Gravitational field equations near an arbitrary null surface expressed as a thermodynamic identity

Previous work has demonstrated that the gravitational field equations in all Lanczos-Lovelock models imply a thermodynamic identity TdS=dE+PdV (where the variations are interpreted as changes due to virtual displacement along the affine parameter) in the near-horizon limit in static spacetimes. Here we generalize this result to any arbitrary null surface in an arbitrary spacetime and show that certain components of the Einstein's equations can be expressed in the form of the above thermodynamic identity. We also obtain an explicit expression for the thermodynamic energy associated with the null surface. Under appropriate limits, our expressions reduce to those previously derived in the literature. The components of the field equations used in obtaining the current result are orthogonal to the components used previously to obtain another related result, viz. that some components of the field equations reduce to a Navier-Stokes equation on any null surface, in any spacetime. We also describe the structure of Einstein's equations near a null surface in terms of three well-defined projections and show how the different results complement each other.Comment: v2, 25 pages, no figures, to appear in JHE

Network of Recurrent events - A case study of Japan

A recently proposed method of constructing seismic networks from 'record breaking events' from the earthquake catalog of California (Phy. Rev. E, 77 6,066104, 2008) was successfull in establishing causal features to seismicity and arrive at estimates for rupture length and its scaling with magnitude. The results of our implementation of this procedure on the earthquake catalog of Japan establishes the robustness of the procedure. Additionally, we find that the temporal distributions are able to detect heterogeneties in the seismicity of the region.Comment: 13 pages, 6 figures, 1 tabl

The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm

If gravity is an emergent phenomenon, as suggested by several recent results, then the structure of the action principle for gravity should encode this fact. With this motivation we study several features of the Einstein-Hilbert action and establish direct connections with horizon thermodynamics. We begin by introducing the concept of holographically conjugate variables (HCVs) in terms of which the surface term in the action has a specific relationship with the bulk term. In addition to g_{ab} and its conjugate momentum \sqrt{-g} M^{cab}, this procedure allows us to (re)discover and motivate strongly the use of f^{ab}=\sqrt{-g}g^{ab} and its conjugate momentum N^c_{ab}. The gravitational action can then be interpreted as a momentum space action for these variables. We also show that many expressions in classical gravity simplify considerably in this approach. For example, the field equations can be written in a form analogous to Hamilton's equations for a suitable Hamiltonian if we use these variables. More importantly, the variation of the surface term, evaluated on any null surface which acts a local Rindler horizon can be given a direct thermodynamic interpretation. The term involving the variation of the dynamical variable leads to T\delta S while the term involving the variation of the conjugate momentum leads to S\delta T. We have found this correspondence only for the choice of variables (g_{ab}, \sqrt{-g} M^{cab}) or (f^{ab}, N^c_{ab}). We use this result to provide a direct thermodynamical interpretation of the boundary condition in the action principle, when it is formulated in a spacetime region bounded by the null surfaces. We analyse these features from several different perspectives and provide a detailed description, which offers insights about the nature of classical gravity and emergent paradigm.Comment: 31 pages, published version with typos fixe

A New Simplified Algorithm Suitable for Implementation on FPGA for Turbo Codes

In this thesis, a new algorithm for Turbo codes and a novel implementation of turbo decoder employed with this algorithm is developed. The decoder has an optimal performance in terms of Bit Error Rate(BER) in all Signal to Noise Ratio(SNR) for all frame sizes and any states of Turbo codes. In hardware implementation, we combine the normalization and matrices modules in a single module in order to minimize the internal connection delay which is the bottleneck in hardware implementation, so that the result can be obtained in one single clock signal. Having implemented in this fashion, data rate of 28Mbps for16 state decoder has been achieved. This can be further improved by changing the algorithm for the normalization modules and LLR modules with MAX operator. The matrices modules with the proposed algorithm and the normalization and LLR modules with MAX-LOG-MAP algorithm have been implemented to achieve a data rate of 60Mbps

A Survey of Applications of Blockchain in Collective Decision-Making Scenarios in Swarm Robotics

Blockchain is a distributed ledger that was introduced to decentralize monetary systems. However, with time, the applications of blockchain in different realms have been identified. Swarm robotics is a field that combines swarm intelligence and robotics to solve real-world problems that cannot be solved by monolithic robots. Collective decision-making is one of the major behaviors implemented by swarm robotics. This study analyzes existing literature on the applications of blockchain in the collective decision-making scenarios in swarm robotics. Consequently, this study introduces a novel taxonomy to study the different applications effectively. The taxonomy categorizes existing literature into (i) application of blockchain in other areas of swarm robotics, (ii) application of blockchain in continuous collective decision-making scenarios, (iii) application of blockchain in discrete collective decision-making scenarios, (iv) application of blockchain in other discrete collective decision-making scenarios, and (v) application of blockchain in the collective perception scenario. Finally, the limitations of existing work such as excessive resource consumption and violation of swarm robotics principles are discussed