Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

Implementing a structural continuity constraint and a halting method for the topology optimization of energy absorbers

This study investigates topology optimization of energy absorbing structures in which material damage is accounted for in the optimization process. The optimization objective is to design the lightest structures that are able to absorb the required mechanical energy. A structural continuity constraint check is introduced that is able to detect when no feasible load path remains in the finite element model, usually as a result of large scale fracture. This assures that designs do not fail when loaded under the conditions prescribed in the design requirements. This continuity constraint check is automated and requires no intervention from the analyst once the optimization process is initiated. Consequently, the optimization algorithm proceeds towards evolving an energy absorbing structure with the minimum structural mass that is not susceptible to global structural failure. A method is also introduced to determine when the optimization process should halt. The method identifies when the optimization method has plateaued and is no longer likely to provide improved designs if continued for further iterations. This provides the designer with a rational method to determine the necessary time to run the optimization and avoid wasting computational resources on unnecessary iterations. A case study is presented to demonstrate the use of this method.

Secure Full-Duplex Small-Cell Networks in a Spectrum Sharing Environment

In this paper, we propose three relay selection schemes for full-duplex heterogeneous networks in the presence of multiple cognitive radio eavesdroppers. In this setup, the cognitive small-cell nodes (secondary network) can share the spectrum licensed to the macro-cell system (primary network) on the condition that the quality-of-service of the primary network is always satisfied subjected to its outage probability constraint. The messages are delivered from one small-cell base station to the destination with the help of full-duplex small-cell base stations, which act as relay nodes. Based on the availability of the network’s channel state information at the secondary information source, three different selection criteria for full-duplex relays, namely: 1) partial relay selection; 2) optimal relay selection; and 3) minimal self-interference relay selection, are proposed. We derive the exact closed-form and asymptotic expressions of the secrecy outage probability for the three criteria under the attack of non-colluding/colluding eavesdroppers. We demonstrate that the optimal relay selection scheme outperforms the partial relay selection and minimal self-interference relay selection schemes at the expense of acquiring full channel state information knowledge. In addition, increasing the number of the full-duplex small-cell base stations can improve the security performance. At the illegitimate side, deploying colluding eavesdroppers and increasing the number of eavesdroppers put the confidential information at a greater risk. Besides, the transmit power and the desire outage probability of the primary network have great influences on the secrecy outage probability of the secondary network. 

An analysis of wind curtailment and constraint at a nodal level

Many countries have set challenging wind power targets to achieve by 2020. This paper implements a realistic analysis of curtailment and constraint of wind energy at a nodal level using a unit commitment and economic dispatch model of the Irish Single Electricity Market in 2020. The key findings show that significant reduction in curtailment can be achieved when the system non-synchronous penetration limit increases from 65% to 75%. For the period analyzed, this results in a decreased total generation cost and a reduction in the dispatch-down of wind. However, some nodes experience significant dispatch-down of wind, which can be in the order of 40%. This work illustrates the importance of implementing analysis at a nodal level for the purpose of power system planning.

Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition-an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers.

Screened Hybrid Exact Exchange Correction Scheme for Adsorption Energies on Perovskite Oxides

The bond formation between an oxide surface and oxygen, which is of importance for numerous surface reactions including catalytic reactions, is investigated within the framework of hybrid density functional theory that includes nonlocal Fock exchange. We show that there exists a linear correlation between the adsorption energies of oxygen on LaMO3 (M = Sc–Cu) surfaces obtained using a hybrid functional (e.g., Heyd–Scuseria–Ernzerhof) and those obtained using a semilocal density functional (e.g., Perdew–Burke–Ernzerhof) through the magnetic properties of the bulk phase as determined with a hybrid functional. The energetics of the spin-polarized surfaces follows the same trend as corresponding bulk systems, which can be treated at a much lower computational cost. The difference in adsorption energy due to magnetism is linearly correlated to the magnetization energy of bulk, that is, the energy difference between the spin-polarized and the non-spin-polarized solutions. Hence, one can estimate the correction ...