Asymptotics of Wigner 3nj-symbols with Small and Large Angular Momenta: an Elementary Method

Yu and Littlejohn recently studied in arXiv:1104.1499 some asymptotics of Wigner symbols with some small and large angular momenta. They found that in this regime the essential information is captured by the geometry of a tetrahedron, and gave new formulae for 9j, 12j and 15j-symbols. We present here an alternative derivation which leads to a simpler formula, based on the use of the Ponzano-Regge formula for the relevant tetrahedron. The approach is generalized to Wigner 3nj-symbols with some large and small angular momenta, where more than one tetrahedron is needed, leading to new asymptotics for Wigner 3nj-symbols. As an illustration, we present 15j-symbols with one, two and four small angular momenta, and give an alternative formula to Yu's recent 15j-symbol with three small spins.Comment: 17 page

Harmonic Superspace from the AdS5×S5AdS_5\times S^5 Pure Spinor Formalism

On-shell supergravity vertex operators in an $AdS_5\times S^5$ background are described in the pure spinor formalism by the zero mode cohomology of a BRST operator. After expanding the pure spinor BRST operator in terms of the $AdS_5$ radius variable, this cohomology is computed using N=4 harmonic superspace variables and explicit superfield expressions are obtained for the behavior of supergravity vertex operators near the boundary of $AdS_5$.Comment: Fixed typos and added reference

Zero refractive index in space-time acoustic metamaterials

New scientific investigations of artificially structured materials and experiments have exhibit wave manipulation to the extreme. In particular, zero refractive index metamaterials have been on the front line of wave physics research for their unique wave manipulation properties and application potentials. Remarkably, in such exotic materials, time-harmonic fields have infinite wavelength and do not exhibit any spatial variations in their phase distribution. This unique feature can be achieved by forcing a Dirac cone to the center of the Brillouin zone ( point), as previously predicted and experimentally demonstrated in time-invariant metamaterials by means of accidental degeneracy between three different modes. In this article, we propose a different approach that enables true conical dispersion at with twofold degeneracy, and generates zero index properties. We break time-reversal symmetry and exploit a space-time modulation scheme to demonstrate a time-Floquet acoustic metamaterial with zero refractive index. This behavior, predicted using stroboscopic analysis, is confirmed by fullwave finite elements simulations. Our results establish the relevance of space-time metamaterials as a novel reconfigurable platform for wave control

Non-Reciprocal gain in non-Hermitian time-Floquet Systems

We explore the unconventional wave scattering properties of non-Hermitian systems in which amplification or damping are induced by time-periodic modulation. These non- Hermitian time-Floquet systems are capable of non-reciprocal operations in the frequency domain, which can be exploited to induce novel physical phenomena such as unidirectional wave amplification and perfect non-reciprocal response with zero or even negative insertion losses. This unique behavior is obtained by imparting a specific low-frequency time-periodic modulation to the coupling between lossless resonators, promoting only upward frequency conversion, and leading to non-reciprocal parametric gain. We provide a full-wave demonstration of our findings in a one-way microwave amplifier, and establish the potential of non-Hermitian time-Floquet devices for insertion-loss free microwave isolation and unidirectional parametric amplification.Comment: 15 pages, 4 figure

Fuzzy Logic Control of Adaptive ARQ for Video Distribution over a Bluetooth Wireless Link

Bluetooth's default automatic repeat request (ARQ) scheme is not suited to video distribution resulting in missed display and decoded deadlines. Adaptive ARQ with active discard of expired packets from the send buffer is an alternative approach. However, even with the addition of cross-layer adaptation to picture-type packet importance, ARQ is not ideal in conditions of a deteriorating RF channel. The paper presents fuzzy logic control of ARQ, based on send buffer fullness and the head-of-line packet's deadline. The advantage of the fuzzy logic approach, which also scales its output according to picture type importance, is that the impact of delay can be directly introduced to the model, causing retransmissions to be reduced compared to all other schemes. The scheme considers both the delay constraints of the video stream and at the same time avoids send buffer overflow. Tests explore a variety of Bluetooth send buffer sizes and channel conditions. For adverse channel conditions and buffer size, the tests show an improvement of at least 4 dB in video quality compared to nonfuzzy schemes. The scheme can be applied to any codec with I-, P-, and (possibly) B-slices by inspection of packet headers without the need for encoder intervention.</jats:p