The role of monopoles in quenched compact QED has been studied by measuring the cluster susceptibility and the order parameter n max /n tot previously introduced by Hands and Wensley in the study of the percolation transition observed in non-compact QED. A correlation between these parameters and the energy (action) at the phase transition has been observed. We conclude that the order parameter...

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

We derive a family of sixth-order compact finite-difference schemes for the three-dimensional Poisson’s equation. As opposed to other research regarding higher-order compact difference schemes, our approach includes consideration of the discretization of the source function on a compact finite-difference stencil. The schemes derived approximate the solution to Poisson’s equation on a compact st...

Abstract. In a compact space with non-trivial cycles, for sufficiently small values of the compact dimensions, charge conjugation (C ), spatial reflection (P) and time reversal (T ) are spontaneously broken in QCD. The order parameter for the symmetry breaking is the trace of the Wilson line wrapping around the compact dimension, which acquires an imaginary part in the broken phase. We show tha...

A class of generalized high order finite compact difference schemes is proposed for shock/vortex, shock/boundary layer interaction problems. The finite compact difference scheme takes the region between two shocks as a compact stencil. The high order WENO fluxes on shock stencils are used as the internal boundary fluxes for the compact scheme. A lemma of the property of smoothness estimators on...

This article presents a family of very high-order non-uniform grid compact finite difference schemes with spatial orders of accuracy ranging from 4th to 20th for the incompressible Navier–Stokes equations. The high-order compact schemes on non-uniform grids developed in Shukla and Zhong [R.K. Shukla, X. Zhong, Derivation of high-order compact finite difference schemes for non-uniform grid using...

We present an explicit sixth order compact finite difference scheme for fast high accuracy numerical solutions of the two dimensional convection diffusion equation with variable coefficients. The sixth order scheme is based on the well-known fourth order compact scheme, the Richardson extrapolation technique, and an operator interpolation scheme. For a particular implementation, we use multisca...

Higher-order compact difference schemes can achieve higher order accuracy on uniform grids. However, in some cases these may not achieve the desired accuracy. Therefore, this paper proposes a multigrid method based on higher-order compact difference scheme for 3D Helmholtz equation on nonuniform grids. Interpolation and restriction operators are designed accordingly. The suggested scheme has up...