Monitoring-of-conservation-laws.md

 **VERSION>=2022.04.05**  
 
 The W-SLDA Toolkit uses conserved quantities to monitor the stability of time integration. The quantities of special interest are:
-* _Particle number_ ($`N_a+N_b`$): this quantity is conserved almost for all cases. The special case when the total particle number may not be conserved is the situation when an external pairing field is activated. 
+* _Particle number_ ($`N_a+N_b`$): this quantity is conserved for almost all cases. The special case in which the total particle number may not be conserved arises when an external pairing field is applied. 
 * _Total energy_: if there is no time-dependent external potential, the energy is conserved. 
 
 To avoid situations where the code uses computing resources for generating trajectories that are incorrect (violation of conservation laws) there is build in mechanism for monitoring conservation laws. This option is controlled by the following tags in the input file:
@@ -17,7 +17,7 @@ To avoid situations where the code uses computing resources for generating traje
 # Nconservation_stop        10000    # Stop to monitor total particle number conservation at time*eF, default=1e12 (infinity)
 # Nconservation_tol         0.05     # if |[N(t)-N(start_t)]/N(start_t)|>tol then the code will terminate, default=0.05
 ``` 
-Note that the energy conservation checking is disabled by default while particle number conservation monitoring is activated. If the violation (measured as deviation from the initial value) is detected, the code terminates. The information will be displays in `stdout` file:
+Note that the energy conservation checking is disabled by default, while particle number conservation monitoring is activated. If the violation (measured as deviation from the initial value) is detected, the code terminates. The information will be displayed in the `stdout` file:
 ```
 # SIMULATION INSTABILITY CRITERIA MET FOR PARTICLE NUMBER!!!
 # INITIAL VALUE=19.000000, PRESENT VALUE=20.351277, RELATIVE CHANGE=0.07112 [> 0.050000]
@@ -29,7 +29,7 @@ If the checkpoint tag is selected
 ```bash
 checkpoint              1       # do checkpoint at the end of the calculation?
 ```
-then immediately after terminating the code, the checkpoint files will be created
+then, immediately after terminating the code, the checkpoint files will be created
 ```
 # SIMULATION INSTABILITY CRITERIA MET FOR PARTICLE NUMBER!!!
 # INITIAL VALUE=19.000000, PRESENT VALUE=20.351277, RELATIVE CHANGE=0.07112 [> 0.050000]