scholarly journals Stochastic multi-particle Brownian Dynamics simulation of biological ion channels: A Finite Element approach

2009 ◽  
Author(s):  
May Siksik ◽  
Vikram Krishnamurthy
Keyword(s):  
Finite Element ◽  
Ion Channels ◽  
Brownian Dynamics ◽  
Dynamics Simulation ◽  
Brownian Dynamics Simulation ◽  
Finite Element Approach ◽  
Element Approach

Finite Element-Based Brownian Dynamics Simulation of Nanofiber Suspensions Using Monte Carlo Method1

2015 ◽  
Vol 3 (4) ◽  
Author(s):  
Dongdong Zhang ◽  
Douglas E. Smith
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Brownian Dynamics ◽  
Element Model ◽  
Dynamics Simulation ◽  
Brownian Dynamics Simulation ◽  
Fiber Motion ◽  
Newton Raphson ◽  
Raphson Method ◽  
Surrounding Fluid

This paper presents a computational approach for simulating the motion of nanofibers during fiber-filled composites processing. A finite element-based Brownian dynamics simulation (BDS) is proposed to solve for the motion of nanofibers suspended within a viscous fluid. We employ a Langevin approach to account for both hydrodynamic and Brownian effects. The finite element method (FEM) is used to compute the hydrodynamic force and torque exerted from the surrounding fluid. The Brownian force and torque are regarded as the random thermal disturbing effects which are modeled as a Gaussian process. Our approach seeks solutions using an iterative Newton–Raphson method for a fiber's linear and angular velocities such that the net forces and torques, including both hydrodynamic and Brownian effects, acting on the fiber are zero. In the Newton–Raphson method, the analytical Jacobian matrix is derived from our finite element model. Fiber motion is then computed with a Runge–Kutta method to update fiber position and orientation as a function of time. Instead of remeshing the fluid domain as a fiber migrates, the essential boundary condition is transformed on the boundary of the fluid domain, so the tedious process of updating the stiffness matrix of finite element model is avoided. Since the Brownian disturbance from the surrounding fluid molecules is a stochastic process, Monte Carlo simulation is used to evaluate a large quantity of motions of a single fiber associated with different random Brownian forces and torques. The final fiber motion is obtained by averaging numerous fiber motion paths. Examples of fiber motions with various Péclet numbers are presented in this paper. The proposed computational methodology may be used to gain insight on how to control fiber orientation in micro- and nanopolymer composite suspensions in order to obtain the best engineered products.

Finite Element-Based Brownian Dynamics Simulation of Nano-Fiber Suspensions in Nano-Composites Processing Using Monte-Carlo Method

2012 ◽  
Author(s):  
Dongdong Zhang ◽  
Douglas E. Smith
Keyword(s):  
Finite Element ◽  
Brownian Dynamics ◽  
Element Model ◽  
Dynamics Simulation ◽  
Nano Composites ◽  
Brownian Dynamics Simulation ◽  
Fiber Motion ◽  
Newton Raphson ◽  
Composites Processing ◽  
Raphson Method

This paper presents a computational approach for simulating the motion of nano-fibers during polymer nano-composites processing. A finite element-based Brownian dynamics simulation is proposed to solve the motion of nano-fibers suspended within a viscous fluid. In this paper, a Langevin approach is used to account for both hydrodynamic and Brownian effects. We develop a stand-alone Finite Element Method (FEM) for modeling the hydrodynamic effect exerted from the surrounding fluid. The Brownian effects are regarded as the random thermal disturbing forces/torques, which are modeled as a Gaussian process. Our approach seeks solutions using an iterative Newton-Raphson method for the fiber’s linear and angular velocities such that the net forces and torques, i.e. the combination of hydrodynamic and Brownian effects, acting on the fiber are zero. In the Newton-Raphson method, the analytical Jacobian matrix is derived from our finite element model. Fiber motion is then computed with a Runge-Kutta method to update the fiber positions and orientations as a function of time. Instead of re-meshing the fluid domain as fiber moves, we applied the transformed essential boundary conditions on the boundary of fluid domain, so the tedious process of updating stiffness matrix of finite element model is avoided. Since Brownian disturbance from the fluid molecules is a stochastic process, Monte-Carlo simulation is used to evaluate the motion of a great many fibers associated with different random Brownian forces and torques. The final fiber motion is obtained by averaging a numerous fiber motion paths. Examples of fiber motions with various Péclet numbers are presented in this paper. The proposed computational methodology will be used to gain insight on how to control fiber orientations in micro- and nano-polymer composite suspensions in order to obtain the best engineered products.

scholarly journals Influence of Global and Local Membrane Curvature on Mechanosensitive Ion Channels: A Finite Element Approach

Membranes ◽  
2016 ◽  
Vol 6 (1) ◽  
pp. 14 ◽  
Author(s):  
Omid Bavi ◽  
Charles Cox ◽  
Manouchehr Vossoughi ◽  
Reza Naghdabadi ◽  
Yousef Jamali ◽  
...  
Keyword(s):  
Finite Element ◽  
Ion Channels ◽  
Membrane Curvature ◽  
Finite Element Approach ◽  
Mechanosensitive Ion Channels ◽  
Element Approach ◽  
Global And Local

A Finite Element Approach to the Transient Dynamics of Rolling Tires with Emphasis on Rolling Noise Simulation4

2007 ◽  
Vol 35 (3) ◽  
pp. 165-182 ◽  
Author(s):  
Maik Brinkmeier ◽  
Udo Nackenhorst ◽  
Heiner Volk
Keyword(s):  
Finite Element ◽  
Traffic Noise ◽  
Complex Eigenvalue ◽  
Arbitrary Lagrangian Eulerian ◽  
Finite Element Approach ◽  
Road Systems ◽  
Element Approach ◽  
Road Surface Roughness ◽  
Complex Eigenvalue Analysis ◽  
Rolling Noise

Abstract The sound radiating from rolling tires is the most important source of traffic noise in urban regions. In this contribution a detailed finite element approach for the dynamics of tire/road systems is presented with emphasis on rolling noise prediction. The analysis is split into sequential steps, namely, the nonlinear analysis of the stationary rolling problem within an arbitrary Lagrangian Eulerian framework, and a subsequent analysis of the transient dynamic response due to the excitation caused by road surface roughness. Here, a modal superposition approach is employed using complex eigenvalue analysis. Finally, the sound radiation analysis of the rolling tire/road system is performed.

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