isotropy

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isotropy

physics

Also known as: isotropic material

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June 29, 2026

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In physics, isotropy refers to the quality of exhibiting properties with the same values when measured along axes in different directions. This is in contrast to anisotropy, where properties differ depending on the direction of measurement.1

Liquids and gases, due to the random distribution of their particles, are generally isotropic. In contrast, many single crystals are anisotropic because their atoms, ions, or molecules are arranged in regular lattices.1

A key example of isotropy is observed in the cosmic microwave background (CMB) radiation, which fills the universe. While there are minute fluctuations, the CMB is remarkably uniform in all directions, supporting the idea that the universe is largely homogeneous and isotropic on large scales.2

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cosmic microwave background
Isotropy in the cosmic background
Apart from the small fluctuations discussed above (one part in 100,000), the observed cosmic microwave background radiation exhibits a high degree of isotropy, a zeroth order fact that presents both satisfaction and difficulty for a comprehensive theory. On the one…
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Apart from the small fluctuations discussed above (one part in 100,000), the observed cosmic microwave background radiation exhibits a high degree of isotropy, a zeroth order fact that presents both satisfaction and difficulty for a comprehensive theory. On the one…
Read More

fluid mechanics
Basic properties of fluids
…(including air and water) are isotropic. In fluid mechanics, the state of an isotropic fluid may be completely described by defining its mean mass per unit volume, or density (ρ), its temperature (T), and its velocity (v) at every point in space, and just what the connection is between these…
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…(including air and water) are isotropic. In fluid mechanics, the state of an isotropic fluid may be completely described by defining its mean mass per unit volume, or density (ρ), its temperature (T), and its velocity (v) at every point in space, and just what the connection is between these…
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industrial glass
Properties of glass
…importance may be called the isotropicity of properties, meaning that such properties as tensile strength, electrical resistance, and thermal expansion are of equal magnitude in any direction through the material.
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…importance may be called the isotropicity of properties, meaning that such properties as tensile strength, electrical resistance, and thermal expansion are of equal magnitude in any direction through the material.
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mechanics
Lagrange’s and Hamilton’s equations
Furthermore, if the problem is isotropic (H does not depend on direction in space) and homogeneous (H does not change with uniform translation in space), then Hamilton’s equations immediately yield the laws of conservation of angular momentum and linear momentum, respectively.
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Furthermore, if the problem is isotropic (H does not depend on direction in space) and homogeneous (H does not change with uniform translation in space), then Hamilton’s equations immediately yield the laws of conservation of angular momentum and linear momentum, respectively.
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rock
Texture
…throughout) and the degree of isotropy. The latter is the extent to which the bulk structure and composition are the same in all directions in the rock.
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…throughout) and the degree of isotropy. The latter is the extent to which the bulk structure and composition are the same in all directions in the rock.
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mechanics of solids
Linear elastic isotropic solid
…which |∂u_i/∂X_j|<< 1 and for isotropic materials, whose mechanical response is independent of the direction of stressing. If a material point sustains a stress state σ₁₁ = σ, with all other σ_ij = 0, it is subjected to uniaxial tensile stress. This can be realized in a homogeneous bar loaded…
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…which |∂u_i/∂X_j|<< 1 and for isotropic materials, whose mechanical response is independent of the direction of stressing. If a material point sustains a stress state σ₁₁ = σ, with all other σ_ij = 0, it is subjected to uniaxial tensile stress. This can be realized in a homogeneous bar loaded…
Read More