Mathematics with Only Rods

We discuss in this expository paper the rod system used in ancient China based on the mathematical classic work of Sun Zi, with a focus on application to solving systems of linear equations. The mathematics involved is authentic and beautiful, and we believe it is also of interest from historical, cultural, and pedagogical perspectives

Mathematics with Only Rods

We discuss in this expository paper the rod system used in ancient China based on the mathematical classic work of Sun Zi, with a focus on application to solving systems of linear equations. The mathematics involved is authentic and beautiful, and we believe it is also of interest from historical, cultural, and pedagogical perspectives

Stability Analysis and Variational Integrator for Real-Time Formation Based on Potential Field

This paper investigates a framework of real-time formation of autonomous vehicles by using potential field and variational integrator. Real-time formation requires vehicles to have coordinated motion and efficient computation. Interactions described by potential field can meet the former requirement which results in a nonlinear system. Stability analysis of such nonlinear system is difficult. Our methodology of stability analysis is discussed in error dynamic system. Transformation of coordinates from inertial frame to body frame can help the stability analysis focus on the structure instead of particular coordinates. Then, the Jacobian of reduced system can be calculated. It can be proved that the formation is stable at the equilibrium point of error dynamic system with the effect of damping force. For consideration of calculation, variational integrator is introduced. It is equivalent to solving algebraic equations. Forced Euler-Lagrange equation in discrete expression is used to construct a forced variational integrator for vehicles in potential field and obstacle environment. By applying forced variational integrator on computation of vehicles' motion, real-time formation of vehicles in obstacle environment can be implemented. Algorithm based on forced variational integrator is designed for a leader-follower formation

A micromechanics and machine learning coupled approach for failure prediction of unidirectional CFRP composites under triaxial loading: A preliminary study

This study presents a hybrid method based on artificial neural network (ANN) and micro-mechanics for the failure prediction of IM7/8552 unidirectional (UD) composite lamina under triaxial loading. The ANN is trained offline by numerical data from a high-fidelity micromechanics-based representative volume element (RVE) model using the finite element method (FEM). The RVE adopts identified constituent parameters from inverse analysis and calibrated interface strengths form uniaxial and biaxial tests. A hybrid loading strategy is proposed for the RVE under triaxial loading to obtain the failure points on sliced surfaces whilst maintaining the constant stress at different surfaces. It has been found that the ANN algorithm is robust in the failure prediction of the UD lamina when subjected to different triaxial loading conditions, with over 97.5% accuracy being achieved by the shallow ANN model, where only two hidden layers and 560 samples are used. The predicted 3D failure surface based on trained ANN model has an elliptical paraboloid shape and shows an extremely high strength in biaxial compression. The approach could be used to inform the modification of existing failure criteria and to propose ANN-based failure criteria

An improved closed-form solution to interfacial stresses in plated beams using a two-stage approach

The shear stress and the normal stresses in the thickness direction at interfaces (referred as interfacial shear and transverse normal stresses hereafter) have played a significant role in understanding the premature debonding failure of beams strengthened by bonding steel/composite plates at their tension surfaces. Due to the occurrence of dissimilar materials and the abrupt change of the cross section, the stress distribution at plate ends becomes singular and hence is considerably complicated. Extensive experimental and analytical analyses have been undertaken to investigate this problem. Large discrepancies have been found from various studies, particularly from experimental results due to the well-acknowledged difficulty in measuring interfacial stresses. Numerical analyses, e.g. 2-D or 3-D finite element analysis (FEA), may predict accurate results, but they demand laborious work on meshing and sensitivity analysis. Analytical solutions, in particular those in a closed form, are more desirable by engineering practitioners, as they can be readily incorporated into design equations. This paper reports an improved closed-form solution to interfacial stresses in plated beams using a two-stage approach. In this solution, beams and bonded plates can be further divided into a number of sub-layers to facilitate the inclusion of steel bars or multiple laminae. Thermal effects may also be considered by using equivalent mechanical loads, i.e. equivalent axial loads and end moments. Numerical examples are presented to show interfacial stresses in concrete or cast iron beams bonded with steel or FRP plates under mechanical and/or thermal loads. The effect of including the steel reinforcement with various ratios in the RC beam on the interfacial stresses is also investigated. Compared with previously published analytical results, this one improves the accuracy of predicting the transverse normal stresses in both adhesive-beam and plate-adhesive interfaces and the solution is in a closed form

