def system_jacobian(self, state_vars, time):
current, theta, potential=state_vars
if self.simulation_options["method"]=="sinusoidal":
Et=isolver_martin_brent.et(self.nd_param.nd_param_dict["E_start"],self.nd_param.nd_param_dict["nd_omega"], self.nd_param.nd_param_dict["phase"], self.nd_param.nd_param_dict["d_E"], time)
dEdt=isolver_martin_brent.dEdt(self.nd_param.nd_param_dict["nd_omega"], self.nd_param.nd_param_dict["phase"], self.nd_param.nd_param_dict["d_E"], time)
elif self.simulation_options["method"]=="ramped":
Et=isolver_martin_brent.c_et(self.nd_param.nd_param_dict["E_start"], self.nd_param.nd_param_dict["E_reverse"], (self.nd_param.nd_param_dict["E_reverse"]-self.nd_param.nd_param_dict["E_start"]) ,self.nd_param.nd_param_dict["nd_omega"], self.nd_param.nd_param_dict["phase"], 1,self.nd_param.nd_param_dict["d_E"],time)
dEdt=isolver_martin_brent.c_dEdt(self.nd_param.nd_param_dict["tr"] ,self.nd_param.nd_param_dict["nd_omega"], self.nd_param.nd_param_dict["phase"], 1,self.nd_param.nd_param_dict["d_E"],time)
elif self.simulation_options["method"]=="dcv":
Et=isolver_martin_brent.dcv_et(self.nd_param.nd_param_dict["E_start"], self.nd_param.nd_param_dict["E_reverse"], (self.nd_param.nd_param_dict["E_reverse"]-self.nd_param.nd_param_dict["E_start"]) , 1,time)
dEdt=isolver_martin_brent.dcv_dEdt(self.nd_param.nd_param_dict["tr"],1,time)
Er=Et-(self.nd_param.nd_param_dict["Ru"]*current)
ErE0=Er-self.nd_param.nd_param_dict["E_0"]
alpha=self.nd_param.nd_param_dict["alpha"]
exp11=self.nd_param.nd_param_dict["k_0"]*np.exp((1-alpha)*ErE0)
exp12=self.nd_param.nd_param_dict["k_0"]*np.exp((-alpha)*ErE0)
Cdlp=self.nd_param.nd_param_dict["Cdl"]*(1+self.nd_param.nd_param_dict["CdlE1"]*Er+self.nd_param.nd_param_dict["CdlE2"]*(Er**2)+self.nd_param.nd_param_dict["CdlE3"]*(Er**3))
jacobian=np.zeros((2, 2))
dtheta_dI=(-(1-theta)*(1-alpha)*exp11*self.nd_param.nd_param_dict["Ru"])-(theta*alpha*self.nd_param.nd_param_dict["Ru"]*exp12)
#dtheta_dE=((1-theta)*(1-alpha)*exp11)+(theta*alpha*exp12)
dtheta_dtheta=-exp11-exp12
jacobian[1, :]=[dtheta_dI, dtheta_dtheta]
jacobian[0, 0]=(-1/(self.nd_param.nd_param_dict["Ru"]*Cdlp))+(self.nd_param.nd_param_dict["gamma"]/Cdlp*self.nd_param.nd_param_dict["Ru"])*dtheta_dI
#jacobian[0, 1]=(self.nd_param.nd_param_dict["gamma"]/Cdlp*self.nd_param.nd_param_dict["Ru"])*dtheta_dE
jacobian[0, 1]=(self.nd_param.nd_param_dict["gamma"]/Cdlp*self.nd_param.nd_param_dict["Ru"])*dtheta_dtheta
return jacobian
def voltage_query(self, time):
if self.current_class.simulation_options["method"] == "sinusoidal":
Et = isolver_martin_brent.et(
self.nd_param.nd_param_dict["E_start"],
self.nd_param.nd_param_dict["nd_omega"],
self.nd_param.nd_param_dict["phase"],
self.nd_param.nd_param_dict["d_E"], time)
dEdt = isolver_martin_brent.dEdt(
self.nd_param.nd_param_dict["nd_omega"],
self.nd_param.nd_param_dict["phase"],
self.nd_param.nd_param_dict["d_E"], time)
elif self.current_class.simulation_options["method"] == "ramped":
