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Related Concept Videos

Stress: General Loading Conditions01:15

Stress: General Loading Conditions

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To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes....
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General State of Stress01:21

General State of Stress

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The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...
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Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

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Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
If...
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First Law: Particles in Two-dimensional Equilibrium01:18

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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
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Components of Stress01:23

Components of Stress

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Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σx, σy, σz act perpendicularly to the x, y, and z axes. Shearing stress components τxy and τxz are exerted on faces perpendicular to these axes.
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Long-range order in two-dimensional systems with fluctuating active stresses.

Yann-Edwin Keta1, Silke Henkes1

  • 1Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, 2333 CA Leiden, The Netherlands. keta@lorentz.leidenuniv.nl.

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This summary is machine-generated.

Pair-wise active forces in 2D tissues stabilize long-range order and create hyperuniformity, defying traditional physics theorems. This hidden order is observed in both analytical models and numerical simulations of cell tissues.

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Area of Science:

  • Soft Matter Physics
  • Biophysics
  • Materials Science

Background:

  • Two-dimensional tissues exhibit active stresses from cytoskeletal contractions.
  • Standard active matter models often assume particle-wise independent fluctuating forces.
  • Dissipation in these systems is typically provided by the surrounding three-dimensional environment.

Purpose of the Study:

  • To analytically and numerically investigate the effects of pair-wise active stresses in two-dimensional elastic systems.
  • To explore the emergence of long-range order and hyperuniformity.
  • To study phase transitions in cell tissue models with active stresses.

Main Methods:

  • Analytical derivation of conserved center-of-mass dynamics from pair-wise stochastic forces.
  • Development and simulation of a vertex model with stochastic junctional contractions.
  • Development and simulation of an active disk model based on active Brownian particles.

Main Results:

  • Pair-wise active forces damp large-wavelength fluctuations, stabilizing long-range translational order in 2D.
  • Emergence of hyperuniformity with a specific structure factor (S(q) ~ q^2) in the q → 0 limit.
  • Numerical models confirm long-range order and hyperuniformity, even in disordered phases, indicating hidden order.
  • A first-order phase transition between ordered and disordered phases was observed in the active disk model.

Conclusions:

  • Pair-wise active stresses can lead to long-range order and hyperuniformity in 2D systems, challenging the Mermin-Wagner theorem.
  • The discovered mechanism of hidden order is general and applicable to both biological and artificial systems.
  • Results are expected to be experimentally testable in living organisms and synthetic active matter.