KMCSolver< R, State, T > Class Template Reference

Class for running Kinetic Monte-Carlo simulations. More...

#include <CD_KMCSolver.H>

Public Types
using	ReactionList = std::vector< std::shared_ptr< const R > >
	Alias for the list of reactions.

Public Member Functions
	KMCSolver () noexcept
	Default constructor. Must subsequently call define.
	KMCSolver (const KMCSolver &)=default
	Copy constructor.
	KMCSolver (const KMCSolver &&)=delete
	Disallowed move constructor.
	KMCSolver (const ReactionList &a_reactions) noexcept
	Full constructor.
virtual	~KMCSolver () noexcept
	Destructor.
KMCSolver &	operator= (const KMCSolver &a_other)=default
	Copy assignment operator.
KMCSolver &	operator= (const KMCSolver &&)=delete
	Disallowed move assignment operator.
void	define (const ReactionList &a_reactions) noexcept
	Define function. Sets the reactions.
void	setSolverParameters (T a_numCrit, T a_numSSA, T a_maxIter, Real a_eps, Real a_SSAlim, Real a_exitTol) noexcept
	Set solver parameters.
std::vector< std::vector< T > >	getNu (const State &a_state, const ReactionList &a_reactions) const noexcept
	Compute the state vector changes for all reactions.
std::vector< Real >	propensities (const State &a_state) const noexcept
	Compute propensities for ALL reactions.
std::vector< Real >	propensities (const State &a_state, const ReactionList &a_reactions) const noexcept
	Compute propensities for a subset of reactions.
Real	totalPropensity (const State &a_state) const noexcept
	Compute the total propensity for ALL reactions.
Real	totalPropensity (const State &a_state, const ReactionList &a_reactions) const noexcept
	Compute the total propensity for a subset of reactions.
std::pair< ReactionList, ReactionList >	partitionReactions (const State &a_state) const noexcept
	Partition reactions into critical and non-critical reactions.
std::pair< ReactionList, ReactionList >	partitionReactions (const State &a_state, const ReactionList &a_reactions) const noexcept
	Partition reactions into critical and non-critical reactions.
Real	getCriticalTimeStep (const State &a_state) const noexcept
	Get the time to the next critical reaction.
Real	getCriticalTimeStep (const State &a_state, const ReactionList &a_criticalReactions) const noexcept
	Get the time to the next critical reaction.
Real	getCriticalTimeStep (const std::vector< Real > &a_propensities) const noexcept
	Get the time to the next critical reaction.
Real	getCriticalTimeStep (const Real &a_totalPropensity) const noexcept
	Get the time to the next critical reaction.
Real	getNonCriticalTimeStep (const State &a_state) const noexcept
	Get the non-critical time step.
Real	getNonCriticalTimeStep (const State &a_state, const ReactionList &a_reactions) const noexcept
	Get the non-critical time step.
Real	getNonCriticalTimeStep (const State &a_state, const ReactionList &a_nonCriticalReactions, const std::vector< Real > &a_nonCriticalPropensities) const noexcept
	Get the non-critical time step.
Real	computeDt (const State &a_state, const ReactionList &a_reactions, const std::vector< Real > &a_propensities, Real a_epsilon) const noexcept
	Compute a time step using the leap condition on the mean value.
void	stepSSA (State &a_state) const noexcept
	Perform a single SSA step.
void	stepSSA (State &a_state, const ReactionList &a_reactions) const noexcept
	Perform a single SSA step.
void	stepSSA (State &a_state, const ReactionList &a_reactions, const std::vector< Real > &a_propensities) const noexcept
	Perform a single SSA step with pre-computed propensities.
void	advanceSSA (State &a_state, Real a_dt) const noexcept
	Advance with the SSA over the input time. This can end up using substepping.
void	advanceSSA (State &a_state, const ReactionList &a_reactions, Real a_dt) const noexcept
	Advance with the SSA over the input time. This can end up using substepping.
void	stepExplicitEuler (State &a_state, Real a_dt) const noexcept
	Perform one plain tau-leaping step using ALL reactions.
void	stepExplicitEuler (State &a_state, const ReactionList &a_reactions, Real a_dt) const noexcept
	Perform one plain tau-leaping step over the input reactions.
void	stepMidpoint (State &a_state, Real a_dt) const noexcept
	Perform one leaping step using the midpoint method for ALL reactions.
void	stepMidpoint (State &a_state, const ReactionList &a_reactions, Real a_dt) const noexcept
	Perform one leaping step using the midpoint method for the input reactions.
void	stepPRC (State &a_state, Real a_dt) const noexcept
	Perform one leaping step using the PRC method for ALL reactions.
void	stepPRC (State &a_state, const ReactionList &a_reactions, Real a_dt) const noexcept
	Perform one leaping step using the PRC method for the input reactions.
void	stepImplicitEuler (State &a_state, Real a_dt) const noexcept
	Perform one implicit Euler tau-leaping step using ALL reactions.
void	stepImplicitEuler (State &a_state, const ReactionList &a_reactions, Real a_dt) const noexcept
	Perform one implicit Euler tau-leaping step over the input reactions.
void	advanceTau (State &a_state, const Real &a_dt, const KMCLeapPropagator &a_leapPropagator=KMCLeapPropagator::ExplicitEuler) const noexcept
	Advance using a specified tau-leaping algorithm.
void	advanceTau (State &a_state, const ReactionList &a_reactions, const Real &a_dt, const KMCLeapPropagator &a_leapPropagator=KMCLeapPropagator::ExplicitEuler) const noexcept
	Advance using a specified tau-leaping algorithm.
void	advanceHybrid (State &a_state, Real a_dt, const KMCLeapPropagator &a_leapPropagator=KMCLeapPropagator::ExplicitEuler) const noexcept
	Advance using Cao et. al. hybrid algorithm over the input time. This can end up using substepping.
void	advanceHybrid (State &a_state, const ReactionList &a_reactions, Real a_dt, const KMCLeapPropagator &a_leapPropagator=KMCLeapPropagator::ExplicitEuler) const noexcept
	Advance using Cao et. al. hybrid algorithm over the input time. This can end up using substepping.
void	advanceHybrid (State &a_state, const ReactionList &a_reactions, Real a_dt, const std::function< void(State &, const ReactionList &a_reactions, const Real a_dt)> &a_propagator) const noexcept
	Advance using Cao et. al. hybrid algorithm over the input time. This can end up using substepping.

