Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State

Many problems in the fields of science and engineering, particularly in materials science and fluid dynamic, involve flows with multiple phases and components. From mathematical modeling point of view, it is a challenge to perform numerical simulations of multiphase flows and study interfaces between phases, due to the topological changes, inherent nonlinearities and complexities of dealing with moving interfaces. In this work, we investigate numerical solutions of a diffuse interface model with Peng-Robinson equation of state. Based on the invariant energy quadratization approach, we develop first and second order time stepping schemes to solve the liquid-gas diffuse interface problems for both pure substances and their mixtures. The resulting temporal semi-discretizations from both schemes lead to linear systems that are symmetric and positive definite at each time step, therefore they can be numerically solved by many efficient linear solvers. The unconditional energy stabilities in the discrete sense are rigorously proven, and various numerical simulations in two and three dimensional spaces are presented to validate the accuracies and stabilities of the proposed linear schemes

Effect of Inclination Angle on the Response of Double-row Retaining Piles: Experimental and Numerical Investigation

The excavation depth of foundation pits has been increasing along with the continuous development of underground space and high-rise buildings. As a result, traditional double-row vertical piles cannot meet the ground settlement and deflection requirements. This study proposed a double-row pile optimization method to extend the suitability of double-row retaining piles to greater excavation depth. The optimization model was established by adjusting the inclination angle of the front and rear piles. Physical scale model tests were performed to analyze the effect of the inclination angle on the pile head displacements and bending moments during excavations and step loadings using three schemes, namely, traditional double-row piles with vertical piles, double-row contiguous retaining piles with batter pile in the front row, and double-row contiguous retaining piles with batter pile in both rows. Numerical simulations were also conducted to verify the effectiveness of the inclination angle adjustment in optimizing the double-row piles. Results indicate that the increase in the displacement and bending moment of the double-row contiguous retaining batter piles is not evident during excavation and step loading when compared with those of the double-row vertical piles and the double-row contiguous retaining piles with batter pile in the front row. Thus, double-row contiguous retaining batter piles can be used in deep foundation pits. The tilt angle is also excessively small to reduce the lateral displacement of the foundation pit, and the optimal tilt angle is 8° – 16°. Although the embedment depth can influence the deformation of the double-row contiguous retaining batter piles significantly, a critical embedment depth may be reached. The findings of this study can provide references for the optimization of double-row piles in foundation pits

A temporal Convolutional Network for EMG compressed sensing reconstruction

Electromyography (EMG) plays a vital role in detecting medical abnormalities and analyzing the biomechanics of human or animal movements. However, long-term EMG signal monitoring will increase the bandwidth requirements and transmission system burden. Compressed sensing (CS) is attractive for resource-limited EMG signal monitoring. However, traditional CS reconstruction algorithms require prior knowledge of the signal, and the reconstruction process is inefficient. To solve this problem, this paper proposed a reconstruction algorithm based on deep learning, which combines the Temporal Convolutional Network (TCN) and the fully connected layer to learn the mapping relationship between the compressed measurement value and the original signal, and it has been verified in the Ninapro database. The results show that, for the same subject, compared with the traditional reconstruction algorithms orthogonal matching pursuit (OMP), basis pursuit (BP), and Modified Compressive Sampling Matching Pursuit (MCo), the reconstruction quality and efficiency of the proposed method is significantly improved under various compression ratios (CR)

{\pi}-{\pi} Interaction-facilitated formation of interwoven trimeric cage-catenanes with topological chirality

Catenanes as interlocked molecules with a nonplanar graph have gained increasing attention for their unique features such as topological chirality. To date, the majority of research in this field has been focusing on catenanes comprising monocyclic rings. Due to the lack of rational synthetic strategy, catenanes of cage-like monomers are hardly accessible. Here we report on the construction of an interwoven trimeric catenane that is composed of achiral organic cages, which exhibits topological chirality. Our rational design begins with a pure mathematical analysis, revealing that the formation probability of the interwoven trimeric catenane surpasses that of its chain-like analogue by 20%; while driven by efficient template effect provided by strong {\pi}-{\pi} stacking of aromatic panels, the interwoven structure emerges as the dominant species, almost ruling out the formation of the chain-like isomer. Its topological chirality is unambiguously unravelled by chiral-HPLC, CD spectroscopy and X-ray diffraction. Our probability analysis-aided rational design strategy would pave a new venue for the efficient synthesis of topologically sophisticated structures in one pot