Langlands duality for finite-dimensional representations of quantum affine algebras

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this duality for the Kirillov-Reshetikhin modules and their irreducible tensor products. In the course of the proof we introduce and construct "interpolating (q,t)-characters" depending on two parameters which interpolate between the q-characters of a quantum affine algebra and its Langlands dual.Comment: 40 pages; several results and comments added. Accepted for publication in Letters in Mathematical Physic

Symmetric and Asymmetric Coalescence of Drops on a Substrate

The coalescence of viscous drops on a substrate is studied experimentally and theoretically. We consider cases where the drops can have different contact angles, leading to a very asymmetric coalescence process. Side view experiments reveal that the "bridge" connecting the drops evolves with self-similar dynamics, providing a new perspective on the coalescence of sessile drops. We show that the universal shape of the bridge is accurately described by similarity solutions of the one-dimensional lubrication equation. Our theory predicts a bridge that grows linearly in time and stresses the strong dependence on the contact angles. Without any adjustable parameters, we find quantitative agreement with all experimental observations.Comment: 5 pages, 4 figure

Copyright Protection of Color Imaging Using Robust-Encoded Watermarking

In this paper we present a robust-encoded watermarking method applied to color images for copyright protection, which presents robustness against several geometric and signal processing distortions. Trade-off between payload, robustness and imperceptibility is a very important aspect which has to be considered when a watermark algorithm is designed. In our proposed scheme, previously to be embedded into the image, the watermark signal is encoded using a convolutional encoder, which can perform forward error correction achieving better robustness performance. Then, the embedding process is carried out through the discrete cosine transform domain (DCT) of an image using the image normalization technique to accomplish robustness against geometric and signal processing distortions. The embedded watermark coded bits are extracted and decoded using the Viterbi algorithm. In order to determine the presence or absence of the watermark into the image we compute the bit error rate (BER) between the recovered and the original watermark data sequence. The quality of the watermarked image is measured using the well-known indices: Peak Signal to Noise Ratio (PSNR), Visual Information Fidelity (VIF) and Structural Similarity Index (SSIM). The color difference between the watermarked and original images is obtained by using the Normalized Color Difference (NCD) measure. The experimental results show that the proposed method provides good performance in terms of imperceptibility and robustness. The comparison among the proposed and previously reported methods based on different techniques is also provided

Vibrating soap films: An analog for quantum chaos on billiards

We present an experimental setup based on the normal modes of vibrating soap films which shows quantum features of integrable and chaotic billiards. In particular, we obtain the so-called scars -narrow linear regions with high probability along classical periodic orbits- for the classically chaotic billiards. We show that these scars are also visible at low frequencies. Finally, we suggest some applications of our experimental setup in other related two-dimensional wave phenomena.Comment: 5 pages, 7 figures. Better Postscript figures available on reques