An Analytic Probability Density for Particle Size in Human Mastication

1996 ◽  
Vol 181 (2) ◽  
pp. 169-178 ◽  
Author(s):  
F.A. Baragar (retired) ◽  
A. van der Bilt ◽  
H.W. van der Glas
Keyword(s):  
Particle Size ◽  
Probability Density ◽  
Human Mastication

Comparison of functions for evaluating the effect of Fe and Al oxides on the particle size distribution of kaolin and quartz

Clay Minerals ◽  
1997 ◽  
Vol 32 (1) ◽  
pp. 3-11 ◽  
Author(s):  
M. Arias ◽  
E. Lopez ◽  
M. T. Barral
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Probability Density ◽  
Size Distribution ◽  
Probability Density Functions ◽  
Density Functions ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Soil Particles ◽  
Quartz Substrates

AbstractAlthough it is generally agreed that Fe and Al can act to bind soil particles, their relative efficiencies as aggregants are still disputed. In this work, the aggregating efficiencies of both aged and non-aged Fe and Al oxides precipitated on kaolin or quartz substrates were characterized by comparing their effects on particle size distributions (PSD). To facilitate comparison of PSD data, these were parameterized by fitting them with five different probability density functions (the normal, lognormal, Jaky, fractal and Rosin-Rammler functions). The best fits were given by the Rosin-Rammler function (R2 = 0.997), whose α parameter was used to compare the aggregating efficiency of Fe and Al oxides: in order of decreasing efficiency, non-aged Al > non-aged Fe ≈ aged Fe > aged Al-precipitates.

scholarly journals Wintertime hygroscopicity and volatility of ambient urban aerosol particles

2018 ◽  
Vol 18 (7) ◽  
pp. 4533-4548 ◽  
Author(s):  
Joonas Enroth ◽  
Jyri Mikkilä ◽  
Zoltán Németh ◽  
Markku Kulmala ◽  
Imre Salma
Keyword(s):  
Particle Size ◽  
Probability Density Function ◽  
Probability Density ◽  
Atmospheric Aerosol ◽  
Particle Number ◽  
Aerosol Particles ◽  
Particle Diameter ◽  
Bimodal Distribution ◽  
Combustion Particles ◽  
Hygroscopic Particles

Abstract. Hygroscopic and volatile properties of atmospheric aerosol particles with dry diameters of (20), 50, 75, 110 and 145 nm were determined in situ by using a volatility–hygroscopicity tandem differential mobility analyser (VH-TDMA) system with a relative humidity of 90 % and denuding temperature of 270 ∘C in central Budapest during 2 months in winter 2014–2015. The probability density function of the hygroscopic growth factor (HGF) showed a distinct bimodal distribution. One of the modes was characterised by an overall mean HGF of approximately 1.07 (this corresponds to a hygroscopicity parameter κ of 0.033) independently of the particle size and was assigned to nearly hydrophobic (NH) particles. Its mean particle number fraction was large, and it decreased monotonically from 69 to 41 % with particle diameter. The other mode showed a mean HGF increasing slightly from 1.31 to 1.38 (κ values from 0.186 to 0.196) with particle diameter, and it was attributed to less hygroscopic (LH) particles. The mode with more hygroscopic particles was not identified. The probability density function of the volatility GF (VGF) also exhibited a distinct bimodal distribution with an overall mean VGF of approximately 0.96 independently of the particle size, and with another mean VGF increasing from 0.49 to 0.55 with particle diameter. The two modes were associated with less volatile (LV) and volatile (V) particles. The mean particle number fraction for the LV mode decreased from 34 to 21 % with particle diameter. The bimodal distributions indicated that the urban atmospheric aerosol contained an external mixture of particles with a diverse chemical composition. Particles corresponding to the NH and LV modes were assigned mainly to freshly emitted combustion particles, more specifically to vehicle emissions consisting of large mass fractions of soot likely coated with or containing some water-insoluble organic compounds such as non-hygroscopic hydrocarbon-like organics. The hygroscopic particles were ordinarily volatile. They could be composed of moderately transformed aged combustion particles consisting of partly oxygenated organics, inorganic salts and soot. The larger particles contained internally mixed non-volatile chemical species as a refractory residual in 20–25 % of the aerosol material (by volume).

scholarly journals Acceleration statistics of finite-sized particles in turbulent flow: the role of Faxén forces

2009 ◽  
Vol 630 ◽  
pp. 179-189 ◽  
Author(s):  
E. CALZAVARINI ◽  
R. VOLK ◽  
M. BOURGOIN ◽  
E. LÉVÊQUE ◽  
J.-F. PINTON ◽  
...  
Keyword(s):  
Experimental Data ◽  
Particle Size ◽  
Probability Density Function ◽  
Numerical Simulations ◽  
Probability Density ◽  
Detailed Comparison ◽  
Point Particle ◽  
Dynamics Of Particles ◽  
Dissipative Scale

The dynamics of particles in turbulence when the particle size is larger than the dissipative scale of the carrier flow are studied. Recent experiments have highlighted signatures of particles' finiteness on their statistical properties, namely a decrease of their acceleration variance, an increase of correlation times (at increasing the particles size) and an independence of the probability density function of the acceleration once normalized to their variance. These effects are not captured by point-particle models. By means of a detailed comparison between numerical simulations and experimental data, we show that a more accurate description is obtained once Faxén corrections are included.

