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Approximate Integration01:24

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In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
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Rotational equilibrium provides a natural framework for defining the center of mass of a system. For a plank balanced on a pivot with two unequal masses, equilibrium is achieved when the net torque about the pivot is zero. Torque is defined as the product of a force and its perpendicular distance from the pivot. When the torques due to all forces cancel, the pivot coincides with the center of mass of the system.For a system composed of several discrete point masses, the center of mass lies at...
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Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
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Geometric integrator for simulations in the canonical ensemble.

Diego Tapias1, David P Sanders1, Alessandro Bravetti2

  • 1Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México 04510, Mexico.

The Journal of Chemical Physics
|September 3, 2016
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Summary

We developed a novel geometric integrator for molecular dynamics simulations. This method accurately preserves the invariant distribution, ensuring correct ensemble sampling for various thermostats in physical systems.

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Area of Science:

  • Computational Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Molecular dynamics simulations are crucial for understanding physical systems.
  • Accurate sampling of the canonical ensemble is essential for reliable thermodynamic results.
  • Existing integrators can introduce drift, compromising ensemble accuracy.

Purpose of the Study:

  • To introduce a novel geometric integrator for molecular dynamics simulations.
  • To preserve the invariant distribution in the canonical ensemble for density dynamics.
  • To provide a unified framework for studying thermostat effects.

Main Methods:

  • Developed a geometric integrator preserving invariant distribution.
  • Implemented a second-order, time-reversible method.
  • Applied to Lennard-Jones system simulations with three thermostats.

Main Results:

  • The geometric integrator demonstrated good conservation of geometrical properties.
  • Expected thermodynamic results were accurately recovered.
  • Compared to the Gear integrator, our method showed no drift in the invariant quantity.

Conclusions:

  • The proposed geometric integrator effectively samples the correct ensemble.
  • This unified framework facilitates the study of different thermostats and their impact.
  • The integrator offers an advantage over non-geometric methods for canonical ensemble simulations.