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In chemistry, the dispersity is a measure of the heterogeneity of sizes of molecules or particles in a mixture. A collection of objects is called uniform if the objects have the same size, shape, or mass. A sample of objects that have an inconsistent size, shape and mass distribution is called non-uniform.
Homogeneity and heterogeneity; only ' b ' is homogeneous Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image.A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, income, disease, temperature, radioactivity, architectural design, etc.); one that is heterogeneous ...
On a theoretical level, refinements to the abstract definition of scale-free have been proposed. For example, Li et al. (2005) offered a potentially more precise "scale-free metric". Briefly, let G be a graph with edge set E , and denote the degree of a vertex v {\displaystyle v} (that is, the number of edges incident to v {\displaystyle v ...
The term hyperuniformity (also independently called super-homogeneity in the context of cosmology [22]) was coined and studied by Salvatore Torquato and Frank Stillinger in a 2003 paper, [1] in which they showed that, among other things, hyperuniformity provides a unified framework to classify and structurally characterize crystals, quasicrystals, and exotic disordered varieties.
Many of these systems evolve in a self-similar fashion in the sense that data obtained from the snapshot at any fixed time is similar to the respective data taken from the snapshot of any earlier or later time. That is, the system is similar to itself at different times. The litmus test of such self-similarity is provided by the dynamic scaling.
Diffusion is of fundamental importance in many disciplines of physics, chemistry, and biology. Some example applications of diffusion: Sintering to produce solid materials (powder metallurgy, production of ceramics) Chemical reactor design; Catalyst design in chemical industry; Steel can be diffused (e.g., with carbon or nitrogen) to modify its ...
In uniform scaling with a non-zero scale factor, all non-zero vectors retain their direction (as seen from the origin), or all have the direction reversed, depending on the sign of the scaling factor. In non-uniform scaling only the vectors that belong to an eigenspace will retain their direction. A vector that is the sum of two or more non ...
Use of the term "scale" is unrelated to the concept of weighing; rather it is related to cognate terms in mathematics (e.g., geometric scaling, the linear transformation that enlarges or shrinks objects, and scale parameters in probability theory), and in applied areas (e.g., in the scaling of images in architecture, engineering, cartography ...