Difference between revisions of "Output parameters"
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*The order of surface and mid-point values for square prisms is: <math>X_{\mathrm{W},1} \, X_{\mathrm{W},2} \, ... \, X_{\mathrm{S},1} \, X_{\mathrm{S},2} \, ... \, X_{\mathrm{E},1} \, X_{\mathrm{E},2} \, ... \, X_{\mathrm{N},1} \, X_{\mathrm{N},2} \, ... </math> and the order of corner values: <math>X_{\mathrm{NW},1} \, X_{\mathrm{NW},2} \, ... \, X_{\mathrm{NE},1} \, X_{\mathrm{NE},2} \, ... \, X_{\mathrm{SE},1} \, X_{\mathrm{SE},2} \, ... \, X_{\mathrm{SW},1} \, X_{\mathrm{SW},2} \, ... </math> where <math>X_{k,g}</math> refers to parameter <math>X</math> on surface/corner ''k'' and energy group ''g''. | *The order of surface and mid-point values for square prisms is: <math>X_{\mathrm{W},1} \, X_{\mathrm{W},2} \, ... \, X_{\mathrm{S},1} \, X_{\mathrm{S},2} \, ... \, X_{\mathrm{E},1} \, X_{\mathrm{E},2} \, ... \, X_{\mathrm{N},1} \, X_{\mathrm{N},2} \, ... </math> and the order of corner values: <math>X_{\mathrm{NW},1} \, X_{\mathrm{NW},2} \, ... \, X_{\mathrm{NE},1} \, X_{\mathrm{NE},2} \, ... \, X_{\mathrm{SE},1} \, X_{\mathrm{SE},2} \, ... \, X_{\mathrm{SW},1} \, X_{\mathrm{SW},2} \, ... </math> where <math>X_{k,g}</math> refers to parameter <math>X</math> on surface/corner ''k'' and energy group ''g''. | ||
*The order of surface and mid-point values for Y-type hexagonal prims runs clockwise starting from the north. The corner values start from the next corner in clockwise direction. | *The order of surface and mid-point values for Y-type hexagonal prims runs clockwise starting from the north. The corner values start from the next corner in clockwise direction. | ||
− | *The order of surface and mid-point values for X-type hexagonal prims runs counterclockwise starting from the east. | + | *The order of surface and mid-point values for X-type hexagonal prims runs counterclockwise starting from the east. ''Confirm the direction of corner values.'' |
*'''Note that one should confirm the order of values in the hexagonal prisms.''' | *'''Note that one should confirm the order of values in the hexagonal prisms.''' | ||
Revision as of 14:04, 16 October 2018
This page lists the output parameters in the main [input]_res.m output file.
Contents
- 1 Homogenized group constants
- 2 Miscellaneous notes for other outputs
- 3 References
Homogenized group constants
Notes:
- Group constants are calculated by first homogenizing the geometry using a multi-group structure with H energy groups. The data is then collapsed into the final few-group structure with G groups using the infinite and B_{1} leakage-corrected flux spectra.
- The methodology used in Serpent for spatial homogenization is described in a paper published in Annals of Nuclear Energy in 2016.^{[1]}
- The B_{1} calculation is off by default, and invoked by the set fum option.
- The intermediate multi-group structure is defined using option set micro.
- The few-group structure is defined using option set nfg.
- The universes in which the group constants are calculated are listed in option set gcu. The calculation is performed for root universe 0 by default, and can be switched off with "set gcu -1".
- If data is produced in multiple universes within a single run, the data is assigned with different run indexes (idx)
- The parameter names can be listed in the set coefpara option, and they will be included in the group constant output file when the automated burnup sequence is invoked.
- The order in which two-dimensional data (scattering matrices, ADF and pin-power parameters) is printed in the [input].coe output file is different from what is listed below in update 2.1.24 and earlier versions.