COMPARISON OF POINT-, LINE- AND BOUNDARY-SAMPLED INTERCEPTS INSIDE A CIRCLE OR SPHERE

2003 ◽  
Vol 17 (02) ◽  
pp. 319-330
Author(s):  
ZHENG-WEI YANG ◽  
GUI-WU WEI
Keyword(s):  
Particle Size ◽  
Distribution Function ◽  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Coefficient Of Variation ◽  
Probability Distribution Function ◽  
Geometric Probability ◽  
Particle Sizes ◽  
Point Line

Point-, line- or boundary-sampled intercepts may be measured inside a particle as a measure of particle size. Each intercept is primarily characterized by three geometric properties: length, location and orientation. Circle and sphere models are used in the present study to analyze these properties. The probability distribution function, probability density function, expectation and coefficient of variation for each of the properties were presented based on geometric probability and mathematical statistics. Such presentation would be helpful for potential users of stereology to better understand the concept of intercepts and implement stereological intercept measurement for estimation of particle sizes in practice.

METHODOLOGY OF CALCULATION THE TERMINAL SETTLING VELOCITY DISTRIBUTION OF SPHERICAL PARTICLES FOR HIGH VALUES OF THE REYNOLD’S NUMBER

2014 ◽  
Vol 59 (1) ◽  
pp. 269-282 ◽  
Author(s):  
Agnieszka Surowiak ◽  
Marian Brożek
Keyword(s):  
Particle Size ◽  
Probability Density Function ◽  
Velocity Distribution ◽  
Density Distribution ◽  
Probability Density ◽  
Settling Velocity ◽  
Particle Density ◽  
Random Variable ◽  
Spherical Particles ◽  
Settling Velocity Distribution

Abstract The particle settling velocity is the feature of separation in such processes as flowing classification and jigging. It characterizes material forwarded to the separation process and belongs to the so-called complex features because it is the function of particle density and size. i.e. the function of two simple features. The affiliation to a given subset is determined by the values of two properties and the distribution of such feature in a sample is the function of distributions of particle density and size. The knowledge about distribution of particle settling velocity in jigging process is as much important factor as knowledge about particle size distribution in screening or particle density distribution in dense media beneficiation. The paper will present a method of determining the distribution of settling velocity in the sample of spherical particles for the turbulent particle motion in which the settling velocity is expressed by the Newton formula. Because it depends on density and size of particle which are random variable of certain distributions, the settling velocity is a random variable. Applying theorems of probability, concerning distributions function of random variables, the authors present general formula of probability density function of settling velocity for the turbulent motion and particularly calculate probability density function for Weibull’s forms of frequency functions of particle size and density. Distribution of settling velocity will calculate numerically and perform in graphical form. The paper presents the simulation of calculation of settling velocity distribution on the basis of real distributions of density and projective diameter of particles assuming that particles are spherical.

The Effect of Particle Size Reduction on the Jaw Gape in Human Mastication

1991 ◽  
Vol 70 (5) ◽  
pp. 931-937 ◽  
Author(s):  
A. Van Der Bilt ◽  
H.W. Van Der Glas ◽  
L.W. Olthoff ◽  
F. Bosman
Keyword(s):  
Particle Size ◽  
Size Reduction ◽  
Particle Size Reduction ◽  
Human Mastication ◽  
Effect Of Particle Size

Exponentially decreasing distributions for the logarithm of particle size

1977 ◽  
Vol 353 (1674) ◽  
pp. 401-419 ◽  
Keyword(s):  
Particle Size ◽  
Probability Density Function ◽  
Probability Density ◽  
Aeolian Sand ◽  
Normal Distributions ◽  
Continuous Type ◽  
The Family ◽  
Mixture Of Normal Distributions ◽  
Mass Size ◽  
Distribution Family

The family of continuous type distributions such that the logarithm of the probability (density) function is a hyperbola (or, in several dimensions, a hyperboloid) is introduced and investigated. It is, among other things, shown that a distribution of this kind is a mixture of normal distributions. As to applications, the paper focuses on the mass-size distribution of aeolian sand deposits, with particular reference to the findings of R. A. Bagnold. The distribution family seems, however, to be of some potential usefulness in other concrete contexts too.

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