Study of Stability of a Charged Topological Soliton in the System of Two Interacting Scalar Fields

An analytical-numerical analysis of the singular self-adjoint spectral problem for a system of three linear ordinary second-order differential equations defined on the entire real exis is presented. This problem comes to existence in the nonlinear field theory. The dependence of the differential equations on the spectral parameter is nonlinear, which results in a quadratic operator Hermitian pencil.Comment: 22 pages, 2 figure

Delivery and reveal of localization of upconversion luminescent microparticles and quantum dots in the skin in vivo by fractional laser microablation, multimodal imaging, and optical clearing

Delivery and spatial localization of upconversion luminescent microparticles [Y 2 O 3 ;Yb, Er] (mean size ~1.6 μm) and quantum dots (QDs) (CuInS 2 ZnS nanoparticles coated with polyethylene glycol-based amphiphilic polymer, mean size ~20 nm) inside rat skin was studied in vivo using a multimodal optical imaging approach. The particles were embedded into the skin dermis to the depth from 300 to 500 μm through microchannels performed by fractional laser microablation. Low-frequency ultrasound was applied to enhance penetration of the particles into the skin. Visualization of the particles was revealed using a combination of luminescent spectroscopy, optical coherence tomography, confocal microscopy, and histochemical analysis. Optical clearing was used to enhance the image contrast of the luminescent signal from the particles. It was demonstrated that the penetration depth of particles depends on their size, resulting in a different detection time interval (days) of the luminescent signal from microparticles and QDs inside the rat skin in vivo. We show that luminescent signal from the upconversion microparticles and QDs was detected after the particle delivery into the rat skin in vivo during eighth and fourth days, respectively. We hypothesize that the upconversion microparticles have created a long-time depot localized in the laser-created channels, as the QDs spread over the surrounding tissues