Future global conflict risk hotspots between biodiversity conservation and food security: 10 countries and 7 Biodiversity Hotspots

Balancing biodiversity conservation and food security is the key to global sustainable development. However, we know little about the future global conflict risk hotspots between biodiversity and food security at both country and Biodiversity Hotspots (BHs) levels. First we calculated land use intensity index (LUII) based on future land use simulation, incorporated data on species richness(including birds, mammals and amphibians) and introduced the Global Food Security Index (GFSI). Then we used local indicators of spatial association (LISA) and bivariate choropleth map to identify the future global conflict risk hotspots between biodiversity conservation and food security. These include 10 countries (including Congo (Kinshasa), Sierra Leone, Malawi, Togo, Zambia, Angola, Guinea, Nigeria, Laos, Cambodia) and 7 BHs (Eastern Afromontane, Guinean Forests of West Africa, Horn of Africa, Indo-Burma, Mediterranean Basin, Maputaland-Pondoland-Albany and Tropical Andes). Special attention needs to be paid to these hotspots to balance biodiversity conservation and food security

Identifying Potential Cropland Losses When Conserving 30% and 50% Earth with Different Approaches and Spatial Scales

Biodiversity conservation is the cornerstone for sustainable development. Bold conservation targets provide the last opportunities to halt the human-driven mass extinction. Recently, bold conservation targets have been proposed to protect 30% or 50% of Earth. However, little is known about its potential impacts on cropland. We identify potential cropland losses when 30% and 50% of global terrestrial area is given back to nature by 2030/2050, at three spatial scales (global, biome and country) and using two approaches (“nature-only landscapes” and “shared landscapes”). We find that different targets, applied scales and approaches will lead to different cropland losses: (1) At the global scale, it is possible to protect 50% of the Earth while having minimum cropland losses. (2) At biome scale, 0.64% and 8.54% cropland will be lost globally in 2030 and 2050 under the nature-only approach while by contrast, the shared approach substantially reduces the number of countries confronted by cropland losses, demanding only 0% and 2.59% of global cropland losses in 2030 and 2050. (3) At the national scale, the nature-only approach causes losses of 3.58% and 10.73% of global cropland in 2030 and 2050, while the shared approach requires 0.77% and 7.55% cropland in 2030 and 2050. Our results indicate that bold conservation targets could be considered, especially when adopting the shared approach, and we suggest adopting ambitious targets (protecting at least 30% by 2030) at the UN Biodiversity Conference (COP 15) to ensure a sustainable future for Earth

Denoising Analysis of Partial Discharge Acoustic Signal Based on SVMD-PCA

Partial discharge (PD) acoustic signal detection is one of the effective means to assess the insulation status of power transformers. In actual monitoring, white noise is likely to cause strong interference to the partial discharge acoustic signal of the transformer, which seriously affects the discharge fault identification and monitoring results. In order to suppress the interference of white noise in partial discharge detection, this paper proposes an adaptive partial discharge based on the combination of variational mode decomposition (VMD) and principal component analysis (PCA) based on improved Spearman correlation coefficient. The white noise suppression method is analyzed for the separation and denoising of partial discharge acoustic signals in the environment of −10 ∼ 10 dB. Firstly, the Spearman correlation coefficient is used to determine the optimal number of decomposing modes of VMD. Then the decomposed modal components are adaptively reduced and reconstructed by principal component analysis to remove redundant clutter interference and reduce the influence of human error. Finally, through the simulation signal and actual discharge pulse acoustic signal are tested for denoising. The results show that SVMD-PCA can suppress the interference of white noise in partial discharge acoustic signals and extract clean discharge pulse signal characteristics, the method has enhanced anti-noise performance and can effectively suppress white noise interference