Bäcklund Transformations and Solution Hierarchies for the Third Painlevé Equation

In this article our concern is with the third Painlevé equation
d² y /d x ²= (1/ y )(d y /d x )²− (1/ x )(d y /d x ) + ( αy ²+ β )/ x + γy ³+ δ / y
where α, β, γ, and δ are arbitrary constants. It is well known that this equation admits a variety of types of solution and here we classify and characterize many of these. Depending on the values of the parameters the third Painlevé equation can admit solutions that may be either expressed as the ratio of two polynomials in either x or x ^1/3 or related to certain Bessel functions. It is thought that all exact solutions of (1) can be categorized into one or other of these hierarchies. We show how, given a few initial solutions, it is possible to use the underlying structures of these hierarchies to obtain many other solutions. In addition, we show how this knowledge concerning the continuous third Painlevé equation (1) can be adapted and used to derive exact solutions of a suitable discretized counterpart of (1). Both the continuous and discrete solutions we find are of potential importance as it is known that the third Painlevé equation has a large number of physically significant applications.     

Dissociation constant of aqueous trifluoroacetic acid by cryoscopy and conductivity

The dissociation constant of trifluoroacetic acid in aqueous solution has been determined at 25°C by electrical conductivity (0.65 mol-l^–1) and at 0°C by cryoscopy (1.05 mol-l^–1) and electrical conductivity (0.98 mol-l^–1). The good agreement between the values of the constant determined by cryoscopy and conductivity at 0°C lends confidence to the value at 25°C determined by electrical conductivity. The constant determined at 25°C is in reasonable agreement with values determined by differential refractometry (0.92 mol-l^–1) and from acidity function data (0.80 mol-l^–1) reported by other workers. This work renews confidence in the electrical conductivity method for determining dissociation constants of moderately strong acids.     

The NCI Drug Information System. 1. System overview

An interactive computer system has been designed to handle all the data associated with the National Cancer Institute's (NCI) drug screening program. The system resides on the NIH DEC System 10 computers and allows interactive access to the entire NCI screening data system. This contains over 20 separate databases, including a chemistry file of about 400,000 structures and a biology file of approximately 1.5 million test records. New compounds and test data are added daily to the files, and the system also controls and records all the daily operations of the screening program, such as acquisition, shipping, and biological testing of chemicals.     

The NCI Drug Information System. 6. System maintenance

The NCI Drug Information System (DIS) is a collection of 24 interactively searchable databases which contain all the data associated with NCI's drug screening program. Data flow into all of these databases upon a daily basis, and maintenance procedures have been developed which provide a high degree of currency to the files. An extensive security system controls both write access and read access to the DIS and matches both to the authorization possessed by each specific user. Detailed usage statistics are collected automatically. The cost of the overall system in terms of both manpower and machine time is discussed briefly.     

Detonation in heterogeneous mixtures of liquids and particles

The mechanisms of detonation propagation in heterogeneous systems comprising closely packed particles and a liquid explosive are not fully understood. Recent experimental work has suggested the presence of two distinct modes of detonation propagation. One mode is valid for small particles (which is the regime we will address in this paper) with another mode for large particles. In this work we model numerically the detail of the wave interactions between the detonating liquid and the solid particles. The generic system of interest in our work is nitromethane and aluminium but our methodology can be applied to other liquids and particles. We have exercised our numerical models on the experiments described above. Our models can now qualitatively explain the observed variation in critical diameter with particle size. We also report some initial discrepancies in our predictions of wave speeds in nominally one dimensional experiments which can be explained by detailed modelling. We find that the complex wave interaction in the flow behind the leading shock in the detonating system of liquid and particles is characterised by at least two sonic points. The first is the standard CJ point in the reacting liquid. The second is a sonic point with respect to the sound speed in the inert material. This leads to a steady state zone in the flow behind the leading shock which is much longer than the reaction zone in the liquid alone. The width of this region scales linearly with particle size. Since the width of the subsonic region strongly influences the failure diameter we believe that this property of the flow is the origin of the observed increase in failure diameter with particle size for small inert particles. Received 3 December 1999 / Accepted 5 July 2000     

Deposition and characterization of sputtered ZnO films

Zinc oxide thin films were deposited by radio frequency magnetron sputtering at room temperature using a metallic zinc target in a gas mixture of argon and oxygen. Plasma power, oxygen /argon gas ratio, gas pressure, and substrate temperature were varied, and an experimental design method was used to optimize these deposition parameters by considering their interdependence. Crystalline structures and film stresses were examined. Post-deposition rapid thermal annealing was also carried out to observe its effects on the film properties. Statistical analysis was then used to find the optimal sputtering conditions. Results indicated that plasma power and gas pressure have the largest effects on film crystallization and stress and that postdeposition annealing can be used to improve the quality of the film properties.     

Dynamic fragmentation of blast mitigants

Experimental evidence from a wide range of sources shows that the expanding cloud of explosively disseminated material comprises “particles” or fragments which have different dimensions from those associated with the original material. Powders and liquids have often been used to surround explosives to act as blast mitigants, and this is the main driver for our research. There are also many other areas of interest where an initially intact material surrounding an explosive charge is dynamically fragmented into a distribution of fragment sizes. Examples of such areas include fuel air explosives and enhanced blast explosives as well as quasi-static pressure mitigation systems, and our studies are thus also relevant to these applications. In this paper, we consider the processes occurring as an explosive interacts with a surrounding layer of liquid or powder and identify why it is important to model these processes as a multiphase material problem as opposed to a single phase, single material velocity problem. We shall present results from this class of numerical modelling. In this paper we shall explore what determines the particle or fragment size distribution resulting from explosive dissemination of a layer of material and discuss reasons why clouds from disseminated liquids and powders look similar. We shall support our analysis with results from recent explosives trials and introduce early results from some ongoing small scale explosive mitigation experiments.     

Leed crystallographic investigations of the surface structure designated Zr(0 0 0 1)-(2 x 2)-O

Initial crystallographic investigations have been made with low-energy electron diffraction for the (2 x 2) structure obtained by adsorbing oxygen on the (0 0 0 1) surface of zirconium. Intensity vs energy curves were measured for six diffracted beams at normal incidence, and levels of correspondence with calculated curves for models in which O atoms occupy octahedral holes between close-packed Zr layers were assessed with the reliability index proposed by Pendry. This analysis suggests that O atoms incorporate into the zirconium structure, and that the metal atoms pack as the f.c.c. structure for the region probed by LEED.