Single-Molecule Localization Microscopy of 3D Orientation and Anisotropic Wobble using a Polarized Vortex Point Spread Function

Within condensed matter, single fluorophores are sensitive probes of their chemical environments, but it is difficult to use their limited photon budget to image precisely their positions, 3D orientations, and rotational diffusion simultaneously. We demonstrate the polarized vortex point spread function (PSF) for measuring these parameters, including characterizing the anisotropy of a molecule’s wobble, simultaneously from a single image. Even when imaging dim emitters (∼500 photons detected), the polarized vortex PSF is able to obtain 12 nm localization precision, 4-8° orientation precision, and 26° wobble precision. We use the vortex PSF to measure the emission anisotropy of fluorescent beads, the wobble dynamics of Nile red (NR) within supported lipid bilayers, and the distinct orientation signatures of NR in contact with amyloid-beta fibrils, oligomers, and tangles. The unparalleled sensitivity of the vortex PSF transforms single-molecule microscopes into nanoscale orientation imaging spectrometers, where the orientations and wobbles of individual probes reveal structures and organization of soft matter that are nearly impossible to perceive using molecular positions alone.

Standing waves for a gauged nonlinear Schrödinger equation with a vortex point

This paper is motivated by a gauged Schrödinger equation in dimension 2. We are concerned with radial stationary states under the presence of a vortex at the origin. Those states solve a nonlinear nonlocal PDE with a variational structure. We will study the global behavior of that functional, extending known results for the regular case.

Investigation of the localized co-interchange instabilities in a rotamak plasma

If the rotamak is regarded as a spherical field-reversed mirror then, according to conventional ideal MHD analysis, it should be unstable to co-interchange modes localized near the vortex point of the magnetic field. It is shown that to study these instabilities in a typical rotamak plasma, the Hall term in Ohm's law cannot be ignored. The effect of the Hall term on the ideal MHD analysis of co-interchange modes is investigated and a stability criterion is derived.