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lectures17_18 - Introduction to Simulation Molecular...

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Introduction to Simulation - Lectures 17, 18 Molecular Dynamics Nicolas Hadjiconsta nti nou
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Molecular Dynamics Molecular dynamics is a technique for computing the equilibrium and non-equilibrium properties of classical* many-body systems. * The nuclear motion of the constituent particles obeys the laws of classical mechanics (Newton). References: 1) Computer Simulation of Liquids , M.P. Allen & D.J. Tildesley, Clarendon, Oxford, 1987. 2) Understanding Molecular Simulation: From Algorithms to Applications , D. Frenkel and B. Smit, Academic Press, 1997. 3) Moldy manual
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3 • A free and easy to use molecular dynamics simulation package can be found at the CCP5 program library ( http://www.ccp5.ac.uk/librar.shtml ), under the name Moldy. At this site a variety of very useful information as well as molecular simulation tools can be found. • Moldy is easy to use and comes with a very well written manual which can help as a reference. I expect the homework assignments to be completed using Moldy. Moldy
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4 Why Do We Need Molecular Dynamics? Similar to real experiments. 1. Allows us to study and understand material behavior so that we can model it. 2. Tells us what the answer is when we do not have models. Example: Diffusion equation Conservation of mass: d dt ndxdydz F F dydz x x dx ( ) = ( ) + | | n F = = number density, flux F x | F x dx | + dy x dx + x
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5 This equation cannot be solved unless a relation between n and F is provided. Experiments or consideration of molecular behavior shows that under a variety of conditions = n t D n x 2 2 diffusion equation! d dt ndxdydz F F F x dx F x dx dydz F x dxdydz F x dx dydzdx x x x ( ) + + = − | | | 2 2 2 2 2 2 2 in the limit dx n t F x + = 0 0 , F D n x = −
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6 F D n x = − Breakdown of linear gradient constitutive law • Large gradients • Far from equilibrium gaseous flows - Shockwaves - Small scale flows (high Knudsen number flow) - Rarefied flows (low density) (high Knudsen number flow) High Knudsen number flows (gases) • Kn is defined as the ratio of the molecular mean-free path to a characteristic lengthscale • The molecular mean-free path is the average distance traveled by molecules between collisions • Collisions tend to restore equilibrium • When Kn « 1 particle motion is diffusive (near equilibrium) • When Kn » 1 particle motion is ballistic (far from equilibrium) • 0.1 ¡ Kn ¡ 10 physics is transitional (hard to model)
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7 Example: Re-entry vehicle aerobraking maneuver in the upper atmosphere • In the upper atmosphere density is low (collision rate is low) • Long mean-free path • High Knudsen number flows typical Other high Knudsen number flows • Small scale flows (mean-free path of air molecules at atmospheric pressure is approximately 60 nanometers) • Vacuum science (low pressure)
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8 From Dr. M. Gallis of Sandia National Laboratories
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9 Brief Intro to Statistical Mechanics Statistical mechanics provides the theoretical connection between the microscopic description of matter (e.g. positions and velocities of molecules)
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