A Study of Multibody Systems involving Optical Tweezers

Many modern research fields make use of optical tweezers in order to surgically manipulate microscopically sized particles, yet only the dynamics of single particle manipulation within an optical trap has been widely theoretically studied. A study of such systems would help more accurately mathematically describe a variety of natural stochastic processes, such as the formation of covalent bonds or the manipulation of DNA strands while splicing genes onto it, which could help optimize the way research is done at the microscopic level. After establishing the necessary tools from stochastic analysis to understand the modeling dynamics equations, we will present the explicit solution for physically relevant cases (elastic attraction and coulombic attraction) as well as a mathematically viable simulation to illustrate this motion. This newly established mathematical framework can also be used to understand other instances of Brownian motion, such as the motion of motion of stars in galaxies, the movement of holes of electrical charge in electrical conductors, or the motion of plasma particles in cells.

This research is supported by the Simons Summer Research Program at Stony Brook University .