Symmetry-regularized neural ordinary differential equations

Neural Ordinary Differential Equations (Neural ODEs) is a class of deep neural network models that interpret the hidden state dynamics of neural networks as an ordinary differential equation, thereby capable of capturing system dynamics in a continuous time framework. In this work, I integrate symmetry regularization into Neural ODEs. In particular, I use continuous Lie symmetry of ODEs and PDEs associated with the model to derive conservation laws and add them to the loss function, making it physics-informed. This incorporation of inherent structural properties into the loss function could significantly improve robustness and stability of the model during training. To illustrate this method, I employ a toy model that utilizes a cosine rate of change in the hidden state, showcasing the process of identifying Lie symmetries, deriving conservation laws, and constructing a new loss function

Effect of Different Water-Binder Ratios and Fiber Contents on the Fluidity and Mechanical Properties of PVA-ECC Materials

With the development of fiber-reinforced cement composites, the diversity and complexity of application scenarios require enhanced strength and ductility and tough materials in practical engineering. To explore the effects of different water-binder ratios and fiber contents on the fluidity, bending resistance, tensile properties, fracture toughness, and fracture behavior of polyvinyl alcohol (PVA) fiber cement composites, several groups of high ductility test blocks (PVA-engineering cementitious composites (ECC)) with different mixing ratios were designed in this study. Based on the expansion degree, the mechanical experimental data, and the electron microscopy scanning image results, K-value analysis was performed on the strain hardening strength criterion. The effect of the water–binder ratio and the fiber dosing on the PVA-ECC material was determined. Results show that the greater the water-binder ratio is, the better the fluidity of the ECC matrix is. In the same cement system and at the same water-binder ratio, the fluidity of the ECC paste gradually deteriorates with the increase of the fiber content. The water-binder ratio significantly affects the flexural tensile strength of the composite. The flexural and tensile strengths of the PVA-ECC gradually increase as the water-binder ratio decreases, but the ductility gradually decreases. The water-binder ratio of the substrate directly influences the damage behavior of the fibers within the substrate. With the gradual increase of the water-binder ratio, the fiber at the crack interface gradually changes from pull-out morphology to fracture morphology. The strain capacity and the multi-crack cracking performance decrease. To achieve improved working performance in the actual project, the matrix water-binder ratio should be controlled at approximately 0.45, and the PVA fiber dose of 1.7% is optimal. This study can provide a good reference for the optimization of practical engineering components

The deformation mechanism in the western Qiangtang terrane and its surroundings: evidence from magnetotelluric data

Located in the central part of the Tibetan Plateau, the Qiangtang terrane preserves important record of the uplift and deformation history of the Plateau, and therefore remains an attractive area of research. However, deep geophysical investigations of its western part are still limited. To further understand the deep structure of the western Qiangtang terrane and its surroundings, we use magnetotelluric array data to generate a 3D electrical structure. It reveals high resistivity anomalies in the upper crust and scattered high conductivity anomalies in the mid-lower crust. The electrical structure also suggests that the Longmu Co-Gozha Co fault once believed to be a major regional deformation boundary, may not have cut through the crust. The melt content and rheological parameters derived from the electrical structures show dominant ductile-type deformation in most of the study area, which contributes to block extrusion along the slip faults. Viscous deformation regions formed by mantle melt upwelling in the mid-lower crust may contribute to the formation of the N-S directed normal faults on the surface

3-D electrical structure and tectonic dynamics in the Yangbajing area based on the array magnetotelluric data

The well-known N-S-trending fault in the Yangbajing area plays a crucial role in the tectonic evolution of the Tibetan Plateau. Previous researches on a few E-W geophysical profiles suggested that the eastern shear at the base of the upper crust and/or lithosphere deformation brought on by asthenosphere upwelling are the major causes of the Yadong-Gulu rift’s creation. Here we propose a 3-D electrical resistivity model derived from the magnetotelluric (MT) array data spanning the Yadong-Gulu rift (YGR), and the distribution of temperature and melt fraction is estimated by the experimental calibrated relationships bridging electrical conductivity and temperature/melt fraction. The result reveals that the Indian slab subducted steeply in the east of the Yadong-Gulu rift, while Indian slab may have delaminated with a flat subduction angle in the west. The temperature distribution shows that the upper mantle of the northern Lhasa terrane is hotter than that of the southern Lhasa terrane. This is likely the result of mantle upwelling caused by either the subduction of the Indian slab or thickened Tibetan lithosphere delamination. Moreover, the strength of the mid-lower crust is so low that it may meet the conditions of the local crust flow in the west-east direction. The local crustal flow and the pulling force from the upwelling asthenosphere jointly contributed to the formation of the Yadong-Gulu rift. These main factors exist in different stages of the evolution of the Yadong-Gulu rift

In situ synthesis of interlinked three-dimensional graphene foam/polyaniline nanorod supercapacitor

Three-dimensional (3-D) graphene foam/PANI nanorods were fabricated by hydrothermal treatment of graphene oxide (GO) solution and sequentially in-situ synthesis of PANI nanorods on the surface of graphene hydrogel. 3-D graphene foam was used as substrate for the growth of PANI nanorods and it increases the specific surface area as well as the double layer capacitance performance of the graphene foam/PANI nanorod composite. The length of the PANI nanorod is about 340 nm. PANI nanorods exhibited a short stick shape. These PANI nanorods agglomerate together and the growth orientation is anisotropic. The highest specific capacitance of 3-D graphene/PANI nanorod composite electrodes is 352 F g−1 at the scan rate of 10 mV s−1.Institute of Textiles and Clothin