Particle-size distribution model wherein random samples are drawn from the doubly-truncated exponential probability density function: More...

Inheritance diagram for exponential:

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Collaboration diagram for exponential:

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Public Member Functions
	TypeName ("exponential")

	exponential (const dictionary &dict, Random &rndGen)

	exponential (const exponential &p)

virtual autoPtr< distributionModel >	clone () const

void	operator= (const exponential &)=delete

virtual	~exponential ()=default

virtual scalar	sample () const

virtual scalar	meanValue () const

Public Member Functions inherited from distributionModel
	TypeName ("distributionModel")

	declareRunTimeSelectionTable (autoPtr, distributionModel, dictionary,(const dictionary &dict, Random &rndGen),(dict, rndGen))

	distributionModel (const word &name, const dictionary &dict, Random &rndGen)

	distributionModel (const distributionModel &p)

virtual	~distributionModel ()=default

virtual scalar	minValue () const

virtual scalar	maxValue () const

Additional Inherited Members
Static Public Member Functions inherited from distributionModel
static autoPtr< distributionModel >	New (const dictionary &dict, Random &rndGen)

Protected Member Functions inherited from distributionModel
virtual void	check () const

Protected Attributes inherited from distributionModel
const dictionary	distributionModelDict_

Random &	rndGen_

scalar	minValue_

scalar	maxValue_

Detailed Description

Particle-size distribution model wherein random samples are drawn from the doubly-truncated exponential probability density function:

$f(x; \lambda, A, B) = \lambda \frac{\exp(-\lambda (x - A))}{1 - \exp(-\lambda(B-A))}$

where

$f(x; \lambda, A, B)$	=	Exponential probability density function
$\lambda$	=	Rate parameter
	=	Sample
	=	Minimum of the distribution
	=	Maximum of the distribution

Constraints:

$\infty > B > A > 0$
$x \in [B,A]$
$\lambda > 0$

Random samples are generated by the inverse transform sampling technique by using the quantile function of the doubly-truncated exponential probability density function:

$x = - \frac{1}{\lambda} \ln (r)$

with

$r = q_{min} + u (q_{max} - q_{min})$

$q_{min} = \exp(-\lambda A)$

$q_{max} = \exp(-\lambda B)$

where $ u $ is a sample drawn from the uniform probability density function on the unit interval $ (0, 1) $ .

Usage

Minimal example by using constant/<CloudProperties>:

subModels
{
    injectionModels
    {
        <name>
        {
            ...

            sizeDistribution
            {
                type        exponential;
                exponentialDistribution
                {
                    lambda      <lambdaValue>;
                    minValue    <minValue>;
                    maxValue    <maxValue>;
                }
            }
        }
    }
}

where the entries mean:

Property	Description	Type	Reqd	Deflt
`type`	Type name: exponential	word	yes	-
`exponentialDistribution`	Distribution settings	dict	yes	-
`lambda`	Rate parameter	scalar	yes	-
`minValue`	Minimum of the distribution	scalar	yes	-
`maxValue`	Maximum of the distribution	scalar	yes	-