The Regularity Criteria and the A Priori Estimate on the 3D Incompressible Navier-Stokes Equations in Orthogonal Curvilinear Coordinate Systems by Fan Geng, Shu Wang, Yongxin Wang

“…The paper considers the regularity problem on three-dimensional incompressible Navier-Stokes equations in general orthogonal curvilinear coordinate systems. We establish one regularity criteria of the weak solutions involving only in a vorticity component ω3 and one a priori estimate on the solution that H3u3L∞0,T;Lpℝ3 is bounded for 1≤p≤∞ to three-dimensional incompressible Navier-Stokes equations in orthogonal curvilinear coordinate systems. …”
Get full text

Spatially Formulated Connected Automated Vehicle Trajectory Optimization with Infrastructure Assistance by Ran Yi, Yang Zhou, Xin Wang, Zhiyuan Liu, Xiaotian Li, Bin Ran

“…Specifically, this paper systematically formulates trajectory optimization problems in a spatial domain and a curvilinear coordinate. As an alternative of temporal domain and Cartesian coordinate formulation, our formulation provides the constrained trajectory optimization flexibility to describe complex road geometries, traffic regulations, and road obstacles, which are usually spatially varying rather than temporal varying, with assistances vehicle to infrastructure (V2I) communication. …”
Get full text

Nematic Liquid Crystal Locking Menisci by Milan Svetec, Mitja Slavinec

“…We study meniscus driven locking of point defects of nematic liquid crystals confined within a cylindrical tube with free ends. Curvilinear coordinate system is introduced in order to focus on the phenomena of both (convex and concave) types of menisci. …”
Get full text

Varying parameterization of an ellipsoidal thin shell with FEM-based implementation by Yu. V. Klochkov, A. P. Nikolaev, O. V. Vakhnina, T. A. Sobolevskaya, A. Sh. Dzhabrailov, M. Yu. Klochkov

“…A quadrangular fragment of the shell mid-surface with nodal unknowns in the form of displacements and their first derivatives along the curvilinear coordinates was used as the discretization element.When approximating the displacements through the nodal values, two variants were considered. …”
Get full text

Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels by Salvatore Brischetto

“…The exact solution is developed for the differential equations of equilibrium written in orthogonal curvilinear coordinates for the free vibrations of simply supported structures. …”
Get full text

Exploring the dynamics of seasonal surface features using coastal and regional ocean community model by D. Jaishree, P.T. Ravichandran, D.V. Thattai

“…The high-resolution numerical model for ocean circulation is three-dimensional and uses hydrostatic primitive equations in generalized curvilinear coordinates. Simulations were conducted over 8 years using a grid comprising 256 x 249 horizontal surface points to model a range of ocean-atmospheric parameters. …”
Get full text