Common parameters
Parameter | Size | Description |
---|---|---|
GC_UNIVERSE_NAME | (string) | Name of the universe where spatial homogenization was performed |
MICRO_NG | 1 | Number of energy groups in the intermediate multi-group structure (referred to as H below) |
MICRO_E | H + 1 | Group boundaries in the intermediate multi-group structure (in ascending order) |
MACRO_NG | 1 | Number of energy groups in the final few-group structure (referred to as G below) |
MACRO_E | G + 1 | Group boundaries in the final few-group structure (in descending order) |
Group constants homogenized in infinite spectrum
Parameter | Size | Description |
---|---|---|
INF_MICRO_FLX | 2H | Multi-group flux spectrum (integral, un-normalized) |
INF_FLX | 2G | Few-group flux (integral, normalized) |
INF_KINF | 2 | Infinite multiplication factor |
Reaction cross sections
Parameter | Size | Description |
---|---|---|
INF_TOT | 2G | Total cross section |
INF_CAPT | 2G | Capture cross section |
INF_FISS | 2G | Fission cross section |
INF_NSF | 2G | Fission neutron production cross section |
INF_KAPPA | 2G | Average deposited fission energy (MeV) |
INF_INVV | 2G | Inverse neutron speed (s/cm) |
INF_NUBAR | 2G | Average neutron yield |
INF_ABS | 2G | Absorption cross section (capture + fission) |
INF_REMXS | 2G | Removal cross section (group-removal + absorption) |
INF_RABSXS | 2G | Reduced absorption cross section (total - scattering production) |
Fission spectra
Parameter | Size | Description |
---|---|---|
INF_CHIT | 2G | Fission spectrum (total) |
INF_CHIP | 2G | Fission spectrum (prompt neutrons) |
INF_CHID | 2G | Fission spectrum (delayed neutrons) |
Scattering cross sections
Notes:
- Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.
Parameter | Size | Description |
---|---|---|
INF_SCATT0 | 2G | Total P_{0} scattering cross section |
INF_SCATT1 | 2G | Total P_{1} scattering cross section |
INF_SCATT2 | 2G | Total P_{2} scattering cross section |
INF_SCATT3 | 2G | Total P_{3} scattering cross section |
INF_SCATT4 | 2G | Total P_{4} scattering cross section |
INF_SCATT5 | 2G | Total P_{5} scattering cross section |
INF_SCATT6 | 2G | Total P_{6} scattering cross section |
INF_SCATT7 | 2G | Total P_{7} scattering cross section |
INF_SCATTP0 | 2G | Total P_{0} scattering production cross section |
INF_SCATTP1 | 2G | Total P_{1} scattering production cross section |
INF_SCATTP2 | 2G | Total P_{2} scattering production cross section |
INF_SCATTP3 | 2G | Total P_{3} scattering production cross section |
INF_SCATTP4 | 2G | Total P_{4} scattering production cross section |
INF_SCATTP5 | 2G | Total P_{5} scattering production cross section |
INF_SCATTP6 | 2G | Total P_{6} scattering production cross section |
INF_SCATTP7 | 2G | Total P_{7} scattering production cross section |
Scattering matrices
Notes:
- Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.
- The order of values ([input].coe) or value pairs ([input]_res.m) is: where refers to scattering from group g to g'.
- The data in the [input]_res.m file can be read into a G by G matrix with Matlab reshape-command, for example:
reshape(INF_S0(idx,1:2:end), G, G);
Parameter | Size | Description |
---|---|---|
INF_S0 | 4G^{2} | P_{0} scattering matrix |
INF_S1 | 4G^{2} | P_{1} scattering matrix |
INF_S2 | 4G^{2} | P_{2} scattering matrix |
INF_S3 | 4G^{2} | P_{3} scattering matrix |
INF_S4 | 4G^{2} | P_{4} scattering matrix |
INF_S5 | 4G^{2} | P_{5} scattering matrix |
INF_S6 | 4G^{2} | P_{6} scattering matrix |
INF_S7 | 4G^{2} | P_{7} scattering matrix |
INF_SP0 | 4G^{2} | P_{0} scattering production matrix |
INF_SP1 | 4G^{2} | P_{1} scattering production matrix |
INF_SP2 | 4G^{2} | P_{2} scattering production matrix |
INF_SP3 | 4G^{2} | P_{3} scattering production matrix |
INF_SP4 | 4G^{2} | P_{4} scattering production matrix |
INF_SP5 | 4G^{2} | P_{5} scattering production matrix |
INF_SP6 | 4G^{2} | P_{6} scattering production matrix |
INF_SP7 | 4G^{2} | P_{7} scattering production matrix |
Diffusion parameters
Notes:
- Calculation of sensible values for INF_TRANSPXS and INF_DIFFCOEF requires fine enough intermediate multi-group structure.
- The cumulative migration method ^{[2]} was first developed for the OpenMC code. Currently the method works only when the homogenized region covers the entire geometry, and is surrounded by periodic or reflective boundary conditions.
- Calculation of TRC_TRANSPXS and TRC_DIFFCOEF requires defining energy-dependent correction factors using the set trc option.
- Calculation of CMM_TRANSPXS and CMM_DIFFCOEF requires that their calculation is not switched off using the set cmm option.
Parameter | Size | Description |
---|---|---|
INF_TRANSPXS | 2G | Transport cross section (calculated using the out-scattering approximation) |
INF_DIFFCOEF | 2G | Diffusion coefficient (calculated using the out-scattering approximation) |
CMM_TRANSPXS | 2G | Transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation) |
CMM_TRANSPXS_X | 2G | X-component of the directional transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation) |
CMM_TRANSPXS_Y | 2G | Y-component of the directional transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation) |
CMM_TRANSPXS_Z | 2G | Z-component of the directional transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation) |
CMM_DIFFCOEF | 2G | Diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation) |
CMM_DIFFCOEF_X | 2G | X-component of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation) |
CMM_DIFFCOEF_Y | 2G | Y-component of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation) |
CMM_DIFFCOEF_Z | 2G | Z-component of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation) |
TRC_TRANSPXS | 2G | Transport cross section calculated by applying user-defined transport correction factors to total cross section |
TRC_DIFFCOEF | 2G | Diffusion coefficient calculated by applying user-defined transport correction factors to total cross section |
Poison cross sections
Notes:
- Printed only if poison cross section option is on (see set poi).
Parameter | Size | Description |
---|---|---|
INF_I135_YIELD | 2G | Fission yield of I-135 (cumulative, includes all precursors) |
INF_XE135_YIELD | 2G | Fission yield of Xe-135 |
INF_PM149_YIELD | 2G | Fission yield of Pm-149 (cumulative, includes all precursors) |
INF_SM149_YIELD | 2G | Fission yield of Sm-149 |
INF_I135_MICRO_ABS | 2G | Microscopic absorption cross section of I-135 |
INF_XE135_MICRO_ABS | 2G | Microscopic absorption cross section of Xe-135 |
INF_PM149_MICRO_ABS | 2G | Microscopic absorption cross section of Pm-149 |
INF_SM149_MICRO_ABS | 2G | Microscopic absorption cross section of Sm-149 |
INF_XE135_MACRO_ABS | 2G | Macroscopic absorption cross section of Xe-135 |
INF_SM149_MACRO_ABS | 2G | Macroscopic absorption cross section of Sm-149 |
Group constants homogenized in B_{1} leakage-corrected spectrum
Parameter | Size | Description |
---|---|---|
B1_MICRO_FLX | 2H | Multi-group flux spectrum (integral, un-normalized) |
B1_FLX | 2G | Few-group flux (integral, normalized) |
B1_KINF | 2 | Infinite multiplication factor |
B1_KEFF | 2 | Effective multiplication factor |
B1_B2 | 2 | Critical buckling |
B1_ERR | 2 | Absolute deviation of k_{eff} from unity |
Reaction cross sections
Parameter | Size | Description |
---|---|---|
B1_TOT | 2G | Total cross section |
B1_CAPT | 2G | Capture cross section |
B1_FISS | 2G | Fission cross section |
B1_NSF | 2G | Fission neutron production cross section |
B1_KAPPA | 2G | Average deposited fission energy (MeV) |
B1_INVV | 2G | Inverse neutron speed (s/cm) |
B1_NUBAR | 2G | Average neutron yield |
B1_ABS | 2G | Absorption cross section (capture + fission) |
B1_REMXS | 2G | Removal cross section (group-removal + absorption) |
B1_RABSXS | 2G | Reduced absorption cross section (total - scattering production) |
Fission spectra
Parameter | Size | Description |
---|---|---|
B1_CHIT | 2G | Fission spectrum (total) |
B1_CHIP | 2G | Fission spectrum (prompt neutrons) |
B1_CHID | 2G | Fission spectrum (delayed neutrons) |
Scattering cross sections
Notes:
- Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.
Parameter | Size | Description |
---|---|---|
B1_SCATT0 | 2G | Total P_{0} scattering cross section |
B1_SCATT1 | 2G | Total P_{1} scattering cross section |
B1_SCATT2 | 2G | Total P_{2} scattering cross section |
B1_SCATT3 | 2G | Total P_{3} scattering cross section |
B1_SCATT4 | 2G | Total P_{4} scattering cross section |
B1_SCATT5 | 2G | Total P_{5} scattering cross section |
B1_SCATT6 | 2G | Total P_{6} scattering cross section |
B1_SCATT7 | 2G | Total P_{7} scattering cross section |
B1_SCATTP0 | 2G | Total P_{0} scattering production cross section |
B1_SCATTP1 | 2G | Total P_{1} scattering production cross section |
B1_SCATTP2 | 2G | Total P_{2} scattering production cross section |
B1_SCATTP3 | 2G | Total P_{3} scattering production cross section |
B1_SCATTP4 | 2G | Total P_{4} scattering production cross section |
B1_SCATTP5 | 2G | Total P_{5} scattering production cross section |
B1_SCATTP6 | 2G | Total P_{6} scattering production cross section |
B1_SCATTP7 | 2G | Total P_{7} scattering production cross section |
Scattering matrices
Notes:
- Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.
- The order of values ([input].coe) or value pairs ([input]_res.m) is: where refers to scattering from group g to g'.
- The data in the _res.m file can be read into a G by G matrix with Matlab reshape-command, for example:
reshape(B1_S0(idx,1:2:end), G, G).
Parameter | Size | Description |
---|---|---|
B1_S0 | 4G^{2} | P_{0} scattering matrix |
B1_S1 | 4G^{2} | P_{1} scattering matrix |
B1_S2 | 4G^{2} | P_{2} scattering matrix |
B1_S3 | 4G^{2} | P_{3} scattering matrix |
B1_S4 | 4G^{2} | P_{4} scattering matrix |
B1_S5 | 4G^{2} | P_{5} scattering matrix |
B1_S6 | 4G^{2} | P_{6} scattering matrix |
B1_S7 | 4G^{2} | P_{7} scattering matrix |
B1_SP0 | 4G^{2} | P_{0} scattering production matrix |
B1_SP1 | 4G^{2} | P_{1} scattering production matrix |
B1_SP2 | 4G^{2} | P_{2} scattering production matrix |
B1_SP3 | 4G^{2} | P_{3} scattering production matrix |
B1_SP4 | 4G^{2} | P_{4} scattering production matrix |
B1_SP5 | 4G^{2} | P_{5} scattering production matrix |
B1_SP6 | 4G^{2} | P_{6} scattering production matrix |
B1_SP7 | 4G^{2} | P_{7} scattering production matrix |
Diffusion parameters
Parameter | Size | Description |
---|---|---|
B1_TRANSPXS | 2G | Transport cross section (calculated from diffusion coefficient) |
B1_DIFFCOEF | 2G | Diffusion coefficient |
Poison cross sections
Notes:
- Printed only if poison cross section option is on (see set poi).
Parameter | Size | Description |
---|---|---|
B1_I135_YIELD | 2G | Fission yield of I-135 (cumulative, includes all precursors) |
B1_XE135_YIELD | 2G | Fission yield of Xe-135 |
B1_PM149_YIELD | 2G | Fission yield of Pm-149 (cumulative, includes all precursors) |
B1_SM149_YIELD | 2G | Fission yield of Sm-149 |
B1_I135_MICRO_ABS | 2G | Microscopic absorption cross section of I-135 |
B1_XE135_MICRO_ABS | 2G | Microscopic absorption cross section of Xe-135 |
B1_PM149_MICRO_ABS | 2G | Microscopic absorption cross section of Pm-149 |
B1_SM149_MICRO_ABS | 2G | Microscopic absorption cross section of Sm-149 |
B1_XE135_MACRO_ABS | 2G | Macroscopic absorption cross section of Xe-135 |
B1_SM149_MACRO_ABS | 2G | Macroscopic absorption cross section of Sm-149 |
Delayed neutron data
Notes:
- The output always consists of 9 values: total, followed by precursor group-wise values. If the number of groups is 6, the last two values are zero.
