The effectiveness of combining rolling deformation with wire-arc additive manufacture on β-Grain refinement and texture modification in Ti-6Al-4V

In Additive Manufacture (AM), with the widely used titanium alloy Ti–6Al–4V, the solidification conditions typically result in undesirable, coarse-columnar, primary β grain structures. This can result in a strong texture and mechanical anisotropy in AM components. Here, we have investigated the efficacy of a new approach to promote β grain refinement in Wire–Arc Additive Manufacture (WAAM) of large scale parts, which combines a rolling step sequentially with layer deposition. It has been found that when applied in-process, to each added layer, only a surprisingly low level of deformation is required to greatly reduce the β grain size. From EBSD analysis of the rolling strain distribution in each layer and reconstruction of the prior β grain structure, it has been demonstrated that the normally coarse centimetre scale columnar β grain structure could be refined down to < 100 μm. Moreover, in the process both the β and α phase textures were substantially weakened to close to random. It is postulated that the deformation step causes new β orientations to develop, through local heterogeneities in the deformation structure, which act as nuclei during the α → β transformation that occurs as each layer is re-heated by the subsequent deposition pass

Diagrammatic Approach for the High-Temperature Regime of Quantum Hall Transitions

We use a general diagrammatic formalism based on a local conductivity approach to compute electronic transport in continuous media with long-range disorder, in the absence of quantum interference effects. The method allows us then to investigate the interplay of dissipative processes and random drifting of electronic trajectories in the high-temperature regime of quantum Hall transitions. We obtain that the longitudinal conductance \sigma_{xx} scales with an exponent {\kappa}=0.767\pm0.002 in agreement with the value {\kappa}=10/13 conjectured from analogies to classical percolation. We also derive a microscopic expression for the temperature-dependent peak value of \sigma_{xx}, useful to extract {\kappa} from experiments.Comment: 4+epsilon pages, 5 figures, attached with Supplementary Material. A discussion and a plot of the temperature-dependent longitudinal conductance was added in the final versio

Residual stress of as-deposited and rolled Wire + Arc Additive Manufacturing Ti–6Al–4V components

Wire + arc additive manufacturing components contain significant residual stresses, which manifest in distortion. High-pressure rolling was applied to each layer of a linear Ti–6Al–4V wire + arc additive manufacturing component in between deposition passes. In rolled specimens, out-of-plane distortion was more than halved; a change in the deposits' geometry due to plastic deformation was observed and process repeatability was increased. The Contour method of residual stresses measurements showed that although the specimens still exhibited tensile stresses (up to 500 MPa), their magnitude was reduced by 60%, particularly at the interface between deposit and substrate. The results were validated with neutron diffraction measurements, which were in good agreement away from the baseplate

Gradient porosity poly(dicyclopentadiene)

This article describes the preparation of gradient porosity thermoset polymers. The technique used is based on polymerizing a solution of cross-linkable dicyclopentadiene and 2-propanol. The forming polymer being insoluble in 2-propanol, phase separation occurs. Subsequent drying of the 2-propanol gives porosities up to 80%. An apparatus was built to produce a gradient in 2-propanol concentration in a flask, resulting in polymerized gradient porosity rods. The resulting materials have been characterized by scanning electron microscopy (SEM) and density measurements. A mathematical model which allows prediction of the gradient produced is also presente

Transferability of Graph Neural Networks using Graphon and Sampling Theories

Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained network can swap in information from a different graph without retraining and retain its accuracy. A recent method of capturing transferability of GNNs is through the use of graphons, which are symmetric, measurable functions representing the limit of large dense graphs. In this work, we contribute to the application of graphons to GNNs by presenting an explicit two-layer graphon neural network (WNN) architecture. We prove its ability to approximate bandlimited signals within a specified error tolerance using a minimal number of network weights. We then leverage this result, to establish the transferability of an explicit two-layer GNN over all sufficiently large graphs in a sequence converging to a graphon. Our work addresses transferability between both deterministic weighted graphs and simple random graphs and overcomes issues related to the curse of dimensionality that arise in other GNN results. The proposed WNN and GNN architectures offer practical solutions for handling graph data of varying sizes while maintaining performance guarantees without extensive retraining

Fermi Edge Singularities in the Mesoscopic Regime: II. Photo-absorption Spectra

We study Fermi edge singularities in photo-absorption spectra of generic mesoscopic systems such as quantum dots or nanoparticles. We predict deviations from macroscopic-metallic behavior and propose experimental setups for the observation of these effects. The theory is based on the model of a localized, or rank one, perturbation caused by the (core) hole left behind after the photo-excitation of an electron into the conduction band. The photo-absorption spectra result from the competition between two many-body responses, Anderson's orthogonality catastrophe and the Mahan-Nozieres-DeDominicis contribution. Both mechanisms depend on the system size through the number of particles and, more importantly, fluctuations produced by the coherence characteristic of mesoscopic samples. The latter lead to a modification of the dipole matrix element and trigger one of our key results: a rounded K-edge typically found in metals will turn into a (slightly) peaked edge on average in the mesoscopic regime. We consider in detail the effect of the "bound state" produced by the core hole.Comment: 16 page

Pseudo-classical theory for fidelity of nearly resonant quantum rotors

Using a semiclassical ansatz we analytically predict for the fidelity of delta-kicked rotors the occurrence of revivals and the disappearance of intermediate revival peaks arising from the breaking of a symmetry in the initial conditions. A numerical verification of the predicted effects is given and experimental ramifications are discussed.Comment: Shortened and improved versio

The Darboux-Backlund transformation for the static 2-dimensional continuum Heisenberg chain

We construct the Darboux-Backlund transformation for the sigma model describing static configurations of the 2-dimensional classical continuum Heisenberg chain. The transformation is characterized by a non-trivial normalization matrix depending on the background solution. In order to obtain the transformation we use a new, more general, spectral problem.Comment: 12 page