First-principles study of stability and electronic properties of single-element 2D materials

We have estimated stability of single-element 2D materials (C2, N2, Si2, P2, Ge2, As2, Sn2, Sb2, Pb2, and Bi2) by ab initio calculations. The calculations of structural and mechanical properties of 2D materials were performed using the VASP software package. The results of calculations of stiffness tensors, Young's modulus, and Poisson's ratios show that all studied single-element 2D materials are mechanically stable. Dynamic stability was investigated by calculating the phonon dispersion of the materials using the finite displacement method. Only Pb2 has imaginary modes in the phonon dispersion curves and therefore it has dynamic unstable structure at low temperatures. The analysis of the band structures indicates the presence of insulators (N2), semiconductors (P2, As2, Bi2, Sb2), semimetals, and metals among the studied group of single-element 2D materials.

APPLICATION OF ANALYTICAL SOLUTIONS FOR BENDING BEAMS IN THE METHOD OF MOVEMENT

Introduction: Usually, to analyze statically indeterminate rod systems, the classical displacement method and preprepared tables for two types of rods of the main system are used. A mathematically correct representation of local loads with the use of generalized functions makes it possible to find an accurate solution of the differential equation for the equilibrium of a beam exposed to an arbitrary transverse load. Purpose of the study: We aimed to obtain analytical expressions for functions of deflection, rotation angles, transverse forces, and bending moments depending on four types of local loads for beams with different boundary conditions, so as to apply accurate solutions in the displacement method. Methods: We propose an analytical form of the displacement method to analyze rod structural models. For beams exposed to different types of transverse load (uniformly distributed force, concentrated force, or a couple of forces), accurate analytical solutions were obtained for functions of deflection, bending moments, and transverse forces at different types of beam ends’ restraint. This is possible due to the fact that concentrated load and load in the form of the moment of force can be specified by using unit column functions. By transforming Mohr’s integrals, using integration by parts, we show that the system of canonical equations of the displacement method was obtained based on the Lagrange principle. Results: Based on the analysis of a statically indeterminate frame, the effectiveness of the proposed analytical method is shown as compared with the classical displacement method.

A Solution of Subgrade Modulus for Response Displacement Method of Circular Underground Structures

In the seismic analysis and design of the underground structure, the response displacement method, as a pseudostatic method, has been widely adopted for its solid theoretical background, clear physical concept, and ease of implementation. The subgrade modulus is an essential parameter to the response displacement method, and a few approaches are available to determine its value. However, the existing methods neglect the interaction between the radial and tangential subgrade modulus and the influence of actual ground deformation, resulting in an inaccurate estimation. This study presents a solution to overcome these defects for the response displacement method adopted in the transverse seismic analysis of the shield tunnel with a circular cross section. First, the analytical solutions of subgrade modulus for ground deformation modes described by the Fourier series are derived based on the theory of elasticity. The ratio of the radial displacement to tangential displacement is introduced to create a link between the radial and tangential subgrade modulus. Based on the solutions of subgrade modulus for different ground deformation modes, the displacement fitting method is proposed to derive the subgrade modulus corresponding to the actual ground deformation. With this method, the subgrade modulus would adjust according to the ground displacement. Finally, a case study is conducted to illustrate the validity of the displacement fitting method.

Comparison of Preoperative Measurement Methods of Alveolar Cleft Volume Using Cone Beam Computed Tomography between Computer Simulation and Water Displacement Methods

Objective To compare the use of a computer simulation by Mimics software and the water displacement method as means for measurement of alveolar cleft volume on cone beam computed tomography (CBCT) data. Design Prospective study. Settling Institutional research. Patients Patients with unilateral complete cleft lip and palate (UCCLP) who would undergo alveolar bone grafting. Interventions CBCT images of twenty patients with UCCLP were included in the study. In the first method, the water displacement method was adopted to measure volume of plasticine filled in the alveolar cleft imprinted on 3D printed model of maxilla. In the second method a volumetric assessment function in Mimics software was adopted to measure volume of 3D virtual model of alveolar cleft constructed from CBCT images. A comparison on the alveolar cleft volumes derived from the two methods was assessed using the statistical paired t-test. Main Outcome Measure The paired-t test showed no statistically significant difference between alveolar cleft volumes measured by the two methods ( P = 0.075). Results Mean volume of the alveolar cleft measured by the water displacement method was 1.03 ± 0.31 ml whereas by the computer simulation using Mimics software the value was 1.00 ± 0.31 ml. The mean difference between the two methods was 0.03 ± 0.08 ml. Conclusion The computer simulation by Mimics software as a means for measurement of alveolar cleft volume on CBCT data is as accurate as the measurement by the water displacement method.

Measuerment of CO2-crude oil minimum miscible pressure in YC Oilfield by core displacement method

Aiming at the defect of measuring the CO2-crude oil MMP(minimum miscible pressure) by the slim tube test, the core displacement method is established based on indoor physical simulation and homogeneous rectangular core in the low permeability block of YC oilfield. For comparison, the MMP is measured by the slim tube test in the same block. Experimental results show that the method has good repeatability and can simulate porous media and reservoir water content, which is more consistent with the actual reservoir conditions. The MMP in the target block of YC oilfield was 19.85MPa, which was 1.87MPa lower than that measured by traditional slim tube test.