Cross-Newell equations for hexagons and triangles
نویسنده
چکیده
The Cross-Newell equations for hexagons and triangles are derived for general real gradient systems, and are found to be in fluxdivergence form. Specific examples of complex governing equations that give rise to hexagons and triangles and which have Lyapunov functionals are also considered, and explicit forms of the Cross-Newell equations are found in these cases. The general nongradient case is also discussed; in contrast with the gradient case, the equations are not flux-divergent. In all cases, the phase stability boundaries and modes of instability for general distorted hexagons and triangles can be recovered from the Cross-Newell equations. 1
منابع مشابه
A Comparison Between Fourier Transform Adomian Decomposition Method and Homotopy Perturbation ethod for Linear and Non-Linear Newell-Whitehead-Segel Equations
In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...
متن کاملRouting on Triangles, Tori and Honeycombs
The standard n n torus consists of two sets of axes: horizontal and vertical ones. For routing h-relations, the bisection bound gives a lower bound of h n=4. Several algorithms nearly matching this bound have been given. In this paper we analyze the routing capacity of modiied tori: tes-sellations of the plane with triangles or hexagons and tori with added diagonals. On some of these networks t...
متن کاملEnumerating some symmetry classes of rhombus tilings of holey hexagons
This extended abstract presents some recent (exact and asymptotic) enumerative results concerning rhombus tilings of hexagons that have had symmetrically distributed inward pointing triangles of side length 2 removed from their interiors. These results form part of a larger article that is currently available online (arXiv:1501.05772). Résumé. Ce résumé détaillé présente quelques résultats énum...
متن کاملStability of Oscillating Hexagons in Rotating Convection
Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons. We study the stability of the oscillating hexagons using three coupled Ginzburg-Landau equations. Close to the bifurcation point we derive reduced equations for the amplitude of the oscillation, coupled to the phase of the underlying hexagons...
متن کاملRhombus Tilings of a Hexagon with Three Missing Border Triangles
The interest in rhombus tilings has emerged from the enumeration of plane partitions in a given box (which was first carried out by MacMahon [5]). The connection comes from looking at the stacks of cubes of a plane partition from the right direction and projecting the picture to the plane. Then the box becomes a hexagon, where opposite sides are equal, and the cubes become a rhombus tiling of t...
متن کامل