Synchrotron X‐ray CT characterization of titanium parts fabricated by additive manufacturing. Part II. Defects

Synchrotron X‐ray tomography (SXRT) has been applied to the study of defects within three‐dimensional printed titanium parts. These parts were made using the Arcam EBM^® (electron beam melting) process which uses powdered titanium alloy, Ti64 (Ti alloy with approximately 6%Al and 4%V) as the feed and an electron beam for the sintering/welding. The experiment was conducted on the Imaging and Medical Beamline of the Australian Synchrotron. The samples represent a selection of complex shapes with a variety of internal morphologies. Inspection via SXRT has revealed a number of defects which may not otherwise have been seen. The location and nature of such defects combined with detailed knowledge of the process conditions can contribute to understanding the interplay between design and manufacturing strategy. This fundamental understanding may subsequently be incorporated into process modelling, prediction of properties and the development of robust methodologies for the production of defect‐free parts.     

Edge of chaos in a parallel shear flow

We study the transition between laminar and turbulent states in a Galerkin representation of a parallel shear flow, where a stable laminar flow and a transient turbulent flow state coexist. The regions of initial conditions where the lifetimes show strong fluctuations and a sensitive dependence on initial conditions are separated from the ones with a smooth variation of lifetimes by an object in phase space which we call the "edge of chaos." We describe techniques to identify and follow the edge, and our results indicate that the edge is a surface. For low Reynolds numbers we find that the surface coincides with the stable manifold of a periodic orbit, whereas at higher Reynolds numbers it is the stable set of a higher-dimensional chaotic object.     

Charge density waves in PbTe in strong magnetic fields

It is found that in a strong magnetic field the parameters of PbTe allow for a Peierls-type transition at a few degrees Kelvin.     

Preturbulence: A regime observed in a fluid flow model of Lorenz

This paper studies a forced, dissipative system of three ordinary differential equations. The behavior of this system, first studied by Lorenz, has been interpreted as providing a mathematical mechanism for understanding turbulence. It is demonstrated that prior to the onset of chaotic behavior there exists a preturbulent state where turbulent orbits exist but represent a set of measure zero of initial conditions. The methodology of the paper is to postulate the short term behavior of the system, as observed numerically, to establish rigorously the behavior of particular orbits for all future time. Chaotic behavior first occurs when a parameter exceeds some critical value which is the first value for which the system possesses a homoclinic orbit. The arguments are similar to Smale's horseshoe.Research supported by NSF Grant MCS 76-24432     

The topology of stirred fluids

There are simple idealized mathematical models representing the stirring of fluids. The models we consider involve two fluids entering a chamber, with the overflow leaving it. The stirring creates a Cantor-like, but connected, boundary between the fluids that is best described point-set topologically. We prove that in many cases the boundary between the fluids is an indecomposable continuum.     

Catalytic applications of 1,2,4-diazaphospholide-based ruthenium complexes in the Heck reaction

The palladium-catalyzed Heck reaction was effected with two ruthenium complexes bearing unique heterocyclic 1,2,4-diazaphospholide ligands that contain sp²-hybridized phosphorus atoms.     

A scaling law: How an attractor's volume depends on noise level

We investigate the meaning of the dimension of a strange attractor for systems with noise. More specifically, we investigate the effect of adding noise of magnitude ε to a deterministic system with D degrees of freedom. If the attractor has dimension d and d < D, then its volume is zero. The addition of noise may be an important physical probe for experimental situations, useful for determining how much of the observed phenomena in a system is due to noise already present. When the noise is added, the attractor A_ε has positive volume. We conjecture that the generalized volume of A_ε is proportional to ε_{D ? d} for ε near 0 and show this relationship is valid in several cases. For chaotic attractors there are a variety of ways of defining d and the generalized volume definition must be chosen accordingly.     

Fractal basin boundaries generated by basin cells and the geometry of mixing chaotic flows

Experiments and computations indicate that mixing in chaotic flows generates certain coherent spatial structures. If a two-dimensional basin has a basin cell (a trapping region whose boundary consists of pieces of the stable and unstable manifold of some periodic orbit) then the basin consists of a central body (the basin cell) and a finite number of channels attached to it and the basin boundary is fractal. We demonstrate an amazing property for certain global structures: A basin has a basin cell if and only if every diverging curve comes close to every basin boundary point of that basin.