The semi-discrete AKNS system: Conservation laws, reductions and continuum limits

In this paper, the semi-discrete Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy is shown in spirit composed by the Ablowitz-Ladik flows under certain combinations. Furthermore, we derive its explicit Lax pairs and infinitely many conservation laws, which are non-trivial in light of continuum limit. Reductions of the semi-discrete AKNS hierarchy are investigated to include the semi-discrete Korteweg-de Vries (KdV), the semi-discrete modified KdV, and the semi-discrete nonlinear Schr\"odinger hierarchies as its special cases. Finally, under the uniform continuum limit we introduce in the paper, the above results of the semi-discrete AKNS hierarchy, including Lax pairs, infinitely many conservation laws and reductions, recover their counterparts of the continuous AKNS hierarchy

IPSO-ELM intelligent prediction of landslide displacement in complex and unstable area of karst landform

In southern China, the karst landform areas possess a complex geological and topographic environment, a fragile ecosystem, poor surface stability, and frequent occurrences of landslides and other geological disasters. To effectively monitor and predict such events, it is crucial to process landslide monitoring data and establish reliable prediction models. This paper presents an IPSO-ELM displacement prediction model that integrates the improved particle swarm optimization algorithm (IPSO) and extreme learning machine (ELM). The proposed coupling model predicts decomposed displacement subsequences individually, which are then reconstructed to obtain the total displacement prediction value. In this study, displacement monitoring data from a typical landslide in the karst landform area between 2007 and 2012 were selected. Various prediction and verification scenarios were established to validate the accuracy and stability of the prediction model. The MAPE of the IPSO-ELM model is 0.18%, which outperforms the ELM and BPNN models with MAPEs of 0.56% and 0.65%, respectively, in predicting landslide displacement in karst landform areas. This study provides a solid theoretical foundation and practical value for landslide displacement prediction

Microyielding of Core-Shell Crystal Dendrites in a Bulk-metallic-glass Matrix Composite

In-situ synchrotron x-ray experiments have been used to follow the evolution of the diffraction peaks for crystalline dendrites embedded in a bulk metallic glass matrix subjected to a compressive loading-unloading cycle. We observe irreversible diffraction-peak splitting even though the load does not go beyond half of the bulk yield strength. The chemical analysis coupled with the transmission electron microscopy mapping suggests that the observed peak splitting originates from the chemical heterogeneity between the core (major peak) and the stiffer shell (minor peak) of the dendrites. A molecular dynamics model has been developed to compare the hkl-dependent microyielding of the bulk metallic-glass matrix composite. The complementary diffraction measurements and the simulation results suggest that the interface, as Maxwell damper, between the amorphous matrix and the (211) crystalline planes relax under prolonged load that causes a delay in the reload curve which ultimately catches up with the original path

A Comprehensive Survey on Deep Graph Representation Learning

Graph representation learning aims to effectively encode high-dimensional sparse graph-structured data into low-dimensional dense vectors, which is a fundamental task that has been widely studied in a range of fields, including machine learning and data mining. Classic graph embedding methods follow the basic idea that the embedding vectors of interconnected nodes in the graph can still maintain a relatively close distance, thereby preserving the structural information between the nodes in the graph. However, this is sub-optimal due to: (i) traditional methods have limited model capacity which limits the learning performance; (ii) existing techniques typically rely on unsupervised learning strategies and fail to couple with the latest learning paradigms; (iii) representation learning and downstream tasks are dependent on each other which should be jointly enhanced. With the remarkable success of deep learning, deep graph representation learning has shown great potential and advantages over shallow (traditional) methods, there exist a large number of deep graph representation learning techniques have been proposed in the past decade, especially graph neural networks. In this survey, we conduct a comprehensive survey on current deep graph representation learning algorithms by proposing a new taxonomy of existing state-of-the-art literature. Specifically, we systematically summarize the essential components of graph representation learning and categorize existing approaches by the ways of graph neural network architectures and the most recent advanced learning paradigms. Moreover, this survey also provides the practical and promising applications of deep graph representation learning. Last but not least, we state new perspectives and suggest challenging directions which deserve further investigations in the future

Strengthening Methods of Room and Cryogenic Temperatures Mechanical Properties of Fe45Mn15Cr15Ni25 High Entropy Alloy

In order to develop cobalt-free low-cost high entropy alloys(HEAs), non equiatomic ratio Fe45Mn15Cr15Ni25 high entropy alloy was designed and prepared through thermodynamic parameters and phase diagram calculation, cold rolling and annealing processes, and the mechanical properties at ambient (293 K) and cryogenic temperatures (77 K) were analyzed. The results show that the single-phase face-centered cubic (FCC) high entropy alloy has excellent mechanical properties at room temperature and cryogenic temperatures. In particular, at 77 K, the cold-rolled alloy achieves the comprehensive properties of yield strength 1 020 MPa, tensile strength 1 180 MPa, and elongation 20%. For recrystallized alloy at ambient temperature, the intrinsic lattice stress is 86 MPa, the Hall-Petch coefficient is 534 MPa·μm1/2, and the grain boundary strengthening is obvious. For the cold-rolled alloy at cryogenic temperature, the strain hardening ability is restored, the dislocation strengthening is significant, and the strength and ductility are improved simultaneously

High-Entropy Alloys (HEAs)

High-entropy alloys (HEAs) [1,2] loosely refer to multi-principal-element solid solution alloys due to their high configurational entropy, in contrast to traditional alloys, which focus on the edge or corner of phase diagrams with one principal component[...