Reconstruction approximating method by biquadratic splines of offset surfaces holes

Standard Offset surfaces are defined as locus of the points which are at constant distance along the unit normal direction from the generator surfaces. Offset are widely used in various practical applications, such as tolerance analysis, geometric optics and robot path-planning. In some of the engineering applications, we need to extend the concept of standard offset to the generalized offset where distance offset is not necessarily constant and offset direction are not necessarily along the normal direction. Normally, a generalized offset is functionally more complex than its progenitor because of the square root appears in the expression of the unit normal vector. For this, an approximation method of its construction is necessary. In many situation it is necessary to fill or reconstruct certain function defined in a domain in which there is a lack of information inside one or several sub-domains (holes). In some practical cases, we may have some specific geometrical constrains, of industrial or design type, for example, the case of a specified volume inside each one of these holes. The problem of filling holes or completing a 3D surface arises in all sorts of computational graphics areas, like CAGD, CAD-CAM, Earth Sciences, computer vision in robotics, image reconstruction from satellite and radar information, etc. In this work we present an approximation method of filling holes of the generalized offset of a surface when there is a lack information in a sub-domain of the function that define it. We prove the existence and uniqueness of solution of this problem, we show how to compute it and we establish a convergence result of this approximation method. Finally, we give some graphical and numerical examples.

Characterization of the Propagation Route of Light Passing Through Convex Lens

Existing optical theory states that the light directed to the optical center of the convex lens will travel in a straight line. Does the theory hold? If this is true, then why the images formed by the camera lens tends to be distorted? To answer the question, this paper studied the propagation mode of light passing through convex lens. Specifically, assuming the propagation medium on both sides of convex lens is homogeneous, we propose an angular affine transformation (AAT) theory. Based on the proposed theory, we first derive the refractive index of convex lens as well as the method of calculating the normal direction of each point within the radius of convex lens radius and then derive the refraction direction of each point within the radius of convex lens, thus completely characterizing the path diagram of light directed to the optical center. The correctness of the proposed theory has been verified using two sets of experiments: characterization of the route of light passing through the convex lens as well as camera imaging experiment. From the results, it can be concluded that the light directed to the optical center of convex lens does not travel in a straight line, but in a refraction line.

(Non-)convergence of solutions of the convective Allen–Cahn equation

We consider the sharp interface limit of a convective Allen–Cahn equation, which can be part of a Navier–Stokes/Allen–Cahn system, for different scalings of the mobility $$m_\varepsilon =m_0\varepsilon ^\theta $$ m ε = m 0 ε θ as $$\varepsilon \rightarrow 0$$ ε → 0 . In the case $$\theta >2$$ θ > 2 we show a (non-)convergence result in the sense that the concentrations converge to the solution of a transport equation, but they do not behave like a rescaled optimal profile in normal direction to the interface as in the case $$\theta =0$$ θ = 0 . Moreover, we show that an associated mean curvature functional does not converge to the corresponding functional for the sharp interface. Finally, we discuss the convergence in the case $$\theta =0,1$$ θ = 0 , 1 by the method of formally matched asymptotics.

Temperature Dependency on the Microscopic Mechanism in the Normal Direction of Wrought AZ31 Sheet under Dynamic Compressive Behavior

In order to analyze the competitive relationship of different deformation mechanisms in wrought AZ31 magnesium alloy, the dynamic compressive experiments were conducted by a Split Hopkinson Pressure Bar (SHPB) apparatus and a resistance-heated furnace in the range of temperature between 20 and 350 °C at the strain rate of 1000 s−1. With the help of Electron Backscattered Diffraction (EBSD) observation, theoretical calculated Schmid Factor (SF), Critical Resolved Shear Stress (CRSS), and critical equivalent stress (σ0.2), the dynamic compressive deformation behavior and corresponding mechanism of wrought AZ31 magnesium alloy along the normal direction (ND) were revealed in the current study. The results demonstrate that the c-axis of grains are gradually reoriented parallel to the normal direction of wrought AZ31-ND sheet with the temperature increasing, except the dynamic recrystallization (DRX) mechanism was activated or grains grew up. The non-basal slip and 101¯2 tension twinning are respectively the predominant deformation mechanisms at lower temperatures (≤250 °C) and higher temperatures (≥250 °C). The predominant type of DRX mechanism of wrought AZ31-ND sheet is rotational dynamic recrystallization (RDRX), which is regarded as an obstacle for the kernel misorientation concentration region enhancement.

