Asymptotic properties of a new Sturm–Liouville problem with retarded argument

In this work, we study the asymptotic properties of a new Sturm–Liouville problem with retarded argument. Contrary to previous works, differential equation includes eigenparameter as a quadratic function. In the considered problem arise new difficulties. Copyright © 2013 John Wiley & Sons, Ltd.     

Tail asymptotics of random sum and maximum of log-normal risks

In this paper we derive the asymptotic behaviour of the survival function of both random sum and random maximum of log-normal risks. As for the case of finite sum and maximum investigated in Asmussen and Rojas-Nandayapa (2008) also for the more general setup of random sums and random maximum the principle of a single big jump holds. We investigate both the log-normal sequences and some related dependence structures motivated by stationary Gaussian sequences.     

An efficient task allocation framework for scheduled data in edge based Internet of Things using hybrid optimization algorithm approach

Allocation of tasks in IoT is an integral and critical approach to finding a perfect match between scheduled tasks of a particular application and Edge-based processing devices for instant response and efficient utilization of resources to make them renewable. We need a protocol to help optimize the problem of allocating processing devices to the tasks, as task allocation is considered an NP-hard problem to prevent problems with energy consumption and response time problems. For this, a hybrid bio-inspired Swarm-based approach will improve the solution to optimize the matching of a task to a particular device. This paper proposed a Meta-heuristic algorithm to optimize Energy and Time-delay for allocating tasks to the edge-based Processing device in IoT. The proposed algorithm called the Hybrid Artificial Bee Colony whales Optimization algorithm (HAWO) is formulated by integrating Artificial Bee Colony with the Whales Optimization algorithm to overcome the search process of an Artificial Bee Colony, which converges too soon due to the local search of Employee Bee phase and Onlooker Bee phase causing the problem of looping. From the simulation results conducted in Matlab, it is observed that the integrated HAWO method shows promising results in terms of Energy and Time Delay when compared with Artificial Bee Colony and Whales Optimization algorithms separately. Also, proposed method when compared with the benchmark work shows significant improvements of 50%, 25% and 60% in terms of Energy, Time Delay and Best cost, respectively.     

Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points

We examine - both experimentally and numerically - a two-dimensional nonlinear driven electrical lattice with honeycomb structure. Drives are considered over a range of frequencies both outside (below and above) and inside the band of linear modes. We identify a number of discrete breathers both existing in the bulk and also (predominantly) ones arising at the domain boundaries, localized either along the arm-chair or along the zig-zag edges. The types of edge-localized breathers observed and computed emerge in distinct frequency bands near the Dirac-point frequency of the dispersion surface while driving the lattice subharmonically (in a spatially homogeneous manner). These observations/computations can represent a starting point towards the exploration of the interplay of nonlinearity and topology in an experimentally tractable system such as the honeycomb electrical lattice.     

Edge states at the interface between monolayer and bilayer graphene

The electronic properties for monolayer-bilayer hybrid graphene with zigzag interface are studied by both the Dirac equation and numerical calculation in zero field and in a magnetic field. Basically there are two types of zigzag interface dependent on the way of lattice stacking at the edge. Our study shows they have different locations of the localized edge states. Accordingly, the energy-momentum dispersion and local density of states behave quit differently along the interface near the Fermi energy EF=0.     

Uniform theory of the boundary diffraction wave

A uniform version of the potential function of the Maggi-Rubinowicz boundary diffraction wave theory is obtained by using the large argument expansion of the Fresnel integral. The derived function is obtained for the problem of diffraction of plane waves by a circular edge. The results are plotted numerically.     

Research on Multi-Terminal’s AC Offloading Scheme and Multi-Server’s AC Selection Scheme in IoT

Mobile Edge Computing (MEC) technology and Simultaneous Wireless Information and Power Transfer (SWIPT) technology are important ones to improve the computing rate and the sustainability of devices in the Internet of things (IoT). However, the system models of most relevant papers only considered multi-terminal, excluding multi-server. Therefore, this paper aims at the scenario of IoT with multi-terminal, multi-server and multi-relay, in which can optimize the computing rate and computing cost by using deep reinforcement learning (DRL) algorithm. Firstly, the formulas of computing rate and computing cost in proposed scenario are derived. Secondly, by introducing the modified Actor-Critic (AC) algorithm and convex optimization algorithm, we get the offloading scheme and time allocation that maximize the computing rate. Finally, the selection scheme of minimizing the computing cost is obtained by AC algorithm. The simulation results verify the theoretical analysis. The algorithm proposed in this paper not only achieves a near-optimal computing rate and computing cost while significantly reducing the program execution delay, but also makes full use of the energy collected by the SWIPT technology to improve energy utilization.     

First-principles calculations of magnetic edge states in zigzag CrI3 nanoribbons

CrI₃ monolayer has recently drawn much attention due to its two-dimensional long range ferromagnetic order. We find that CrI₃ nanoribbons, which are strips of CrI₃ monolayer, can be used as building blocks of nanodevices. In this paper, we studied the atomic and electronic structures of CrI₃ zigzag nanoribbons by using first-principles calculations. CrI₃ zigzag nanoribbons are also ferromagnet. Interestingly, edge states exist in the system and play an important role in their electronic structures. They dominate the band structures around Fermi level and can be tuned by edge atomic structures. The intrinsic ferromagnetism and rich electronic structures enable CrI₃ zigzag nanoribbons a group of promising candidate materials for spintronics.     

Numerical investigations of the vortex interactions for a flow over a pitching foil at different stages

The fluid–structure interaction is investigated numerically for a two-dimensional flow (Re=2.5·10⁶) over a sinusoid-pitching foil by the SST (Shear Stress Transport) k–ω model. Although discrepancies in the downstroke phase, which are also documented in other numerical studies, are observed by comparing with experimental results, our current numerical results are sufficient to predict the mean features and qualitative tendencies of the dynamic stall phenomenon. These discrepancies are evaluated carefully from the numerical and experimental viewpoints.In this study, we have utilized Λ, which is the normalized second invariant of the velocity gradient tensor, to present the evolution of the Leading Edge Vortex (LEV) and Trailing Edge Vortex (TEV). The convective, pressure, and diffusion terms during the dynamic stall process are discussed based on the transport equation of Λ. It is found that the pressure term dominates the rate of the change of the rotation strength inside the LEV. This trend can hardly be observed directly by using the vorticity transport equation due to the zero baroclinic term for the incompressible flow.The mechanisms to delay the stall are categorized based on the formation of the LEV. At the first stage before the formation of the LEV in the upper surface, the pitching foil provides extra momentum into the fluid flows to resist the flow separation, and hence the stall is delayed. At the second stage, a low-pressure area travels with the evolution of the LEV such that the lift still can be maintained. Three short periods at the second stage corresponds to different flow patterns during the dynamic stall, and these short periods can be distinguished according to the trend of the pressure variation inside the LEV. The lift stall occurs when a reverse flow from the lower surface is triggered during the shedding of the LEV. For a reduced frequency k_f=0.15, the formation of the TEV happens right after the lift stall, and the lift can drop dramatically. With a faster reduced frequency k_f=0.25, the shedding of the LEV is postponed into the downstroke, and the interaction between the LEV and TEV becomes weaker correspondingly. Thus, the lift drops more gently after the stall. In order to acquire more reliable numerical results within the downstroke phase, the Large Eddy Simulation (LES), which is capable of better predictions for the laminar-to-turbulent transition and flow reattachment process, will be considered as the future work.