تماثل الخواص

في الفيزياء والهندسة، تماثل الخواص (Isotropy ؛ من يونانية قديمة ἴσος (ísos)، وتعني "equal", و τρόπος (trópos)، وتعني "turn, way") تُطلق على الجسم أو الوسط الذي تكون خواصه واحدة في جميع الاتجاهات. و هو وصف لكل وسط متساوي الخصائص في جميع الاتجاهات ، وفي بصريات البلورات يقصد به تساوي الخصائص الضوئية أو عدم تغيرها في الاتجاهات البلورية المختلفة، ومثال ذلك انتشار الضوء في المادة بسرعة واحدة في كل الاتجاهات كما هي الحال في بلورات الفصيلة المكعبية .

الرياضيات

في الرياضيات، تماثل الخواص له عدة معاني:

Isotropic manifolds: A manifold is isotropic if the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity.
صيغة تربيعية متماثلة الخواص: A quadratic form q is said to be isotropic if there is a non-zero vector v such that q(v) = 0; such a v is an isotropic vector or null vector. 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.^{[محل شك]}^[1] An isotropy representation is a representation of an isotropy group.
Isotropic position: A probability distribution over a vector space is in isotropic position if its covariance matrix is the الوحدة.
Isotropic vector field: The vector field generated by a point source is said to be isotropic if, for any spherical neighborhood centered at the point source, the magnitude of the vector determined by any point on the sphere is invariant under a change in direction. For an example, starlight appears to be isotropic.

الفيزياء

Quantum mechanics or particle physics: When a spinless particle (or even an unpolarized particle with spin) decays, the resulting decay distribution must be isotropic in the rest frame of the decaying particle - regardless of the detailed physics of the decay. This follows from rotational invariance of the Hamiltonian, which in turn is guaranteed for a spherically symmetric potential.

Gases: The kinetic theory of gases also exemplifies isotropy. It is assumed that the molecules move in random directions and as a consequence, there is an equal probability of a molecule moving in any direction. Thus when there are many molecules in the gas, with high probability there will be very similar numbers moving in one direction as any other, demonstrating approximate isotropy.

Fluid dynamics: Fluid flow is isotropic if there is no directional preference (e.g. in fully developed 3D turbulence). An example of anisotropy is in flows with a background density as gravity works in only one direction. The apparent surface separating two differing isotropic fluids would be referred to as an isotrope.

Thermal expansion: A solid is said to be isotropic if the expansion of solid is equal in all directions when thermal energy is provided to the solid.

الكهرومغناطيسية: An isotropic medium is one such that the permittivity, ε, and permeability, μ, of the medium are uniform in all directions of the medium, the simplest instance being free space.

الخلية الحية: إذا كانت خواص جدار الخلية واحدة تقريباً في كافة الاتجاهات المدروسة يمكن الحديث حينها عن خلية متوحدة الخواص.
علم البصريات: يعني توحد الخواص البصرية لمادة ما أن هذه الخواص واحدة في مختلف الاتجاهات. يمكن أخذ متوسط الانعكاس أو الانتشار المحلي للوسط المدروس في الحسابات.

علم المواد

This sand grain made of volcanic glass is isotropic, and thus, goes extinct when looking through a doubly polarized petrographic microscope

المواد الهندسية: هذا المصطلح هام جداً في توصيف الخواص الميكانيكية للمواد الهندسية. إن توحد الخواص هنا يعني أن أية خاصية ميكانيكية ستكون واحدة في مختلف الاتجاهات البلورية ولها نفس القيمة. يمكن القول حينئذٍ إن المادة تسلك نفس السلوك تحت تأثير الحمولات المطبقة في أي اتجاه كان.

التصنيع الدقيق

In industrial processes, such as etching steps, "isotropic" means that the process proceeds at the same rate, regardless of direction. Simple chemical reaction and removal of a substrate by an acid, a solvent or a reactive gas is often very close to isotropic. Conversely, "anisotropic" means that the attack rate of the substrate is higher in a certain direction. Anisotropic etch processes, where vertical etch-rate is high but lateral etch-rate is very small, are essential processes in microfabrication of integrated circuits and MEMS devices.

هوائي الراديو

An isotropic antenna is an idealized "radiating element" used as a reference; an antenna that broadcasts power equally (calculated by the Poynting vector) in all directions. The gain of an arbitrary antenna is usually reported in decibels relative to an isotropic antenna, and is expressed as dBi or dB(i).

In cells (a.k.a. muscle fibers), the term "isotropic" refers to the light bands (I bands) that contribute to the striated pattern of the cells.

علم الصيدلة

While it is well established that the skin provides an ideal site for the administration of local and systemic drugs, it presents a formidable barrier to the permeation of most substances.^[2] Recently, isotropic formulations have been used extensively in dermatology for drug delivery.^[3]

علم الحاسب

التصوير: A volume such as a computed tomography is said to have isotropic voxel spacing when the space between any two adjacent voxels is the same along each axis x, y, z. E.g., voxel spacing is isotropic if the center of voxel (i, j, k) is 1.38 mm from that of (i+1, j, k), 1.38 mm from that of (i, j+1, k) and 1.38 mm from that of (i, j, k+1) for all indices i, j, k.^[4]

العلوم الأخرى

Economics and geography: An isotropic region is a region that has the same properties everywhere. Such a region is a construction needed in many types of models.

انظر أيضاً

المراجع

^ A groupoid $𝒢$ is a category where all morphisms are isomorphisms, i.e., invertible. If $G \in 𝒢$ is any object, then $𝒢 (G, G)$ denotes its isotropy group: the group of isomorphisms from $G$ to $G$ .
^ Landman L. "The Epidermal Permeability Barrier". Anatomy and Embryology (Berl) 1988; 178:1-13 [1]
^ Gregoriadis G. "Liposomes in Drug Delivery". Harwood Academic Publishers, 1993. [2]
^ Zwanenburg, Alex; Leger, Stefan; Vallières, Martin; Löck, Steffen (2016-12-21). "Image biomarker standardisation initiative". Radiology. 295 (2): 328–338. arXiv:1612.07003. doi:10.1148/radiol.2020191145. PMC 7193906. PMID 32154773.

[1] A groupoid $𝒢$ is a category where all morphisms are isomorphisms, i.e., invertible. If $G \in 𝒢$ is any object, then $𝒢 (G, G)$ denotes its isotropy group: the group of isomorphisms from $G$ to $G$ .

[2] Landman L. "The Epidermal Permeability Barrier". Anatomy and Embryology (Berl) 1988; 178:1-13 [1]

[3] Gregoriadis G. "Liposomes in Drug Delivery". Harwood Academic Publishers, 1993. [2]

[4] Zwanenburg, Alex; Leger, Stefan; Vallières, Martin; Löck, Steffen (2016-12-21). "Image biomarker standardisation initiative". Radiology. 295 (2): 328–338. arXiv:1612.07003. doi:10.1148/radiol.2020191145. PMC 7193906. PMID 32154773.

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