a generalization of the modified KP hierarchy proposed in
\cite{3}.Comment: 19 page
Casimir interaction between two concentric cylinders at nonzero temperature
We study the finite temperature Casimir interaction between two concentric
cylinders. When the separation between the cylinders is much smaller than the
radii of the cylinders, the asymptotic expansions of the Casimir interaction
are derived. Both the low temperature and the high temperature regions are
considered. The leading terms are found to agree with the proximity force
approximations. The low temperature leading term of the temperature correction
is also computed and it is found to be independent of the boundary conditions
imposed on the larger cylinder.Comment: 6 pages, 1 figur
On the corrections beyond proximity force approximation (PFA)
We recalculate the first analytic correction beyond PFA for a sphere in front
of a plane for a scalar field and for the electromagnetic field. We use the
method of Bordag and Nikolaev [J.Phys.A, {\bf 41} (2008) p.164002]. We confirm
their result for Dirichlet boundary conditions whereas we find a different one
for Robin, Neumann and conductor boundary conditions. The difference can be
traced back to a sign error. As a result, the corrections depend on the Robin
parameter. Agreement is found with a very recent method of derivative
expansion.Comment: 9 pages. Some changes in the conclusio
Casimir effect of electromagnetic field in D-dimensional spherically symmetric cavities
Eigenmodes of electromagnetic field with perfectly conducting or infinitely
permeable conditions on the boundary of a D-dimensional spherically symmetric
cavity is derived explicitly. It is shown that there are (D-2) polarizations
for TE modes and one polarization for TM modes, giving rise to a total of (D-1)
polarizations. In case of a D-dimensional ball, the eigenfrequencies of
electromagnetic field with perfectly conducting boundary condition coincides
with the eigenfrequencies of gauge one-forms with relative boundary condition;
whereas the eigenfrequencies of electromagnetic field with infinitely permeable
boundary condition coincides with the eigenfrequencies of gauge one-forms with
absolute boundary condition. Casimir energy for a D-dimensional spherical shell
configuration is computed using both cut-off regularization and zeta
regularization. For a double spherical shell configuration, it is shown that
the Casimir energy can be written as a sum of the single spherical shell
contributions and an interacting term, and the latter is free of divergence.
The interacting term always gives rise to an attractive force between the two
spherical shells. Its leading term is the Casimir force acting between two
parallel plates of the same area, as expected by proximity force approximation.Comment: 28 page
Spin texture on the Fermi surface of tensile strained HgTe
We present ab initio and k.p calculations of the spin texture on the Fermi
surface of tensile strained HgTe, which is obtained by stretching the
zincblende lattice along the (111) axis. Tensile strained HgTe is a semimetal
with pointlike accidental degeneracies between a mirror symmetry protected
twofold degenerate band and two nondegenerate bands near the Fermi level. The
Fermi surface consists of two ellipsoids which contact at the point where the
Fermi level crosses the twofold degenerate band along the (111) axis. However,
the spin texture of occupied states indicates that neither ellipsoid carries a
compensating Chern number. Consequently, the spin texture is locked in the
plane perpendicular to the (111) axis, exhibits a nonzero winding number in
that plane, and changes winding number from one end of the Fermi ellipsoids to
the other. The change in the winding of the spin texture suggests the existence
of singular points. An ordered alloy of HgTe with ZnTe has the same effect as
stretching the zincblende lattice in the (111) direction. We present ab initio
calculations of ordered Hg_xZn_1-xTe that confirm the existence of a spin
texture locked in a 2D plane on the Fermi surface with different winding
numbers on either end.Comment: 8 pages, 8 figure
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