Protected Attributes
ReactionList	m_reactions
	List of reactions used when advancing states.
T	m_Ncrit
	Definition of critical reactions.
T	m_numSSA
	Maximum number of SSA steps to run when switching into SSA-based advancement for non-critical reactions.
T	m_maxIter
	Maximum number of iterations for implicit solvers.
Real	m_eps
	Maximum permitted change in propensities for non-critical reactions.
Real	m_SSAlim
	Threshold for switching to SSA-based algorithm within the Cao algorithm.
Real	m_exitTol
	Exit tolerance for implicit solvers.
std::vector< std::vector< int > >	m_nu
	List of state changes for each reaction.

Detailed Description

template<typename R, typename State, typename T = long long>
class KMCSolver< R, State, T >

Class for running Kinetic Monte-Carlo simulations.

The template parameter State is the underlying state type that KMC operators on. There are rather simple required member functions on the State parameter, but the reaction type (template parameter R) MUST be able to operate on the state through the following functions:

1. Real R::propensity(State) const -> Computes the reaction propensity for the input state.
2. T R::computeCriticalNumberOfReactions(State) const -> Computes the minimum number of reactions that exhausts one of the reactants.
3. void R::advanceState(State&, const T numReactions) const -> Advance state by numReactions.
4. std::<some_container> getReactants() const -> Get reactants involved in the reactions.
5. static T R::population(const <some_type> reactant, const State& a_state) -> Get the population of the input reactant in the input state.

The template parameter T should agree across both R, State, and KMCSolver. Note that this must be a signed integer type.

