A new micromechanical approach of micropolar continuum modeling for 2-D periodic cellular material

In this paper, we present a new united approach to formulate the equivalent micropolar constitutive relation of two-dimensional（2-D） periodic cellular material to capture its non-local properties and to explain the size effects in its structural analysis. The new united approach takes both the displacement compatibility and the equilibrium of forces and moments into consideration, where Taylor series expansion of the displacement and rotation fields and the extended averaging procedure with an explicit enforcement of equilibrium are adopted in the micromechanical analysis of a unit cell.In numerical examples, the effective micropolar constants obtained in this paper and others derived in the literature are used for the equivalent micropolar continuum simulation of cellular solids. The solutions from the equivalent analysis are compared with the discrete simulation solutions of the cellular solids. It is found that the micropolar constants developed in this paper give satisfying results of equivalent analysis for the periodic cellular material.

Improved third-order nonlinear effect in graphene based on bound states in the continuum

The scattering matrix theory has been developed to calculate the third-order nonlinear effect in sphere-grapheneslab structures. By designing structural parameters, we have demonstrated that the incident electromagnetic wave can be well confined in the graphene in these structures due to the formation of a bound state in the continuum(BIC) of radiation modes. Based on such a bound state, third-harmonic(TH) generation and four-wave mixing(FWM) have been studied. It is found that the efficiency of TH generation in monolayer graphene can be enhanced about 7 orders of magnitude. It is interesting that we can design structure parameters to make all beams(the pump beam, probe beam, and generated FWM signal) be BICs at the same time. In such a case, the efficiency of FWM in monolayer graphene can be enhanced about 9 orders of magnitude. Both the TH and FWM signals are sensitive to the wavelength, and possess high Q factors, which exhibit very good monochromaticity. By taking suitable BICs, the selective generation of TH and FWM signals for S-and P-polarized waves can also be realized,which is beneficial for the design of optical devices.

Triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis

A triaxially deformed relativistic Hartree–Bogoliubov theory in the Woods–Saxon basis is developed with the aim of treating the triaxial deformation,pairing correlations and continuum in a unified way.In order to consider the triaxial deformation,the deformed potentials are expanded in terms of spherical harmonic functions in the coordinate space.In order to take the pairing correlations into account and treat the continuum properly,by using the Dirac Woods–Saxon basis,which has correct asymptotic behavior,the relativistic Hartree–Bogoliubov equation with triaxial deformation is solved.The formalism of triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is presented.Taking an axially deformed nucleus24Ne and a triaxially deformed nucleus76Ge as examples,the numerical checks are performed.A weakly bound nucleus112Ge is taken as an example to carry out the necessary converge checks for the numerical parameters.In addition,the ground-state properties of even–even germanium isotopes are investigated.The evolutions of two-neutron separation energy,deformation,root-mean-square radii and density distribution with mass number are analyzed.The comparison between the calculations from the relativistic Hartree–Bogoliubov theory based on harmonic-oscillator basis and the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is performed.It is found that the neutron drip line is extended from114Ge to118Ge in the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis.