TEMPLATE, NOT IMPLEMENTED: waiting times for periodic rates by inverting the integrated escape rate (BEP R. Paiders, nhKMC, Algorithms 3 and 4; Prados, Brey, Sanchez-Rey 1997). More...
#include <kmcwaitingtime.h>
Classes | |
| struct | Settings |
Public Member Functions | |
| IntegratedRateInversion (const Settings &settings) | |
| std::string | Name () const override |
| void | Prepare (const TimeDependentRates &rates) override |
| double | NextTime (Index site, double t, KMCRandom &random) const override |
| Index | ChooseHop (Index site, double t, KMCRandom &random) const override |
| Public Member Functions inherited from votca::xtp::WaitingTimeStrategy | |
| virtual | ~WaitingTimeStrategy ()=default |
Private Attributes | |
| Settings | settings_ |
| const TimeDependentRates * | rates_ = nullptr |
Detailed Description
TEMPLATE, NOT IMPLEMENTED: waiting times for periodic rates by inverting the integrated escape rate (BEP R. Paiders, nhKMC, Algorithms 3 and 4; Prados, Brey, Sanchez-Rey 1997).
For a carrier on site i at time t0 the waiting time dt solves -ln u = int_{t0}^{t0+dt} lambda_i(s) ds, u ~ U(0,1], lambda_i(t) = TimeDependentRates::EscapeRate(i, t) > 0 with period T. With Lambda_i(t) = int_0^t lambda_i, I_T = Lambda_i(T) and t0 = l T + t0*: m = floor((g + Lambda_i(t0*)) / I_T) ... (BEP eqs. 11-18) so only Lambda_i on [0, T) (or [0, 2T)) and I_T are needed, precomputed per site in Prepare() (quadrature + monotone PCHIP interpolant), and the remainder is a bounded, monotone root search.
ChooseHop(i, t): edge e with probability w_e(t) / lambda_i(t) at the event time t (never -1, apart from rounding).
Notes for the implementation:
- Prepare(): rates.Period() must be > 0, else throw. Store per site what the inversion needs (e.g. the PCHIP coefficients of Lambda_i on [0, T] and I_T); memory is per site, not per edge.
- Tolerances relative to T and I_T that double precision can reach (about 1e-14 relative, not 1e-20). The phase rem(t0, T) loses about log10(t0/T) digits for t0 >> T; document the accuracy or keep the time split into periods and phase.
- Validation (see test_kmcwaitingtime.cc, disabled test cases):
- static rates (Period() any > 0): identical statistics to ExponentialWaitingTime and the GRW hitting times;
- uniformly scaled rates w_e(t) = s(t) w_e: hitting times are the static ones mapped through the inverse of int s (exact reference);
- any periodic rates: same statistics as ThinningWaitingTime;
- f -> infinity: the GRW with period-averaged rates; f -> 0: the average over the phase of the static result.
Definition at line 149 of file kmcwaitingtime.h.
Constructor & Destructor Documentation
◆ IntegratedRateInversion()
|
inlineexplicit |
Definition at line 156 of file kmcwaitingtime.h.
Member Function Documentation
◆ ChooseHop()
|
overridevirtual |
Implements votca::xtp::WaitingTimeStrategy.
Definition at line 161 of file kmcwaitingtime.cc.
◆ Name()
|
inlineoverridevirtual |
Implements votca::xtp::WaitingTimeStrategy.
Definition at line 158 of file kmcwaitingtime.h.
◆ NextTime()
|
overridevirtual |
Implements votca::xtp::WaitingTimeStrategy.
Definition at line 155 of file kmcwaitingtime.cc.
◆ Prepare()
|
overridevirtual |
Implements votca::xtp::WaitingTimeStrategy.
Definition at line 137 of file kmcwaitingtime.cc.
Member Data Documentation
◆ rates_
|
private |
Definition at line 165 of file kmcwaitingtime.h.
◆ settings_
|
private |
Definition at line 164 of file kmcwaitingtime.h.
The documentation for this class was generated from the following files:
- xtp/include/votca/xtp/kmcwaitingtime.h
- xtp/src/libxtp/kmcwaitingtime.cc
