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Cumulative mass distribution function

The ANN model had four neurones in the input layer one for each operating variable and one for the bias. The output was selected to be cumulative mass distribution thirteen neurones were used to represent it. A sigmoid functional... [Pg.274]

The values of 2.84%, Lso%( = Lm) and Li % may be obtained from a cumulative mass distribution curve, as described in section 2.14.4. The higher the CV the broader the spread, CV = 0 denoting a monosized distribution. The CV for a Gaussian distribution is 52%, but the product from an MSMPR crystallizer, which generally conforms more to a gamma function distribution (equation 2.78), has a CFof 50%. [Pg.412]

Three distinct methods are therefore available for calculating the mass distribution of particles in suspension for a series of sector-shaped tubes filled to a series of levels. First, the mass fraction of particles larger than a known diameter may be calculated from equation (8.77) and the distribution function determined from the slope of the cumulative mass deposited against S. Secondly, the distribution function may be calculated directly in terms of the first and second derivatives of the fraction sedimented with respect to the length of the column of suspension centrifuged by use of equation (8.77). Thirdly, from the sedimentation -time curve at a series of levels, the distribution functions may be calculated by the use of equation (8.77). [Pg.437]

Every possible outcome of a random variable is associated with a probability for that event occurring. Two functions map outcome to probability for continuous random variables the probability density function (pdf) and cumulative distribution function (cdf). In the discrete case, the pdf and cdf are referred to as the probability mass function and cumulative mass function, respectively. A function f(x) is a pdf for some continuous random variable X if and only if... [Pg.347]

Common distribution functions are Wj (r), the number of nuclei found in a spherical shell of width dr, with a volume Aiir dr he number of nuclei found in an element of volume dr at a distance r from the origin and n ir), a cumulative function measuring the number of nuclei within a sphere of radius r centered at the center of mass. The radius r takes values between 0 and the span R. [Pg.202]

The median diameter corresponds with the 50 % value of a cumulative number, volume or mass percent distribution as function of the diameter. Fifty percent of the volume (number or mass) of the aerosol is in larger, and 50 % is in smaller particles than the median diameter. For a volume distribution it is the volume median diameter, for a mass distribution the mass median diameter. When the mass percent is expressed as a function of the aerod3mamic diameter, reference can be made to the mass median aerodynamic diameter (MMAD). [Pg.103]

All currently marketed inhaler devices produce polydisperse aerosols of which the individual particles have different sizes. Therefore, they cannot be characterised by a single diameter. In fact, for most solid aerosols from dry powder inhalers the particles may have different shapes too, which is the reason to characterise them with aerodynamic diameters. To be able to express polydisperse aerosols with a single parameter, the median aerodynamic diameter (MAD) was introduced. When the aerodynamic size range which covers the population of particles in the aerosol is divided into different classes and the volume or mass fraction within each size class is expressed as function of the class mean diameter, a volume or mass distribution as function of the aerodynamic diameter is obtained. This volume or mass frequency distribution can be transferred into a cumulative percent distribution of which the 50 % value corresponds with the volume or mass median aerodynamic diameter (VMAD or MMAD). This is the diameter indicating that 50 % of the total aerosol volume or mass is in larger, and 50 % is in smaller particles. When particles of all sizes in the aerosol have the same density, which is mostly the case, then VMAD equals MMAD. [Pg.109]

We begin with examining Equation (4.6.19) and recognize that the cumulative volume fraction F x, t) of particles of mass at most x is a cumulative distribution function that can be attributed to a random process X (t), which may be interpreted as the mass of a single particle at time t. We imagine that this particle, whose initial size is a random variable with... [Pg.187]

Discrete and continuous variables and probability distributions From Clause 5.3.3 of Chapter I, we get the probability mass function and cumulative distribution functions. For a single dimension, discrete random variable X, the discrete probability function is defined by/(xi), such that/(xi) > 0, for all xie R (range space), and f xi) = F(x) where F(x) is known as cumulative... [Pg.957]

Figure 13.15 Cumulative distribution function W n), i.e. the mass fraction of linear chains shorter than n for polyethylene with 1.5% of chain defects. Figure 13.15 Cumulative distribution function W n), i.e. the mass fraction of linear chains shorter than n for polyethylene with 1.5% of chain defects.
Figure 9.6 example9 2.m file that evaluates and graphically presents both the point mass and cumulative mass function of the binomial distribution. [Pg.252]

Complementary to differential distribution functions, it might be useful to establish integral (cumulative) distribution functions (Figure 3.8)—in particular, when one is interested in the proportion of the population to which a property value applies or not. The most probable molar mass (molar mass at the peak in Figure 3.7) corresponds to the inflection point of the curve (Figure 3.8). [Pg.38]

Cumulative distribution function of a discrete random variable Probability mass function of a discrete random variable Derivative of Gx(z) with respect to z... [Pg.13]

A cumulative distribution function similar to Fig. 4.5 can be constructed for the distribution of mass. The vertical axis is changed to represent the fraction of total - mass attributable to particles less than the indicated size. Figures 4.6 and 4.7 show the distribution of mass and the cumulative distribution of mass for the particle size data given in Table 4.1 and shown in Figs. 4.1-4.5. [Pg.41]


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