On the scaling behaviour of cross-tie domain wall structures in patterned NiFe elements

The cross-tie domain wall structure in micrometre and sub-micrometre wide patterned elements of NiFe, and a thickness range of 30 to 70nm, has been studied by Lorentz microscopy. Whilst the basic geometry of the cross-tie repeat units remains unchanged, their density increases when the cross-tie length is constrained to be smaller than the value associated with a continuous film. This occurs when element widths are sufficiently narrow or when the wall is forced to move close to an edge under the action of an applied field. To a very good approximation the cross-tie density scales with the inverse of the distance between the main wall and the element edge. The experiments show that in confined structures, the wall constantly modifies its form and that the need to generate, and subsequently annihilate, extra vortex/anti-vortex pairs constitutes an additional source of hysteresis.Comment: 4 pages, 5 figures, accepted for publication in Europhysics Letters (EPL

Learn While You Earn: Two Approaches to Learning Auction Parameters in Take-it-or-leave-it Auctions

Much of the research in auction theory assumes that the auctioneer knows the distribution of participants ’ valuations with complete certainty. However, this is unrealistic. Thus, we analyse cases in which the auctioneer is uncertain about the valuation distributions; specifically, we consider a repeated auction setting in which the auctioneer can learn these distributions. Using take-it-or-leave-it auctions (Sandholm and Gilpin, 2006) as an exemplar auction format, we consider two auction design criteria. Firstly, an auctioneer could maximise expected revenue each time the auction is held. Secondly, an auctioneer could maximise the information gained in earlier auctions (as measured by the Kullback-Liebler divergence between its posterior and prior) to develop good estimates of the unknowns, which are later exploited to improve the revenue earned in the long-run. Simulation results comparing the two criteria indicate that setting offers to maximise revenue does not significantly detract from learning performance, but optimising offers for information gain substantially reduces expected revenue while not producing significantly better parameter estimates

Four bugs on a rectangle

The problem of four bugs in cyclic pursuit starting from a 2-by-1 rectangle is considered, and asymptotic formulas are derived to describe the motion. In contrast to the famous case of four bugs on a square, here the trajectories quickly freeze to essentially one dimension. After the first rotation about the centre point, the scale of the configuration has shrunk by a factor of 10^427907250, and this number is then exponentiated four more times with each successive cycle. Relations to Knuth’s double-arrow notation and level-index arithmetic are discussed

Comment on Bramwell et al, "Universal Fluctuations in Correlated Systems"

This is a comment on "Universal Fluctuations in Correlated Systems", by Bramwell et al, Phys. Rev. Lett., 84, 3744 (2000.Comment: To appear in Phys. Rev. Let

A computer program for systematically analyzing free-flight data to determine the aerodynamics of axisymmetric bodies

Computer program for analyzing free flight motions of axisymmetric bodies to determine aerodynamic coefficient

Servo-controlled intravital microscope system

A microscope system is described for viewing an area of a living body tissue that is rapidly moving, by maintaining the same area in the field-of-view and in focus. A focus sensing portion of the system includes two video cameras at which the viewed image is projected, one camera being slightly in front of the image plane and the other slightly behind it. A focus sensing circuit for each camera differentiates certain high frequency components of the video signal and then detects them and passes them through a low pass filter, to provide dc focus signal whose magnitudes represent the degree of focus. An error signal equal to the difference between the focus signals, drives a servo that moves the microscope objective so that an in-focus view is delivered to an image viewing/recording camera

Automatically-focusing microscope system for live tissue observation

System includes focus-sensing arrangement which controls servo to keep microscope constantly focused on target. Microscope objective is moved along optical axis. System includes two video cameras that are used as transducers for sensing focus. Incoming visual image is split by beam splitter so that one-half of information is fed to each camera