- The actual number of groups depends on the cross section library used in the calculations. JEFF-3.1, JEFF.3.2 and later evaluations use 8 precursor groups, while earlier evaluations, as well as all ENDF/B and JENDL data is based on 6 groups.
Parameter | Size | Description |
---|---|---|
BETA_EFF | 9 | Effective delayed neutron fraction (currently calculated using the Meulekamp method) |
LAMBDA | 9 | Decay constants |
Assembly discontinuity factors
Notes:
- Calculation of assembly discontinuity factors requires the set adf option.
- Surface flux and current tallies are used to calculate the boundary currents and fluxes. Mid-point and corner values are approximated by integrating over a small surface segment.
- Fluxes and currents are normalized average values.
- When the homogenized region is surrounded by reflective boundary conditions (zero net-current) the homogeneous flux becomes flat and equal to the volume-averaged heterogeneous flux. When the net currents are non-zero, the homogeneous flux is obtained using the Built-in diffusion flux solver.
- The calculation currently supports only a limited number of surface types: infinite planes and square and hexagonal prisms.
- The order of surface and mid-point values for square prisms is: and the order of corner values: where refers to parameter on surface/corner k and energy group g.
- The order of surface and mid-point values for Y-type hexagonal prims runs clockwise starting from the north. The corner values start from the next corner in clockwise direction.
- The order of surface and mid-point values for X-type hexagonal prims runs counterclockwise starting from the east. Confirm the direction of corner values.
- Note that one should confirm the order of values in the hexagonal prisms.
Parameter | Size | Description |
---|---|---|
DF_SURFACE | (string) | Name of the surface used for the calculation |
DF_SYM | 1 | Symmetry option defined in the input |
DF_N_SURF | 1 | Number of surface values (denoted as N_{S} below) |
DF_N_CORN | 1 | Number of corner values (denoted as N_{C} below) |
DF_VOLUME | 1 | Volume (3D) or cross sectional area (2D) of the homogenized cell |
DF_SURF_AREA | N_{S} | Area (3D) or perimeter length (2D) of the surface region |
DF_MID_AREA | N_{S} | Area (3D) or perimeter length (2D) of the mid-point region |
DF_CORN_AREA | N_{S} | Area (3D) or perimeter length (2D) of the corner region |
DF_SURF_IN_CURR | 2G N_{S} | Inward surface currents |
DF_SURF_OUT_CURR | 2G N_{S} | Outward surface currents |
DF_SURF_NET_CURR | 2G N_{S} | Net surface currents |
DF_MID_IN_CURR | 2G N_{S} | Inward mid-point currents |
DF_MID_OUT_CURR | 2G N_{S} | Outward mid-point currents |
DF_MID_NET_CURR | 2G N_{S} | Net mid-point currents |
DF_CORN_IN_CURR | 2G N_{C} | Inward corner currents |
DF_CORN_OUT_CURR | 2G N_{C} | Outward corner currents |
DF_CORN_NET_CURR | 2G N_{C} | Net corner currents |
DF_HET_VOL_FLUX | 2G | Heterogeneous flux over homogenized cell |
DF_HET_SURF_FLUX | 2G N_{S} | Heterogeneous surface flux |
DF_HET_CORN_FLUX | 2G N_{C} | Heterogeneous corner flux |
DF_HOM_VOL_FLUX | 2G | Homogeneous flux over homogenized cell |
DF_HOM_SURF_FLUX | 2G N_{C} | Homogeneous surface flux |
DF_HOM_CORN_FLUX | 2G N_{C} | Homogeneous corner flux |
DF_SURF_DF | 2G N_{C} | Surface discontinuity factors |
DF_CORN_DF | 2G N_{C} | Corner discontinuity factors |
Pin-power form factors
Notes:
- Calculation of pin-power form factors requires the set ppw option.
