Spin and charge Nernst effect in a four-terminal double-dot interferometer

We investigate the spin and charge Nernst effect of a four-terminal Aharonov–Bohm interferometer with Rashba spin–orbit interaction (RSOI). It is shown that a pure spin Nernst effect or a fully spin-polarized Nernst effect can be obtained by modulating the magnetic flux phase ? and the RSOI induced phase φ. It is also demonstrated that some windows of ? (or φ) for maintaining an almost fully spin-polarized Nernst effect exist and their width is under the control of the other phase. Moreover, for the charge Nernst coefficient $N_c$ and spin Nernst coefficient $N_s$ the relationship $N_c(?,\phi )=?N_s(\phi ,?)$ always holds. These results suggest that our proposal may act as a controllable thermospin generator.     

Leibniz algebras associated with representations of filiform Lie algebras

In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra $n_{n,1}$. We introduce a Fock module for the algebra $n_{n,1}$ and provide classification of Leibniz algebras $L$ whose corresponding Lie algebra $L/I$ is the algebra $n_{n,1}$ with condition that the ideal $I$ is a Fock $n_{n,1}$-module, where $I$ is the ideal generated by squares of elements from $L$.We also consider Leibniz algebras with corresponding Lie algebra $n_{n,1}$ and such that the action $I\times n_{n,1}\to I$ gives rise to a minimal faithful representation of $n_{n,1}$. The classification up to isomorphism of such Leibniz algebras is given for the case of $n=4$.     

Exact PsTd invariant and PsTd symmetric breaking solutions,symmetry reductions and Bäcklund transformations for an AB–KdV system

In natural and social science, many events happened at different space–times may be closely correlated. Two events, A (Alice) and B (Bob) are defined as correlated if one event is determined by another, say, $B=\stackrel{?}{f}A$ for suitable $\stackrel{?}{f}$ operators. A nonlocal AB–KdV system with shifted-parity ($P_s$, parity with a shift), delayed time reversal ($T_d$, time reversal with a delay) symmetry where $B=\stackrel{?}{P_s}\stackrel{?}{T_d}A$ is constructed directly from the normal KdV equation to describe two-area physical event. The exact solutions of the AB–KdV system, including $P_s{T}_d$ invariant and $P_s{T}_d$ symmetric breaking solutions are shown by different methods. The $P_s{T}_d$ invariant solution show that the event happened at A will happen also at B. These solutions, such as single soliton solutions, infinitely many singular soliton solutions, soliton–cnoidal wave interaction solutions, and symmetry reduction solutions etc., show the AB–KdV system possesses rich structures. Also, a special Bäcklund transformation related to residual symmetry is presented via the localization of the residual symmetry to find interaction solutions between the solitons and other types of the AB–KdV system.     

Sustained high βN plasmas on EAST tokamak

Sustained high normalized beta (${\beta }_N～1.9$) plasmas with an ITER-like tungsten divertor have been achieved on EAST tokamak recently. The high power NBI heating system of 4.8 MW and the 4.6 GHz lower hybrid wave of 1 MW were developed and applied to produce edge and internal transport barriers in high ${\beta }_N$ discharges. The central flat q profile with $q(\rho )～1$ at $\rho <0.3$ region and edge safety factor $q_{95}=4.7$ is identified by the multi-channel far-infrared laser polarimeter and the EFIT code. The fraction of non-inductive current is about 40%. The relation between fishbone activity and ITB formation is observed and discussed.