Recurrence in generic staircases

The straight-line flow on almost every staircase and on almost every square tiled staircase is recurrent. For almost every square tiled staircase the set of periodic orbits is dense in the phase space

Smoke Study of Nozzle Secondary Flows in a Low-speed Turbine

Still and motion pictures were made of boundary-layer and wake secondary-flow phenomena visualized by smoke. Two annular cascades of turbine nozzles were used, both designed for constant discharge angle but differing in blade shape and suction-surface velocity distribution. Flows were similar to those obtained with pressure and angle measurements at near-sonic airspeeds. Boundary-layer cross-channel and trailing-edge radial flows caused vortices and an accumulation of low-momentum air at the hub, which may affect flow in following blade rows. Motion of a downstream rotor blade row produced pulsations in trailing-edge radial flow. The motion-picture supplement may be obtained on loan from NACA Headquarters, Washington, D.C

Domain wall propagation through spin wave emission

We theoretically study field-induced domain wall (DW) motion in an electrically insulating ferromagnet with hard- and easy-axis anisotropies. DWs can propagate along a dissipationless wire through spin wave emission locked into the known soliton velocity at low fields. In the presence of damping, the mode appears before the Walker breakdown field for strong out-of-plane magnetic anisotropy, and the usual Walker rigid-body propagation mode becomes unstable when the field is between the maximal-DW-speed field and Walker breakdown field.Comment: 4 pages, 4 figure

Dimensional analysis using toric ideals: Primitive invariants

© 2014 Atherton et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units M, L, T etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer K matrix from the initial integer A matrix holding the exponents for the derived quantities. The K matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups) is obtained directly from the toric ideal defined by A. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of K, is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.The third author received funding from Leverhulme Trust Emeritus Fellowship (1-SST-U445) and United Kingdom EPSRC grant: MUCM EP/D049993/1

Existence of vertical spin stiffness in Landau-Lifshitz-Gilbert equation in ferromagnetic semiconductors

We calculate the magnetization torque due to the spin polarization of the itinerant electrons by deriving the kinetic spin Bloch equations based on the $s$-$d$ model. We find that the first-order gradient of the magnetization inhomogeneity gives rise to the current-induced torques, which are consistent to the previous works. At the second-order gradient, we find an effective magnetic field perpendicular to the spin stiffness filed. This field is proportional to the nonadiabatic parameter $\beta$. We show that this vertical spin stiffness term can significantly modify the domain-wall structure in ferromagnetic semiconductors and hence should be included in the Landau-Lifshitz-Gilbert equation in studying the magnetization dynamics.Comment: 7 pages, 4 figure

Comparison of secondary flows and boundary-layer accumulations in several turbine nozzles

An investigation was made of losses and secondary flows in three different turbine nozzle configurations in annular cascade. Appreciable outer shroud loss cores (passage vortices) were found to exist at the discharge of blades which had thickened suction surface boundary layers near the outer shroud. Blade designs having thinner boundary layers did not show such outer shroud loss cores, but indicated greater inward radial flow of low momentum air, in the wake loss is to this extent an indication of the presence or absence of radial flow. The blade wake was a combination of profile loss and low momentum air from the outer shroud, and the magnitude of the wake loss is to this extent an indication of the presence or absence of radial flow. At a high Mach number, shock-boundary-layer thickening on the blade suction surfaces provided an additional radial flow path for low momentum air, which resulted in large inner shroud loss regions accompanied by large deviations from design values of discharge angle. (author

Probing fractal magnetic domains on multiple length scales in Nd2Fe14B

Using small-angle neutron scattering, we demonstrate that the complex magnetic domain patterns at the surface of Nd2Fe14B, revealed by quantitative Kerr and Faraday microscopy, propagate into the bulk and exhibit structural features with dimensions down to 6 nm, the domain wall thickness. The observed fractal nature of the domain structures provides an explanation for the anomalous increase in the bulk magnetization of Nd2Fe14B below the spin-reorientation transition. These measurements open up a rich playground for studies of fractal structures in highly anisotropic magnetic systems.Comment: Accepted for publication in Phys. Rev. Lett. (4 pages, 4 figures

Public Price Reporting, Marketing Channel Selection, and Price Discovery: The Perspective of Cow/Calf Producers in the Dakotas

Cow/calf producers operating in the Dakotas were surveyed on their price discovery strategies, marketing channel preferences, and their perceptions of how regime change in the public price reporting system for fed cattle affected the beef industry in general and the cow/calf industry in particular. Survey results indicate cow/calf producers consider local institutions (auction barns, etc.) to be more reliable for price discovery than regional or national institutions (futures market, USDA public price reports, satellite auctions, etc.). The auction barn marketing channel is the preferred channel for marketing cattle and is considered the most reliable source of market information by producers. Dakota cow/calf producers perceive livestock mandatory price reporting as benefiting the beef industry in general, but consider public price reports to be less reliable than local sources of market information.beef supply chain, cow-calf marketing, marketing channel, price discovery, public price reporting, Livestock Production/Industries,