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

In Vitro and in Vivo Visualization and Trapping of Fluorescent Magnetic Microcapsules in a Bloodstream

Remote navigation and targeted delivery of biologically active compounds is one of the current challenges in the development of drug delivery systems. Modern methods of micro- and nanofabrication give us new opportunities to produce particles and capsules bearing cargo to deploy and possess magnetic properties to be externally navigated. In this work we explore multilayer composite magnetic microcapsules as targeted delivery systems in vitro and in vivo studies under natural conditions of living organism. Herein, we demonstrate magnetic addressing of fluorescent composite microcapsules with embedded magnetite nanoparticles in blood flow environment. First, the visualization and capture of the capsules at the defined blood flow by the magnetic field are shown in vitro in an artificial glass capillary employing a wide-field fluorescence microscope. Afterward, the capsules are visualized and successfully trapped in vivo into externally exposed rat mesentery microvessels. Histological analysis shows that capsules infiltrate small mesenteric vessels whereas large vessels preserve the blood microcirculation. The effect of the magnetic field on capsule preferential localization in bifurcation areas of vasculature, including capsule retention at the site once external magnet is switched off is discussed. The research outcome demonstrates that microcapsules can be effectively addressed in a blood flow, which makes them a promising delivery system with remote navigation by the magnetic field