scholarly journals Modeling of a Nanoparticle Motion in a Newtonian Fluid: A Comparison Between Fluctuating Hydrodynamics and Generalized Langevin Procedures

2012 ◽  
Author(s):  
B. Uma ◽  
P. S. Ayyaswamy ◽  
R. Radhakrishnan ◽  
D. M. Eckmann
Keyword(s):  
Cylindrical Tube ◽  
Langevin Dynamics ◽  
Solid Sphere ◽  
Thermal Fluctuations ◽  
Velocity Autocorrelation Function ◽  
Fluctuating Hydrodynamics ◽  
Arbitrary Lagrangian Eulerian ◽  
Particle Decay ◽  
Numerical Predictions ◽  
Generalized Langevin Dynamics

A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed to simulate the motion of a nanocarrier in a quiescent fluid contained in a cylindrical tube. The nanocarrier is treated as a solid sphere. Thermal fluctuations are implemented using two different approaches: (1) fluctuating hydrodynamics; (2) generalized Langevin dynamics (Mittag-Leffler noise). At thermal equilibrium, the numerical predictions for temperature of the nanoparticle, velocity distribution of the particle, decay of the velocity autocorrelation function, diffusivity of the particle and particle-wall interactions are evaluated and compared with analytical results, where available. For a neutrally buoyant nanoparticle of 200 nm radius, the comparisons between the results obtained from the fluctuating hydrodynamics and the generalized Langevin dynamics approaches are provided. Results for particle diffusivity predicted by the fluctuating hydrodynamics approach compare very well with analytical predictions. Ease of computation of the thermostat is obtained with the Langevin approach although the dynamics gets altered.

scholarly journals A Hybrid Approach for the Simulation of the Thermal Motion of a Nearly Neutrally Buoyant Nanoparticle in an Incompressible Newtonian Fluid Medium

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
B. Uma ◽  
R. Radhakrishnan ◽  
D. M. Eckmann ◽  
P. S. Ayyaswamy
Keyword(s):  
Newtonian Fluid ◽  
Brownian Particle ◽  
Equations Of Motion ◽  
Hybrid Approach ◽  
Thermal Motion ◽  
Fluctuating Hydrodynamics ◽  
Arbitrary Lagrangian Eulerian ◽  
Fluid Medium ◽  
Incompressible Newtonian Fluid ◽  
Neutrally Buoyant

A hybrid approach consisting of a Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein–Uhlenbeck noise perturbing the translational and rotational equations of motion of a nanoparticle is employed to study the thermal motion of a nearly neutrally buoyant nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian–Eulerian based finite element method is employed for the simulation of the hybrid approach. The instantaneous flow around the particle and the particle motion are fully resolved. The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obey Stokes–Einstein and Stokes–Einstein–Debye relations, respectively; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available. The study has important implications for designing nanocarriers for targeted drug delivery. A major advantage of our novel hybrid approach employed in this paper as compared to either the fluctuating hydrodynamics approach or the generalized Langevin approach by itself is that only the hybrid method has been shown to simultaneously preserve both hydrodynamic correlations and equilibrium statistics in the incompressible limit.

Comparison of rate theories for generalized Langevin dynamics

1991 ◽  
Vol 95 (8) ◽  
pp. 5809-5826 ◽  
Author(s):  
Susan C. Tucker ◽  
Mark E. Tuckerman ◽  
Bruce J. Berne ◽  
Eli Pollak
Keyword(s):  
Langevin Dynamics ◽  
Generalized Langevin Dynamics

scholarly journals Uncertainty quantification for generalized Langevin dynamics

2016 ◽  
Vol 145 (22) ◽  
pp. 224108 ◽  
Author(s):  
Eric J. Hall ◽  
Markos A. Katsoulakis ◽  
Luc Rey-Bellet
Keyword(s):  
Uncertainty Quantification ◽  
Langevin Dynamics ◽  
Generalized Langevin Dynamics
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