The contravariant form of the Navier–Stokes equations in a fixed curvilinear coordinate system is well known. However, when the curvilinear coordinate system is time-varying, such as when a body-fitted grid is used to compute the flow over a compliant surface, considerable care is needed to handle the momentum term correctly. The present paper derives the complete contravariant form of the Navi...

Combinatorial interpretation of the fibonomial coefficients recently proposed by the present author [1,2] here results in combinatorial derivation of the recurrence relation for fibonomial coefficients . The presentation is provided with quite an exhaustive context with reference to classical attitude of [3,4]. This note apart from plane grid coordinate system used is fitted with several figure...

The model of the homogenous and isotropic universe is considered in which the coordinate system of reference is not defined by the matter but is a priori specified. The scale factor of the universe changes following the linear law. The scale of mass changes proportional to the scale factor of the universe. The model under consideration avoids the flatness and horizon problems. The predictions o...

A toy model for gamma-ray burst-supernovae (GRB-SN) is discussed by considering the coexistence of baryon poor outflows from black holes (BHs) and a powerful spin-connection to surrounding disk, giving rise to consistent calorimetry as described by van Putten (2001a) in a variant of the Blandford-Znajek process (BZ, 1977). In this model the half-opening angle of the magnetic flux tube on the ho...

In this paper, we present a surface-fitting based smoothing algorithm for discrete, general-purpose mesh models. The surface patch around a mesh vertex is defined in a local coordinate system and fitted with a quadratic polynomial function. An initial mesh smoothing is achieved by projecting each vertex onto the fitted surface. At each vertex of the initial mesh, the curvature is estimated and ...

We introduce several modifications of conic fitting in Geometric algebra for conics by incorporating additional conditions into the optimisation problem. Each these extra ensure geometric properties a fitted conic, particular, centre point position at origin coordinate system, axial alignment with axes, or, eventually, combination both. All derived algorithms are accompanied discussion underlyi...

Understanding galaxies, the basic components of the universe, is one of the most challenging tasks we meet. There are two major phenomena of spiral galaxies which are not given acceptable explanation. One is the almost constant rotation curve and the other is the bar pattern. In my previous work, I proposed to use curvilinear coordinate system and a symmetry principle to study galaxy patterns. ...

We describe the reinforcement learning problem, motivate algorithms which seek an approximation to the Q function, and present new convergence results for two such algorithms.

A Volume Tracking (VT) and a Front Tracking (FT) algorithm are implemented and compared for locating the interface between two immiscible, incompressible, Newtonian fluids in a tube with a periodically varying, circular cross-section. Initially, the fluids are stationary and stratified in an axisymmetric arrangement so that one is around the axis of the tube (core fluid) and the other one surro...