Posts Tagged ‘spring’

Modeling Physical Behavior with an Atomic Engine

May 13th, 2013 by Sara Remsen

Our Next-Generation Molecular Workbench (MW) software usually models molecular dynamics—from states of matter and phase changes to diffusion and gas laws. Recently, we adapted the Molecular Dynamics 2D engine to model macroscale physics mechanics as well, including pendulums and springs.

In order to scale up the models from microscopic to macroscopic, we employ specific unit-scaling conventions. The Next-Generation Molecular Workbench (MW) engine simulates molecular behavior by treating atoms as particles that obey Newton’s laws. For example, the bond between two atoms is treated as a spring that obeys Hooke’s law, and electrostatic interactions between charged ions follow Coulomb’s Law.

Dipole-dipole interactions simulated using Coulomb’s Law.

At the microscale, the Next-Generation MW engine calculates the forces between molecules or atoms using atomic mass units (amu), nanometers (10−9 meters) and femtoseconds (10-15 seconds), and depicts their motion. To simulate macroscopic particles that follow the same laws, we can imagine them as microscopic particles with masses in amu, distance in nanometers, and timescales measured in femtoseconds. Once the Next-Generation MW engine calculates the movement of these atomic-scale particles, we simply multiply the length, mass and time units by the correct scaling factors. This motion satisfies the same physical laws as the atomic motion but is now measured in meters, kilograms and seconds.

In the pendulum simulation below, the Next-Generation MW engine models the behavior of a pendulum by treating it as two atoms connected by a very stiff bond with a very long equilibrium length. The topmost atom is restrained to become a “pivot” while the bottom atom “swings” because of the stiff bond. Once the engine has calculated the force using the atomic-scale units, it converts the mass, velocity and acceleration to the appropriate units for large, physical objects like the pendulum.

Large-scale physical behavior simulated with a molecular dynamics engine.

In order to appropriately model the physical behavior of a pendulum or a spring, we use specific scaling constants. Independent scaling constants for mass, distance and time enable us to convert nanometers to meters, atomic mass units to kilograms and femtoseconds to model seconds. Using the same scaling constants, we can derive other physical conversions, such as elementary charge unit to Coulomb. In order to make one model second pass for every real second, we adjusted the amount of model time between each page refresh. We also chose to simulate a gravitation field—a feature usually absent in molecular dynamics simulators—because it is relevant to macroscopic phenomena.

From microscale to macroscale, the Next-Generation Molecular Workbench engine is a powerful modeling tool that we can use to simulate a wide variety of biological, chemical, and physical phenomena.  Find more simulations at mw.concord.org/nextgen/interactives.