Update README.md

examples/nonconvex/tidalfarm/README.md

@@ -7,7 +7,7 @@ using the conditional gradient method.
 
 ![](output/26-January-2023-12-12-15_solution_best_N=100_online_version.png)
 |:--:| 
-*Optimal turbine density*
+*Optimal turbine friction*
 
 Using the conditional gradient method, we can compute a tidal-stream farm layout
 which maximizes energy extraction. The setting used for this application is descriped
@@ -81,21 +81,28 @@ We use $u=c_t(d)$, the turbine friction, as the control, not the turbine density
 The power function $J_{\text{power}}$ is defined by (see [eq. (3.10)](https://link.springer.com/book/10.1007/978-3-319-59483-5))
 
 $$
- J_{\text{power}}(y, u) = \int_{\text{array}} u(x) \|y(x)\|_2^3 \mathrm{d} x
+ J_{\text{power}}(y, u) = \int_{\text{array}} \rho u(x) \|y(x)\|_2^3 \mathrm{d} x
 $$
 
 where $\rho$ is the water density. See also [power_functionals.py](https://github.com/OpenTidalFarm/OpenTidalFarm/blob/master/opentidalfarm/functionals/power_functionals.py) and [steady_sw.py](https://github.com/OpenTidalFarm/OpenTidalFarm/blob/ca1aa59ee17818dc3b1ab94a9cbc735527fb2961/opentidalfarm/problems/steady_sw.py#L60).
 
-The objective function $J$, the profit, is defined by (see [eq. (3.11)](https://link.springer.com/book/10.1007/978-3-319-59483-5))
+The profit $J_{profit}$ to be maximized is defined by (see [eq. (3.11)](https://link.springer.com/book/10.1007/978-3-319-59483-5))
 
 $$
-	J_{profit}(y, u) = \text{revenue}(y, u) - \text{cost}(u)  = I \cdot k \cdot T \cdot J_{\text{power}}(y, u) - C \int_{D} u(x) \mathrm{d} x,
+	J_{profit}(y, u) = \text{revenue}(y, u) - \text{cost}(u)  = I \cdot k \cdot T \cdot J_{\text{power}}(y, u) - C \int_{D} d(x) \mathrm{d} x,
 $$
 
 where $T$ is a turbine's average lifetime, $k \in (0,1)$ is a turbine efficiency coefficient, $I$ is an income factor, and $C$ is the cost of installing and maintaining one turbine. 
 
-We use [$C = 4800$](https://www.wolframalpha.com/input?i=1*%281-0.4%29*1000*2%5E3) (see [cost_coefficient in model_turbine.py](https://zenodo.org/record/224251)).
+We obtain 
 
+$$
+	J(y,u) = - J_{\text{power}}(y, u).
+$$
+
+We use [$\beta = 4800 = C/(I \cdot k \cdot T)$](https://www.wolframalpha.com/input?i=1*%281-0.4%29*1000*2%5E3) (see [cost_coefficient in model_turbine.py](https://zenodo.org/record/224251)).
+
+Note that the 
 
 ## References