On the Production of Flux Vortices and Magnetic Monopoles in Phase Transitions

We examine the basic assumptions underlying a scenario due to Kibble that is widely used to estimate the production of topological defects. We argue that one of the crucial assumptions, namely the geodesic rule, although completely valid for global defects, becomes ill defined for the case of gauged defects. We address the issues involved in formulating a suitable geodesic rule for this case and argue that the dynamics plays an important role in the production of gauge defects.Comment: 9 pages, in LATEX, UMN-TH-1028/92, TPI-MINN-92/20-

Probing shapes of microbes using liquid crystal textures

Topological defects in nematic liquid crystals are routinely investigated using a cross-polarizer set-up in optical microscopes. Characteristic signature of topology and structure of the defect is contained in the structure of dark brushes emanating from the core of topological defects. Even with defect core of size of few tens of nanometers, simple optical microscopy is able to identify the defects using these brushes. We propose to use this property to identify shapes of microbes embedded in a nematic liquid crystal (NLC) sample. Assuming certain anchoring conditions for the NLC director at the surface of the microbe, we determine the resulting shapes of brushes using numerical simulations. Our results suggest that for asymmetrical microbes (such as cylindrical shaped bacteria/viruses), resulting brushes may carry the imprints of this asymmetry (e.g. the aspect ratio of cylindrical shape) at relatively large distances to be able to be seen using simple optical microscopy, even for microbe sizes in few tens to few hundred nanometer range. For more complicated shapes, such as spiral shape bacterias or Filovirus such as Ebola virus, even the topology of brushes may be non-trivial depending on the spiral nature/folding of the virus along its length. For roughly spherical microbes, such as the corona virus, complete symmetry of brushes can help distinguishing from general asymmetric impurities/microbes. Further, information about the size of a spherical microbe may possibly be probed using brush deformations near the core in the presence of external electric/magnetic field.Comment: 12 pages, 7 figures, Electric field interaction term corrected, discussion improved/corrected, e.g. for intensity of light in the cross-polarizer setu