title: Generalized Scaling and the Master Variable for Brownian Magnetic Nanoparticle Dynamics.
abstract: Understanding the dynamics of magnetic particles can help to advance several biomedical nanotechnologies. Previously, scaling relationships have been used in magnetic spectroscopy of nanoparticle Brownian motion (MSB) to measure biologically relevant properties (e.g., temperature, viscosity, bound state) surrounding nanoparticles in vivo. Those scaling relationships can be generalized with the introduction of a master variable found from non-dimensionalizing the dynamical Langevin equation. The variable encapsulates the dynamical variables of the surroundings and additionally includes the particles' size distribution and moment and the applied field's amplitude and frequency. From an applied perspective, the master variable allows tuning to an optimal MSB biosensing sensitivity range by manipulating both frequency and field amplitude. Calculation of magnetization harmonics in an oscillating applied field is also possible with an approximate closed-form solution in terms of the master variable and a single free parameter.
authors.affiliation: Department of Physics and Astronomy, Dartmouth College, Hanover, NH, 03755 United States of America.
authors.forename: Daniel B
authors.initials: DB
authors.lastname: Reeves
authors.affiliation: Department of Physics and Astronomy, Dartmouth College, Hanover, NH, 03755 United States of America.
authors.forename: Yipeng
authors.initials: Y
authors.lastname: Shi
authors.affiliation: Department of Physics and Astronomy, Dartmouth College, Hanover, NH, 03755 United States of America.|Department of Radiology, Geisel School of Medicine, Hanover, NH, 03755 United States of America.
authors.forename: John B
authors.initials: JB
authors.lastname: Weaver
mesh_terms: D015374:Biosensing Techniques; D003198:Computer Simulation; D060526:Magnetic Fields; D058185:Magnetite Nanoparticles / Q000737:chemistry*; D008962:Models, Theoretical; D015203:Reproducibility of Results; D013696:Temperature
chemical_list: D058185:Magnetite Nanoparticles