This chapter is an introduction to phase transitions in two-dimensional (2D) systems. In contrast to three dimensions (3D), microscopic theories of melting exist in 2D. The most well known of them was developed more than 30 years ago by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY theory). This theory predicts the unbinding of topological defects to break the symmetry in two steps a...

Imaging systems that construct an image from phase information in received signals include synthetic aperture radar (SAR) and optical Doppler tomography (ODT) systems. A fundamental problem in the image formation is phase ambiguity; i.e. it is impossible to distinguish between phases that differ by 2π. Phase unwrapping in two dimensions essentially consists of detecting the pixel locations of t...

So far it has been found by using lattice techniques that in the anisotropic five– dimensional Abelian Higgs model, a layered Higgs phase exists in addition to the expected five–dimensional one. The exploration of the phase diagram has shown that the two Higgs phases are separated by a phase transition from the confining phase. This transition is known to be first order. In this paper we explor...

In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D time-dependent initial-boundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used the triple convolution of a one dimensional wavelet. Using convolution we get a scaling function ...