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Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As a column of the medium is displaced, its successive columns are also displaced. As the successive displacements differ relatively, a pressure difference with the surrounding pressure is created. The gauge pressure varies across the medium.
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When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the...
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Methane Hydrate Crystallization on Sessile Water Droplets
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Fluctuating shells under pressure.

Jayson Paulose1, Gerard A Vliegenthart, Gerhard Gompper

  • 1Harvard School of Engineering and Applied Sciences, Cambridge, MA 02138, USA. jpaulose@fas.harvard.edu

Proceedings of the National Academy of Sciences of the United States of America
|November 15, 2012
PubMed
Summary
This summary is machine-generated.

Thermal fluctuations significantly alter the elasticity of thin spherical shells, especially under pressure. These effects are crucial for understanding microcapsule behavior and collapse.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Thermal fluctuations impact large-scale elastic behavior in cross-linked membranes.
  • Thin elastic shells, unlike flat membranes, possess non-zero curvature, coupling in-plane and out-of-plane deformations.
  • The influence of thermal fluctuations on shell elasticity remains largely unexplored.

Purpose of the Study:

  • Investigate the statistical mechanics of shape fluctuations in pressurized spherical shells.
  • Analyze the effects of curvature and inward pressure on shell elasticity.
  • Predict novel behaviors of fluctuating shells under mechanical stress.

Main Methods:

  • Utilized perturbation theory to analyze shell behavior.
  • Employed Monte Carlo computer simulations for detailed analysis.
  • Explicitly incorporated curvature and inward pressure effects.

Main Results:

  • Predicted scale-dependent elastic moduli due to thermal fluctuations.
  • Demonstrated that thermal contributions increase with the shell radius-to-thickness ratio.
  • Observed enhanced thermal effects and divergence near the buckling transition under inward pressure.

Conclusions:

  • Thermal fluctuations play a critical role in the elasticity of thin shells, particularly under pressure.
  • Results are pertinent to the elasticity and osmotic collapse of microcapsules.
  • Curvature and inward pressure significantly modify thermal fluctuation effects in shells.