Et = -1 * isolver_martin_brent.c_et(
self.nd_param.nd_param_dict["E_start"],
self.nd_param.nd_param_dict["E_reverse"],
(self.nd_param.nd_param_dict["E_reverse"] -
self.nd_param.nd_param_dict["E_start"]),
self.nd_param.nd_param_dict["nd_omega"],
self.nd_param.nd_param_dict["phase"], 1,
self.nd_param.nd_param_dict["d_E"], time)
dEdt = -1 * isolver_martin_brent.c_dEdt(
self.nd_param.nd_param_dict["tr"],
self.nd_param.nd_param_dict["nd_omega"],
self.nd_param.nd_param_dict["phase"], 1,
self.nd_param.nd_param_dict["d_E"], time)
elif self.current_class.simulation_options["method"] == "dcv":
Et = isolver_martin_brent.dcv_et(
self.nd_param.nd_param_dict["E_start"],
self.nd_param.nd_param_dict["E_reverse"],
(self.nd_param.nd_param_dict["E_reverse"] -
self.nd_param.nd_param_dict["E_start"]), 1, time)
dEdt = isolver_martin_brent.dcv_dEdt(
self.nd_param.nd_param_dict["tr"], 1, time)
elif self.current_class.simulation_options["method"] == "square_wave":
time_position = int(np.ceil(time))
Et = SWV_surface.potential(
time_position, self.nd_param.nd_param_dict["sampling_factor"],
self.nd_param.nd_param_dict["scan_increment"],
self.nd_param.nd_param_dict["SW_amplitude"], self.nd_param.
nd_param_dict["E_start"]) / self.nd_param.sw_class.c_E0
dEdt = None
elif self.current_class.simulation_options[
"method"] == "square_wave_fourier":
Et = SWV_surface.fourier_Et(
math.pi, self.nd_param.nd_param_dict["scan_increment"],
self.nd_param.nd_param_dict["fourier_order"],
self.nd_param.nd_param_dict["SW_amplitude"],
self.nd_param.nd_param_dict["E_start"], time)
dEdt = SWV_surface.fourier_dEdt(
math.pi, self.nd_param.nd_param_dict["scan_increment"],
self.nd_param.nd_param_dict["fourier_order"],
self.nd_param.nd_param_dict["SW_amplitude"], time)
#print(Et)
Et = Et / self.nd_param.sw_class.c_E0
dEdt = dEdt / self.nd_param.sw_class.c_E0
return Et, dEdt
def define_voltages(self):
voltages=np.zeros(len(self.time_vec))
if self.simulation_options["method"]=="sinusoidal":
for i in range(0, len(self.time_vec)):
voltages[i]=isolver_martin_brent.et(self.nd_param.E_start,self.nd_param.nd_omega, self.nd_param.phase, self.nd_param.d_E, (self.time_vec[i]))
elif self.simulation_options["method"]=="ramped":
for i in range(0, len(self.time_vec)):
voltages[i]=isolver_martin_brent.c_et(self.nd_param.E_start, self.nd_param.E_reverse, (self.nd_param.E_reverse-self.nd_param.E_start) ,self.nd_param.nd_omega, self.nd_param.phase, 1,self.nd_param.d_E,(self.time_vec[i]))
elif self.simulation_options["method"]=="dcv":
for i in range(0, len(self.time_vec)):
voltages[i]=isolver_martin_brent.dcv_et(self.nd_param.E_start, self.nd_param.E_reverse, (self.nd_param.E_reverse-self.nd_param.E_start) , 1,(self.time_vec[i]))
return voltages
def define_voltages(self, transient=False):
voltages=np.zeros(len(self.time_vec))
if self.simulation_options["method"]=="sinusoidal":
for i in range(0, len(self.time_vec)):
