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Equations Supported by GlobalWorks™
Fitting of up to five species is possible using the Olis Global Fitting Program. Listed below are the equations offered for each possible number of species. If you know of any fitting equation that is not currently supported by the Olis software, please let us know.
Color Key
Species shown in color (red, blue, green, & purple) indicate colored species. Species shown in gray indicate colorless species.
A®B
Single Colored Species Cases
| Pure First Order Process |
A®B |
| Pure Second Order Process |
A®B |
| First Order Rise |
A®B |
| Polynomial Fit |
A®B |
| Pure Zeroth Order Process |
A®B |
A®P,
Multiple Rates, Special Cases
| 2 Exponentials, 1 Species |
A®P |
| 2 Exponentials with Background, 1 Species |
A®P |
| 3 Exponentials, 1 species |
A®P |
| 3 Exponentials with Background, 1 Species |
A®P |
Two Species Cases
| First Order with Growing in |
A®B |
| Reversible First Order |
A«B |
| First Order with Background |
A®C, B |
| Two First Order Decays |
A®C, B®C |
| Second Order with Growing in |
A+A®B |
| Second Order Decay with Background |
A+A®C, B |
Three Species Cases
| Normal Rise Fall |
A®B®C |
| Special Rise Fall |
A®B+C,
B®C |
| Rise-Fall, Step 1 Reversible |
A«B®C |
| Rise-Fall, Step 2 Reversible |
A®B«C |
| Reversible Rise-Fall |
A«B«C |
| 1 Exponential Growing In, 1 Independent Exponential Decaying |
A®B, C®D |
| 1 Exponential Decaying, 1 Independent Exponential Growing in |
A®D, B®C |
| 2 Independent Exponentials, Same Product |
A®B, C®B |
| 2 Independent Exponentials with Background |
A®D, B®D, C®D |
| 3 Independent Exponentials |
A®D, B®D, C®D |
| Irreversible Heterogeneous Second, 3 Concentrations |
A+B®C |
| Reversible Heterogeneous Second, 3 Concentrations |
A+B«C |
| 1 Exponential Rise, Second Order Fall |
A®B, B+B®C+A |
| Mixed Reduction Reactions |
A®B, C®D, B+C®A+D |
Four Species Cases
| Irreversible 4 Species Sequential |
A®B®C®D |
| 4 Species Sequential with First Process Reversible |
A«B®C®D |
| Reversible 4 Species Sequential |
A«B«C«D |
| 3 Independent Exponentials with Background |
A®E, B®E, C®E, D |
| 4 Independent Exponentials |
A®E, B®E, C®E, D®E |
| 4 Species Branching Reaction |
A«B, B«C, B«D |
| Enzyme Reaction with Second Order Terms, 4 Species |
A+B«C«D+A |
Five Species Cases
| Irreversible 5 Species Sequential |
A® B® C® D® E |
| Reversible 5 Species Sequential |
A« B« C« D« E |
| 4 Independent Exponentials with Background |
A® F,
B®
F, C® F,
D®
F, E® F |
| 5 Independent Exponentials |
A® F,
B®
F, C® F,
D®
F, E® F |
Enzyme Reactions with Second Order Terms,
6 Species |
A+B« C« D« E+A |
Formation of Differential Matrix
Mechanism
Rate equation in differential form
| dA/dt = -k1(A) |
+0 |
+0 |
| dB/dt = +k1(A) |
-k2(B) |
+0 |
| dC/dt = 0 |
+k2(B) |
+0 |
Matrix derived from above by removing the concentration terms
| -k1 |
0 |
0 |
| +k1 |
-k2 |
0 |
| 0 |
+k2 |
0 |
It is this matrix itself which is solved by Matrix Exponentiation!
In this way, Matrix Exponentiation provides an exact solution of the rate equation.
We could say "instantaneous" and be fully accurate!
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