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This type of mixture, being a finite sum, is called a finite mixture, and in applications, an unqualified reference to a "mixture density" usually means a finite mixture. The case of a countably infinite set of components is covered formally by allowing n = ∞ {\displaystyle n=\infty \!} .
For example, a mixture of two normal distributions with different means may result in a density with two modes, which is not modeled by standard parametric distributions. Another example is given by the possibility of mixture distributions to model fatter tails than the basic Gaussian ones, so as to be a candidate for modeling more extreme events.
J i is the diffusion flux vector of the i th species (for example in mol/m 2-s), M i is the molar mass of the i th species, ρ is the mixture density (for example in kg/m 3). The is outside the gradient operator. This is because: =, where ρ si is the partial density of the i th species.
Increasing the pressure always increases the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalization. For example, the density of water increases between its melting point at 0 °C and 4 °C; similar behavior is observed in silicon at low temperatures.
In chemistry, the mass concentration ρ i (or γ i) is defined as the mass of a constituent m i divided by the volume of the mixture V. [1]= For a pure chemical the mass concentration equals its density (mass divided by volume); thus the mass concentration of a component in a mixture can be called the density of a component in a mixture.
The hyperexponential distribution is an example of a mixture density. An example of a hyperexponential random variable can be seen in the context of telephony, where, if someone has a modem and a phone, their phone line usage could be modeled as a hyperexponential distribution where there is probability p of them talking on the phone with rate ...
This page contains tables of azeotrope data for various binary and ternary mixtures of solvents. The data include the composition of a mixture by weight (in binary azeotropes, when only one fraction is given, it is the fraction of the second component), the boiling point (b.p.) of a component, the boiling point of a mixture, and the specific gravity of the mixture.
In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material. [ 1 ] [ 2 ] [ 3 ] It provides a theoretical upper- and lower-bound on properties such as the elastic modulus , ultimate tensile strength , thermal conductivity , and electrical conductivity . [ 3 ]