The Sorting Index and Permutation Codes

In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced a new Mahonian statistic $sor$, called the sorting index. Petersen proved that the pairs of statistics $(sor,cyc)$ and $(inv,rl\textrm{-}min)$ have the same joint distribution over the symmetric group, and asked for a combinatorial proof of this fact. In answer to the question of Petersen, we observe a connection between the sorting index and the B-code of a permutation defined by Foata and Han, and we show that the bijection of Foata and Han serves the purpose of mapping $(inv,rl\textrm{-}min)$ to $(sor,cyc)$. We also give a type $B$ analogue of the Foata-Han bijection, and we derive the quidistribution of $(inv_B,{\rm Lmap_B},{\rm Rmil_B})$ and $(sor_B,{\rm Lmap_B},{\rm Cyc_B})$ over signed permutations. So we get a combinatorial interpretation of Petersen's equidistribution of $(inv_B,nmin_B)$ and $(sor_B,l_B')$. Moreover, we show that the six pairs of set-valued statistics $\rm (Cyc_B,Rmil_B)$, $\rm(Cyc_B,Lmap_B)$, $\rm(Rmil_B,Lmap_B)$, $\rm(Lmap_B,Rmil_B)$, $\rm(Lmap_B,Cyc_B)$ and $\rm(Rmil_B,Cyc_B)$ are equidistributed over signed permutations. For Coxeter groups of type $D$, Petersen showed that the two statistics $inv_D$ and $sor_D$ are equidistributed. We introduce two statistics $nmin_D$ and $\tilde{l}_D'$ for elements of $D_n$ and we prove that the two pairs of statistics $(inv_D,nmin_D)$ and $(sor_D,\tilde{l}_D')$ are equidistributed.Comment: 25 page

Selecting the power electronic interface for a supercapattery based energy storage system

This paper presents the initial investigations in selecting the topology of the power electronic interface for an energy storage system for power levelling applications based on a novel storage device, the supercapattery. The particularities of the supercapattery device are summarized leading to a multistage power converter structure. A review of the two stage DC/DC converter structure to interface with the supercapattery and of various DC/AC inverters and conversion techniques suitable for connection to a medium voltage and high power AC grid, is given. Simulation results prove the capability of the power electronic interface to control independently and fast the active and reactive power flow which are vital in power peak leveling and power grid stabilization

Mechanisms and designs of asymmetrical electrochemical capacitors

Different charge storage mechanisms in electrochemical energy storage devices are reviewed, including non-Faradaic capacitive, Faradaic capacitive, Faradaic non-capacitive, and their combinations. Specifically, Faradaic capacitive (pseudocapacitive) storage and Faradaic non-capacitive (Nernstian) storage are attributed to the transfer of delocalised and localised valence electrons, respectively. Mathematical and graphical expressions of the respective storage performances are presented. The account is made especially for asymmetrical electrochemical capacitors (AECs), supercapattery and supercabattery. Both hypothetical and experimental examples are presented to demonstrate the merits of supercapattery that combines capacitive and Nernstian electrodes. Enhanced storage performance is shown by properly pairing and balancing the properties of the negatrode (negative electrode) and positrode (positive electrode) in the AEC or supercapattery. In addition, the design, laboratory manufacturing and performance of several stacks of bipolarly connected AEC cells are assessed in terms of commercial feasibility and promise

Redox electrolytes in supercapacitors

Most methods for improving supercapacitor performance are based on developments of electrode materials to optimally exploit their storage mechanisms, namely electrical double layer capacitance and pseudocapacitance. In such cases, the electrolyte is supposed to be electrochemically as inert as possible so that a wide potential window can be achieved. Interestingly, in recent years, there has been a growing interest in the investigation of supercapacitors with an electrolyte that can offer redox activity. Such redox electrolytes have been shown to offer increased charge storage capacity, and possibly other benefits. There are however some confusions, for example, on the nature of contributions of the redox electrolyte to the increased storage capacity in comparison with pseudocapacitance, or by expression of the overall increased charge storage capacity as capacitance. This report intends to provide a brief but critical review on the pros and cons of the application of such redox electrolytes in supercapacitors, and to advocate development of the relevant research into a new electrochemical energy storage device in parallel with, but not the same as that of supercapacitors

