scholarly journals Effects of Imprinting Pressure on the Damage of Flexible Composite Mould and Pattern Quality during UV Nanoimprinting

Micromachines ◽  
2019 ◽  
Vol 10 (10) ◽  
pp. 706 ◽  
Author(s):  
Xu Zheng ◽  
Qing Wang ◽  
Wenquan Du
Keyword(s):  
Complex Surfaces ◽  
Small Pressure ◽  
Experiment And Simulation

Imprinting pressure is the significant factor for composite mould durability and pattern quality during UV nanoimprinting on complex surfaces. To solve these problems, the effects of imprinting pressure on the damage of flexible composite mould and pattern quality-encountering particles were investigated through experiment and simulation. It was found that increasing the pressure could improve the pattern quality, but it will damage the mould and reduce the durability. Moreover, too small pressure could lead to serious pattern defects. Therefore, the imprint pressure of 30 kPa was suitable for use in the imprinting process from the viewpoints of protecting the mould and reducing pattern defects. These findings will be useful for improving the pattern quality and mould durability.

scholarly journals Verlinde formulae on complex surfaces: K-theoretic invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Göttsche ◽  
M. Kool ◽  
R. A. Williams
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Complex Surfaces ◽  
Type Formula ◽  
Verlinde Formula ◽  
Donaldson Invariants

Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).

Experiment and Simulation of Erosion Behavior and Deformation Characteristics in Al6061-T6 Beam Due to Rhomboid Particle Impacts

2021 ◽  
Vol 69 (3) ◽  
Author(s):  
Mingchao Du ◽  
Zengliang Li ◽  
Xiangwei Dong ◽  
Chunyong Fan ◽  
Jiaqi Che ◽  
...  
Keyword(s):  
Deformation Characteristics ◽  
Erosion Behavior ◽  
Experiment And Simulation

scholarly journals Conversion Between Cubic Bezier Curves and Catmull–Rom Splines

2021 ◽  
Vol 2 (5) ◽  
Author(s):  
Soroosh Tayebi Arasteh ◽  
Adam Kalisz
Keyword(s):  
Computer Graphics ◽  
Geometric Design ◽  
The Other ◽  
Control Points ◽  
Complex Surfaces ◽  
Linear Transformations ◽  
Computer Aided Geometric Design ◽  
Cubic Curves ◽  
Original Curve ◽  
Computer Aided

AbstractSplines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier and Catmull–Rom splines are the most common in the sub-fields of engineering. In this paper, we focus on conversion between cubic Bézier and Catmull–Rom curve segments, rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of either of the Catmull–Rom or Bézier cubic curves to a new set of control points, which corresponds to approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples.

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