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In complex geometry, a line through the origin in the direction of an isotropic vector is an isotropic line. Isotropic coordinates Isotropic coordinates are coordinates on an isotropic chart for Lorentzian manifolds. Isotropy group An isotropy group is the group of isomorphisms from any object to itself in a groupoid.
Isotropic solids tend to be of interest when developing models for physical behavior of materials, as they tend to allow for dramatic simplifications of theory; for example, conductivity in metals of the cubic crystal system can be described with single scalar value, rather than a tensor. [1]
Therefore, for cubic materials, we can think of anisotropy, , as the ratio between the empirically determined shear modulus for the cubic material and its (isotropic) equivalent: = / [(+)] = (+). The latter expression is known as the Zener ratio , a r {\displaystyle a_{r}} , where C i j {\displaystyle C_{ij}} refers to elastic constants in ...
Since neutral particles attack the wafer from all angles, this process is isotropic. Plasma etching can be isotropic, i.e., exhibiting a lateral undercut rate on a patterned surface approximately the same as its downward etch rate, or can be anisotropic, i.e., exhibiting a smaller lateral undercut rate than its downward etch rate.
Isotropic formulations are thermodynamically stable microemulsions possessing lyotropic liquid crystal properties. [1] They inhabit a state of matter and physical behaviour somewhere between conventional liquids and that of solid crystals . [ 2 ]
Optical activity is reciprocal, i.e. it is the same for opposite directions of wave propagation through an optically active medium, for example, clockwise polarization rotation from the point of view of an observer. In case of optically active isotropic media, the rotation is the same for any direction of wave propagation.
The term microemulsion was first used by T. P. Hoar and J. H. Shulman, professors of chemistry at Cambridge University, in 1943. Alternative names for these systems are often used, such as transparent emulsion, swollen micelle, micellar solution, and solubilized oil. More confusingly still, the term microemulsion can refer to the single ...
At high temperatures, liquid crystals become an isotropic liquid and at low temperatures, they tend to glassify. In a thermotropic crystal, those phase transitions occur only at temperature extremes; the phase is insensitive to concentration.