With tangent angle perturbation approach the axial symmetry deformation of a spherical vesicle in large under the pressure changes is studied by the elasticity theory of Helfrich spontaneous curvature model. Three main results in axial symmetry shape: biconcave shape, peanut shape, and one type of myelin are obtained. These axial symmetry morphology deformations are in agreement with those obse...

With tangent angle perturbation approach the axial symmetry deformation of a spherical vesicle in large under the pressure changes is studied by the elasticity theory of Helfrich spontaneous curvature model. Three main results in axial symmetry shape: biconcave shape, peanut shape, and one type of myelin are obtained. These axial symmetry morphology deformations are in agreement with those obse...

Numerical simulations of the geodynamo in the presence of heterogeneous heating are presented. We study the dynamics and the structure of the magnetic field when the equatorial symmetry of the flow is broken. If the symmetry breaking is sufficiently strong, the m=0 axial dipolar field is replaced by a hemispherical magnetic field, dominated by an oscillating m=1 magnetic field. Moreover, for mo...

A electroweak theory without spontaneous symmetry breaking is studied in this paper. A new symmetry breaking of SU(2)L × U(1), axial-vector symmetry breaking, caused by the combination of the axial-vector component of the intermediate boson and the fermion mass is found in electroweak theory. The mass of the W boson is resulted in the combination of the axial-vector symmetry breaking and the ex...

A electroweak theory without spontaneous symmetry breaking is studied in this paper. A new symmetry breaking of SU(2)L × U(1), axial-vector symmetry breaking, caused by the combination of the axial-vector component of the intermediate boson and the fermion mass is found in electroweak theory. The mass of the W boson is resulted in the combination of the axial-vector symmetry breaking and the ex...

This paper is organized in two parts. The first part (Sections 2–5) is dedicated to the theory at T = 0 and contains a pedagogical review of some fundamental aspects related with the chiral symmetries of QCD, the U(1) problem and its solution proposed by ’tHooft, Witten and Veneziano. In the second part (Sections 6–14) we discuss the role of the U(1) axial symmetry for the phase structure of QC...

For trees, we define the notion of the so-called symmetry number to measure the size of the maximum subtree that exhibits an axial symmetry in graph drawing. For unrooted unordered trees, we are able to demonstrate a polynomial time algorithm for computing the symmetry number.  2001 Elsevier Science B.V. All rights reserved.