Demonstration of light reflection concepts for rendering realistic 3D tree images

With advancements in computer graphics, creating natural images has always been the main purpose, image rendering is all based on principles of physics. So, understanding the physics of image rendering will enable us to create the most realistic images. A ray of light hit a surface with different orientation and reflects as per the rules of physics. It is difficult to calculate the light reflection of complex foliage, such as trees, so, the reflection of this natural complexity needs to be adapted to rendering situations. In this research, the researchers provide demonstrations to enable students to understand the light reflection in nature, light calculation in computer graphics and methods to apply them to render realistic tree images. The researchers assign students to render 3D realistic tree images to assess the students’ understanding by applying the diffuse reflection value, specular reflection value and surface normal direction to render realistic tree images. The researchers find that most students understand of diffuse reflection, specular reflection, and surface normal direction causes the rendering results to be most realistic.

Statistical Study of Small-Scale Interplanetary Magnetic Flux Ropes in the Vicinity of the Heliospheric Current Sheet

The small-scale interplanetary magnetic flux ropes (SIMFRs) are common magnetic structures in the interplanetary space, yet their origination is still an open question. In this article, we surveyed 63 SIMFRs found within 6-day window around the heliospheric current sheet (HCS) and investigated their axial direction, as well as the local normal direction of the HCS. Results showed that the majority (48/63) of the SIMFRs were quasi-parallel to the associated HCS (i.e., the axial direction of SIMFRs was quasi-perpendicular to the normal direction of the associated HCS). They also showed that the SIMFRs quasi-parallel to the associated HCS statistically had shorter duration than the cases quasi-perpendicular. The results indicate that most of these SIMFRs may be generated in the nearby HCSs.

Waveguided nematic liquid crystal random lasers

In waveguided nematic liquid crystal random lasers (NLCRLs), we realize polarized random laser (RL) emission and discover that the waveguide effect reduces the transmission loss of the RL whose polarization is parallel to the liquid crystal molecules (LCMs). Compared with the traditional liquid crystal random lasers, the waveguide NLCRLs can achieve the regulation of RLs strength, polarization, and wavelength in the same structure. The electric field can drive the rotation of LCMs to control the RL polarization and intensity. The drop of horizontal polarization laser and the increase of vertical polarization laser prove the role of the waveguide effect. In addition, the disorder of the waveguided NLCRLs is highly sensitive to temperature, which makes it easy to control the wavelength and intensity of the RL. As the temperature rises, the waveguide effect is weakened, resulting in a weakening of the restriction along liquid crystal (LC) cell normal direction. The reduced laser intensity verifies the role of the waveguide effect.

Multidimensional Aligned Nanowires Array: Toward Bendable and Stretchable Strain Sensors

Micropatterns based on the oriented nanowires have attracted research interests for their unique physicochemical advantages in various applications of electric microdevices. Here, we proposed a facile fibrous dewetting strategy by spreading and dewetting of the silver nanowire (AgNW) solution on the vertical aligned carbon nanotube array (ACNTs) for preparing multidimensional aligned nanowires array, based on the elastocapillary coalescence. The unidirectional shrinking of the liquid film on the top of ACNTs happens during the dewetting process, as a result of the elastocapillary coalescence of ACNTs, which drives the AgNWs aligned along normal direction of liquid film shrinkage on the top of ACNTs. Thus, a multidimensional aligned NWs array was prepared, composing of the horizontally oriented NWs of top layer and vertical ACNT bundles of under layer connected by CNT yarns. A bendable flexible electrode was prepared using the as-prepared multidimensional aligned nanowires array, showing high stability during bending cycles (1800 cycles). Moreover, the multidimensional aligned nanowires array is also applicable for fabricating strain sensors, which show stable resistance response under strain. We envision that the as-developed approach shed new light on easy manufacture NW-based micropatterns.

Cutting State Estimation via Chatter Mark on End Milled Surface and Analysis of Its Formation Mechanism Using Voxel Model Simulation

When chatter vibrations occur during cutting, a characteristic pattern called chatter mark appears on the machined surface. In our previous studies, it was estimated that this chatter mark is formed by the tool (or workpiece) vibration in the normal direction with respect to the machined surface. We thus proposed a method to inversely analyze the chatter vibration information during cutting through the chatter mark using two-dimensional discrete Fourier transform. Previous studies confirmed that the analysis results of this method are in good agreement with those of the information obtained via conventional sensing. However, the correctness of the pattern formation mechanism is yet to be directly verified, as it is difficult to measure the cutting phenomenon directly. In this study, the chatter vibration during cutting was measured by the displacement of the tool-shank. Then, based on the results obtained in the static stiffness test, the movement of the tool edge was estimated. A cutting simulation using a voxel model was executed based on this tool-edge movement. When the simulation using the chatter vibration in the normal direction was performed, a chatter mark appeared on the simulated surface. It could thus be confirmed more directly that the analytical model is correct compared with the previous methods.