voltages[i]=isolver_martin_brent.et(self.nd_param.nd_param_dict["E_start"],self.nd_param.nd_param_dict["nd_omega"], self.nd_param.nd_param_dict["phase"], self.nd_param.nd_param_dict["d_E"], (self.time_vec[i]))
elif self.simulation_options["method"]=="ramped":
for i in range(0, len(self.time_vec)):
voltages[i]=isolver_martin_brent.c_et(self.nd_param.nd_param_dict["E_start"], self.nd_param.nd_param_dict["E_reverse"], (self.nd_param.nd_param_dict["E_reverse"]-self.nd_param.nd_param_dict["E_start"]) ,self.nd_param.nd_param_dict["nd_omega"], self.nd_param.nd_param_dict["phase"], 1,self.nd_param.nd_param_dict["d_E"],(self.time_vec[i]))
elif self.simulation_options["method"]=="dcv":
for i in range(0, len(self.time_vec)):
voltages[i]=isolver_martin_brent.dcv_et(self.nd_param.nd_param_dict["E_start"], self.nd_param.nd_param_dict["E_reverse"], (self.nd_param.nd_param_dict["E_reverse"]-self.nd_param.nd_param_dict["E_start"]) , 1,(self.time_vec[i]))
if transient==True:
voltages=voltages[self.time_idx]
return voltages
def current_ode_sys(self, state_vars, time):
current, theta, potential=state_vars
if self.simulation_options["method"]=="sinusoidal":
Et=isolver_martin_brent.et(self.nd_param.nd_param_dict["E_start"],self.nd_param.nd_param_dict["nd_omega"], self.nd_param.nd_param_dict["phase"], self.nd_param.nd_param_dict["d_E"], time)
dEdt=isolver_martin_brent.dEdt(self.nd_param.nd_param_dict["nd_omega"], self.nd_param.nd_param_dict["phase"], self.nd_param.nd_param_dict["d_E"], time)
elif self.simulation_options["method"]=="ramped":
Et=isolver_martin_brent.c_et(self.nd_param.nd_param_dict["E_start"], self.nd_param.nd_param_dict["E_reverse"], (self.nd_param.nd_param_dict["E_reverse"]-self.nd_param.nd_param_dict["E_start"]) ,self.nd_param.nd_param_dict["nd_omega"], self.nd_param.nd_param_dict["phase"], 1,self.nd_param.nd_param_dict["d_E"],time)
dEdt=isolver_martin_brent.c_dEdt(self.nd_param.nd_param_dict["tr"] ,self.nd_param.nd_param_dict["nd_omega"], self.nd_param.nd_param_dict["phase"], 1,self.nd_param.nd_param_dict["d_E"],time)
elif self.simulation_options["method"]=="dcv":
Et=isolver_martin_brent.dcv_et(self.nd_param.nd_param_dict["E_start"], self.nd_param.nd_param_dict["E_reverse"], (self.nd_param.nd_param_dict["E_reverse"]-self.nd_param.nd_param_dict["E_start"]) , 1,time)
dEdt=isolver_martin_brent.dcv_dEdt(self.nd_param.nd_param_dict["tr"],1,time)
Er=Et-(self.nd_param.nd_param_dict["Ru"]*current)
ErE0=Er-self.nd_param.nd_param_dict["E_0"]
alpha=self.nd_param.nd_param_dict["alpha"]
self.Cdlp=self.nd_param.nd_param_dict["Cdl"]*(1+self.nd_param.nd_param_dict["CdlE1"]*Er+self.nd_param.nd_param_dict["CdlE2"]*(Er**2)+self.nd_param.nd_param_dict["CdlE3"]*(Er**3))
d_thetadt=((1-theta)*self.nd_param.nd_param_dict["k_0"]*np.exp((1-alpha)*ErE0))-(theta*self.nd_param.nd_param_dict["k_0"]*np.exp((-alpha)*ErE0))
dIdt=(dEdt-(current/self.Cdlp)+self.nd_param.nd_param_dict["gamma"]*d_thetadt*(1/self.Cdlp))/self.nd_param.nd_param_dict["Ru"]
f=[dIdt, d_thetadt, dEdt]
return f