Constructor & Destructor Documentation

KMCSolver()

template<typename R , typename State , typename T >

KMCSolver< R, State, T >::KMCSolver ( const ReactionList &  a_reactions )

inlinenoexcept

Full constructor.

Parameters

[in]

a_reactions

List of reactions.

Member Function Documentation

advanceHybrid() [1/3]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::advanceHybrid ( State &  a_state, const ReactionList &  a_reactions, Real  a_dt, const KMCLeapPropagator &  a_leapPropagator = KMCLeapPropagator::ExplicitEuler  ) const

inlinenoexcept

Advance using Cao et. al. hybrid algorithm over the input time. This can end up using substepping.

Parameters

[in,out]	a_state	State vector to advance.
[in]	a_reactions	Reactions to advance.
[in]	a_dt	Time increment.
[in]	a_leapPropagator	Which leap propagator to use.

Note

Calls the other version with stepTau as the leap propagator.

advanceHybrid() [2/3]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::advanceHybrid ( State &  a_state, const ReactionList &  a_reactions, Real  a_dt, const std::function< void(State &, const ReactionList &a_reactions, const Real a_dt)> &  a_propagator  ) const

inlinenoexcept

Advance using Cao et. al. hybrid algorithm over the input time. This can end up using substepping.

Parameters

[in,out]	a_state	State vector to advance.
[in]	a_reactions	Reactions to advance with.
[in]	a_dt	Time increment.
[in]	a_propagator	Leaping propagator function.

advanceHybrid() [3/3]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::advanceHybrid ( State &  a_state, Real  a_dt, const KMCLeapPropagator &  a_leapPropagator = KMCLeapPropagator::ExplicitEuler  ) const

inlinenoexcept

Advance using Cao et. al. hybrid algorithm over the input time. This can end up using substepping.

Parameters

[in,out]	a_state	State vector to advance.
[in]	a_dt	Time increment.
[in]	a_leapPropagator	Which leap propagator to use.

Note

Calls the other version with m_reactions.

advanceSSA() [1/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::advanceSSA ( State &  a_state, const ReactionList &  a_reactions, Real  a_dt  ) const

inlinenoexcept

Advance with the SSA over the input time. This can end up using substepping.

Parameters

[in,out]	a_state	State vector to advance.
[in]	a_reactions	Reactions to advance with.
[in]	a_dt	Time increment.

advanceSSA() [2/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::advanceSSA ( State &  a_state, Real  a_dt  ) const

inlinenoexcept

Advance with the SSA over the input time. This can end up using substepping.

Parameters

[in,out]	a_state	State vector to advance.
[in]	a_dt	Time increment.

Note

Calls the other version with m_reactions.

advanceTau() [1/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::advanceTau ( State &  a_state, const ReactionList &  a_reactions, const Real &  a_dt, const KMCLeapPropagator &  a_leapPropagator = KMCLeapPropagator::ExplicitEuler  ) const

inlinenoexcept

Advance using a specified tau-leaping algorithm.

Parameters

[in,out]	a_state	State vector to advance.
[in]	a_reactions	Reactions to advance.
[in]	a_dt	Time increment.
[in]	a_leapPropagator	Which leap propagator to use.

Note

Calls the other version with stepTau as the leap propagator.

advanceTau() [2/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::advanceTau ( State &  a_state, const Real &  a_dt, const KMCLeapPropagator &  a_leapPropagator = KMCLeapPropagator::ExplicitEuler  ) const

inlinenoexcept

Advance using a specified tau-leaping algorithm.

Parameters

[in,out]	a_state	State vector to advance.
[in]	a_dt	Time increment.
[in]	a_leapPropagator	Which leap propagator to use.

Note

Calls the other version with m_reactions.

computeDt()

template<typename R , typename State , typename T >

Real KMCSolver< R, State, T >::computeDt ( const State &  a_state, const ReactionList &  a_reactions, const std::vector< Real > &  a_propensities, Real  a_epsilon  ) const

inlinenoexcept

Compute a time step using the leap condition on the mean value.

This is just like getNonCriticalTimeStep EXCEPT that the leap condition is not applied for the deviation.

