A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations

A Hamiltonian pair with arbitrary constants is proposed and thus a sort of hereditary operators is resulted. All the corresponding systems of evolution equations possess local bi-Hamiltonian formulation and a special choice of the systems leads to the KdV hierarchy. Illustrative examples are given.Comment: 8 pages, late

Extension of Hereditary Symmetry Operators

Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commutative symmetries may be generated. Some concrete structures of hereditary symmetry operators are carefully analyzed on the base of the resulting general conditions and several corresponding nonlinear systems are explicitly given out as illustrative examples.Comment: 13 pages, LaTe

Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras

Polynomial-in-time dependent symmetries are analysed for polynomial-in-time dependent evolution equations. Graded Lie algebras, especially Virasoro algebras, are used to construct nonlinear variable-coefficient evolution equations, both in 1+1 dimensions and in 2+1 dimensions, which possess higher-degree polynomial-in-time dependent symmetries. The theory also provides a kind of new realisation of graded Lie algebras. Some illustrative examples are given.Comment: 11 pages, latex, to appear in J. Phys. A: Math. Ge

Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with Rashba Interaction in a Perpendicular Magnetic Field

We study transport properties of a two-dimensional electron system with Rashba spin-orbit coupling in a perpendicular magnetic field. The spin orbit coupling competes with Zeeman splitting to introduce additional degeneracies between different Landau levels at certain magnetic fields. This degeneracy, if occuring at the Fermi level, gives rise to a resonant spin Hall conductance, whose height is divergent as 1/T and whose weight is divergent as $-\ln T$ at low temperatures. The Hall conductance is unaffected by the Rashba coupling.Comment: 4 pages, 4 figure

Information processing with topologically protected vortex memories in exciton-polariton condensates

We show that in a non-equilibrium system of an exciton-polariton condensate, where polaritons are generated from incoherent pumping, a ring-shaped pump allows for stationary vortex memory elements of topological charge $m = 1$ or $m = -1$. Using simple potential guides we can choose whether to copy the same charge or invert it onto another spatially separate ring pump. Such manipulation of binary information opens the possibility of a new type processing using vortices as topologically protected memory components

Decomposition process in a FeAuPd alloy nanostructured by severe plastic deformation

The decomposition process mechanisms have been investigated in a Fe50Au25Pd25 (at.%) alloy processed by severe plastic deformation. Phases were characterized by X-ray diffraction and microstructures were observed using transmission electron microscopy. In the coarse grain alloy homogenized and aged at $450 ^{circ}\mathrm{C}$, the bcc \alpha-Fe and fcc AuPd phases nucleate in the fcc supersaturated solid solution and grow by a discontinuous precipitation process resulting in a typical lamellar structure. The grain size of the homogenized FeAuPd alloy was reduced in a range of 50 to 100nm by high pressure torsion. Aging at $450 ^{circ}\mathrm{C}$ this nanostructure leads to the decomposition of the solid solution into an equi-axed microstructure. The grain growth is very limited during aging and the grain size remains under 100nm. The combination of two phases with different crystallographic structures (bcc \alpha-Fe and fcc AuPd) and of the nanoscaled grain size gives rise to a significant hardening of the allo

Binary Nonlinearization of Lax pairs of Kaup-Newell Soliton Hierarchy

Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense, which also provides us with new examples of finite dimensional integrable Hamiltonian systems. A sort of involutive solutions to the Kaup-Newell hierarchy are exhibited through the obtained finite dimensional integrable systems and the general involutive system engendered by binary nonlinearization is reduced to a specific involutive system generated by mono-nonlinearization.Comment: 15 pages, plain+ams tex, to be published in Il Nuovo Cimento

Spatial heterogeneity of piezoelectric properties in fatigued lead zirconate titanate ceramics

A spatial non-uniformity of the switching properties during the fatigue cycling in lead zirconate titanate ceramics was investigated by a quasi-static piezoelectric and a polarization switching measurements. The agreement between the local piezoelectric properties and the switching behavior of segmented samples was demonstrated. The observed spatial variation of the properties and its evolution with cycle number provides clear evidence of the presence of heterogeneous regions that possess a local fatigue state and the local switching behavior. These results can be explained as a result of the build-up of the spatially non-uniform field and the formation of frozen domains in the ceramics during cycling. The statistical analysis of spatial variation of the switching properties and its evolution with cycle number provides the evidence that the heterogeneity of the switching properties during the fatigue cycling in lead zirconate titanate ceramics is mostly related to the non-uniform change of the local characteristic switching time. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim