A Singularity-Avoiding Moving Least Squares Scheme for Two Dimensional Unstructured Meshes

Moving least squares interpolation schemes are in widespread use as a tool for numerical analysis on scattered data. In particular, they are often employed when solving partial differential equations on unstructured meshes, which are typically needed when the geometry defining the domain is complex. It is known that such schemes can be singular if the data points in the stencil happen to be in certain special geometric arrangements, however little research has addressed this issue specifically. In this paper, a moving least squares scheme is presented which is an appropriate tool for use when solving partial differential equations in two dimensions, and the precise conditions under which singularities occur are identified. The theory is then applied in the form of a stencil building algorithm which automatically detects singular stencils and corrects them in an efficient manner, while attempting to maintain stencil symmetry as closely as possible. Finally, the scheme is used in a convection-diffusion equation solver, and the results of a number of simulations are presented

The Utilization of Specially Tailored Air Bubbles as Static Pressure Sensors in a Jet

It is shown that air bubbles of a certain size may be used to measure the fluctuating pressure in a liquid jet. The conditions under which these bubbles accurately reflect the local static pressures are described in detail; the volume shape of the bubbles was determined by holography for a 3.17mm jet and the change in volume is interpreted as a result of the fluctuating pressure. The experimental results revealed that at any one instant, a wide spectrum of static pressure fluctuation intensities exist in the jet. It was also found that the probability distribution of these intensities has a slightly skewed bell shape distribution and that the fluctuating static pressure peaked at a higher positive value than a negative one

Broadband strong optical dichroism in topological Dirac semimetals with Fermi velocity anisotropy

Prototypical three-dimensional (3D) topological Dirac semimetals (DSMs), such as Cd$_3$As$_2$ and Na$_3$Bi, contain electrons that obey a linear momentum-energy dispersion with different Fermi velocities along the three orthogonal momentum dimensions. Despite being extensively studied in recent years, the inherent \emph{Fermi velocity anisotropy} has often been neglected in the theoretical and numerical studies of 3D DSMs. Although this omission does not qualitatively alter the physics of light-driven massless quasiparticles in 3D DSMs, it does \emph{quantitatively} change the optical coefficients which can lead to nontrivial implications in terms of nanophotonics and plasmonics applications. Here we study the linear optical response of 3D DSMs for general Fermi velocity values along each direction. Although the signature conductivity-frequency scaling, $\sigma(\omega) \propto \omega$, of 3D Dirac fermion is well-protected from Fermi velocity anisotropy, the linear optical response exhibits strong linear dichroism as captured by the \emph{universal} extinction ratio scaling law, $\Lambda_{ij} = (v_i/v_j)^2$ (where $i\neq j$ denotes the three spatial coordinates $x,y,z$, and $v_i$ is the $i$-direction Fermi velocity), which is independent of frequency, temperature, doping, and carrier scattering lifetime. For Cd$_3$As$_2$ and Na$_3$Bi$_3$, an exceptionally strong extinction ratio larger than 15 and covering broad terahertz window is revealed. Our findings shed new light on the role of Fermi velocity anisotropy in the optical response of Dirac semimetals and open up novel polarization-sensitive functionalities, such as photodetection and light modulation.Comment: 8 pages, 3 figure

Microcantilever Studies of Angular Field Dependence of Vortex Dynamics in BSCCO

Using a nanogram-sized single crystal of BSCCO attached to a microcantilever we demonstrate in a direct way that in magnetic fields nearly parallel to the {\it ab} plane the magnetic field penetrates the sample in the form of Josephson vortices rather than in the form of a tilted vortex lattice. We further investigate the relation between the Josephson vortices and the pancake vortices generated by the perpendicular field component.Comment: 5 pages, 8 figure

Controlling laser spectra in a phaseonium photonic crystal using maser

We study the control of quantum resonances in photonic crystals with electromagnetically induced transparency driven by microwave field. In addition to the control laser, the intensity and phase of the maser can alter the transmission and reflection spectra in interesting ways, producing hyperfine resonances through the combined effects of multiple scattering in the superstructure.Comment: 7 pages, 4 figure

Residual stress control of multipass welds using low transformation temperature fillers

Low transformation temperature (LTT) weld fillers can be used to replace tensile weld residual stresses with compressive ones and reduce the distortion of single-pass welds in austenitic plates. By contrast, weld fillers in multipass welds experience a number of thermal excursions, meaning that the benefit of the smart LTT fillers may not be realised. Here, neutron diffraction and the contour method are used to measure the residual stress in an eight pass groove weld of a 304 L stainless steel plate using the experimental LTT filler Camalloy 4. Our measurements show that the stress mitigating the effect of Camalloy 4 is indeed diminished during multipass welding. We propose a carefully selected elevated interpass hold temperature and demonstrate that this restores the LTT capability to successfully mitigate residual tensile stresses

The London theory of the crossing-vortex lattice in highly anisotropic layered superconductors

A novel description of Josephson vortices (JVs) crossed by the pancake vortices (PVs) is proposed on the basis of the anisotropic London theory. The field distribution of a JV and its energy have been calculated for both dense ($a\lambda_J$) PV lattices with distance $a$ between PVs, and the nonlinear JV core size $\lambda_J$. It is shown that the ``shifted'' PV lattice (PVs displaced mainly along JVs in the crossing vortex lattice structure), formed in high out-of-plane magnetic fields transforms into the PV lattice ``trapped'' by the JV sublattice at a certain field, lower than $\Phi_0/\gamma^2s^2$, where $\Phi_0$ is the flux quantum, $\gamma$ is the anisotropy parameter and $s$ is the distance between CuO$_2$ planes. With further decreasing $B_z$, the free energy of the crossing vortex lattice structure (PV and JV sublattices coexist separately) can exceed the free energy of the tilted lattice (common PV-JV vortex structure) in the case of $\gamma s<\lambda_{ab}$ with the in-plane penetration depth $\lambda_{ab}$ if the low ($B_x<\gamma\Phi_0/\lambda_{ab}^2$) or high ($B_x\gtrsim \Phi_0/\gamma s^2$) in-plane magnetic field is applied. It means that the crossing vortex structure is realized in the intermediate field orientations, while the tilted vortex lattice can exist if the magnetic field is aligned near the $c$-axis and the $ab$-plane as well. In the intermediate in-plane fields $\gamma\Phi_0/\lambda_{ab}^2\lesssim B_x \lesssim \Phi_0/\gamma s^2$, the crossing vortex structure with the ``trapped'' PV sublattice seems to settle in until the lock-in transition occurs since this structure has the lower energy with respect to the tilted vortex structure in the magnetic field ${\vec H}$ oriented near the $ab$-plane.Comment: 15 pages, 6 figures, accepted for publication in PR