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Microscopic pressure tensor for hard-sphere fluids.

Bjørn Hafskjold1, Tamio Ikeshoji

  • 1Research Institute for Computational Sciences, AIST Tsukuba Central 2, Umezono 1-1-1, Tsukuba, 305-8568, Japan. bjorn.hafskjold@phys.chem.ntnu.no

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
Summary
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The Irving-Kirkwood (IK) pressure tensor definition yields consistent results for hard-sphere fluids across coordinate systems. The Harasima (H) definition, however, proves unreliable in spherical coordinates, indicating it is not a proper pressure tensor.

Area of Science:

  • Statistical Mechanics
  • Computational Physics
  • Fluid Dynamics

Background:

  • The microscopic pressure tensor is crucial for understanding fluid behavior.
  • Its definition is not unique, leading to potential inconsistencies.
  • Hard-sphere models are fundamental in statistical mechanics.

Purpose of the Study:

  • To analyze the microscopic pressure tensor for a uniform hard-sphere fluid.
  • To compare the Irving-Kirkwood (IK) and Harasima (H) definitions.
  • To evaluate coordinate system dependence of pressure tensor definitions.

Main Methods:

  • Analysis of the microscopic pressure tensor in Cartesian and spherical coordinates.
  • Application of the Irving-Kirkwood (IK) definition.
  • Application of the Harasima (H) definition.

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Main Results:

  • The IK definition provides consistent ensemble-averaged local pressure in both coordinate systems for homogeneous hard-sphere systems.
  • The H definition yields different pressures in Cartesian and spherical coordinates.
  • The H pressure in spherical coordinates shows dependence on the distance from the origin (R).

Conclusions:

  • The IK definition is a reliable method for calculating the pressure tensor in hard-sphere fluids.
  • The H definition is not a proper pressure tensor due to its coordinate dependence.
  • Coordinate system choice significantly impacts pressure tensor calculations using certain definitions.