improve equations display

degradation_model/tuning_code/readme.md

@@ -12,7 +12,7 @@ We adopt a sequential tuning process and it includes 4 steps:
 3. The vector of degradation mechanism parameters P to be tuned in step 1 are:
 $$P_\mathrm{cal} = \left[k_{0,\mathrm{SEI}},D_\mathrm{SEI},E_{a,\mathrm{SEI}}\right]^T $$
 4. The vector of data to be fitted against model outputs are:
-$$Y_\R\mathrm{cal} = \left[C, n_\mathrm{Li},y_0,x_{100}\right]^T$$
+$$Y_\mathrm{cal} = \left[C, n_\mathrm{Li},y_0,x_{100}\right]^T$$
 
 ### Input Data Required:
 eSOH parameters $[x_0,x_{100},y_0,y_{100},C_n,C_p,C,n_{Li}]$ at RPTs for calendar aging cells at multiple temperatures
@@ -46,7 +46,7 @@ Initializes the model and experiment for the particular cell number.
 ## Step 2
 1. After step 1, we tune the mechanical damage model parameters and lithium plating model parameters together using the cycling aging data at multiple C-rates
 2. The vector of degradation mechanism parameters P to be tuned in step 2 are:
-$$P_\mathrm{cyc} = \left[\beta^-_{\mathrm{LAM},1},\beta^-_{\mathrm{LAM},2},\beta^+_{\mathrm{LAM},1},\beta^+_{\mathrm{LAM},2},m_{\mathrm{LAM}},k_\mathrm{pl}\right] $$
+$$P_\mathrm{cyc} = \left[\beta^-_{\mathrm{LAM},1},\beta^-_{\mathrm{LAM},2},\beta^+_{\mathrm{LAM},1},\beta^+_{\mathrm{LAM},2},m_{\mathrm{LAM}},k_\mathrm{pl}\right]$$
 3. The vector of data to be fitted against model outputs are:
 $$Y_\mathrm{cyc} = \left[C, n_\mathrm{Li},C_n,C_p\right]^T$$
 4. The parameters $P_{cyc}$ were tuned based on the data sets $Y_{cyc}$ extracted from the RPTs of the cycling cells at charge-discharges rates of C/5-C/5%–100%DOD, 1.5C-1.5C-100%DOD, and C/5-1.5C-100%DOD. The reason for tuning the model using the three cells together is to establish the C-rate dependency of the mechanical damage and Li plating models. Using data from a single C-rate would be insufficient to get the C-rate dependency correct in the model. 
@@ -57,7 +57,7 @@ $$Y_\mathrm{cyc} = \left[C, n_\mathrm{Li},C_n,C_p\right]^T$$
 1. eSOH parameters $[x_0,x_{100},y_0,y_{100},C_n,C_p,C,n_{Li}]$ at RPTs for cycling aging cells at multiple C-rates
 2. Output of step 1 i.e. parameters tuned in step 1.
 ### Output of Tuning:
-$$P_\mathrm{cyc} = \left[\beta^-_{\mathrm{LAM},1},\beta^-_{\mathrm{LAM},2},\beta^+_{\mathrm{LAM},1},\beta^+_{\mathrm{LAM},2},m_{\mathrm{LAM}},k_\mathrm{pl}\right] $$
+$$P_\mathrm{cyc} = \left[\beta^-_{\mathrm{LAM},1},\beta^-_{\mathrm{LAM},2},\beta^+_{\mathrm{LAM},1},\beta^+_{\mathrm{LAM},2},m_{\mathrm{LAM}},k_\mathrm{pl}\right]$$
 
 ### Code for executing step:
 To perform step 2, please run this [notebook](./step_2_cycling.ipynb)
@@ -104,7 +104,7 @@ $$P_\mathrm{expansion} = \left[b_\mathrm{SEI}, b_\mathrm{pl}, b^-_\mathrm{in},b^
 3. Expansion data at RPTs for the chose cells
 
 ### Output of Tuning:
-$$ P_\mathrm{expansion} = \left[b_\SEI, b_\mathrm{pl}, b^-_\mathrm{in},b^+_\mathrm{in}\right]$$
+$$P_\mathrm{expansion} = \left[b_\SEI, b_\mathrm{pl}, b^-_\mathrm{in},b^+_\mathrm{in}\right]$$
 
 ### Code for executing step:
 To perform step 4, please run this [notebook](./step_4_expansion.ipynb)