Punctuated Equilibrium in Software Evolution

The approach based on paradigm of self-organized criticality proposed for experimental investigation and theoretical modelling of software evolution. The dynamics of modifications studied for three free, open source programs Mozilla, Free-BSD and Emacs using the data from version control systems. Scaling laws typical for the self-organization criticality found. The model of software evolution presenting the natural selection principle is proposed. The results of numerical and analytical investigation of the model are presented. They are in a good agreement with the data collected for the real-world software.Comment: 4 pages, LaTeX, 2 Postscript figure

Large-n expansion for m-axial Lifshitz points

The large-n expansion is developed for the study of critical behaviour of d-dimensional systems at m-axial Lifshitz points with an arbitrary number m of modulation axes. The leading non-trivial contributions of O(1/n) are derived for the two independent correlation exponents \eta_{L2} and \eta_{L4}, and the related anisotropy index \theta. The series coefficients of these 1/n corrections are given for general values of m and d with 0<m<d and 2+m/2<d<4+m/2 in the form of integrals. For special values of m and d such as (m,d)=(1,4), they can be computed analytically, but in general their evaluation requires numerical means. The 1/n corrections are shown to reduce in the appropriate limits to those of known large-n expansions for the case of d-dimensional isotropic Lifshitz points and critical points, respectively, and to be in conformity with available dimensionality expansions about the upper and lower critical dimensions. Numerical results for the 1/n coefficients of \eta_{L2}, \eta_{L4} and \theta are presented for the physically interesting case of a uniaxial Lifshitz point in three dimensions, as well as for some other choices of m and d. A universal coefficient associated with the energy-density pair correlation function is calculated to leading order in 1/n for general values of m and d.Comment: 28 pages, 3 figures. Submitted to: J. Phys. C: Solid State Phys., special issue dedicated to Lothar Schaefer on the occasion of his 60th birthday. V2: References added along with corresponding modifications in the text, corrected figure 3, corrected typo

Model of Dirac field interacting with material plane within Symanzik’s approach

The model for the interaction of a spinor field with a material plane is constructed in the framework of the Symanzik’s approach. The characteristics of scattering process of Dirac particles on the plane are calculated. The bounced states localized near the plane are investigated.The model can find application to a wide class of phenomena arising by the interaction of quantum electrodynamics fields with two-dimensional materials