Joint probabilities and mixing of isolated scalars emitted from parallel jets

2015 ◽  
Vol 769 ◽  
pp. 130-153 ◽  
Author(s):  
M. A. Soltys ◽  
J. P. Crimaldi
Keyword(s):  
Probability Distribution ◽  
Joint Probability ◽  
Scalar Fields ◽  
Distribution Functions ◽  
Joint Probability Distribution ◽  
Diffusive Flux ◽  
Ambient Fluid ◽  
Planar Laser ◽  
The Mean ◽  
Shared Structure

Mixing and reaction between two scalars initially separated by scalar-free ambient fluid is important in problems ranging from ecology to engineering. Using a two-channel planar laser-induced fluorescence (PLIF) system the instantaneous spatial structure of two independent scalars emitted from parallel jets into a slow coflow is quantified. Of particular interest is the scalar covariance used to define the correlation coefficient. Joint probability distribution functions (JPDFs) and instantaneous images of the scalar fields demonstrate that initially the flow mainly consists of incursions of fluid from one jet into the other, and vice versa, before scalars have time to assemble in attracting regions of the flow and coalesce due to diffusive flux. Decomposing the joint probability distribution exhibits the effect these events have on scaler overlap and scalar covariance. Along the centreline near where the mean profiles of the jets meet, the scalar covariance is negative; however, the covariance becomes positive as the scalars converge in shared structure and diffusive flux bridges a reduced barrier of ambient fluid. The mixing path between scalar filaments can be probabilistically observed through the conditional diffusion of the two scalars at various points in the flow.

Joint probability distribution functions when a model is available: Fourier syntheses

2013 ◽  
Author(s):  
Carmelo Giacovazzo
Keyword(s):  
Probability Distribution ◽  
Current Model ◽  
Joint Probability ◽  
Distribution Functions ◽  
Joint Probability Distribution ◽  
Conditional Distributions ◽  
Target Structure ◽  
Probability Distribution Functions ◽  
Structure Factors ◽  
Joint Probability Distributions

The title of this chapter may seem a little strange; it relates Fourier syntheses, an algebraic method for calculating electron densities, to the joint probability distribution functions of structure factors, which are devoted to the probabilistic estimate of s.i.s and s.s.s. We will see that the two topics are strictly related, and that optimization of the Fourier syntheses requires previous knowledge and the use of joint probability distributions. The distributions used in Chapters 4 to 6 are able to estimate s.i. or s.s. by exploiting the information contained in the experimental diffraction moduli of the target structure (the structure one wants to phase). An important tool for such distributions are the theories of neighbourhoods and of representations, which allow us to arrange, for each invariant or seminvariant Φ, the set of amplitudes in a sequence of shells, each contained within the subsequent shell, with the property that any s.i. or s.s. may be estimated via the magnitudes constituting any shell. The resulting conditional distributions were of the type, . . . P(Φ| {R}), (7.1) . . . where {R} represents the chosen phasing shell for the observed magnitudes. The more information contained within the set of observed moduli {R}, the better will be the Φ estimate. By definition, conditional distributions (7.1) cannot change during the phasing process because prior information (i.e. the observed moduli) does not change; equation (7.1) maintains the same identical algebraic form. However, during any phasing process, various model structures progressively become available, with different degrees of correlation with the target structure. Such models are a source of supplementary information (e.g. the current model phases) which, in principle, can be exploited during the phasing procedure. If this observation is accepted, the method of joint probability distribution, as described so far, should be suitably modified. In a symbolic way, we should look for deriving conditional distributions . . . P (Φ| {R}, {Rp}) , (7.2) . . . rather than (7.1), where {Rp} represents a suitable subset of the amplitudes of the model structure factors. Such an approach modifies the traditional phasing strategy described in the preceding chapters; indeed, the set {Rp} will change during the phasing process in conjunction with the model changes, which will continuously modify the probabilities (7.2).

The approach of the joint probability distribution functions: the SIR-MIR, SAD-MAD and SIRAS-MIRAS, cases

2002 ◽  
Vol 217 (12) ◽  
Author(s):  
C. Giacovazzo ◽  
M. Ladisa ◽  
D. Siliqi
Keyword(s):  
Probability Distribution ◽  
Joint Probability ◽  
Distribution Functions ◽  
Joint Probability Distribution ◽  
Probability Distribution Functions

AbstractThe method of the joint probability distribution functions has been recently applied to SIR-MIR, SAD-MAD and SIRAS-MIRAS cases. The capacity of the method to treat various forms of errors (i.e., errors in measurements, possible lack of isomorphism, errors in a substructure model when a model is

Reliability analysis of a telecommunication tower

1999 ◽  
Vol 26 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Kamal El-Fashny ◽  
Luc E Chouinard ◽  
Ghyslaine McClure
Keyword(s):  
Wind Speed ◽  
Probability Distribution ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Joint Probability ◽  
Distribution Functions ◽  
Sensitivity Analyses ◽  
Ice Thickness ◽  
Joint Probability Distribution ◽  
Type I

This study presents a structural reliability analysis of a microwave tower subject to wind and freezing-rain hazards. The tower (name code CEBJ, owned by Hydro-Québec) is a 66 m tall, three-legged, steel lattice structure located in the James Bay area. The reliability analysis is performed conditionally with respect to wind speed and ice thickness accretion, and the results are integrated over the domain of wind and ice values using their joint probability distribution. This approach makes it possible to perform sensitivity analyses with respect to various assumptions on the joint probability distribution function of the climatological variable, without having to repeat the detailed coupled reliability - structural analysis of the tower. The probability distribution functions assumed for the wind speed and the ice thickness accretion on the tower members are both extreme-value type I (Gumbel) distributions. Adopting a weakest link model, the failure of the tower is assumed to occur when any of the members fails either in tension, compression, or global buckling. Without loss of generality, the proposed procedure can be applied with more refined probability distribution functions.Key words: reliability, telecommunication towers, wind, ice.