Parameters

[in]	a_state	State vector.
[in]	a_reactions	Reactions.
[in]	a_propensities	Propensities.
[in]	a_epsilon	Epsilon value for maximum change in propensities.

Returns

Tau-leaping time step.

define()

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::define ( const ReactionList &  a_reactions )

inlinenoexcept

Define function. Sets the reactions.

Parameters

[in]

a_reactions

List of reactions.

getCriticalTimeStep() [1/4]

template<typename R , typename State , typename T >

Real KMCSolver< R, State, T >::getCriticalTimeStep ( const Real &  a_totalPropensity ) const

inlinenoexcept

Get the time to the next critical reaction.

Parameters

[in]

a_totalPropensity

Total propensity.

Returns

Time step for the next critical reaction.

getCriticalTimeStep() [2/4]

template<typename R , typename State , typename T >

Real KMCSolver< R, State, T >::getCriticalTimeStep ( const State &  a_state ) const

inlinenoexcept

Get the time to the next critical reaction.

Parameters

[in]

a_state

State vector.

Returns

Time step for the next critical reaction.

Note

Calls the other version with m_reactions.

getCriticalTimeStep() [3/4]

template<typename R , typename State , typename T >

Real KMCSolver< R, State, T >::getCriticalTimeStep ( const State &  a_state, const ReactionList &  a_criticalReactions  ) const

inlinenoexcept

Get the time to the next critical reaction.

Parameters

[in]	a_state	State vector.
[in]	a_criticalReactions	Reaction list.

Returns

Time step for the next critical reaction.

Note

Computes the total propensity and calls the other version.

getCriticalTimeStep() [4/4]

template<typename R , typename State , typename T >

Real KMCSolver< R, State, T >::getCriticalTimeStep ( const std::vector< Real > &  a_propensities ) const

inlinenoexcept

Get the time to the next critical reaction.

Parameters

[in]

a_propensities

Reaction propensities.

Returns

Time step for the next critical reaction.

getNonCriticalTimeStep() [1/3]

template<typename R , typename State , typename T >

Real KMCSolver< R, State, T >::getNonCriticalTimeStep ( const State &  a_state ) const

inlinenoexcept

Get the non-critical time step.

Parameters

[in]

a_state

State vector.

Returns

Non-critical tau-leaping time step.

Note

Calls the other version with m_reactions.

getNonCriticalTimeStep() [2/3]

template<typename R , typename State , typename T >

Real KMCSolver< R, State, T >::getNonCriticalTimeStep ( const State &  a_state, const ReactionList &  a_nonCriticalReactions, const std::vector< Real > &  a_nonCriticalPropensities  ) const

inlinenoexcept

Get the non-critical time step.

Parameters

[in]	a_state	State vector.
[in]	a_nonCriticalReactions	Non-critical reactions.
[in]	a_nonCriticalPropensities	Non-critical propensities.

Returns

Non-critical tau-leaping time step.

getNonCriticalTimeStep() [3/3]

template<typename R , typename State , typename T >

Real KMCSolver< R, State, T >::getNonCriticalTimeStep ( const State &  a_state, const ReactionList &  a_reactions  ) const

inlinenoexcept

Get the non-critical time step.

Parameters

[in]	a_state	State vector.
[in]	a_reactions	Reaction list.

Returns

Non-critical tau-leaping time step.

Note

Computes propensities and calls the other version.

getNu()

template<typename R , typename State , typename T >

std::vector< std::vector< T > > KMCSolver< R, State, T >::getNu ( const State &  a_state, const ReactionList &  a_reactions  ) const

inlinenoexcept

Compute the state vector changes for all reactions.

Parameters

[in]	a_state	Input state.
[in]	a_reactions	Reaction list.

Returns

State change vectors for each reaction.

Note

The input parameter a_state can be a dummy state because the state change vector does not depend on it.

operator=()

template<typename R , typename State , typename T = long long>

KMCSolver & KMCSolver< R, State, T >::operator= ( const KMCSolver< R, State, T > &  a_other )

default

Copy assignment operator.

Parameters

[in]

a_other

Other solver.

