The Galerkin weighted residuals method is extended solve the laminar, fully developed flow and heat transfer of Al2O3-water nanofluid inside polygonal ducts with round corners for the constant heat flux and uniform wall temperature boundary conditions. Using the method, semi-analytical, closed-form solutions are obtained for the friction coefficient and the Nusselt number in terms of the radius...

In this article, we construct traveling-rotating helical vortices with small cross-section to the 3D incompressible Euler equations in an infinite pipe, which tend asymptotically singular vortex filament evolved by binormal curvature flow. The construction is based on studying a general semilinear elliptic problem divergence form{??2div(K(x)?u)=(u?q|ln??|)+p,x??,u=0,x???, for values of ?. Helic...

In this paper we improve the cubature rules discussed in Sommariva and Vianello (2021) for computation of integrals by radial basis functions (RBFs). More precisely, introduce context meshless a leave-one-out cross validation criterion optimization RBF shape parameter. This choice allows us to get highly reliable accurate results any kind both infinity finite regularity RBF. The efficacy approx...

In this paper we introduce a new algorithm for simplification of polygonal meshes. It generates a variable resolution structure called hierarchical 4-K mesh. This structure is a powerful representation for non-uniform level of detail that, among other things, allows simple and efficient extraction of conforming meshes.

A new algorithm to identify the neighbours of polygons on 4-connected raster images of 2D polygonal networks is presented in this paper. It is mainly based on mathematical morphology operators and can be indistinctively applied to networks of tri and tetravalent nature (with three and four edges at each vertex, respectively). The algorithm is tested on a varied set of polygonal terrains occurri...

We consider the problem of planning smooth paths for a vehicle in a region bounded by polygonal chains. The paths are represented as B-spline functions. A path is found by solving an optimization problem using a cost function designed to care for both the smoothness of the path and the safety of the vehicle. Smoothness is defined as small magnitude of the derivative of curvature and safety is d...