Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Quaternized and Thiazole-Functionalized Free Radical-Generating Organometallic Dendrimers as Antimicrobial Platform against Multidrug-Resistant Microorganisms

New macromolecules such as dendrimers are increasingly needed to drive breakthroughs in diverse areas, for example, healthcare. Here, the authors report hybrid antimicrobial dendrimers synthesized by functionalizing organometallic dendrimers with quaternary ammonium groups or 2-mercaptobenzothiazole. The functionalization tunes the glass transition temperature and antimicrobial activities of the dendrimers. Electron paramagnetic resonance spectroscopy reveals that the dendrimers form free radicals, which have significant implications for catalysis and biology. In vitro antimicrobial assays indicate that the dendrimers are potent antimicrobial agents with activity against multidrug-resistant pathogens such as methicillin-resistant Staphylococcus aureus and vancomycin-resistant Enterococcus faecium as well as other microorganisms. The functionalization increases the activity, especially in the quaternary ammonium group-functionalized dendrimers. Importantly, the activities are selective because human epidermal keratinocytes cells and BJ fibroblast cells exposed to the dendrimers are viable after 24 h