Dose-dependent Transmissibility of Chromosome Aberrations at First Mitosis after Exposure to Gamma Rays. I. Modeling and Implications Related to Risk Assessment

2022 ◽  
Author(s):  
Bradford D. Loucas ◽  
Igor Shuryak ◽  
Stephen R. Kunkel ◽  
Michael N. Cornforth
Keyword(s):  
Probability Distribution ◽  
Gamma Rays ◽  
Dose Response ◽  
Human Lymphocytes ◽  
Radiation Risk ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Linear Quadratic ◽  
Response Curves ◽  
The Mean

The relationship between certain chromosomal aberration (CA) types and cell lethality is well established. On that basis we used multi-fluor in situ hybridization (mFISH) to tally the number of mitotic human lymphocytes exposed to graded doses of gamma rays that carried either lethal or nonlethal CA types. Despite the fact that a number of nonlethal complex exchanges were observed, the cells containing them were seldom deemed viable, due to coincident lethal chromosome damage. We considered two model variants for describing the dose responses. The first assumes independent linear-quadratic (LQ) dose response shapes for the yields of both lethal and nonlethal CAs. The second (simplified) variant assumes that the mean number of nonlethal CAs per cell is proportional to the mean number of lethal CAs per cell, meaning that the shapes and magnitudes of both aberration types differ only by a multiplicative proportionality constant. Using these models allowed us to assemble dose response curves for the frequency of aberration-bearing cells that would be expected to survive. This took the form of a joint probability distribution for cells containing ≥1 nonlethal CAs but having zero lethal CAs. The simplified second model variant turned out to be marginally better supported than the first, and the joint probability distribution based on this model yielded a crescent-shaped dose response reminiscent of those observed for mutagenesis and transformation for cells “at risk” (i.e. not corrected for survival). Among the implications of these findings is the suggestion that similarly shaped curves form the basis for deriving metrics associated with radiation risk models.

scholarly journals Multiple-wavelength anomalous dispersion techniques applied to powder data: a probabilistic method for finding the substructureviajoint probability distribution functions

2008 ◽  
Vol 42 (1) ◽  
pp. 30-35 ◽  
Author(s):  
Angela Altomare ◽  
Benny Danilo Belviso ◽  
Maria Cristina Burla ◽  
Gaetano Campi ◽  
Corrado Cuocci ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Probabilistic Method ◽  
Joint Probability ◽  
Direct Methods ◽  
Distribution Functions ◽  
Joint Probability Distribution ◽  
Probability Distribution Functions ◽  
Multiple Wavelength ◽  
Joint Probability Distribution Function

A new joint probability distribution function method is described to find the anomalous scatterer substructure from powder data. The method requires two wavelengths; the conclusive formulas provide estimates of the substructure structure factor moduli, from which the anomalous scatterer positions can be found by Patterson or direct methods. The theory has been preliminarily applied to two compounds, the first having Pt and the second having Fe as anomalous scatterer. Both substructures were correctly identified.

The joint probability distribution function of structure factors with rational indices. IV. The P1 case

1999 ◽  
Vol 55 (3) ◽  
pp. 512-524
Author(s):  
Carmelo Giacovazzo ◽  
Dritan Siliqi ◽  
Cristina Fernández-Castaño
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Joint Probability ◽  
Distribution Functions ◽  
Accurate Estimation ◽  
Joint Probability Distribution ◽  
Structure Factors ◽  
Joint Probability Distributions ◽  
The Hilbert Transform

The method of the joint probability distribution functions of structure factors has been extended to reflections with rational indices. The most general case, space group P1, has been considered. The positional parameters are the primitive random variables of our probabilistic approach, while the reflection indices are kept fixed. Quite general joint probability distributions have been considered from which conditional distributions have been derived: these proved applicable to the accurate estimation of the real and imaginary parts of a structure factor, given prior information on other structure factors. The method is also discussed in relation to the Hilbert-transform techniques.

scholarly journals Parametric Modeling and Simulation of Joint Price-Production Distributions under Non-Normality, Autocorrelation and Heteroscedasticity: A Tool for Assessing Risk in Agriculture

2000 ◽  
Vol 32 (2) ◽  
pp. 283-297 ◽  
Author(s):  
Octavio A. Ramirez
Keyword(s):  
Probability Distribution ◽  
Agricultural Production ◽  
Time Trends ◽  
Joint Probability ◽  
Parametric Modeling ◽  
Joint Probability Distribution ◽  
Agricultural Risk ◽  
Multivariate Distributions ◽  
West Texas ◽  
The Mean

AbstractThis study presents a way to parametrically model and simulate multivariate distributions under potential non-normality, autocorrelation and heteroscedasticity and illustrates its application to agricultural risk analysis. Specifically, the joint probability distribution (pdf) for West Texas irrigated cotton, corn, sorghum, and wheat production and prices is estimated and applied to evaluate the changes in the risk and returns of agricultural production in the region resulting from observed and predicted price and production trends. The estimated pdf allows for time trends on the mean and the variance and varying degrees of autocorrelation and non-normality (kurtosis and right- or left-skewness) in each of the price and production variables. It also allows for any possible price-price, production-production, or price-production correlation.

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