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In the present work, the scattering of water waves by undulating bottom in a two-layer fluid system is investigated by the inclusion of current, surface tension and interfacial tension to better understand the phenomenon of wave blocking. The perturbation technique followed by the Fourier transform method is applied to solve the coupled boundary value problem. The associated velocity potentials, Bragg reflection coefficients, and Bragg transmission coefficients are obtained in integral forms. A particular case of the undulating bottom, namely sinusoidal bottom undulation, has been taken into consideration for showing the effects of current speed and surface tension. A shift in the Bragg resonant frequency is observed with a change in the current speed. Further, the combined effects of Bragg resonance and wave blocking are investigated. For some values of opposing current, the group velocity vanishes at two distinct points in the frequency space; the maxima is known as the primary blocking point and the minima is called as the secondary blocking point. For each frequency, there exist three propagating modes between these two blocking points. Certain abnormalities and a sharp increase in the Bragg reflection and transmission coefficients are caused by the superposition of various propagating wave modes and triad interaction within the blocking points as well as a change in the incident wave mode. Mathematics Subject Classification: 76B15, 42A38, 35Q35.

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With the increased use of social media platforms by people across the world, many new interesting NLP problems have come into existence. One such being the detection of sarcasm in the social media texts. We present a corpus of tweets for training custom word embeddings and a Hinglish dataset labelled for sarcasm detection. We propose a deep learning based approach to address the issue of sarcasm detection in Hindi-English code mixed tweets using bilingual word embeddings derived from FastText and Word2Vec approaches. We experimented with various deep learning models, including CNNs, LSTMs, Bi-directional LSTMs (with and without attention). We were able to outperform all state-of-the-art performances with our deep learning models, with attention based Bi-directional LSTMs giving the best performance exhibiting an accuracy of 78.49%.