Returns

Reference to this object.

partitionReactions() [1/2]

template<typename R , typename State , typename T >

std::pair< typename KMCSolver< R, State, T >::ReactionList, typename KMCSolver< R, State, T >::ReactionList > KMCSolver< R, State, T >::partitionReactions ( const State &  a_state ) const

inlinenoexcept

Partition reactions into critical and non-critical reactions.

First member in the pair is the critical reactions, then the non-critical reactions.

Parameters

[in]

a_state

State vector.

Returns

Pair of (critical reactions, non-critical reactions).

Note

Calls the other version with m_reactions.

partitionReactions() [2/2]

template<typename R , typename State , typename T >

std::pair< typename KMCSolver< R, State, T >::ReactionList, typename KMCSolver< R, State, T >::ReactionList > KMCSolver< R, State, T >::partitionReactions ( const State &  a_state, const ReactionList &  a_reactions  ) const

inlinenoexcept

Partition reactions into critical and non-critical reactions.

First member in the pair is the critical reactions, then the non-critical reactions.

Parameters

[in]	a_state	State vector.
[in]	a_reactions	Reaction list to be partitioned.

Returns

Pair of (critical reactions, non-critical reactions).

propensities() [1/2]

template<typename R , typename State , typename T >

std::vector< Real > KMCSolver< R, State, T >::propensities ( const State &  a_state ) const

inlinenoexcept

Compute propensities for ALL reactions.

Parameters

[in]

a_state

State vector.

Returns

Propensities for each reaction.

Note

Calls the other version with m_reactions.

propensities() [2/2]

template<typename R , typename State , typename T >

std::vector< Real > KMCSolver< R, State, T >::propensities ( const State &  a_state, const ReactionList &  a_reactions  ) const

inlinenoexcept

Compute propensities for a subset of reactions.

Parameters

[in]	a_state	State vector.
[in]	a_reactions	Reaction list.

Returns

Propensities for each reaction.

setSolverParameters()

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::setSolverParameters ( T  a_numCrit, T  a_numSSA, T  a_maxIter, Real  a_eps, Real  a_SSAlim, Real  a_exitTol  )

inlinenoexcept

Set solver parameters.

Parameters

[in]	a_numCrit	Determines critical reactions. This is the number of reactions that need to fire before depleting a reactant.
[in]	a_numSSA	Maximum number of SSA steps to run when switching from tau-leaping to SSA (hybrid algorithm only).
[in]	a_maxIter	Maximum permitted number of iterations for the implicit solver.
[in]	a_eps	Maximum permitted change in propensities when performing tau-leaping for non-critical reactions.
[in]	a_SSAlim	Threshold for switching from tau-leaping of non-critical reactions to SSA for all reactions (hybrid algorithm only).
[in]	a_exitTol	Exit tolerance for implicit solvers.

stepExplicitEuler() [1/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::stepExplicitEuler ( State &  a_state, const ReactionList &  a_reactions, Real  a_dt  ) const

inlinenoexcept

Perform one plain tau-leaping step over the input reactions.

Parameters

[in,out]	a_state	State vector to be advanced.
[in]	a_reactions	List of reactions to advance with.
[in]	a_dt	Time increment.

stepExplicitEuler() [2/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::stepExplicitEuler ( State &  a_state, Real  a_dt  ) const

inlinenoexcept

Perform one plain tau-leaping step using ALL reactions.

Parameters

[in,out]	a_state	State vector to be advanced.
[in]	a_dt	Time increment.

Note

Calls the other version with m_reactions.

stepImplicitEuler() [1/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::stepImplicitEuler ( State &  a_state, const ReactionList &  a_reactions, Real  a_dt  ) const

inlinenoexcept

Perform one implicit Euler tau-leaping step over the input reactions.

Parameters

[in,out]	a_state	State vector to be advanced.
[in]	a_reactions	List of reactions to advance with.
[in]	a_dt	Time increment.

stepImplicitEuler() [2/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::stepImplicitEuler ( State &  a_state, Real  a_dt  ) const

inlinenoexcept

Perform one implicit Euler tau-leaping step using ALL reactions.

