298 research outputs found

### Plus-minus construction leads to perfect invisibility

Recent theoretical advances applied to metamaterials have opened new avenues
to design a coating that hides objects from electromagnetic radiation and even
the sight. Here, we propose a new design of cloaking devices that creates
perfect invisibility in isotropic media. A combination of positive and negative
refractive indices, called plus-minus construction, is essential to achieve
perfect invisibility (i.e., no time delay and total absence of reflection).
Contrary to the common understanding that between two isotropic materials
having different refractive indices the electromagnetic reflection is
unavoidable, our method shows that surprisingly the reflection phenomena can be
completely eliminated. The invented method, different from the classical
impedance matching, may also find electromagnetic applications outside of
cloaking devices, wherever distortions are present arising from reflections.Comment: 24 pages, 10 figure

### A lower bound in Nehari's theorem on the polydisc

By theorems of Ferguson and Lacey (d=2) and Lacey and Terwilleger (d>2),
Nehari's theorem is known to hold on the polydisc D^d for d>1, i.e., if H_\psi
is a bounded Hankel form on H^2(D^d) with analytic symbol \psi, then there is a
function \phi in L^\infty(\T^d) such that \psi is the Riesz projection of \phi.
A method proposed in Helson's last paper is used to show that the constant C_d
in the estimate \|\phi\|_\infty\le C_d \|H_\psi\| grows at least exponentially
with d; it follows that there is no analogue of Nehari's theorem on the
infinite-dimensional polydisc

### Conformal mapping of ultrasonic crystals: confining ultrasound and cochlear-like wave guiding

Conformal mapping of a slab of a two-dimensional ultrasonic crystal generate
a closed geometrical arrangement of ultrasonic scatterers with appealing
acoustic properties. This acoustic shell is able to confine ultrasonic modes.
Some of these internal resonances can be induced from an external wave source.
The mapping of a linear defect produces a wave-guide that exhibits a
spatial-frequency selection analogous to that characteristic of a synthetic
"cochlea". Both, experimental and theoretical results are reported here.Comment: 4 pages, 4 figure

### Wilson Loops and QCD/String Scattering Amplitudes

We generalize modern ideas about the duality between Wilson loops and
scattering amplitudes in ${\cal N}=4$ SYM to large $N$ QCD by deriving a
general relation between QCD meson scattering amplitudes and Wilson loops. We
then investigate properties of the open-string disk amplitude integrated over
reparametrizations. When the Wilson loop is approximated by the area behavior,
we find that the QCD scattering amplitude is a convolution of the standard
Koba-Nielsen integrand and a kernel. As usual poles originate from the first
factor, whereas no (momentum dependent) poles can arise from the kernel. We
show that the kernel becomes a constant when the number of external particles
becomes large. The usual Veneziano amplitude then emerges in the kinematical
regime where the Wilson loop can be reliably approximated by the area behavior.
In this case we obtain a direct duality between Wilson loops and scattering
amplitudes when spatial variables and momenta are interchanged, in analogy with
the $\cal N$=4 SYM case.Comment: 39pp., Latex, no figures; v2: typos corrected; v3: final, to appear
in PR

### Koebe 1/4-Theorem and Inequalities in N=2 Super-QCD

The critical curve ${\cal C}$ on which ${\rm Im}\,\hat\tau =0$,
$\hat\tau=a_D/a$, determines hyperbolic domains whose Poincar\'e metric is
constructed in terms of $a_D$ and $a$. We describe ${\cal C}$ in a parametric
form related to a Schwarzian equation and prove new relations for $N=2$ Super
$SU(2)$ Yang-Mills. In particular, using the Koebe 1/4-theorem and Schwarz's
lemma, we obtain inequalities involving $u$, $a_D$ and $a$, which seem related
to the Renormalization Group. Furthermore, we obtain a closed form for the
prepotential as function of $a$. Finally, we show that $\partial_{\hat\tau}
\langle {\rm tr}\,\phi^2\rangle_{\hat \tau}={1\over 8\pi i b_1}\langle
\phi\rangle_{\hat\tau}^2$, where $b_1$ is the one-loop coefficient of the beta
function.Comment: 11 pages, LaTex file, Expanded version: new results, technical
details explained, misprints corrected and references adde

