Lorentz transformation in Maxwell equations for slowly moving media

We use the method of field decomposition, a technique widely used in relativistic magnetohydrodynamics, to study the small velocity approximation (SVA) of the Lorentz transformation in Maxwell equations for slowly moving media. The "deformed" Maxwell equations derived under the SVA in the lab frame can be put into the conventional form of Maxwell equations in the medium's comoving frame. Our results show that the Lorentz transformation in the SVA up to $O(v/c)$ ($v$ is the speed of the medium and $c$ is the speed of light in vacuum) is essential to derive these equations: the time and charge density must also change when transforming to a different frame even in the SVA, not just the position and current density as in the Galilean transformation. This marks the essential difference of the Lorentz transformation from the Galilean one. We show that the integral forms of Faraday and Ampere equations for slowly moving surfaces are consistent with Maxwell equations. We also present Faraday equation the covariant integral form in which the electromotive force can be defined as a Lorentz scalar independent of the observer's frame. No evidences exist to support an extension or modification of Maxwell equations.Comment: 16 pages, 1 figure, 3 tables. Section VI is added about integral forms of Faraday and Ampere laws for moving surfaces. Part of Section IV and V are rewitte

Learning Complex Motor Skills for Legged Robot Fall Recovery

Falling is inevitable for legged robots in challenging real-world scenarios, where environments are unstructured and situations are unpredictable, such as uneven terrain in the wild. Hence, to recover from falls and achieve all-terrain traversability, it is essential for intelligent robots to possess the complex motor skills required to resume operation. To go beyond the limitation of handcrafted control, we investigated a deep reinforcement learning approach to learn generalized feedback-control policies for fall recovery that are robust to external disturbances. We proposed a design guideline for selecting key states for initialization, including a comparison to the random state initialization. The proposed learning-based pipeline is applicable to different robot models and their corner cases, including both small-/large-size bipeds and quadrupeds. Further, we show that the learned fall recovery policies are hardware-feasible and can be implemented on real robots

Application of Fibonacci Sequence and Lucas Sequence on the Design of the Toilet Siphon Pipe Shape

The purpose of this study was to explore the method for designing the toilet siphon pipe shape to improve flushing performance. The Fibonacci sequence and the Lucas sequence were used to design the structural parameters of the siphon pipe. The flushing processes of the toilet were simulated using the computational fluid dynamics (CFD) method to analyze the flushing performance under different siphon pipe shapes. Experimental studies were conducted to verify the reliability of the simulation results. The results indicated that when the Lucas numbers and the Fibonacci numbers were utilized to regulate the curvature of the siphon pipe in the Xi direction and the Yj direction respectively, the flushing performance of the toilet was optimal. In order to obtain better flushing performance, the curvature of the siphon pipe should be smooth and have obvious transitions at the connections of different sections. When the overall size of the siphon pipe is kept constant, a short siphon pipe length is helpful for the improvement of toilet flushing performance

Convex Hull-Based Multi-objective Genetic Programming for Maximizing ROC Performance

ROC is usually used to analyze the performance of classifiers in data mining. ROC convex hull (ROCCH) is the least convex major-ant (LCM) of the empirical ROC curve, and covers potential optima for the given set of classifiers. Generally, ROC performance maximization could be considered to maximize the ROCCH, which also means to maximize the true positive rate (tpr) and minimize the false positive rate (fpr) for each classifier in the ROC space. However, tpr and fpr are conflicting with each other in the ROCCH optimization process. Though ROCCH maximization problem seems like a multi-objective optimization problem (MOP), the special characters make it different from traditional MOP. In this work, we will discuss the difference between them and propose convex hull-based multi-objective genetic programming (CH-MOGP) to solve ROCCH maximization problems. Convex hull-based sort is an indicator based selection scheme that aims to maximize the area under convex hull, which serves as a unary indicator for the performance of a set of points. A selection procedure is described that can be efficiently implemented and follows similar design principles than classical hyper-volume based optimization algorithms. It is hypothesized that by using a tailored indicator-based selection scheme CH-MOGP gets more efficient for ROC convex hull approximation than algorithms which compute all Pareto optimal points. To test our hypothesis we compare the new CH-MOGP to MOGP with classical selection schemes, including NSGA-II, MOEA/D) and SMS-EMOA. Meanwhile, CH-MOGP is also compared with traditional machine learning algorithms such as C4.5, Naive Bayes and Prie. Experimental results based on 22 well-known UCI data sets show that CH-MOGP outperforms significantly traditional EMOAs

