There has been a considerable amount of work carried out on two-dimensional laser forming. In order to advance the process further for industrial applications, however, it is necessary to consider more general cases and especially their process planning aspect. This paper presents an optimal approach to laser scanning paths and heating condition determination for laser forming of doubly curved shapes. Important features of the approach include the strain field calculation based on principal curvature formulation and minimal strain optimization, and scanning paths and heating condition (laser power and scanning velocity) determination by combining analytical and practical constraints. The overall methodology is presented first, followed by more detailed descriptions of each step of the approach. Two distinctive types of doubly curved shape, pillow and saddle shapes are focused on and the effectiveness of the proposed approach is validated by forming experiments.

In this work, we present a systematic search for stellar groups in the Taurus field by applying the DBSCAN algorithm to the data from Gaia DR2. We find 22 groups, consisting of 8 young groups (Groups 1–8) at ages of 2–4 Myr and distances of ∼130–170 pc, and 14 old groups (Groups 9–22) at ages of 8–49 Myr and distances of ∼110–210 pc. We characterize the disk properties of group members and find 19 new disk-bearing stars, 8 of which are in the young groups with 11 others belonging to the comparatively old groups at the ages of 8–11 Myr. We characterize the accretion properties of the group members with Hα emission lines in their Large Sky Area Multi-Object Fibre Spectroscopic Telescope spectra, and discover one source in Group 10 at an age of 10 Myr which still shows accretion activity. We investigate the kinematic relations among the old groups, find that Group 9 is kinematically related to the known Taurus members, and exclude any kinematic relations between Groups 10–22 and the known Taurus members.

In this paper, an interpolating complex variable moving least-squares (ICVMLS) method is presented. In the ICVMLS method, the trial function of a two-dimensional problem is formed with a one-dimensional basis function, and the shape function of the ICVMLS method satisfies the property of Kronecker δ function. The ICVMLS method has greater computational efficiency than the moving least-squares (MLS) approximation. Then combining the ICVMLS method with the Galerkin weak form of temperature field problems, an interpolating complex variable element-free Galerkin (ICVEFG) method is proposed. In the ICVEFG method, we can obtain the equation system by applying the essential boundary conditions directly. Compared with the element-free Galerkin (EFG) method and the complex variable element-free Galerkin (CVEFG) method, the ICVEFG method in this paper has higher accuracy and efficiency.

In this paper, we propose an adjustable liquid aperture to eliminate the undesirable light in a holographic projection. The aperture is based on hydrodynamic actuation. A chamber is formed with a cylindrical tube. A black droplet is filled in the sidewall of the cylinder tube and the outside space is the transparent oil which is immiscible with the black droplet. An ultrathin glass sheet is attached on the bottom substrate of the device and a black shading film is secured to the central area of the glass sheet. By changing the volume of the black droplet, the black droplet will move to the middle or sidewall due to hydrodynamic actuation, so the device can be used as an adjustable aperture. A divergent spherical wave and a solid lens are used to separate the focus planes of the reconstructed image and diffraction beams induced by the liquid crystal on silicon in the holographic projection. Then the aperture is used to eliminate the diffraction beams by adjusting the size of the liquid aperture and the holographic projection does not have undesirable light.

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Summary Existing solutions to Mandel's problem focus on isotropic, transversely isotropic, and orthotropic materials, the last two of which have one of the material symmetry axes coincide with the vertical loading direction. The classical plane strain condition holds for all these cases. In this work, analytical solution to Mandel's problem with the most general matrix anisotropy is presented. This newly derived analytical solution for fully anisotropic materials has all the three nonzero shear strains. Warping occurs in the cross sections, and a generalized plane strain condition is fulfilled. This solution can be applied to transversely isotropic and orthotropic materials whose material symmetry axes are not aligned with the vertical loading direction. It is the first analytical poroelastic solution considering mechanical general anisotropy of elasticity. The solution captures the effects of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction on the responses of pore pressure, stress, strain, and displacement. It can be used to match, calibrate, and simulate experimental results to estimate anisotropic poromechanical parameters. This generalized solution is capable of reproducing the existing solutions as special cases. As an application, the solution is used to study the responses of transversely isotropic and orthotropic materials whose symmetry axes are not aligned with the vertical loading direction. Examples on anisotropic shale rocks show that the effects of material anisotropy are significant. Mandel‐Cryer's effects are highly impacted by the degree of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction.

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Motivated by the future stability problem of solutions of the Einstein-Yang-Mills (EYM) system with arbitrary dimension, we aim to (1) construct a tensorial symmetric hyperbolic formulation for the (n + 1)-dimensional EYM system in the temporal gauge; (2) establish the local well-posedness for the Cauchy problem of EYM equations in the temporal gauge using this tensorial symmetric hyperbolic system. By introducing certain auxiliary variables, we extend essentially the (n + 1)-dimensional Yang-Mills system to a tensorial symmetric hyperbolic system. On the contrary, this symmetric hyperbolic system with data satisfying some constraints (extending the Yang-Mills constraints) reduces to the Yang-Mills system. Consequently, an equivalence between the EYM and the tensorial symmetric hyperbolic system with a class of specific data set is concluded. Furthermore, a general symmetric hyperbolic system over tensor bundles is studied, with which, we conclude the local well-posedness of the EYM system. It turns out the idea of symmetric hyperbolic formulation of the Yang-Mills field is very useful in prompting a tensorial Fuchsian formalism and proving the future stability for the EYM system with arbitrary dimension (i.e., this new symmetric hyperbolic formulation of EYM manifests well behaved lower order terms for long time evolution), see our companion article [21] with Todd A. Oliynyk.