Bipartite flocking for multi-agent systems

This paper addresses the bipartite flock control problem where a multi-agent system splits into two clusters upon internal or external excitations. Using structurally balanced signed graph theory, LaSalle’s invariance principle and Barbalat’s Lemma, we prove that the proposed algorithm guarantees a bipartite flocking behavior. In each of the two disjoint clusters, all individuals move with the same direction. Meanwhile, every pair of agents in different clusters moves with opposite directions. Moreover, all agents in the two separated clusters approach a common velocity magnitude, and collision avoidance among all agents is ensured as well. Finally, the proposed bipartite flock control method is examined by numerical simulations. The bipartite flocking motion addressed by this paper has its references in both natural collective motions and human group behaviors such as predator–prey and panic escaping scenarios.     

Simple laser vision sensor calibration for surface profiling applications

Due to the relatively large structures in the Oil and Gas industry, original equipment manufacturers (OEMs) have been implementing custom-designed laser vision sensor (LVS) surface profiling systems as part of quality control in their manufacturing processes. The rough manufacturing environment and the continuous movement and misalignment of these custom-designed tools adversely affect the accuracy of laser-based vision surface profiling applications. Accordingly, Oil and Gas businesses have been raising the demand from the OEMs to implement practical and robust LVS calibration techniques prior to running any visual inspections. This effort introduces an LVS calibration technique representing a simplified version of two known calibration techniques, which are commonly implemented to obtain a calibrated LVS system for surface profiling applications. Both calibration techniques are implemented virtually and experimentally to scan simulated and three-dimensional (3D) printed features of known profiles, respectively. Scanned data is transformed from the camera frame to points in the world coordinate system and compared with the input profiles to validate the introduced calibration technique capability against the more complex approach and preliminarily assess the measurement technique for weld profiling applications. Moreover, the sensitivity to stand-off distances is analyzed to illustrate the practicality of the presented technique.     

Interbasis expansions for isotropic harmonic oscillator

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.     

Organic Positive Materials for Magnesium Batteries: A Review

Magnesium batteries, like lithium-ion batteries, with higher abundance and similar efficiency, have drawn great interest for large-scale applications such as electric vehicles, grid energy storage and many more. On the other hand, the use of organic electrode materials allows high energy-performance, metal-free, environmentally friendly, versatile, lightweight, and economically efficient magnesium storage devices. In particular, the structural diversity and the simple activity of organic molecules make redox properties, and hence battery efficiency, easy to monitor. While organic magnesium batteries still in their infancy, this field becomes more and more promising because significant results were reported. To summarize the achievements in studies on organic cathodes for magnesium systems, their synthesis is discussed, combined with electrode design to provide the basis for controlling the electrochemical properties. Moreover, the techniques to synthesize organic materials with high-yield are mentioned. Finally, potential problems and prospects are explored to further improve organic cathodes.     

变形谐振子势的能谱方程

讨论了3种变形谐振子势:左右两边不同参数的谐振子势、左边方形势加右边谐振子势和谐振子势中间加δ势中的能量本征态函数.这些函数都可以由厄米函数表示.由波函数及其一次导数在原点的衔接条件,得到了能谱方程.     

FeOOH Nanocubes Anchored on Carbon Ribbons for Use in Li/O2 Batteries

A composite of FeOOH nanocubes anchored on carbon ribbons has been synthesized and used as a cathode material for Li/O₂ batteries. Fe²⁺ ion-exchanged resin serves as a precursor for both FeOOH nanocubes and carbon ribbons, which are formed simultaneously. The as-prepared FeOOH cubes are proposed to have a core–shell structure, with FeOOH as the shell and Prussian blue as the core, based on information from XPS, TEM, and EDS mapping. As a cathode material for Li/O₂ batteries, FeOOH delivers a specific capacity of 14816 mA h g⁻¹_cathode with a cycling stability of 67 cycles over 400 h. The high performance is related to the low overpotential of the oxygen reduction/evolution reaction on FeOOH. The cube structure, the supporting carbon ribbons, and the -OOH moieties all contribute to the low overpotential. The discharge product Li₂O₂ can be efficiently decomposed in the FeOOH cathode after a charging process, leading to higher cycling stability. Its high activity and stability make FeOOH a good candidate for use in non-aqueous Li/O₂ batteries.     

The (S−1,S) inventory model and its counterparts in queueing theory

We explore the relationship between the ($S?1,S$) inventory model and three well-known queueing models: the Erlang loss system, the machine-repair model and a two-node Jackson network. Exploiting this relationship allows us to obtain key performance measures of the ($S?1,S$) model, like the so-called virtual outdating time, the number of items on the shelf in steady state, the long-run rate of unsatisfied demands and the distribution of the empty shelf period.     

Interaction of modulated pulses in nonlinear oscillator chains

We formally derive and rigorously justify the modulation equations of lowest order for the interaction of two modulated pulses on a one-dimensional nonlinear oscillator chain. We show that solutions with the initial form of the assumed ansatz preserve this form over time intervals with positive macroscopic length, and we show a bound on the possible shift of the envelope caused by the interaction. Thus, we rigorously justify and quantify the statement that under the given conditions there is almost no interaction of the modulated pulses.     

Micro-/Mesoporous conjugated polymer based on star-shaped triazine-functional triphenylamine framework as the performance-improved cathode of Li-organic battery

A novel organic conjugated polymer based on star-shaped triazine-functional triphenylamine framework poly[1,3,5-tris(4-diphenylamino-phenyl)triazine] (PTDAPTz) is designed and synthesized successfully by FeCl₃-catalysted chemical oxidative polymerization. The polymer PTDAPTz powder exhibits a compactly packed pleated skirt shape-like morphology with a high surface area (~930 m² g⁻¹) and a bimodal pore size distribution ranging from micropores (~0.55 nm) to small diameter mesopores (~2–6 nm). As explored as the cathode material, the obtained PTDAPTz presents the double charge–discharge process characteristics of both the free radical redox of triphenylamine unit and the bipolar redox of triazine unit in the polymer and a well-defined multistage charge/discharge voltage plateau (~3.8 V for p-doped and ~2.0 V for n-doped) during the charge–discharge process. Also, the PTDAPTz demonstrates an improved capacity (stabilized at 123 mA h g⁻¹ until 50th cycle) and the enhanced rate performance compared to polytriphenylamine (PTPAn). Specially, the discharge curve for the part of triphenylamine unit presents an obviously improved discharge plateau (~3.8 V for PTDAPTz compared to ~3.6 V for PTPAn) due to the electron-withdrawing effect of the triazine unit to triphenylamine. The elaborate structural design and created micro-/mesoporous morphology with the double charge–discharge process make PTDAPTz a potential candidate as the performance-improved cathode of Li-organic battery. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2574–2583     

Fervent Hype behind Magnesium Batteries: An Open Call to Synthetic Chemists—Electrolytes and Cathodes Needed

Magnesium metal is a superior anode which has double the volumetric capacity of lithium metal and has a negative reduction potential of −2.37 V vs. the standard hydrogen electrode. A major benefit of magnesium is the apparent lack of dendrite formation during charging which is one of the crucial concerns of using a lithium metal anode. In this Review, we highlight the foremost research in the development of electrolytes and cathodes and discuss some of the significant challenges which must be overcome in realizing a practical magnesium battery.