Bis[2-(benzyl­imino­meth­yl)-4-chloro­phenolato-κ2 N,O]nickel(II)

In the mononuclear centrosymmetric title compound, [Ni(C14H11ClNO)2], the NiII atom, lying on a center of symmetry, is four-coordinated by two O atoms and two N atoms from two Schiff base ligands, forming a slightly distorted square-planar environment. The dihedral angle between the two aromatic rings of the ligand is 72.0 (2)°. No significant hydrogen bonding or π–π stacking inter­actions are observed

Leveraging Partial Symmetry for Multi-Agent Reinforcement Learning

Incorporating symmetry as an inductive bias into multi-agent reinforcement learning (MARL) has led to improvements in generalization, data efficiency, and physical consistency. While prior research has succeeded in using perfect symmetry prior, the realm of partial symmetry in the multi-agent domain remains unexplored. To fill in this gap, we introduce the partially symmetric Markov game, a new subclass of the Markov game. We then theoretically show that the performance error introduced by utilizing symmetry in MARL is bounded, implying that the symmetry prior can still be useful in MARL even in partial symmetry situations. Motivated by this insight, we propose the Partial Symmetry Exploitation (PSE) framework that is able to adaptively incorporate symmetry prior in MARL under different symmetry-breaking conditions. Specifically, by adaptively adjusting the exploitation of symmetry, our framework is able to achieve superior sample efficiency and overall performance of MARL algorithms. Extensive experiments are conducted to demonstrate the superior performance of the proposed framework over baselines. Finally, we implement the proposed framework in real-world multi-robot testbed to show its superiority.Comment: Accepted by AAAI202

Study on the Influence of Toilet Siphon Pipe Shape on Flushing Performance

The goal of this work was to explore the influence of toilet siphon pipe shape on flushing performance. The flushing processes of a toilet under different shape parameters were simulated by using computational fluid dynamics (CFD) with a volume of fluid (VOF) multiphase model. The effects of siphon pipe shape on flushing performance were analyzed in detail. The interpretation of the simulation results was experimentally validated. The results reveal that a toilet may obtain good flushing performance under one single shape parameter when the climbing angle, the arc width, the arc height, the pipe diameter, the climbing width, and the climbing height are about 48°, 45 mm, 210 mm, 50 mm, 90 mm and 30 mm, respectively. With the increase of the siphon pipe diameter, the toilet flushing performance peaks in the range between 50 and 53 mm rather than continuing to improve. In order to reasonably evaluate the flushing effect of the toilet, all flow parameters on a characteristic cross section of the siphon pipe, including the average velocity, the average pressure and the average mass flow rate, should be comprehensively considered instead of one single parameter. The findings of this study provide a reference for the pipe shape design of toilets

Bis[triaqua­(1H-1,2,4-triazole-3,5-dicarboxyl­ato-κ2 O 3,N 4)copper(II)] di-μ-aqua-bis­[diaqua­(1H-1,2,4-triazole-3,5-dicarboxyl­ato-κ2 O 3,N 4)copper(II)]

In the title compound, [Cu(C4HN3O4)(H2O)3]2[Cu2(C4HN3O4)2(H2O)6], both monomeric and dimeric mol­ecules are present in the solid state. In the monomeric compound, the CuII atom is five-coordinated in a square-pyramidal configuration by one O atom and one N atom from one 1H-1,2,4-triazole-3,5-dicarboxyl­ate (TZDCA2−) ligand and three O atoms from water mol­ecules. In the centrosymmetric binuclear complex, each CuII atom is six-coordinated in an octa­hedral geometry by one O atom and one N atom from one TZDCA2− ligand and four O atoms from water mol­ecules, two of which bridge the CuII atoms. In the structure, there are intra­molecular O—H⋯O and N—H⋯O hydrogen bonds, and in the crystal, inter­molecular O—H⋯O, O—H⋯N and N—H⋯O hydrogen bonds link symmetry-related mol­ecules, forming a three-dimensional supra­molecular structure