Update README.md

README.md

@@ -98,13 +98,13 @@ where \\(\mu\\) is the mean and \\(\sigma\\) is the standard deviation of the pr
 
 **Simulation time-step:** \\(\Delta t\\) is set such that the maximum Courant number is \\(\frac12(CFL_{max}=0.5)\\). Therefore, the time step decreases as the flow accelerates.
 
-**Data are stored separated by (\\(\Delta t\\)):**  varies with the Atwood number.
+**Data are stored separated by ( \\(\Delta t\\)):**  varies with the Atwood number.
 
-**Total time range (\\(t_{min}\\) to \\(t_{max}\\)):** Varies from \\(t_{min}=0\\) to \\(t_{max}\\) between \\(\sim 30s\\) and \\(\sim 100s\\), depending on Atwood number.
+**Total time range ( \\(t_{min}\\) to \\(t_{max}\\)):** Varies from \\(t_{min}=0\\) to \\(t_{max}\\) between \\(\sim 30s\\) and \\(\sim 100s\\), depending on Atwood number.
 
-**Spatial domain size (\\(L_x\\), \\(L_y\\), \\(L_z\\)):** \\([0,1]\times[0,1]\times[0,1]\\).
+**Spatial domain size ( \\(L_x\\), \\(L_y\\), \\(L_z\\)):** \\([0,1]\times[0,1]\times[0,1]\\).
 
-**Set of coefficients or non-dimensional parameters evaluated:** We run simulations with 13 different initializations for five different Atwood number values \\(At\in \{\frac34, \frac12, \frac14, \frac18, \frac{1}{16}\}\\). The first set on initial conditions considers varying the mean \\(\mu\\) and standard deviation \\(\sigma\\) of the profile \\(A(k)\\) with \\(\mu\in{1, 4, 16}\\) and \\(\sigma\in\{\frac14, \frac12, 1\}\\), the phase (argument of the complex Fourier component) \\(\phi\\) was set randomly in the range \\([0,2\pi)\\). The second set of initial conditions considers a fixed mean (\\(\mu=16\\)) and standard deviation (\\(\sigma =0.25\\)) and a varieed range of random phases (complex arguments \\(\phi\in[0,\phi_{max}\\))) given to each Fourier component. The four cases considered are specified by \\(\phi_{max}\in \{ \frac{\pi}{128}, \frac{\pi}{8}, \frac{\pi}{2}, \pi\}\\).
+**Set of coefficients or non-dimensional parameters evaluated:** We run simulations with 13 different initializations for five different Atwood number values \\(At\in \{\frac34, \frac12, \frac14, \frac18, \frac{1}{16}\}\\). The first set on initial conditions considers varying the mean \\(\mu\\) and standard deviation \\(\sigma\\) of the profile \\(A(k)\\) with \\(\mu\in{1, 4, 16}\\) and \\(\sigma\in\{\frac14, \frac12, 1\}\\), the phase (argument of the complex Fourier component) \\(\phi\\) was set randomly in the range \\([0,2\pi)\\). The second set of initial conditions considers a fixed mean ( \\(\mu=16\\)) and standard deviation ( \\(\sigma =0.25\\)) and a varieed range of random phases (complex arguments \\(\phi\in[0,\phi_{max}\\))) given to each Fourier component. The four cases considered are specified by \\(\phi_{max}\in \{ \frac{\pi}{128}, \frac{\pi}{8}, \frac{\pi}{2}, \pi\}\\).
 
 **Approximate time to generate the data:** 1 hour on 128 CPU cores for 1 simulation. 65 hours on 128 CPU cores for all simulations.