### Solutions of the Einstein-Dirac and Seiberg-Witten Monopole Equations

We present unique solutions of the Seiberg-Witten Monopole Equations in which
the U(1) curvature is covariantly constant, the monopole Weyl spinor consists
of a single constant component, and the 4-manifold is a product of two Riemann
surfaces of genuses p_1 and p_2. There are p_1 -1 magnetic vortices on one
surface and p_2 - 1 electric ones on the other, with p_1 + p_2 \geq 2 p_1 =
p_2= 1 being excluded). When p_1 = p_2, the electromagnetic fields are
self-dual and one also has a solution of the coupled euclidean
Einstein-Maxwell-Dirac equations, with the monopole condensate serving as
cosmological constant. The metric is decomposable and the electromagnetic
fields are covariantly constant as in the Bertotti-Robinson solution. The
Einstein metric can also be derived from a K\"{a}hler potential satisfying the
Monge-Amp\`{e}re equations.Comment: 22 pages. Rep. no: FGI-99-

### Superantenna made of transformation media

We show how transformation media can make a superantenna that is either
completely invisible or focuses incoming light into a needle-sharp beam. Our
idea is based on representating three-dimensional space as a foliage of sheets
and performing two-dimensional conformal maps on each shee

### Texture and shape of two-dimensional domains of nematic liquid crystal

We present a generalized approach to compute the shape and internal structure
of two-dimensional nematic domains. By using conformal mappings, we are able to
compute the director field for a given domain shape that we choose from a rich
class, which includes drops with large and small aspect ratios, and sharp
domain tips as well as smooth ones. Results are assembled in a phase diagram
that for given domain size, surface tension, anchoring strength, and elastic
constant shows the transitions from a homogeneous to a bipolar director field,
from circular to elongated droplets, and from sharp to smooth domain tips. We
find a previously unaccounted regime, where the drop is nearly circular, the
director field bipolar and the tip rounded. We also find that bicircular
director fields, with foci that lie outside the domain, provide a remarkably
accurate description of the optimal director field for a large range of values
of the various shape parameters.Comment: 12 pages, 10 figure

### Hydrodynamic object recognition using pressure sensing

Hydrodynamic sensing is instrumental to fish and some amphibians. It also represents, for underwater vehicles, an alternative way of sensing the fluid environment when visual and acoustic sensing are limited. To assess the effectiveness of hydrodynamic sensing and gain insight into its capabilities and limitations, we investigated the forward and inverse problem of detection and identification, using the hydrodynamic pressure in the neighbourhood, of a stationary obstacle described using a general shape representation. Based on conformal mapping and a general normalization procedure, our obstacle representation accounts for all specific features of progressive perceptual hydrodynamic imaging reported experimentally. Size, location and shape are encoded separately. The shape representation rests upon an asymptotic series which embodies the progressive character of hydrodynamic imaging through pressure sensing. A dynamic filtering method is used to invert noisy nonlinear pressure signals for the shape parameters. The results highlight the dependence of the sensitivity of hydrodynamic sensing not only on the relative distance to the disturbance but also its bearing

### A Novel Design of Dielectric Perfect Invisibility Devices

The aim of an invisibility device is to guide light around any object put
inside, being able to hide objects from sight. In this work, we propose a novel
design of dielectric invisibility media based on negative refraction and
optical conformal mapping that seems to create perfect invisibility. This
design has some advantages and more relaxed constraints compared with already
proposed schemes. In particular, it represents an example where the time delay
in a dielectric invisibility device is zero. Furthermore, due to impedance
matching of negatively refracting materials, the reflection should be close to
zero. These findings strongly indicate that perfect invisibility with optically
isotropic materials is possible. Finally, the area of the invisible space is
also discussed

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