A model of competition among more than two languages

We extend the Abrams-Strogatz model for competition between two languages [Nature 424, 900 (2003)] to the case of n(>=2) competing states (i.e., languages). Although the Abrams-Strogatz model for n=2 can be interpreted as modeling either majority preference or minority aversion, the two mechanisms are distinct when n>=3. We find that the condition for the coexistence of different states is independent of n under the pure majority preference, whereas it depends on n under the pure minority aversion. We also show that the stable coexistence equilibrium and stable monopoly equilibria can be multistable under the minority aversion and not under the majority preference. Furthermore, we obtain the phase diagram of the model when the effects of the majority preference and minority aversion are mixed, under the condition that different states have the same attractiveness. We show that the multistability is a generic property of the model facilitated by large n.Comment: 28 pages, 7 figure

金属有機構造体へのイオン液体の導入およびその相挙動とイオン伝導性

京都大学0048新制・論文博士博士(理学)乙第12997号論理博第1553号新制||理||1604(附属図書館)32925(主査)教授 北川 宏, 教授 竹腰 清乃理, 教授 有賀 哲也学位規則第4条第2項該当Doctor of ScienceKyoto UniversityDGA

Low temperature ionic conductor: Ionic liquid incorporated within a metal-organic framework

Ionic liquids (ILs) show promise as safe electrolytes for electrochemical devices. However, the conductivity of ILs decreases markedly at low temperatures because of strong interactions arising between the component ions. Metal-organic frameworks (MOFs) are appropriate microporous host materials that can control the dynamics of ILs via the nanosizing of ILs and tunable interactions of MOFs with the guest ILs. Here, for the first time, we report on the ionic conductivity of an IL incorporated within a MOF. The system studied consisted of EMI-TFSA (1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide) and ZIF-8 (Zn(MeIM)2, H(MeIM) = 2-methylimidazole) as the IL and the MOF, respectively. While the ionic conductivity of bulk EMI-TFSA showed a sharp decrease arising from freezing, the EMI-TFSA@ZIF-8 showed no marked decrease because there was no phase transition. The ionic conductivity of EMI-TFSA@ZIF-8 was higher than that of bulk EMI-TFSA below 250 K. This result points towards a novel method by which to design electrolytes for electrochemical devices such as batteries that can operate at low temperatures

Lithium Ion Diffusion in a Metal–Organic Framework Mediated by an Ionic Liquid

Metal–organic frameworks (MOFs) are desirable host materials to study and control the dynamics of molecules and ions such as lithium ions. We show the first study of a lithium ion-doped ionic liquid (IL) incorporated into a MOF and investigate its phase behavior and ionic conductivity. Moreover, for the first time, we have studied the dynamics of lithium ions in the micropores of the MOF in terms of the self-diffusion coefficient of the lithium ions. The IL was a mixture of EMI-TFSA (1-ethyl-3-methylimidazolium bis­(trifluoromethylsulfonyl)­amide) with LiTFSA (lithium bis­(trifluoromethylsulfonyl)­amide), and the MOF was ZIF-8 (Zn­(MeIM)₂; H­(MeIM) = 2-methylimidazole). The TFSA^– anions showed a gradual decrease of mobility in the micropores at low temperatures, which indicates the absence of the apparent freezing transition. The mobility of the Li⁺ cations showed a slightly steeper decrease than that of the TFSA^– anions at low temperature. The ionic conductivity of the (EMI_0.8Li_0.2)­TFSA in the micropores was 2 orders of magnitude lower than that of the bulk (EMI_0.8Li_0.2)­TFSA. However, the activation energy for the diffusion of lithium ions in the micropores of ZIF-8 was comparable with the bulk (EMI_0.8Li_0.2)­TFSA. These results suggest that the Li⁺ cations diffuse through the micropores via the exchange of the solvating TFSA^– anions, similar to the Grotthuss mechanism in proton conductivity