The notion of a Private Information Retrieval (PIR) code was recently introduced by Fazeli, Vardy and Yaakobi [1] who showed that this class of codes permit PIR at reduced levels of storage overhead in comparison with replicated-server PIR. In the present paper, the construction of an (n, k) τ -server binary, linear PIR code having parameters n = i=0 m i , k = m and τ = 2 is presented. These codes are obtained through homogeneouspolynomial evaluation and correspond to the binary, Projective Reed Muller (PRM) code. The construction can be extended to yield PIR codes for any τ of the form 2 , 2 − 1 and any value of k, through a combination of single-symbol puncturing and shortening of the PRM code. Each of these code constructions above, have smaller storage overhead in comparison with other PIR codes appearing in the literature.For the particular case of τ = 3, 4, we show that the codes constructed here are optimal, systematic PIR codes by providing an improved lower bound on the block length n(k, τ ) of a systematic PIR code. It follows from a result by Vardy and Yaakobi [2], that these codes also yield optimal, systematic primitive multi-set (n, k, τ ) B batch codes for τ = 3, 4. The PIR code constructions presented here also yield upper bounds on the generalized Hamming weights of binary PRM codes.

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We propose a generic model of driven DNA under the influence of an oscillatory force of amplitude F and frequency ν and show the existence of a dynamical transition for a chain of finite length. We find that the area of the hysteresis loop, A_{loop}, scales with the same exponents as observed in a recent study based on a much more detailed model. However, towards the true thermodynamic limit, the high-frequency scaling regime extends to lower frequencies for larger chain length L and the system has only one scaling (A_{loop}≈ν^{-1}F^{2}). Expansion of an analytical expression for A_{loop} obtained for the model system in the low-force regime revealed that there is a new scaling exponent associated with force (A_{loop}≈ν^{-1}F^{2.5}), which has been validated by high-precision numerical calculation. By a combination of analytical and numerical arguments, we also deduce that for large but finite L, the exponents are robust and independent of temperature and friction coefficient.

Geothermal energy is one of the most suitable sources of energy since it is possible to use it continuously for generating power and providing heat. Firstly, recent trends in geothermal energy are discussed and compared with other types of renewable energies. According to the results of this section, geothermal energy is an attractive choice for future power generation due to its low carbon dioxide emission and levelzied cost of electricity in comparison with other renewable energy sources. Afterwards, applications of nanofluid in geothermal-based energy systems are reviewed and their important results are represented. On the basis of literature review, using nanofluids can result in augment in geothermal systems. The enhancement is dependent on several factors including the type of nanofluid, concentration and system specification. According to the results of a study, the effect of using nanofluid on heat transfer rate became more significant at higher flow rates. In addition, using nanofluids can reduce the size of heat exchangers used in geothermal-based system. The main effects of employing nanofluids is increase in convective heat transfer and pressure loss.

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