Numerical simulation of optically trapped particles

Some randomness is present in most phenomena, ranging from biomolecules and nanodevices to financial markets and human organizations. However, it is not easy to gain an intuitive understanding of such stochastic phenomena, because their modeling requires advanced mathematical tools, such as sigma algebras, the Itô formula and martingales. Here, we discuss a simple finite difference algorithm that can be used to gain understanding of such complex physical phenomena. In particular, we simulate the motion of an optically trapped particle that is typically used as a model system in statistical physics and has a wide range of applications in physics and biophysics, for example, to measure nanoscopic forces and torques.

[1]  P. Denti,et al.  Radiation torque and force on optically trapped linear nanostructures. , 2008, Physical review letters.

[2]  J. Wehr,et al.  Noise-Induced Drift in Stochastic Differential Equations with Arbitrary Friction and Diffusion in the Smoluchowski-Kramers Limit , 2011, 1112.2607.

[3]  E. Stelzer,et al.  Trapping and tracking a local probe with a photonic force microscope , 2004 .

[4]  H. Rubinsztein-Dunlop,et al.  Optical application and measurement of torque on microparticles of isotropic nonabsorbing material , 2003, physics/0309122.

[5]  J. Wehr,et al.  Force measurement in the presence of Brownian noise: equilibrium-distribution method versus drift method. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Scott Hottovy,et al.  Thermophoresis of Brownian particles driven by coloured noise , 2012, 1205.1093.

[7]  Edward Nelson.  Dynamical Theories of Brownian Motion , 1967 .

[8]  Giorgio Volpe,et al.  Brownian motion in a nonhomogeneous force field and photonic force microscope. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Ramin Golestanian,et al.  Self-motile colloidal particles: from directed propulsion to random walk. , 2007, Physical review letters.

[10]  G. Volpe,et al.  Torque detection using Brownian fluctuations. , 2006, Physical review letters.

[11]  M. Raizen,et al.  Measurement of the Instantaneous Velocity of a Brownian Particle , 2010, Science.

[12]  E. Purcell.  Life at Low Reynolds Number , 2008 .

[13]  T. Faniran.  Numerical Solution of Stochastic Differential Equations , 2015 .

[14]  Mark Dykman,et al.  Thermally activated transitions in a bistable three-dimensional optical trap , 1999, Nature.

[15]  Michelle D. Wang,et al.  Optical torque wrench: angular trapping, rotation, and torque detection of quartz microparticles. , 2004, Physical review letters.

[16]  G. Volpe,et al.  Simulation of a Brownian particle in an optical trap , 2013 .

[17]  T C Lubensky,et al.  State-dependent diffusion: Thermodynamic consistency and its path integral formulation. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  J. Wehr,et al.  Influence of noise on force measurements. , 2010, Physical review letters.

[19]  G. Volpe,et al.  Singular-point characterization in microscopic flows. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  J. Wehr,et al.  Thermal noise suppression: how much does it cost? , 2007, 0711.0923.

[21]  P. Lancon,et al.  Drift without flux: Brownian walker with a space dependent diffusion coefficient , 2001 .

[22]  Gregoire Nicolis,et al.  Stochastic resonance , 2007, Scholarpedia.

[23]  A. Ashkin,et al.  Optical trapping and manipulation of neutral particles using lasers. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[24]  D. Ermak,et al.  Brownian dynamics with hydrodynamic interactions , 1978 .

[25]  H. Flyvbjerg,et al.  Power spectrum analysis for optical tweezers , 2004 .

[26]  Giorgio Volpe,et al.  Quantitative assessment of non-conservative radiation forces in an optical trap , 2009 .

[27]  Stephen J. Ebbens,et al.  In pursuit of propulsion at the nanoscale , 2010 .

[28]  J. Rubí,et al.  Stochastic resonant damping in a noisy monostable system: theory and experiment. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.