- The power distribution is calculated by tallying the few-group fission energy deposition in each lattice position and dividing the values with the total energy produced in the universe (sum over all values of PPW_POW equals 1).
- The calculation of form factors depends on the boundary conditions:
- If the homogenized region is surrounded by reflective boundary conditions (zero net-current), the homogeneous flux becomes flat and equal to the volume-averaged heterogeneous flux. Variables PPW_HOM_FLUX and PPW_FF are then omitted.
- When the net currents are non-zero, the homogeneous flux is obtained using the built-in diffusion flux solver. The form-factors (PPW_FF) are obtained by dividing the pin- and group-wise powers with the corresponding homogeneous diffusion flux (PPW_HOM_FLUX).
- Running the diffusion flux solver currently requires ADF calculation.
- The order of values is: where refers to parameter of pin n and energy group g. For example, two-group power distributions in a 1717 lattice can be converted into matrix form using the reshape-command in Matlab:
P1 = reshape(PPW_POW(1,1:4:end), 17, 17); P2 = reshape(PPW_POW(1,3:4:end), 17, 17);
Parameter | Size | Description |
---|---|---|
PPW_LATTICE | (string) | Name of the lattice used for the calculation |
PPW_LATTICE_TYPE | 1 | Lattice type (corresponds to the lat-card) |
PPW_PINS | 1 | Number of pin positions in the lattice (denoted as N_{P} below) |
PPW_POW | 2G N_{P} | Pin-wise power distribution |
PPW_HOM_FLUX | 2G N_{P} | Pin-wise homogeneous flux distribution |
PPW_FF | 2G N_{P} | Pin-wise form factors |
Albedos
Notes:
- Calculation of albedos requires the set alb option.
- The order of the surfaces should be the same as for the ADFs.
- The order of ALB_IN_CURR is where refers to incoming partial current of surface k of group g'.
- The order of ALB_OUT_CURR is where refers to outgoing partial current of surface k of group g which has entered the albedo surface through surface k and group g.
- The order of ALB_TOT_ALB is where refers to albedo from group g to g'.
- The order of ALB_PART_ALB is where refers to albedo of surface k of group g which has entered the albedo surface through surface k and group g.
- For example, two-group hexagonal partial albedos can be converted into matrix form using the reshape-command in Matlab with the notation part_alb(g', k', g, k) as
part_alb = reshape(ALB_PART_ALB(1, 1:2:end), 2, 6, 2, 6)
Parameter | Size | Description |
---|---|---|
ALB_SURFACE | (string) | Name of the surface used for the calculation |
ALB_FLIP_DIR | 1 | |
ALB_N_SURF | 1 | Number of albedo surface faces (denoted as N_{S} below) |
ALB_IN_CURR | 2G N_{S} | Groupwise incoming partial currents of albedo surface faces |
ALB_OUT_CURR | 2G^{2} N_{S}^{2} | Outgoing group to group and face to face outgoing partial currents |
ALB_TOT_ALB | 2G^{2} | Total group to group albedos for the entire albedo surface |
ALB_PART_ALB | 2G^{2} N_{S}^{2} | Partial group to group and face to face albedos |
Miscellaneous notes for other outputs
Delayed neutrons accounted for in ANA_KEFF
Since Serpent 2.1.23, ANA_KEFF estimator is calculated separately for delayed neutrons. The first two values are total, 3-4 are prompt neutron multiplication only and 5-6 delayed neutron multiplication only. ^{[3]}
References
- ^ Leppänen, J., Pusa, M. and Fridman, E. "Overview of methodology for spatial homogenization in the Serpent 2 Monte Carlo code." Ann. Nucl. Energy, 96 (2016) 126-136.
- ^ Liu, Z., Smith, K., Forget, B. and Ortensi, J."Cumulative migration method for computing rigorous diffusion coefficients and transport cross sections from Monte Carlo." Ann. Nucl. Energy, 118 (2018) 507-516.
- ^ http://ttuki.vtt.fi/serpent/viewtopic.php?f=25&t=1885&p=4469