Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors

The main objective of the present numerical analysis is to predict the nonlinear frequency ratios associated with the nonlinear free vibration response of porous composite plates at microscale in the presence of different microstructural gradient tensors.To achieve this end,by taking cubic-type elements into account,isogeometric models of porous composite microplates are obtained with and without a central cutout and relevant to various porosity patterns of distribution along the plate thickness.The established unconventional models have the capability to capture the effects of various unconventional gradient tensors continuity on the basis of a refined shear deformable plate formulation.For the simply supported microsized uniform porous functionally graded material(UPFGM)plate having the oscillation amplitude equal to the plate thickness,it is revealed that the rotation gradient tensor causes to reduce the frequency ratio about 0.73%,the dilatation gradient tensor causes to reduce it about 1.93%,and the deviatoric stretch gradient tensor leads to a decrease of it about 5.19%.On the other hand,for the clamped microsized U-PFGM plate having the oscillation amplitude equal to the plate thickness,these percentages are equal to 0.62%,1.64%,and 4.40%,respectively.Accordingly,it is found that by changing the boundary conditions from clamped to simply supported,the effect of microsize on the reduction of frequency ratio decreases a bit.

Geometrical optics approximation of light scattering by large air bubbles

For large spherical bubbles in water, geometrical optics approximation is considered a better method for calculating light scattering patterns. In this paper, the basic theory of geometrical optics approximation is clarified. The change of phase for bubbles is calculated when total reflection occurs, which is different from particles with relative refractive indices larger than 1. Verification of the method was achieved by assuming a spherical particle and comparing present results to Mie scattering and Debye calculation. Agreement with the Mie theory was excellent in all directions when the dimensionless size parameter is larger than 50. Limitations of the geometrical optics approximation are also discussed.

Energy Efficiency Optimization for D2D Communications Based on SCA and GP Method

In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellular user. Taking the maximum allowed transmit power and the minimum data rate requirement into consideration, we formulate the energy efficiency maximization problem as a non-concave fractional programming(FP) problem and then develop a two-loop iterative algorithm to solve it. In the outer loop, we adopt Dinkelbach method to equivalently transform the FP problem into a series of parametric subtractive-form problems, and in the inner loop we solve the parametric subtractive problems based on successive convex approximation and geometric programming method to obtain the solutions satisfying the KarushKuhn-Tucker conditions. Simulation results demonstrate the validity and efficiency of the proposed scheme, and illustrate the impact of different parameters on system performance.

Rendering discrete participating media using geometrical optics approximation

We consider the scattering of light in participating media composed of sparsely and randomly distributed discrete particles.The particle size is expected to range from the scale of the wavelength to several orders of magnitude greater,resulting in an appearance with distinct graininess as opposed to the smooth appearance of continuous media.One fundamental issue in the physically-based synthesis of such appearance is to determine the necessary optical properties in every local region.Since these properties vary spatially,we resort to geometrical optics approximation(GOA),a highly efficient alternative to rigorous Lorenz–Mie theory,to quantitatively represent the scattering of a single particle.This enables us to quickly compute bulk optical properties for any particle size distribution.We then use a practical Monte Carlo rendering solution to solve energy transfer in the discrete participating media.Our proposed framework is the first to simulate a wide range of discrete participating media with different levels of graininess,converging to the continuous media case as the particle concentration increases.