Parameters

[in,out]	a_state	State vector to be advanced.
[in]	a_dt	Time increment.

Note

Calls the other version with m_reactions.

stepMidpoint() [1/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::stepMidpoint ( State &  a_state, const ReactionList &  a_reactions, Real  a_dt  ) const

inlinenoexcept

Perform one leaping step using the midpoint method for the input reactions.

Parameters

[in,out]	a_state	State vector to be advanced.
[in]	a_reactions	List of reactions to advance with.
[in]	a_dt	Time increment.

stepMidpoint() [2/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::stepMidpoint ( State &  a_state, Real  a_dt  ) const

inlinenoexcept

Perform one leaping step using the midpoint method for ALL reactions.

Parameters

[in,out]	a_state	State vector to be advanced.
[in]	a_dt	Time increment.

Note

Calls the other version with m_reactions.

stepPRC() [1/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::stepPRC ( State &  a_state, const ReactionList &  a_reactions, Real  a_dt  ) const

inlinenoexcept

Perform one leaping step using the PRC method for the input reactions.

Parameters

[in,out]	a_state	State vector to be advanced.
[in]	a_reactions	List of reactions to advance with.
[in]	a_dt	Time increment.

stepPRC() [2/2]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::stepPRC ( State &  a_state, Real  a_dt  ) const

inlinenoexcept

Perform one leaping step using the PRC method for ALL reactions.

Parameters

[in,out]	a_state	State vector to be advanced.
[in]	a_dt	Time increment.

Note

Calls the other version with m_reactions.

stepSSA() [1/3]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::stepSSA ( State &  a_state ) const

inlinenoexcept

Perform a single SSA step.

Parameters

[in,out]

a_state

State vector to advance.

Note

Calls the other version with m_reactions.

stepSSA() [2/3]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::stepSSA ( State &  a_state, const ReactionList &  a_reactions  ) const

inlinenoexcept

Perform a single SSA step.

Parameters

[in,out]	a_state	State vector to advance.
[in]	a_reactions	Reactions to advance with.

Note

Computes propensities and calls the other version.

stepSSA() [3/3]

template<typename R , typename State , typename T >

void KMCSolver< R, State, T >::stepSSA ( State &  a_state, const ReactionList &  a_reactions, const std::vector< Real > &  a_propensities  ) const

inlinenoexcept

Perform a single SSA step with pre-computed propensities.

Parameters

[in,out]	a_state	State vector to advance.
[in]	a_reactions	Reactions to advance with.
[in]	a_propensities	Propensities for the reactions.

totalPropensity() [1/2]

template<typename R , typename State , typename T >

Real KMCSolver< R, State, T >::totalPropensity ( const State &  a_state ) const

inlinenoexcept

Compute the total propensity for ALL reactions.

Parameters

[in]

a_state

State vector.

Returns

Sum of all reaction propensities.

Note

Calls the other version with m_reactions.

totalPropensity() [2/2]

template<typename R , typename State , typename T >

Real KMCSolver< R, State, T >::totalPropensity ( const State &  a_state, const ReactionList &  a_reactions  ) const

inlinenoexcept

Compute the total propensity for a subset of reactions.

Parameters

[in]	a_state	State vector.
[in]	a_reactions	Reaction list.

Returns

Sum of propensities for the given reactions.

Member Data Documentation

m_Ncrit

template<typename R , typename State , typename T = long long>

T KMCSolver< R, State, T >::m_Ncrit

protected

Definition of critical reactions.

A reaction is critical if it is m_Ncrit firings away from depleting a reactant.

m_nu

template<typename R , typename State , typename T = long long>

std::vector<std::vector<int> > KMCSolver< R, State, T >::m_nu

protected

List of state changes for each reaction.

The outer vector corresponds to the reactive index. The inner vector describes the change in the population of the state vector, with an indexing given by the State's linearIn/linearOut functions.

---

The documentation for this class was generated from the following files:

• Source/KineticMonteCarlo/CD_KMCSolver.H
• Source/KineticMonteCarlo/CD_KMCSolverImplem.H