Daniel G. Schuster Jr., Mario W. Gomes, Alexandra B. Artusio-Glimpse, Grover A. Swartzlander Jr.
In this paper, the response is found for a semi-cylindrical rod rocking on a level surface while subjected to forces from radiation pressure and gravity. Changes in the oscillation frequency of the rod as a function of light intensity are determined for both a mirrored and non-mirrored rod. The simulation results show that the equilibrium positions for the mirrored and non-mirrored rod exhibit a classic pitchfork and cusp catastrophe type bifurcation at critical laser intensities, respectively. By linearizing the systems equations of motion and sinusoidally modulating the laser intensity, the mathematical model for the rocking semi-cylinder could be transformed in the standard form of Mathieu’s equation. Inspired by the stability regions of the vertically oscillating inverted pendulum, a region of laser modulation parameters was determined, which could stabilize orientations of the lens which were unstable with constant laser intensity. Lastly, a comparison between the bifurcation point and change in natural frequency as functions of intensity between a previous analytical derivation and the full nonlinear model also showed that they agree closely for laser intensities near and below the critical intensity.
DOI
Showing posts with label Nonlinear Dynamics. Show all posts
Showing posts with label Nonlinear Dynamics. Show all posts
Wednesday, March 25, 2015
Wednesday, January 15, 2014
Dynamics of microscopic objects in optical tweezers: experimental determination of underdamped regime and numerical simulation using multiscale analysis
Mahdi Haghshenas-Jaryani, Bryan Black, Sarvenaz Ghaffari, James Drake, Alan Bowling, Samarendra Mohanty
This article presents new experimental observations and numerical simulations to investigate the dynamic behavior of micro–nano-sized objects under the influence of optical tweezers (OTs). OTs are scientific tools that can apply forces and moments to small particles using a focused laser beam. The motions of three polystyrene microspheres of different diameters, 1,950, 990, and 500 nm, are examined. The results show a transition from the overdamped motion of the largest bead to the underdamped motion of the smallest bead. The experiments are verified using a dynamic model of a microbead under the influence of Gaussian beam OTs that is modeled using ray-optics. The time required to numerically integrate the classic Newton–Euler model is quite long because a picosecond step size must be used. This run time can be reduced using a first-order model, and greatly reduced using a new multiscale model. The difference between these two models is the underdamped behavior predicted by the multiscale model. The experimentally observed underdamped behavior proves that the multiscale model predicts the actual physics of a nano-sized particle moving in a fluid environment characterized by a low Reynolds number.
DOI
This article presents new experimental observations and numerical simulations to investigate the dynamic behavior of micro–nano-sized objects under the influence of optical tweezers (OTs). OTs are scientific tools that can apply forces and moments to small particles using a focused laser beam. The motions of three polystyrene microspheres of different diameters, 1,950, 990, and 500 nm, are examined. The results show a transition from the overdamped motion of the largest bead to the underdamped motion of the smallest bead. The experiments are verified using a dynamic model of a microbead under the influence of Gaussian beam OTs that is modeled using ray-optics. The time required to numerically integrate the classic Newton–Euler model is quite long because a picosecond step size must be used. This run time can be reduced using a first-order model, and greatly reduced using a new multiscale model. The difference between these two models is the underdamped behavior predicted by the multiscale model. The experimentally observed underdamped behavior proves that the multiscale model predicts the actual physics of a nano-sized particle moving in a fluid environment characterized by a low Reynolds number.
DOI
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