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Related Concept Videos

Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Viscosity01:27

Viscosity

Viscosity is a property of fluids that measures their resistance to flow. It is influenced by factors such as the surface area of contact, the gradient of flow speed, and the fluid's viscosity constant, called the coefficient of viscosity. The coefficient of viscosity, also known as dynamic viscosity, is denoted by the symbol η. It determines the proportionality between the viscous force and the gradient of flow speed.Newton's law of viscosity states that the viscous force on a faster-moving...
Viscosity01:17

Viscosity

When water is poured into a glass, it falls freely and quickly, whereas if honey or maple syrup is poured over a pancake, it flows slowly and sticks to the surface of the container. This difference in the flow of different kinds of liquids arises due to the fluid friction between the liquid layers and the liquid and the surrounding material. This property of fluids is called fluid viscosity. In this example, water has a lower viscosity than honey and maple syrup.
The SI unit of viscosity is...
Viscosity of Fluid01:19

Viscosity of Fluid

Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
Newtonian Fluid: Problem Solving01:18

Newtonian Fluid: Problem Solving

Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...

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Related Experiment Video

Updated: Jun 27, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

On the dynamic viscous permeability tensor symmetry.

Camille Perrot, Fabien Chevillotte, Raymond Panneton

    The Journal of the Acoustical Society of America
    |December 10, 2008
    PubMed
    Summary

    The dynamic permeability tensor is proven to be symmetric for periodic structures, even with non-orthogonal symmetry axes. This finding aids in validating numerical simulations for materials with complex symmetries.

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    Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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    Published on: February 22, 2018

    Area of Science:

    • Physics
    • Materials Science
    • Electromagnetism

    Background:

    • The symmetry property of the permeability tensor is well-established for static regimes.
    • Extending this understanding to dynamic regimes, especially for complex periodic structures, remains an area of interest.

    Purpose of the Study:

    • To elucidate the underlying reasons for the dynamic permeability tensor's symmetry in spatially periodic structures.
    • To address cases where symmetry axes do not align with orthogonal pairs perpendicular to high-fold symmetry axes (three-, four-, and sixfold).

    Main Methods:

    • Generalization of Torquato's proof for static symmetry properties.
    • Development of analytical framework for dynamic permeability tensor.
    • Numerical simulations for a hexagonal lattice of solid cylinders.

    Main Results:

    • Demonstration that the dynamic permeability tensor remains symmetric under specific conditions of structural symmetry.
    • Confirmation of this nonintuitive property through detailed numerical examples across asymptotic and frequency-dependent regimes.
    • Validation of the theoretical findings with practical computational data.

    Conclusions:

    • The dynamic permeability tensor exhibits symmetry for periodic structures with specific non-orthogonal symmetry axes.
    • This research provides a theoretical basis and numerical evidence for this property.
    • Findings are valuable for validating numerical implementations and assessing convergence in computational electromagnetism and materials science.