The semi-discrete AKNS system: Conservation laws, reductions and continuum limits

In this paper, the semi-discrete Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy is shown in spirit composed by the Ablowitz-Ladik flows under certain combinations. Furthermore, we derive its explicit Lax pairs and infinitely many conservation laws, which are non-trivial in light of continuum limit. Reductions of the semi-discrete AKNS hierarchy are investigated to include the semi-discrete Korteweg-de Vries (KdV), the semi-discrete modified KdV, and the semi-discrete nonlinear Schr\"odinger hierarchies as its special cases. Finally, under the uniform continuum limit we introduce in the paper, the above results of the semi-discrete AKNS hierarchy, including Lax pairs, infinitely many conservation laws and reductions, recover their counterparts of the continuous AKNS hierarchy

Solutions to the complex Korteweg-de Vries equation: Blow-up solutions and non-singular solutions

In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, including blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Korteweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the complex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.Comment: 12 figure

Optically-Nonactive Assorted Helices Array with Interchangeable Magnetic/Electric Resonance

We report here the designing of optically-nonactive metamaterial by assembling metallic helices with different chirality. With linearly polarized incident light, pure electric or magnetic resonance can be selectively realized, which leads to negative permittivity or negative permeability accordingly. Further, we show that pure electric or magnetic resonance can be interchanged at the same frequency band by merely changing the polarization of incident light for 90 degrees. This design demonstrates a unique approach to construct metamaterial.Comment: 15 pages, 4 figure

Modelling the electromagnetic separation of non-metallic particles from liquid metal flowing through a two-stage multichannel

A two-stage multichannel was designed to increase the efficiency of separating non-metallic particles from liquid metal flowing through an alternating magnetic field. Numerical method was developed to calculate the particle concentration and separation efficiency of a zinc melt containing dross particles and verified by the experimental results. The distribution of particle concentration and axial fluid velocity changed significantly due to the added walls in the sub-channel, resulting in an abrupt increase in the residence time of the inner bulk melt with high particle concentrations and a remarkable increase in particle separation efficiency when flowing through the single-channel to sub-channels. A multistage and multichannel arrangement is hence recommended for further increase in the separation efficiency of an electromagnetic separator

Quantum electric-dipole liquid on a triangular lattice

Geometric frustrations and quantum mechanical fluctuations may prohibit the formation of long-range ordering even at the lowest temperature, and therefore liquid-like ground states could be expected. A good example is the quantum spin liquid in frustrated magnets that represents an exotic phase of matter and is attracting enormous interests. Geometric frustrations and quantum fluctuations can happen beyond magnetic systems. Here we propose that quantum electric-dipole liquids, analogs to quantum spin liquids, could emerge in frustrated dielectrics where antiferroelectrically coupled small electric dipoles reside on a triangular lattice. The quantum paraelectric hexaferrite BaFe12O19, in which small electric dipoles originated from the off-center displacement of Fe3+ in the FeO5 bipyramids constitute a two-dimensional triangular lattice, represents a promising candidate to generate the anticipated electric-dipole liquid. We present a series of experimental evidences, including dielectric permittivity, heat capacity, and thermal conductivity measured down to 66 mK, to reveal the existence of a nontrivial ground state in BaFe12O19, characterized by itinerant low-energy excitations with a small gap, to which we interpret as an exotic liquid-like quantum phase. The quantum electric-dipole liquids in frustrated dielectrics open up a fresh playground for fundamental physics and may find applications in quantum information and computation as well.Comment: 13 pages, 6 figure

Poly[[μ2-1,4-bis­(imidazol-1-ylmeth­yl)benzene]bis­(μ4-cyclo­hexane-1,4-dicarboxyl­ato)dicobalt(II)]

In the title compound, [Co2(C8H10O4)2(C14H14N4)]n, the two CoII atoms are both five-coordinated by four carboxyl­ate O atoms, derived from two different cyclo­hexane-1,4-dicarboxyl­ate (chdc) ligands, and an N atom, derived from one end of a 1,4-bis­(imidazol-1-ylmeth­yl)benzene mol­ecule (1,4-bix), in a distorted square-pyramidal environment. Each end of the chdc ligand links pairs of CoII atoms into a paddle-wheel assembly, i.e. Co2(O2CR′)4; these are connected into rows because of the bridging nature of the chdc ligands, and the rows are further connected into a two-dimensional layer through the 1,4-bix ligands. The 1,4-bix ligand, which is disposed about a centre of inversion, is disorderd. Two positions were discerned for the –CH2(C6H4)CH2– residue, with the major component having a site-occupancy factor of 0.512 (9)