In linear anisotropic materials, σ, ρ and D are tensors.

A petrographic microscope, which is a optical microscope fitted with cross-Polarizer | polarizing lenses, a conoscopy | conoscopic lens, and compensators ( plates of anisotropic materials ; gypsum plates and quartz wedges are common ), for crystallographic analysis.

Common anisotropic materials include wood, because its material properties are different parallel and perpendicular to the grain, and layered minerals such as slate.

An extended, structurally rigid, highly anisotropic shape seems to be the main criterion for liquid crystalline behavior, and as a result many liquid crystalline materials are based on benzene rings.

Highly anisotropic materials like regular wood ( as opposed to wood composites ) can easily be wedged apart.

For anisotropic materials the E and D fields are not parallel, and so E and D are related by the permittivity tensor ( a 2nd order tensor field ), in component form:

Polarized light does interact with anisotropic materials, which is the basis for birefringence.

This is to say, the polarizability of anisotropic materials is not equivalent in all directions.

In each of these materials, the anisotropic nature of the pairing is implicated by the power-law dependence of the nuclear magnetic resonance ( NMR ) relaxation rate and specific heat capacity on temperature.

In anisotropic materials, the thermal conductivity typically varies with orientation ; in this case is represented by a second-order tensor.

Image: Working with Nodes Blender. PNG | Using the node editor to create anisotropic metallic materials

The physical properties of composite materials are generally not isotropic ( independent of direction of applied force ) in nature, but rather are typically anisotropic ( different depending on the direction of the applied force or load ).

Techniques that take advantage of the anisotropic properties of the materials include mortise and tenon joints ( in natural composites such as wood ) and Pi Joints in synthetic composites.

These optically anisotropic materials are said to be birefringent.

The more general case of biaxially anisotropic materials, also known as trirefringent materials, is described by crystal optics which is substantially more complex.

While birefringence is often found naturally ( like anisotropic crystals ), there are several ways to create it in optically isotropic materials:

In linear anisotropic materials, σ, ρ and D are tensors.

Ferrimagnetic materials have high resistivity and have anisotropic properties.

These materials then become anisotropic, and Young's modulus will change depending on the direction of the force vector.

Its applicability includes, but is not limited to, linear and non-linear analysis, solid and fluid interactions, materials that are isotropic, orthotropic, or anisotropic, and external effects that are static, dynamic, and environmental factors.

Different materials reflect radar waves with different intensities, but anisotropic materials such as grass often reflect different polarizations with different intensities.

* Granular materials are often inhomogeneous and anisotropic

If the waves are propagating through an anisotropic ( i. e., not rotationally symmetric ) medium, for example a crystal, then the phase velocity vector and group velocity vector may point in different directions.

In anisotropic media such as some crystals, birefringence may split the refracted ray into two rays, the ordinary or o-ray which follows Snell's law, and the other extraordinary or e-ray which may not be co-planar with the incident ray.

In an anisotropic material, the relative permittivity may be a tensor, causing birefringence.

However, when a wave travels through an anisotropic medium, such as light waves through an asymmetric crystal or sound waves through a sedimentary rock, the wave vector may not point exactly in the direction of wave propagation.

A heterogeneous system ( comprising different substances or different phases ) may be anisotropic if the loss tangents of the components are considered.

Rod-shaped molecules have an elongated, anisotropic geometry which allows for preferential alignment along one spatial direction.

By changing the balance it is possible to influence the anisotropy of the etching, since the chemical part is isotropic and the physical part highly anisotropic the combination can form sidewalls that have shapes from rounded to vertical.

In the anisotropic HTS, perhaps NMR measurements have found that the relaxation rate for copper depends on the direction of the applied static magnetic field, with the rate being higher when the static field is parallel to one of the axes in the copper oxide plane.

* liquid crystal phase transitions have been examined in confined geometries and / or during flow using the Gay-Berne potential which describes anisotropic species ;

There are two physical types of ellipticals ; the " boxy " giant ellipticals, whose shapes result from random motion which is greater in some directions than in others ( anisotropic random motion ), and the " disky " normal and low luminosity ellipticals, which have nearly isotropic random velocities but are flattened due to rotation.

The realization that soft matter contains innumerable examples of symmetry breaking, generalized elasticity, and many fluctuating degrees of freedom has re-invigorated classical fields of physics such as fluids ( now generalized to non-Newtonian and structured media ) and elasticity ( membranes, filaments, and anisotropic networks are all important and have common aspects ).

Unlike more general anisotropic filtering, the RIP mapping described for illustration is limited by only supporting anisotropic probes that are axis-aligned in texture space, so diagonal anisotropy still presents a problem, even though real-use cases of anisotropic texture commonly have such screenspace mappings.

For non-isotropic ( anisotropic ) coatings, the optimal coating depends on the shape of the target and the radar direction, but duality, the symmetry of Maxwell's equations between the electric and magnetic fields, tells one that optimal coatings have η < sub > 0 </ sub > × η < sub > 1 </ sub > = 377 < sup > 2 </ sup > Ω < sup > 2 </ sup >, where η < sub > 0 </ sub > and η < sub > 1 </ sub > are perpendicular components of the anisotropic surface impedance, aligned with edges and / or the radar direction.

Materials with anisotropic structures, such as crystals ( with less than cubic symmetry ) and many composites, will generally have different linear expansion coefficients in different directions.

If you have a unit vector D which specifies the global direction of the anisotropic distribution, you can compute the vector T at a given point by the following:

An anisotropic liquid is a liquid which has fluidity and where the molecules have an average structural order relative to each other along their molecular axis, imparting directional qualities that ordinary fluids do not have.

In media with no or little mobility ( e. g. crystals, powders, large membrane vesicles, molecular aggregates ), anisotropic interactions have a substantial influence on the behaviour of a system of nuclear spins.

Many other substances have anisotropic physical properties.

Because the permittivity is anisotropic, polarized light of different orientations will travel at different speeds.

Semi-confined aquifers with one or more aquitards work as an anisotropic system, even when the separate layers are isotropic, because the compound Kh and Kv values are different ( see hydraulic transmissivity and hydraulic resistance ).

Many wood joinery techniques either depend upon or compensate for the fact that wood is anisotropic: its material properties are different along different dimensions.

The device used anisotropic thin magnetic films that required different magnetic pulse combinations for orthogonal propagation directions.

If the resulting electric current is in a different direction from the applied electric field, the material is said to be an anisotropic electrical conductor.

Geometrically, a diagonalizable matrix is an inhomogeneous dilation ( or anisotropic scaling ) – it scales the space, as does a homogeneous dilation, but by a different factor in each direction, determined by the scale factors on each axis ( diagonal entries ).

Vanadinite is anisotropic, meaning that some of its properties differ when measured along different axes.

Angular dependent calculations or measurements on systems consisting of a single crystal of a compound, for example, are anisotropic, meaning the density of states will be different in one crystallographic direction than in another.

Non-uniform scaling ( anisotropic scaling ) is obtained when at least one of the scaling factors is different from the others ; a special case is directional scaling or stretching ( in one direction ).