Topological mechanics in quasicrystals

We study topological mechanics in two-dimensional quasicrystalline parallelogram tilings. Topological mechanics has been studied intensively in periodic lattices in the past a few years, leading to the discovery of topologically protected boundary floppy modes in Maxwell lattices. In this paper we extend this concept to quasicrystalline parallelogram tillings and we use the Penrose tiling as our example to demonstrate how these topological boundary floppy modes arise with a small geometric perturbation to the tiling. The same construction can also be applied to disordered parallelogram tilings to generate topological boundary floppy modes. We prove the existence of these topological boundary floppy modes using a duality theorem which relates floppy modes and states of self stress in parallelogram tilings and fiber networks, which are Maxwell reciprocal diagrams to one another. We find that, due to the unusual rotational symmetry of quasicrystals, the resulting topological polarization can exhibit orientations not allowed in periodic lattices. Our result reveals new physics about the interplay between topological states and quasicrystalline order, and leads to novel designs of quasicrystalline topological mechanical metamaterials.Comment: 16 pages, 8 figure

Secure Decentralized Access Control Policy for Data Sharing in Smart Grid

Smart grid has improved the security, efficiency of the power system and balanced the supply and demand by intelligent management, which enhanced stability and reliability of power grid. The key point to achieve them is real-time data and consume data sharing by using fine-grained policies. But it will bring the leakage of the privacy of the users and losing of control over data for data owners. The reported solutions can not give the best trade-off among the privacy protection, control over the data shared and confidentiality. In addition, they can not solve the problems of large computation overhead and dynamic management such as users’ revocation. This paper aims at these problems and proposes a decentralized attribute-based data sharing scheme. The proposed scheme ensures the secure sharing of data while removing the central authority and hiding user’s identity information. It uses attribute-based signcryption(ABSC) to achieve data confidentiality and authentication. Under this model, attribute-based encryption gives the access policies for users and keeps the data confidentiality, and the attribute-based signature is used for authentication of the primary ciphertextintegrity. It is more efficient than ”encrypt and then sign” or ”sign and then encrypt”. In addition, the proposed scheme enables user’s revocation and public verifiability. Under the random oracle model, the security and the unforgeability against adaptive chosen message attack are demonstrated

Algebraic isomorphic spaces of ideal lattices, reduction of Ring-SIS problem, and new reduction of Ring-LWE problem

The main focus of this article is on an open problem, namely the Ring-SIS reduction problem.We first utilize a spatial isomorphism approach to reduce the Ring-SIS problem to the classic SIS problem in lattices, indirectly reducing it to the classic SIVP in lattices. This provides theoretical assurance to some extent for the difficulty and resistance against quantum attacks of the Ring-SIS problem. Additionally, we reduce the Ring-LWE problem to the Ring-SIS problem, which guarantees the security of encryption schemes based on Ring-LWE to a certain degree. Finally, this article proves that the difficulty of the Ring-SIS problem and the Ring-LWE problem is relatively average with respect to the spatial dimension or polynomial degree

Correlated rigidity percolation and colloidal gels

Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation

Rigidity percolation by next-nearest-neighbor bonds on generic and regular isostatic lattices

Theoretical Physic