In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...

Early fruit fly embryo development begins with the formation of a chemical blueprint that guides cellular movements and the development of organs and tissues. This blueprint sets the intrinsic spatial coordinates of the embryo. The coordinates are curvilinear from the start, becoming more curvilinear as cells start coherent movements several hours into development. This dynamic aspect of the cu...

Modern large-scale \functional genomics" projects are inconceivable without the automated processing and computer-aided analysis of images. The project we are engaged in is aimed at the construction of heuristic models of segment determination in the fruit fly Drosophila melanogaster. The current emphasis in our work is the automated transformation of gene expression data in confocally scanned ...

Purpose: The aim of this paper is to present an alternative approach to the problem of accuracy estimation for smartdesigns’ class (also named space-filling or intelligent design) by making use of the design’s geometrical properties. Design/methodology/approach: The assumed topographical condition: ‘all design cases have to be on the defined surface’ is reversed into a curvilinear coordinate sy...

In order to improve efficiency and accuracy, while maintaining an ease of modeling flows with the lattice Boltzmann approach in domains having complex geometry, a method for modeling equations of 2D flow in curvilinear coordinates has been developed. Both the transformed shallow water equations and the transformed 2D Navier-Stokes equations in the horizontal plane were synchronized with the equ...

The classical problem of description of n-Orthogonal Curvilinear Coordinate System in flat Euclidean space is solved by the Inverse Scattering Method. The developed method allows to describe Hamiltonian and semi-Hamiltonian Integrable systems of Hydrodynamic type.

The reaction path is an important concept of theoretical chemistry. We discuss the definition with the help of the following of the reduced gradient (RGF) [see Quapp et al., Theoret. Chem. Acc. 100 (1998) 285], also named the Newton trajectory. All the important features of the potential energy surface are definable independently of the coordinate system. We demonstrate it for the Newton trajec...

Zusammenfassung 1

In a separate paper, the transformation rules to curvilinear coordinates and the form of common differential operators in these coordinates are derived. In this paper we study transformations that preserve an underlying Lagrangian or Hamiltonian structure by providing transformations to suitably constructed canonical variables. Within the canonical framework, various advanced techniques to stud...

In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...