The Navier-Stokes equations are solved exactly, assuming the Navier slip boundary condition, for flow between coaxial circular cylinders (with possibly different slip lengths at the inner and outer walls), and flow in an equilateral triangular pipe. The velocity fields and total flow rates are found analytically. A relatively small slip length can lead to a large increase in the total rate of f...

We apply periodic orbit theory to a two-dimensional nonintegrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing triangular deformation, it exhibits an astonishingly pronounced shell effect on its way through the shape transition. A semiclassical analysis reveals that this shel...

Here we illustrate the free search for the optimal geometry of flow channel cross-sections that meet two objectives simultaneously: reduced resistances to heat transfer and fluid flow. The element cross section and the wall material are fixed, while the shape of the fluid flow opening, or the wetted perimeter is free to vary. Two element cross sections are considered, square and equilateral tri...

Discrete approximations to hyperbolic partial differential equations governing frictionless two-dimensional fluid flow are developed in Cartesian geometry for use over arbitrary triangular grids. A class of schemes is developed that conserves mass, momentum, and total energy. The terms of the governing equations are also approximated individually and their truncation error is examined. For test...

By Dirichlet's Unit Theorem, under the log embedding units in ring of integers a number field form lattice, called log-unit lattice. We investigate geometry these lattices when is biquadratic or cyclic cubic extension Q. In case, we determine lattice orthogonal. show that always equilateral triangular.