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Related Concept Videos

Basic Equation for Pressure Field01:13

Basic Equation for Pressure Field

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The basic equation for a pressure field in fluid mechanics captures the balance of forces within any segment of fluid, providing a foundational understanding of how pressure changes within fluids under various forces. Generally, two main types of forces act on any part of a fluid: surface forces and body forces. Surface forces arise from pressure differences across points within the fluid, which result in net forces that can vary depending on the local pressure gradient. Body forces, on the...
648
Pressure Variation in a Fluid at Rest01:11

Pressure Variation in a Fluid at Rest

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In a fluid at rest, the pressure at any point beneath the fluid surface depends solely on the depth, not on the container's shape or size. This principle, known as hydrostatic pressure, arises because, in stationary fluids, there is no acceleration, meaning the forces within the fluid balance out. Only vertical forces, caused by the weight of the fluid above, contribute to pressure changes with depth.
When measuring pressure at two different levels within the fluid, the difference in...
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Applications of Integration to Find Hydrostatic Pressure01:30

Applications of Integration to Find Hydrostatic Pressure

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Hydrostatic force is a fluid's total force at rest on a surface. For a horizontal surface submerged at a fixed depth, the pressure is constant and calculated as the product of fluid density, gravitational acceleration, and depth. In the case of a vertical dam wall submerged in water, this force is not evenly distributed due to the increasing pressure with depth. This variation arises from the cumulative weight of the water above each point. Integration is used to account for the continuous...
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Radiation Pressure: Problem Solving01:09

Radiation Pressure: Problem Solving

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The radiation pressure applied by an electromagnetic wave on a perfectly absorbing surface equals the energy density of the wave. The wave's momentum also gets transferred to the surface when an electromagnetic wave is entirely absorbed by it. The rate at which momentum is transmitted to an absorbing surface perpendicular to the propagation direction equals the force on the surface.
The average value of the rate of momentum transfer divided by the absorbing area represents the average force...
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Pressure and Volume in an Adiabatic Process01:27

Pressure and Volume in an Adiabatic Process

3.6K
Free expansion of a gas is an adiabatic process. However, there are few differences between free expansion and adiabatic expansion. During free expansion, no work is done, and there is no change in internal energy. But, for an adiabatic expansion, work is done, and there is a change in internal energy. During an adiabatic process, the relation between the pressure and volume is obtained from the condition for the adiabatic process, that is,
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Application of Linearization and Approximation01:29

Application of Linearization and Approximation

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A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
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Related Experiment Video

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Blast Quantification Using Hopkinson Pressure Bars
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Evaluation of atomic pressure in the multiple time-step integration algorithm.

Yoshimichi Andoh1, Noriyuki Yoshii1,2, Atsushi Yamada2

  • 1Center of Computational Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan.

Journal of Computational Chemistry
|January 21, 2017
PubMed
Summary

This study introduces new equations for calculating atomic pressure in molecular dynamics (MD) simulations using the RESPA multiple time-step (MTS) algorithm. The proposed method accurately determines pressure, improving computational efficiency and reliability in MD calculations.

Keywords:
RESPASHAKE/RATTLEatomic pressuremolecular dynamics calculationmultiple time-step

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Area of Science:

  • Computational Chemistry
  • Molecular Dynamics Simulations
  • Statistical Mechanics

Background:

  • Efficient molecular dynamics (MD) simulations require reducing calculation time per MD loop.
  • The RESPA multiple time-step (MTS) algorithm offers computational savings by reducing the frequency of long-range interaction calculations.
  • Existing RESPA MTS methods present uncertainties in accurately calculating atomic pressure, especially with holonomic constraints.

Purpose of the Study:

  • To develop accurate equations for evaluating atomic pressure within the RESPA MTS integration procedure.
  • To ensure time-reversibility in pressure calculations, even for systems with holonomic constraints.
  • To generalize the pressure calculation method for arbitrary numbers of inner time steps and RESPA levels.

Main Methods:

  • Derivation of new equations for atomic pressure calculation based on equivalence to the Velocity-Verlet single time-step (STS) integration.
  • Validation of the proposed equations against reference values obtained using STS integration.
  • Generalization of the equations for flexible MTS integration and force component levels.

Main Results:

  • The proposed equations accurately calculate atomic pressure in RESPA MTS simulations, showing excellent agreement with STS reference values.
  • Conventional ad hoc equations for pressure calculation in RESPA MTS were found to deviate from reference values.
  • The developed method ensures time-reversibility for systems with holonomic constraints.

Conclusions:

  • The new equations provide a reliable method for atomic pressure calculation in RESPA MTS simulations.
  • This advancement improves the accuracy and applicability of MTS integration for molecular dynamics.
  • The method is readily extendable to isothermal NVT and NPT ensembles in MTS simulations.