Calibration of Discrete Element Heat Transfer Parameters by Central Composite Design

The efficiency and precision of parameter calibration in discrete element method （DEM） are not satisfactory, and parameter calibration for granular heat transfer is rarely involved. Accordingly, parameter calibration for granular heat transfer with the DEM is studied. The heat transfer in granular assemblies is simulated with DEM, and the effective thermal conductivity （ETC） of these granular assemblies is measured with the transient method in simulations. The measurement testbed is designed to test the ETC of the granular assemblies under normal pressure and a vacuum based on the steady method. Central composite design （CCD） is used to simulate the impact of the DEM parameters on the ETC of granular assemblies, and the heat transfer parameters are calibrated and compared with experimental data. The results show that, within the scope of the considered parameters, the ETC of the granular assemblies increases with an increasing particle thermal conductivity and decreases with an increasing particle shear modulus and particle diameter. The particle thermal conductivity has the greatest impact on the ETC of granular assemblies followed by the particle shear modulus and then the particle diameter. The calibration results show good agreement with the experimental results. The error is less than 4%, which is within a reasonable range for the scope of the CCD parameters. The proposed research provides high efficiency and high accuracy parameter calibration for granular heat transfer in DEM.

Discrete spatial solitons formed in periodically poled lithium niobate by electro-optical effect

We report the numerical observation of discrete spatial solitons in a periodically poled lithium niobate waveguide array by applying an electrical field through electro-optical effect. We show that discrete spatial soliton can be controlled by applied voltage in the periodically poled lithium niobate.

Representative elementary volume analysis of polydisperse granular packings using discrete element method

The representative elementary volume （REV） for three-dimensional polydisperse granular packings was determined using discrete element method simulations. Granular mixtures of various sizes and particle size distributions were poured into a cuboid chamber and subjected to uniaxial compression, Findings showed that the minimum REV for porosity was larger compared with the REV for parameters such as coordination number, effective elastic modulus, and pressure ratio. The minimum REV for porosity and other parameters was found to equal 15,10, and 5 times the average grain diameter, respectively. A study of the influence of sample size on energy dissipation in random packing of spheres has also confirmed that the REV size is about 15 times the average grain diameter. The heterogeneity of systems was found to have no effect on the REV for the parameters of interest for the narrow range of coefficient of uniformity analyzed in this paper. As the REV approach is commonly applied in both experimental and numerical studies, determining minimum REV size for polydisperse granular packings remains a crucial issue.

THE DISLOC ATION EQU ATIONS OF A SIMPLE CUBIC CRYSTAL IN THE ISOTROPIC APPROXIMATION-A SOLVABLE MODEL

The dislocation equations of a simple cubic lattice have been obtained by using Green＇s function method based on the discrete lattice theory with the coefficients of the secondorder differential terms and the integral terms have been given explicitly in advance. The simple cubic lattice we have discussed is a solvable model, which is obtained according to the lattice statics and the symmetry principle and can verify and validate the dislocation lattice theory. It can present unified dislocation equations which are suitable for most of metals with arbitral lattice structures. Through comparing the results of the present solvable model with the dislocation lattice theory, it can be seen that, the coefficients of integral terms of the edge and screw components we obtain are in accordance with the results of the dislocation lattice theory, however, the coefficient of the second-order differential term of the screw component is not in agreement with the result of the dislocation lattice theory. This is mainly caused by the reduced dynamical matrix of the surface term, which is the essence to obtain the dislocation equation. According to the simple cubic solvable model, not only the straight dislocations but also the curved dislocations, such as the kink, can be investigated further.