Interactions of molten salts with cathode products in the FFC Cambridge Process

© 2020, University of Science and Technology Beijing and Springer-Verlag GmbH Germany, part of Springer Nature. Molten salts play multiple important roles in the electrolysis of solid metal compounds, particularly oxides and sulfides, for the extraction of metals or alloys. Some of these roles are positive in assisting the extraction of metals, such as dissolving the oxide or sulfide anions, and transporting them to the anode for discharging, and offering the high temperature to lower the kinetic barrier to break the metal-oxygen or metal-sulfur bond. However, molten salts also have unfavorable effects, including electronic conductivity and significant capability of dissolving oxygen and carbon dioxide gases. In addition, although molten salts are relatively simple in terms of composition, physical properties, and decomposition reactions at inert electrodes, in comparison with aqueous electrolytes, the high temperatures of molten salts may promote unwanted electrode-electrolyte interactions. This article reviews briefly and selectively the research and development of the Fray-Farthing-Chen (FFC) Cambridge Process in the past two decades, focusing on observations, understanding, and solutions of various interactions between molten salts and cathodes at different reduction states, including perovskitization, non-wetting of molten salts on pure metals, carbon contamination of products, formation of oxychlorides and calcium intermetallic compounds, and oxygen transfer from the air to the cathode product mediated by oxide anions in the molten salt

Erratum to: Interactions of molten salts with cathode products in the FFC Cambridge Process (International Journal of Minerals, Metallurgy and Materials, (2020), 27, 12, (1572-1587), 10.1007/s12613-020-2202-1)

The copyright information of the print version for this article unfortunately is not the same with that of the online version. The copyright information of the online version is right, which is “© The Author(s) 2020”

Research Progress and Perspectives on High Voltage, Flame Retardant Electrolytes for Lithium-Ion Batteries

© 2017 Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences. The electrolyte is an indispensable constituent in lithium ion batteries, and its role conducts electricity by means of the transportation of charge carries between the pair of electrodes. Its properties directly affect the energy density, cycle life and safety of the battery. However, there are two major challenges to using carbonate-based electrolytes in recent lithium ion batteries (LIBs) to further increase the energy density of the devices without compromising the safety. One is that carbonate- based electrolytes are not sufficiently stable at the positive electrode, and the other is their relatively high flammability. Therefore, developing high voltage and flame retardant electrolytes for LIBs is highly desired. Herein, we review the recent progress and challenges in new electrolytes, focusing on high-voltage electrolytes, flame retardant electrolytes and highly concentrated electrolytes. Among the reported electrolytes, highly concentrated electrolytes are worth a special attention, showing various unusual functionalities, for example, high oxidative stability, low volatility, high reductive stability, and non-corrosive to Al. These special properties are totally different from that of the conventional 1 mol•L-1 LiPF6/EC-based electrolytes, which are result from solution structures. A discussion is also provided in this review on the prospects of further development of new electrolytes for LIBs

Electrolysis of metal oxides in MgCl2 based molten salts with an inert graphite anode

Eletrolysis of solid metal oxides has been demonstrated in MgCl2-NaCl-KCl melt at 700 oC taking the electrolysis of Ta2O5 as an example. Both the cathodic and anodic processes have been investigated using cyclic voltammetry, potentiostatic and constant voltage electrolysis, with the cathodic products analysed by XRD, SEM and the anodic products by GC. Fast electrolysis of Ta2O5 against a graphite anode has been realized at a cell voltage of 2 V , or a total overpotential of about 400 mV. The energy consumption was about 1 kWh/kg-Ta with a nearly 100% Ta recovery. The cathodic product was nanometer Ta powder with sizes of about 50 nm. The main anodic product was Cl2 gas, together with about 1 mol% O2 gas and trace of CO. The graphite anode was found to be an excellent inert anode. These results promise an environment-friendly and energy efficient method for metal extraction by electrolysis of metal oxides in MgCl2 based molten salts

Faradaic processes beyond Nernst’s law: density functional theory assisted modelling of partial electron delocalisation and pseudocapacitance in graphene oxides

The study of electron delocalisation in oxygen atom segregated zones in graphene, aided by the first-principles density functional theory, has revealed extra energy bands of ≥ 2 eV wide around the Fermi level, predicting faradaic charge storage occurring in a wide range of potentials, which disagrees with Nernst’s Law but accounts well for the so called pseudocapacitance of heteroatommodified graphene based electrode materials in supercapacitors