Chiral polymerization: symmetry breaking and entropy production in closed systems

We solve numerically a kinetic model of chiral polymerization in systems closed to matter and energy flow, paying special emphasis to its ability to amplify the small initial enantiomeric excesses due to the internal and unavoidable statistical fluctuations. The reaction steps are assumed to be reversible, implying a thermodynamic constraint among some of the rate constants. Absolute asymmetric synthesis is achieved in this scheme. The system can persist for long times in quasi- stationary chiral asymmetric states before racemizing. Strong inhibition leads to long-period chiral oscillations in the enantiomeric excesses of the longest homopolymer chains. We also calculate the entropy production {\sigma} per unit volume and show that {\sigma} increases to a peak value either before or in the vicinity of the chiral symmetry breaking transition

Critical Dynamics of Magnets

We review our current understanding of the critical dynamics of magnets above and below the transition temperature with focus on the effects due to the dipole--dipole interaction present in all real magnets. Significant progress in our understanding of real ferromagnets in the vicinity of the critical point has been made in the last decade through improved experimental techniques and theoretical advances in taking into account realistic spin-spin interactions. We start our review with a discussion of the theoretical results for the critical dynamics based on recent renormalization group, mode coupling and spin wave theories. A detailed comparison is made of the theory with experimental results obtained by different measuring techniques, such as neutron scattering, hyperfine interaction, muon--spin--resonance, electron--spin--resonance, and magnetic relaxation, in various materials. Furthermore we discuss the effects of dipolar interaction on the critical dynamics of three--dimensional isotropic antiferromagnets and uniaxial ferromagnets. Special attention is also paid to a discussion of the consequences of dipolar anisotropies on the existence of magnetic order and the spin--wave spectrum in two--dimensional ferromagnets and antiferromagnets. We close our review with a formulation of critical dynamics in terms of nonlinear Langevin equations.Comment: Review article (154 pages, figures included

On the Classification of Leptons

peer reviewedaudience: researcherThe formulae giving the electric charge and the neutrinonic charge in terms of T3 and S are generalized in order to apply them to leptons. There remains an unknown parameter. For a particular value of this parameter these formulae assume the particularly symmetric forms (15) and (16). Values for S, T and T3 are assigned to the different leptons. At the time this investigation was carried out the following difficulty arose: in addition to the known leptons (neutrino, electron and muon) there remained a vacancy for an undisovered lepton, which, with regard to the charges, is similar to the neutrino. Yet this has no longer to be considered as a difficulty but well as a prediction of the theory since one was recently led to admit the existence of two neutral leptons instead of one, namely the neutrino