Spectral solver for Cauchy problems in polar coordinates using discrete Hankel transforms

We introduce a Fourier-Bessel-based spectral solver for Cauchy problems featuring Laplacians in polar coordinates under homogeneous Dirichlet boundary conditions. We use FFTs in the azimuthal direction to isolate angular modes, then perform discrete Hankel transform (DHT) on each mode along the radial direction to obtain spectral coefficients. The two transforms are connected via numerical and cardinal interpolations. We analyze the boundary-dependent error bound of DHT; the worst case is $\sim N^{-3/2}$, which governs the method, and the best $\sim e^{-N}$, which then the numerical interpolation governs. The complexity is $O[N^3]$. Taking advantage of Bessel functions being the eigenfunctions of the Laplacian operator, we solve linear equations for all times. For non-linear equations, we use a time-splitting method to integrate the solutions. We show examples and validate the method on the two-dimensional wave equation, which is linear, and on two non-linear problems: a time-dependent Poiseuille flow and the flow of a Bose-Einstein condensate on a disk

Wettability characteristics of carbon steel modified with CO2, Nd:YAG, Excimer and high power diode lasers

Interaction of CO2, Nd:YAG, excimer and high power diode laser (HPDL) radiation with the surface of a common mild steel (EN8) was found to effect changes in the wettability characteristics of the steel, namely changes in the measured contact angle. These modifications are related to changes in the surface roughness, changes in the surface oxygen content and changes in the surface energy of the mild steel. The wettability characteristics of the selected mild steel could be controlled and/or modified by laser surface treatment. A correlation between the change of the wetting properties of the mild steel and the laser wavelength was found

Quantum storage of polarization qubits in birefringent and anisotropically absorbing materials

Storage of quantum information encoded into true single photons is an essential constituent of long-distance quantum communication based on quantum repeaters and of optical quantum information processing. The storage of photonic polarization qubits is, however, complicated by the fact that many materials are birefringent and have polarization-dependent absorption. Here we present and demonstrate a simple scheme that allows compensating for these polarization effects. The scheme is demonstrated using a solid-state quantum memory implemented with an ensemble of rare-earth ions doped into a biaxial yttrium orthosilicate ($Y_2SiO_5$) crystal. Heralded single photons generated from a filtered spontaneous parametric downconversion source are stored, and quantum state tomography of the retrieved polarization state reveals an average fidelity of $97.5 \pm 0.4$, which is significantly higher than what is achievable with a measure-and-prepare strategy.Comment: 7 pages, 3 figures, 1 table, corrected typos and added ref. 3

Learning dislocation dynamics mobility laws from large-scale MD simulations

The computational method of discrete dislocation dynamics (DDD), used as a coarse-grained model of true atomistic dynamics of lattice dislocations, has become of powerful tool to study metal plasticity arising from the collective behavior of dislocations. As a mesoscale approach, motion of dislocations in the DDD model is prescribed via the mobility law; a function which specifies how dislocation lines should respond to the driving force. However, the development of traditional hand-crafted mobility laws can be a cumbersome task and may involve detrimental simplifications. Here we introduce a machine-learning (ML) framework to streamline the development of data-driven mobility laws which are modeled as graph neural networks (GNN) trained on large-scale Molecular Dynamics (MD) simulations of crystal plasticity. We illustrate our approach on BCC tungsten and demonstrate that our GNN mobility implemented in large-scale DDD simulations accurately reproduces the challenging tension/compression asymmetry observed in ground-truth MD simulations while correctly predicting the flow stress at lower straining rate conditions unseen during training, thereby demonstrating the ability of our method to learn relevant dislocation physics. Our DDD+ML approach opens new promising avenues to improve fidelity of the DDD model and to incorporate more complex dislocation motion behaviors in an automated way, providing a faithful proxy for dislocation dynamics several orders of magnitude faster than ground-truth MD simulations

High power diode laser modification of the wettability characteristics of an Al2O3/SiO2 based oxide compound for improved enamelling

High power diode laser (HPDL) surface melting of a thin layer of an amalgamated Al2O3/SiO2 oxide compound (AOC) resulted in significant changes in the wettability characteristics of the material. This behaviour was identified as being primarily due to: (i) the polar component of the AOC surface energy increasing after laser melting from 2.0 to 16.2 mJm-2, (ii) the surface roughness of the AOC decreasing from an Ra value of 25.9 to 6.3 μm after laser melting and (iii) the relative surface oxygen content of the AOC increasing by 36% after laser melting. HPDL melting was consequently identified as affecting a decrease in the enamel contact angle from 1180 prior to laser melting to 330 after laser melting; thus allowing the vitreous enamel to wet the AOC surface. The effective melt depth for such modifications was measured as being from 50 to 125 μm. The morphological, microstructural and wetting characteristics of the AOC were determined using optical microscopy, scanning electron microscopy, energy disperse X-ray analysis, X-ray diffraction techniques and wetting experiments by the sessile drop technique. The work has shown that laser radiation can be used to alter the wetting characteristics of the AOC only when surface melting occurs

Magnetoresistance in Thin Permalloy Film (10nm-thick and 30-200nm-wide) Nanocontacts Fabricated by e-Beam Lithography

In this paper we show spin dependent transport experiments in nanoconstrictions ranging from 30 to 200nm. These nanoconstrictions were fabricated combining electron beam lithography and thin film deposition techniques. Two types of geometries have been fabricated and investigated. We compare the experimental results with the theoretical estimation of the electrical resistance. Finally we show that the magnetoresistance for the different geometries does not scale with the resistance of the structure and obtain drops in voltage of 20mV at 20Oe.Comment: 15 pages, 4 figures. Accepted by AP