A new shell formulation for graphene structures based on existing ab-initio data

An existing hyperelastic membrane model for graphene calibrated from ab-initio data (Kumar and Parks, 2014) is adapted to curvilinear coordinates and extended to a rotation-free shell formulation based on isogeometric finite elements. Therefore, the membrane model is extended by a hyperelastic bending model that reflects the ab-inito data of Kudin et al. (2001). The proposed formulation can be implemented straight-forwardly into an existing finite element package, since it does not require the description of molecular interactions. It thus circumvents the use of interatomic potentials that tend to be less accurate than ab-initio data. The proposed shell formulation is verified and analyzed by a set of simple test cases. The results are in agreement to analytical solutions and satisfy the FE patch test. The performance of the shell formulation for graphene structures is illustrated by several numerical examples. The considered examples are indentation and peeling of graphene and torsion, bending and axial stretch of carbon nanotubes. Adhesive substrates are modeled by the Lennard-Jones potential and a coarse grained contact model. In principle, the proposed formulation can be extended to other 2D materials.Comment: New examples are added and some typos are removed. The previous results are unchanged, International Journal of Solids and Structures (2017

On the handover security key update and residence management in LTE networks

In LTE networks, key update and residence management have been investigated as an effective solution to cope with desynchronization attacks in mobility management entity (MME) handovers. In this paper, we first analyse the impacts of the key update interval (KUI) and MME residence interval (MRI) on the handover performance in terms of the number of exposed packets (NEP) and signaling overhead rate (SOR). By deriving the bounds of the NEP and SOR over the KUI and MRI, it is shown that there exists a tradeoff between the NEP and the SOR, while our aim is to minimise both of them simultaneously. This accordingly motivates us to propose a multiobjective optimisation problem to find the optimal KUI and MRI that minimise both the NEP and SOR. By introducing a relative importance factor between the SOR and NEP along with their derived bounds, we further transform the proposed optimisation problem into a single-objective optimisation problem which can be solved via a simple numerical method. In particular, the results show that a higher accuracy of up to 1 second is achieved with the proposed approach while requiring a lower complexity compared to the conventional approach employing iterative searches

Enhancing security of MME handover via fractional programming and Firefly algorithm

Key update and residence management have been investigated as an effective solution to cope with desynchronisation attacks in Mobility Management Entity (MME) handovers. In this paper, we first analyse the impacts of the Key Update Interval (KUI) and MME Residence Interval (MRI) on handover processes and their secrecy performance in terms of the Number of Exposed Packets (NEP), Signaling Overhead Rate (SOR) and Outage Probability of Vulnerability (OPV). Specifically, the bounds of the derived NEP and SOR not only capture their behaviours at the boundary of the KUI and MRI, but also show the trade-off between the NEP and SOR. Additionally, through the analysis of the OPV, it is shown that the handover security can be enhanced by shortening the KUI and the desynchonisation attacks can be avoided with high-mobility users. The above facts accordingly motivate us to propose a Multi- objective Optimisation (MO) problem to find the optimal KUI and MRI that minimise both the NEP and SOR subject to the constraint on the OPV. To this end, two scalarisation techniques are adopted to transform the proposed MO problem into single- objective optimisation problems, i.e., an achievement-function method via Fractional Programming (FP) and a weighted-sum method. Based on the derived bounds on NEP and SOR, the FP approach can be optimally solved via a simple numerical method. For the weighted-sum method, the Firefly Algorithm (FA) is utilised to find the optimal solution. The results show that both techniques can solve the proposed MO problem with a significantly reduced searching complexity compared to the conventional heuristic iterative search technique

Maximal LpL^p-regularity for stochastic evolution equations

We prove maximal $L^p$-regularity for the stochastic evolution equation \{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t), \qquad t\in [0,T], U(0) & = u_0, {aligned}. under the assumption that $A$ is a sectorial operator with a bounded $H^\infty$-calculus of angle less than $\frac12\pi$ on a space $L^q(\mathcal{O},\mu)$. The driving process $W_H$ is a cylindrical Brownian motion in an abstract Hilbert space $H$. For $p\in (2,\infty)$ and $q\in [2,\infty)$ and initial conditions $u_0$ in the real interpolation space \XAp we prove existence of unique strong solution with trajectories in L^p(0,T;\Dom(A))\cap C([0,T];\XAp), provided the non-linearities F:[0,T]\times \Dom(A)\to L^q(\mathcal{O},\mu) and B:[0,T]\times \Dom(A) \to \g(H,\Dom(A^{\frac12})) are of linear growth and Lipschitz continuous in their second variables with small enough Lipschitz constants. Extensions to the case where $A$ is an adapted operator-valued process are considered as well. Various applications to stochastic partial differential equations are worked out in detail. These include higher-order and time-dependent parabolic equations and the Navier-Stokes equation on a smooth bounded domain \OO\subseteq \R^d with $d\ge 2$. For the latter, the existence of a unique strong local solution with values in (H^{1,q}(\OO))^d is shown.Comment: Accepted for publication in SIAM Journal on Mathematical Analysi

Cellular O-Glycome Reporter/Amplification to explore O-glycans of living cells

Protein O-glycosylation has key roles in many biological processes, but the repertoire of O-glycans synthesized by cells is difficult to determine. Here we describe an approach termed Cellular O-Glycome Reporter/Amplification (CORA), a sensitive method used to amplify and profile mucin-type O-glycans synthesized by living cells. Cells convert added peracetylated benzyl-α-N-acetylgalactosamine to a large variety of modified O-glycan derivatives that are secreted from cells, allowing for easy purification for analysis by HPLC and mass spectrometry (MS). Relative to conventional O-glycan analyses, CORA resulted in an ∼100-1,000-fold increase in sensitivity and identified a more complex repertoire of O-glycans in more than a dozen cell types from Homo sapiens and Mus musculus. Furthermore, when coupled with computational modeling, CORA can be used for predictions about the diversity of the human O-glycome and offers new opportunities to identify novel glycan biomarkers for human diseases