We study the formulation of bond-orientational order in an arbitrary two dimensional geometry. We find that bond-orientational order is properly formulated within the framework of differential geometry with torsion. The torsion reflects the intrinsic frustration for two-dimensional crystals with arbitrary geometry. Within a DebyeHuckel approximation, torsion may be identified as the density of ...

Dissections of simple geometrical forms can be used to train students’ spatial understanding and to teach geometrical modeling as well as some of the practical aspects of rapid prototyping by layered manufacturing. Two types of dissection puzzles have been used as class exercises in a graduate course on computer-aided solid modeling: Helicoidal sectioning of simple geometrical shapes and a burr...

We study a disk amplitude which has a complicated heterogeneous matter configuration on the boundary in a system of the (3, 4) conformal matter coupled to two-dimensional gravity. It is analyzed using the two-matrix chain model in the large N limit. We show that the disk amplitude calculated by Schwinger-Dyson equations can completely be reproduced through purely geometrical consideration. From...

nowadays deep excavations are needed for construction of foundation of high rise buildings, providing space for parking and etc. in some cases deep excavations may be constructed in the vicinity of the subway tunnels and causes unpredicted extra displacements and internal forces in tunnel lining of tunnels which were not designed for them and consequently affect serviceability of tunnel. theref...

This study conducts the modeling and numerical analysis of a screw dislocation in three-dimensional continuous medium. Our is based on differential geometry Weitzenböck manifold, i.e., Riemann-Cartan manifold which equips itself with non-zero torsion affine connection. Following to standard framework geometrical elasto-plasticity, we introduce three smooth manifolds representing reference R, in...

This paper discusses a digital twin-based approach for designing and redesigning flexible assembly systems. The twin allows modeling the parameters of production system at different levels including process, station, line level. dynamically updating in runtime, synthesizing data from multiple 2D–3D sensors order to have up-to-date information about actual process. model integrates both geometri...

Conventional 2D face recognition methods often struggle when a subject's head is turned even slightly to the side. In this study, a face recognition system based on 3D head modeling that is able to tolerate facial rotation angles was constructed by leveraging the Open source graphic library (OpenGL) framework. To minimize the extensive angle searching time that often occurs in conventional 3D m...

While 3D visualization technology is still in its infancy, hardware capabilities have progressed to the point where useful, practical work can be done. However, there exists significant barriers to using 3D visualization, primarily in usability and interfaces. 3D visualization is closely linked with the realization of depth or the distance between the objects along the 3 mutually perpendicular ...

A hybrid numerical scheme has been presented in this paper for channel flow simulation by coupling one-dimensional and two-dimensional models. Both 1D and 2D differential equations have been discretized by applying the finite volume cell-centered method in a collocated grid system and solved along channel axis for all sections and elements. Due to truncation, dissipation and round off errors, u...