A (2 + 1)-dimensional integrable hierarchy and its extending integrable model

A loop algebra is constructed, whose subalgebra is first used to present a Lax pair. By making use of the Tu scheme by Tu Guizhang, a generalized (2 + 1)-dimensional KN hierarchy is worked out. Further, based on the associated relations between the subalgebras in the above loop algebra, an extending integrable model of the generalized (2 + 1)-dimensional KN hierarchy as above is produced.     

Compressible two-pressure two-phase flow models

A central problem for compressible two-pressure two-phase flow models is closure, or the proper definition of averages of nonlinear terms. We propose here new closures for the velocity and momentum equations and discuss their validation.     

Magnetic fluid behavior in uniform DC,AC, and rotating magnetic fields

New flows and instabilities are demonstrated for magnetic fluids and by dual analogy to dielectric fluids. If a fluid drop is contained in a thin gap between two glass plates (Hele–Shaw cell) with a simultaneously applied in-plane rotating field and a DC axial field, smooth spirals or an abrupt transformation to many small droplets can occur. A preliminary minimum magnetization and surface energy analysis is presented to model the abrupt transformation in ferrofluids. An analysis of effective DC magnetoviscosity is also presented for planar Couette flow with an applied uniform DC field transverse to a duct axis with the effective magnetoviscosity and flow spin velocity calculated as a function of field strength. Related Couette viscometer measurements of ferrofluid viscosity show zero and negative magnetoviscosity values for rotating magnetic fields.     

Low temperature static magnetization of an organic ferromagnet, β-p-NPNN

A ³He refrigerator mountable to a commercial SQUID magnetometer has been developed, which enables us to measure static magnetizations of a sample at temperatures below 2 K conveniently. The design and usage of the system are outlined. We have applied this to study static magnetic properties of an organic ferromagnet, β-p-NPNN, and have confirmed that the saturation magnetization is 1 μ_B per molecule. No hysteretic behavior has been detected, when the field was applied along the easy axis. This indicates that β-p-NPNN is a very soft magnet, as expected for an isotropic Heisenberg magnet based on organic radicals.     

Ballistic electron transport in wrinkled superlattices

Inspired by the problem of elastic wave scattering on wrinkled interfaces, we studied the scattering of ballistic electrons on a wrinkled potential energy region. The electron transmission coefficient depends on both wrinkle amplitude and periodicity, having different behaviors for positive and negative scattering potential energies. For scattering on potential barriers, minibands appear in the electron transmission, as in superlattices, whereas for scattering on periodic potential wells the transmission coefficient has a more complex form. Besides suggesting that tuning of electron transmission is possible by modifying the scattering potential via voltages on wrinkled gate electrodes, our results emphasize the analogies between ballistic electrons and elastic waves even in scattering problems on non-typical configurations.