Taking a Leading Role as a “First Mover” to Advance Materials Science and Technology at the Ulsan National Institute of Science & Technology (UNIST)

Abstract

We present a collection of explicit formulas for the minimum volume of Sasaki-Einstein 5manifolds. The cone over these 5-manifolds is a toric Calabi-Yau 3-fold. These toric Calabi-Yau 3-folds are associated with an infinite class of 4d N = 1 supersymmetric gauge theories, which are realized as worldvolume theories of D3-branes probing the toric Calabi-Yau 3-folds. Under the AdS/CFT correspondence, the minimum volume of the Sasaki-Einstein base is inversely proportional to the central charge of the corresponding 4d N = 1 superconformal field theories. The presented formulas for the minimum volume are in terms of geometric invariants of the toric Calabi-Yau 3folds. These explicit results are derived by implementing machine learning regularization techniques that advance beyond previous applications of machine learning for determining the minimum volume. Moreover, the use of machine learning regularization allows us to present interpretable and explainable formulas for the minimum volume. Our work confirms that, even for extensive sets of toric Calabi-Yau 3-folds, the proposed formulas approximate the minimum volume with remarkable accuracy.

Research on the automatic modeling and performance prediction of plain-woven composites based on beam elements

“…5,6 The theoretical method has the advantage of high computational efficiency; however, its disadvantages consist of non-intuitive results and the working conditions that can be solved will be very limited. Much of the research on woven composites relies on the Finite Element Method (FEM), [7][8][9][10][11] as 3D FEM can detail the mechanical behavior of materials, making it a commonly used method. However, the modeling of woven composites is complex, especially the discretization of the matrix mesh and processing of the contact relationship between the matrix and the fibers, which require considerable manual operations.…”