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 $L^{3/2}$ 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 $v(x)$ and magnetic potential $\vec{b}(x)$. 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 $\Gamma$ and the eigenvalues corresponding to a set of impedances in the Robin boundary condition which vary on $\Gamma$. 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 $V$ lie in the disjoint union of two disks in the right and left half plane, respectively, provided that the $L^1-norm$ of $V$ 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 $V$ 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)]