diff --git a/t3/utils/flux.py b/t3/utils/flux.py
index 6ef34655..903614fb 100644
--- a/t3/utils/flux.py
+++ b/t3/utils/flux.py
@@ -304,13 +304,24 @@ def set_batch_p(gas: ct.Solution,
     network.rtol = r_tol
     return network, reactor
 
-def closest_bigger_number(array, target):
-    # Filter the numbers greater than the target
+def closest_bigger_number(array: List[float],
+                          target: float,
+                          ) -> Tuple[Optional[float], Optional[int]]:
+    """
+    Find the min number in an array that is greater than the target number.
+    Args:
+    - array (List[float]): List of numbers to search through.
+    - target (float): The target number.
+    Returns:
+    - Tuple[num[float], i[int]]: A tuple containing the min bigger number (num) and its index (i) in the originaul array.
+      If no number greater than the target is found, both elements in the tuple will be None.
+    """
+    # Filter out the numbers smaller than the target
     candidates = [(num, i) for i, num in enumerate(array) if num > target]
-    # Find the closest bigger number
+    # Find the min bigger number
     if candidates:
-        m, i = min(candidates, key=lambda x: x[0])
-        return m, i
+        num, i = min(candidates, key=lambda x: x[0])
+        return num, i
     else:
         return None, None  # No number greater than the target was found
 
@@ -322,7 +333,7 @@ def run_jsr(gas: ct.Solution,
             V: Optional[float] = None,
             a_tol: float = 1e-16,
             r_tol: float = 1e-10,
-            tau_tolerance: float = 0.1,
+            tau_tolerance: float = 0.005,
             ) -> Dict[float, dict]:
     """
     Run a JSR reactor with constant pressure, constant temperature, and constant volume.
@@ -336,7 +347,9 @@ def run_jsr(gas: ct.Solution,
         V (float, optional): The reactor volume in cm^3.
         a_tol (float, optional): The absolute tolerance for the simulation.
         r_tol (float, optional): The relative tolerance for the simulation.
-        tau_tolerance (float, optional): Cantera will solve JSR equations with step() till tau*tolerance time, after that, it will solve them by advance(t_i). This will adress stiff equestion in which small time steps are required.
+        tau_tolerance (float, optional): Cantera will solve JSR equations with step()
+        till tau * tolerance time, after that, it will solve them by advance(t_i).
+        This will adress stiff equestion in which small time steps are required.
 
     Returns:
         dict: The T, P, X, and ROP profiles (values) at a specific time.
@@ -347,34 +360,29 @@ def run_jsr(gas: ct.Solution,
     stoichiometry = get_rxn_stoichiometry(gas)
     for tau in times:
         t = 0
-        dt = tau/num_steps
+        dt = tau / num_steps
         time_steps_array = np.arange(t, tau+dt, dt) #the last number is tau
         network, reactor = set_jsr(gas=gas, time=tau, composition=composition, T=T, P=P, V=V, a_tol=a_tol, r_tol=r_tol)
-        while t <= tau*tau_tolerance:
+        while t <= tau * tau_tolerance:
             network.step()
-            #update the system's time
-            t = network.time
-        if t > tau*tau_tolerance:
-            #get the current time of the system after step()
-            #find the closest_bigger time value in time_array, and continue with advance func
             t = network.time
-            t_array, t_step_index = closest_bigger_number(time_steps_array, t)
-            t = t_array
-            while t_step_index < len(time_steps_array) -1 : #till t =tau
-                rops = {spc.name: dict() for spc in gas.species()}
-                network.advance(t)
-                t_step_index +=1
-                t = time_steps_array[t_step_index]
-                cantera_reaction_rops = gas.net_rates_of_progress
-                for spc in gas.species():
-                    for i, rxn in enumerate(gas.reactions()):
-                        if stoichiometry[spc.name][i]:
-                            if rxn.equation not in rops[spc.name].keys():
-                                rops[spc.name][rxn.equation] = 0
-                            rops[spc.name][rxn.equation] += cantera_reaction_rops[i] * stoichiometry[spc.name][i]
-                profile = {'P': gas.P, 'T': gas.T, 'X': {s.name: x for s, x in zip(gas.species(), gas.X)}, 'ROPs': rops}
-                if t == tau:
-                    profiles[t] = profile
+        t = network.time
+        t, t_step_index = closest_bigger_number(time_steps_array, t)
+        while t_step_index < len(time_steps_array) -1 : #till t =tau
+            rops = {spc.name: dict() for spc in gas.species()}
+            network.advance(t)
+            t_step_index +=1
+            t = time_steps_array[t_step_index]
+            cantera_reaction_rops = gas.net_rates_of_progress
+            for spc in gas.species():
+                for i, rxn in enumerate(gas.reactions()):
+                    if stoichiometry[spc.name][i]:
+                        if rxn.equation not in rops[spc.name].keys():
+                            rops[spc.name][rxn.equation] = 0
+                        rops[spc.name][rxn.equation] += cantera_reaction_rops[i] * stoichiometry[spc.name][i]
+            profile = {'P': gas.P, 'T': gas.T, 'X': {s.name: x for s, x in zip(gas.species(), gas.X)}, 'ROPs': rops}
+            if t == tau:
+                profiles[t] = profile
     return profiles
 
 def run_batch_p(gas: ct.Solution,