Spatial dispersion and energy in strong chiral medium

Since the discovery of backward-wave materials, people have tried to realize strong chiral medium, which is traditionally thought impossible mainly for the reason of energy and spatial dispersion. We compare the two most popular descriptions of chiral medium. After analyzing several possible reasons for the traditional restriction, we show that strong chirality parameter leads to positive energy without any frequency-band limitation in the weak spatial dispersion. Moreover, strong chirality does not result in a strong spatial dispersion, which occurs only around the traditional limit point. For strong spatial dispersion where higher-order terms of spatial dispersion need to be considered, the energy conversation is also valid. Finally, we show that strong chirality need to be realized from the conjugated type of spatial dispersion.Comment: 6 pages, 2 figure

Axisymmetric Indentation Response of Functionally Graded Material Coating

In this chapter, the indentation response of the functionally graded material (FGM) coating is considered due to the contact between the coating and axisymmetric indenter. The mechanical properties of FGM coating is assumed to vary along the thickness direction. Three kinds of models are applied to simulate the variation of elastic parameter in the FGM coating based on the cylindrical coordinate system. The axisymmetric frictionless and partial slip contact problems are reduced to a set of Cauchy singular integral equations that can be numerically calculated by using the Hankel integral transform technique and the transfer matrix method. The effect of gradient of coating on the distribution of contact stress is presented. The present investigation will provide the guidance for the indentation experiment of coating

Gauss-Bonnet inflation with a constant rate of roll

We consider the constant-roll condition in the model of the inflaton nonminimal coupling to the Gauss-Bonnet term. By assuming the first Gauss-Bonnet flow parameter $\delta_1$ is a constant, we discuss the constant-roll inflation with constant $\epsilon_1$, constant $\epsilon_2$ and constant $\eta_H$, respectively. Using the Bessel function approximation, we get the analytical expressions for the scalar and tensor power spectrum and derive the scalar spectral index $n_{\mathcal{R}}$ and the tensor to scalar ratio $r$ to the first order of $\epsilon_1$. By using the Planck 2018 observations constraint on $n_{\mathcal{R}}$ and $r$, we obtain some feasible parameter space and show the result on the $n_{\mathcal{R}}-r$ region. The scalar potential is also reconstructed in some spectral cases