Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations

The truncation method is a collective name for techniques that arise from truncating a Laurent series expansion (with leading term) of generic solutions of nonlinear partial differential equations (PDEs). Despite its utility in finding Backlund transformations and other remarkable properties of integrable PDEs, it has not been generally extended to ordinary differential equations (ODEs). Here we give a new general method that provides such an extension and show how to apply it to the classical nonlinear ODEs called the Painleve equations. Our main new idea is to consider mappings that preserve the locations of a natural subset of the movable poles admitted by the equation. In this way we are able to recover all known fundamental Backlund transformations for the equations considered. We are also able to derive Backlund transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages

Master-equation approach to the study of phase-change processes in data storage media

We study the dynamics of crystallization in phase-change materials using a master-equation approach in which the state of the crystallizing material is described by a cluster size distribution function. A model is developed using the thermodynamics of the processes involved and representing the clusters of size two and greater as a continuum but clusters of size one (monomers) as a separate equation. We present some partial analytical results for the isothermal case and for large cluster sizes, but principally we use numerical simulations to investigate the model. We obtain results that are in good agreement with experimental data and the model appears to be useful for the fast simulation of reading and writing processes in phase-change optical and electrical memories

Cyclotron resonance of the quasi-two-dimensional electron gas at Hg1-xCdxTe grain boundaries

The magnetotransmission of a p-type Hg0.766Cd0.234Te bicrystal containing a single grain boundary with an inversion layer has been investigated in the submillimetre wavelength range. For the first time the cyclotron resonance lines belonging to the various electric subbands of a quasi-two-dimensional carrier system at a grain boundary could be detected. The measured cyclotron masses and the subband densities determined from Shubnikov-de Haas experiments are compared with theoretical predictions and it is found that the data can be explained very well within the framework of a triangular well approximation model which allows for non-parabolic effects

B\"acklund transformations for the second Painlev\'e hierarchy: a modified truncation approach

The second Painlev\'e hierarchy is defined as the hierarchy of ordinary differential equations obtained by similarity reduction from the modified Korteweg-de Vries hierarchy. Its first member is the well-known second Painlev\'e equation, P2. In this paper we use this hierarchy in order to illustrate our application of the truncation procedure in Painlev\'e analysis to ordinary differential equations. We extend these techniques in order to derive auto-B\"acklund transformations for the second Painlev\'e hierarchy. We also derive a number of other B\"acklund transformations, including a B\"acklund transformation onto a hierarchy of P34 equations, and a little known B\"acklund transformation for P2 itself. We then use our results on B\"acklund transformations to obtain, for each member of the P2 hierarchy, a sequence of special integrals.Comment: 12 pages in LaTeX 2.09 (uses ioplppt.sty), to appear in Inverse Problem

On the magnetic fields generated by experimental dynamos

We review the results obtained by three successful fluid dynamo experiments and discuss what has been learnt from them about the effect of turbulence on the dynamo threshold and saturation. We then discuss several questions that are still open and propose experiments that could be performed to answer some of them.Comment: 40 pages, 13 figure

The Winchcombe meteorite, a unique and pristine witness from the outer solar system.

Direct links between carbonaceous chondrites and their parent bodies in the solar system are rare. The Winchcombe meteorite is the most accurately recorded carbonaceous chondrite fall. Its pre-atmospheric orbit and cosmic-ray exposure age confirm that it arrived on Earth shortly after ejection from a primitive asteroid. Recovered only hours after falling, the composition of the Winchcombe meteorite is largely unmodified by the terrestrial environment. It contains abundant hydrated silicates formed during fluid-rock reactions, and carbon- and nitrogen-bearing organic matter including soluble protein amino acids. The near-pristine hydrogen isotopic composition of the Winchcombe meteorite is comparable to the terrestrial hydrosphere, providing further evidence that volatile-rich carbonaceous asteroids played an important role in the origin of Earth's water

X-ray zone plate fabrication using a focused ion beam

An x-ray zone plate was fabricated using the novel approach of focused ion beam (FIB) milling. The FIB technique was developed in recent years, it has been successfully used for transmission electron microscopy (TEM) sample preparation, lithographic mask repair, and failure analysis of semiconductor devices. During FIB milling, material is removed by the physical sputtering action of ion bombardment. The sputter yield is high enough to remove a substantial amount of material, therefore FIB can perform a direct patterning with submicron accuracy. The authors succeeded in fabricating an x-ray phase zone plate using the Micrion 9500HT FIB station, which has a 50 kV Ga{sup +} column. Circular Fresnel zones were milled in a 1.0-{micro}m-thick TaSiN film deposited on a silicon wafer. The outermost zone width of the zone plate is 170 nm at a radius of 60 {micro}m. An achieved aspect ratio was 6:1