Fermion Generations and Mixing from Dualized Standard Model

We review a possible solution to the fermion generation puzzle based on a nonabelian generalization of electric--magnetic duality derived some years ago. This nonabelian duality implies the existence of another SU(3) symmetry dual to colour, which is necessarily broken when colour is confined and so can play the role of the ``horizontal'' symmetry for fermion generations. When thus identified, dual colour then predicts 3 and only 3 fermion generations, besides suggesting a special Higgs mechanism for breaking the generation symmetry. A phenomenological model with a Higgs potential and a Yukawa coupling constructed on these premises is shown to explain immediately all the salient qualitative features of the fermion mass hierarchy and mixing pattern, excepting for the moment CP-violation. Calculations already carried out to 1-loop order is shown to give with only 3 adjustable parameters the following quantities all to within present experimental error: all 9 CKM matrix elements $|V_{rs}|$ for quarks, the neutrino oscillation angles or the MNS lepton mixing matrix elements $|U_{\mu 3}|, |U_{e 3}|$, and the mass ratios $m_c/m_t, m_s/m_b, m_\mu/m_\tau$. The special feature of this model crucial for deriving the above results is a fermion mass matrix which changes its orientation (rotates) in generation space with changing energy scale, a feature which is shown to have direct empirical support.Comment: updated version of course of lectures given at the 42nd Cracow School of Theoretical Physics, 2002, Polan

General analysis of self-dual solutions for the Einstein-Maxwell-Chern-Simons theory in (1+2) dimensions

The solutions of the Einstein-Maxwell-Chern-Simons theory are studied in (1+2) dimensions with the self-duality condition imposed on the Maxwell field. We give a closed form of the general solution which is determined by a single function having the physical meaning of the quasilocal angular momentum of the solution. This function completely determines the geometry of spacetime, also providing the direct computation of the conserved total mass and angular momentum of the configurations.Comment: 3 pages, REVTEX file, no figure

Theory of enhanced performance emerging in a sparsely-connected competitive population

We provide an analytic theory to explain Anghel et al.'s recent numerical finding whereby a maximum in the global performance emerges for a sparsely-connected competitive population [Phys. Rev. Lett. 92, 058701 (2004)]. We show that the effect originates in the highly-correlated dynamics of strategy choice, and can be significantly enhanced using a simple modification to the model.Comment: This revised version will appear in PRE as a Rapid Com

Three-dimensional finite element analysis for high velocity impact

A finite element algorithm for solving unsteady, three-dimensional high velocity impact problems is presented. A computer program was developed based on the Eulerian hydroelasto-viscoplastic formulation and the utilization of the theorem of weak solutions. The equations solved consist of conservation of mass, momentum, and energy, equation of state, and appropriate constitutive equations. The solution technique is a time-dependent finite element analysis utilizing three-dimensional isoparametric elements, in conjunction with a generalized two-step time integration scheme. The developed code was demonstrated by solving one-dimensional as well as three-dimensional impact problems for both the inviscid hydrodynamic model and the hydroelasto-viscoplastic model