Cocommutative coalgebras: homotopy theory and Koszul duality

We extend a construction of Hinich to obtain a closed model category structure on all differential graded cocommutative coalgebras over an algebraically closed field of characteristic zero. We further show that the Koszul duality between commutative and Lie algebras extends to a Quillen equivalence between cocommutative coalgebras and formal coproducts of curved Lie algebras.Comment: 38 page

Electrostatic rogue waves in double pair plasmas

A nonlinear Schr\"{o}dinger equation is derived to investigate the modulational instability (MI) of ion-acoustic (IA) waves (IAWs) in a double pair plasma system containing adiabatic positive and negative ion fluids along with super-thermal electrons and positrons. The analytical analysis predicts two types of modes, viz. fast ($\omega_f$) and slow ($\omega_s$) IA modes. The possible stable and unstable parametric regions for the IAWs in presence of external perturbation can be observed for both $\omega_f$ and $\omega_s$. The number density of the negative ions and positrons play a vital role in generating the IA rogue waves (IARWs) in the modulationally unstable region. The applications of our present work in astrophysical environments [viz. D-region ($\rm H^+, O_2^-$) and F-region ($\rm H^+, H^-$) of the Earth's ionosphere] as well as in laboratory plasmas [viz. pair-ion Fullerene ($\rm C^+, C^-$)] are pinpointed.Comment: 5 pages; 6 figure