525 research outputs found
A rigorous analysis of high order electromagnetic invisibility cloaks
There is currently a great deal of interest in the invisibility cloaks
recently proposed by Pendry et al. that are based in the transformation
approach. They obtained their results using first order transformations. In
recent papers Hendi et al. and Cai et al. considered invisibility cloaks with
high order transformations. In this paper we study high order electromagnetic
invisibility cloaks in transformation media obtained by high order
transformations from general anisotropic media. We consider the case where
there is a finite number of spherical cloaks located in different points in
space. We prove that for any incident plane wave, at any frequency, the
scattered wave is identically zero. We also consider the scattering of finite
energy wave packets. We prove that the scattering matrix is the identity, i.e.,
that for any incoming wave packet the outgoing wave packet is the same as the
incoming one. This proves that the invisibility cloaks can not be detected in
any scattering experiment with electromagnetic waves in high order
transformation media, and in particular in the first order transformation media
of Pendry et al. We also prove that the high order invisibility cloaks, as well
as the first order ones, cloak passive and active devices. The cloaked objects
completely decouple from the exterior. Actually, the cloaking outside is
independent of what is inside the cloaked objects. The electromagnetic waves
inside the cloaked objects can not leave the concealed regions and viceversa,
the electromagnetic waves outside the cloaked objects can not go inside the
concealed regions. As we prove our results for media that are obtained by
transformation from general anisotropic materials, we prove that it is possible
to cloak objects inside general crystals.Comment: The final version is now published in Journal of Physics A:
Mathematical and Theoretical, vol 41 (2008) 065207 (21 pp). Included in
IOP-Selec
Contemporary antihypertensive therapy
Pharmacotherapy of human hypertension is effective, safe and well-tolerated. Antihypertensive drugs are of three broad classes: diuretics, sympatholytics and vasodilators. The use of each class is discussed and a summary of therapeutic considerations offered for representative agents. Recent trends in antihypertensive therapy are identified.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26517/1/0000055.pd
Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time
We prove that the scattering matrix at a fixed quasi--energy determines
uniquely a time--periodic potential that decays exponentially at infinity. We
consider potentials that for each fixed time belong to in space. The
exponent 3/2 is critical for the singularities of the potential in space. For
this singular class of potentials the result is new even in the
time--independent case, where it was only known for bounded exponentially
decreasing potentials.Comment: In this revised version I give a more detailed motivation of the
class of potentials that I consider and I have corrected some typo
Associations between fruit and vegetable intake and quality of life
Abstract Dysregulation of the immune response to microbiota is associated with inflammatory bowel disease (IBD), which can trigger intestinal fibrosis. MyD88 is a key component of microbiota signalling but its influence on intestinal fibrosis has not been clarified. Small bowel resections from donor-mice were transplanted subcutaneously into the neck of recipients C57BL/6 B6-MyD88tm1 Aki (MyD88−/−) and C57BL/6-Tg(UBC-green fluorescence protein (GFP))30Scha/J (GFP-Tg). Grafts were explanted up to 21 days after transplantation. Collagen layer thickness was determined using Sirius Red stained slides. In the mouse model of fibrosis collagen deposition and transforming growth factor-beta 1 (TGF-β1) expression was equal in MyD88+/+ and MyD88−/−, indicating that MyD88 was not essential for fibrogenesis. Matrix metalloproteinase (Mmp)9 expression was significantly decreased in grafts transplanted into MyD88−/− recipients compared to MyD88+/+ recipients (0.2 ± 0.1 vs. 153.0 ± 23.1, respectively, p < 0.05), similarly recruitment of neutrophils was significantly reduced (16.3 ± 4.5 vs. 25.4 ± 3.1, respectively, p < 0.05). Development of intestinal fibrosis appears to be independent of MyD88 signalling indicating a minor role of bacterial wall compounds in the process which is in contrast to published concepts and theories. Development of fibrosis appears to be uncoupled from acute inflammation
Atrial natriuretic hormone is not elevated during dopamine induced natriuresis
To evaluate the possibility that atrial natriuretic hormone (ANH) is involved in dopamine induced natriuresis and diuresis, we studied five normal male volunteers. Each was studied on two occasions. During the first two hours of each study, normal saline, 25 ml/hr, was infused. During the second two hours either normal saline, 25 ml/hr, or dopamine, 4 [mu]g/kg/min, in normal saline, was infused. Dopamine infusion caused prominent and significant natriuresis and diuresis but plasma levels of immunoreactive ANH levels did not change. We conclude that the ANH is not involved in dopamine induced natriuresis and that dopaminergic stimulation is not responsible for ANH secretion.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26700/1/0000248.pd
Scattering theory for Klein-Gordon equations with non-positive energy
We study the scattering theory for charged Klein-Gordon equations:
\{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x,
D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)=
f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq
n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x),
describing a Klein-Gordon field minimally coupled to an external
electromagnetic field described by the electric potential and magnetic
potential . The flow of the Klein-Gordon equation preserves the
energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+
\bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x)
\d x. We consider the situation when the energy is not positive. In this
case the flow cannot be written as a unitary group on a Hilbert space, and the
Klein-Gordon equation may have complex eigenfrequencies. Using the theory of
definitizable operators on Krein spaces and time-dependent methods, we prove
the existence and completeness of wave operators, both in the short- and
long-range cases. The range of the wave operators are characterized in terms of
the spectral theory of the generator, as in the usual Hilbert space case
Multidimensional Borg-Levinson Theorem
We consider the inverse problem of the reconstruction of a Schr\"odinger
operator on a unknown Riemannian manifold or a domain of Euclidean space. The
data used is a part of the boundary and the eigenvalues corresponding
to a set of impedances in the Robin boundary condition which vary on .
The proof is based on the analysis of the behaviour of the eigenfunctions on
the boundary as well as in perturbation theory of eigenvalues. This reduces the
problem to an inverse boundary spectral problem solved by the boundary control
method
Simplicity of extremal eigenvalues of the Klein-Gordon equation
We consider the spectral problem associated with the Klein-Gordon equation
for unbounded electric potentials. If the spectrum of this problem is contained
in two disjoint real intervals and the two inner boundary points are
eigenvalues, we show that these extremal eigenvalues are simple and possess
strictly positive eigenfunctions. Examples of electric potentials satisfying
these assumptions are given
Eigenvalue estimates for non-selfadjoint Dirac operators on the real line
We show that the non-embedded eigenvalues of the Dirac operator on the real
line with non-Hermitian potential lie in the disjoint union of two disks in
the right and left half plane, respectively, provided that the of
is bounded from above by the speed of light times the reduced Planck
constant. An analogous result for the Schr\"odinger operator, originally proved
by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For
massless Dirac operators, the condition on implies the absence of nonreal
eigenvalues. Our results are further generalized to potentials with slower
decay at infinity. As an application, we determine bounds on resonances and
embedded eigenvalues of Dirac operators with Hermitian dilation-analytic
potentials
Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential
For the Schrodinger equation at fixed energy with a potential supported in a
bounded domain we give formulas and equations for finding scattering data from
the Dirichlet-to-Neumann map with nonzero background potential. For the case of
zero background potential these results were obtained in [R.G.Novikov,
Multidimensional inverse spectral problem for the equation
-\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22,
(1988)]
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