st-wslda-examples-archival.md

@@ -3,37 +3,37 @@
 [[_TOC_]]
 
 # Example 1: gas confined in a tube
-The solution of cold atomic gas in an external potential of the form of a tube. Gas with is in BCS regime with $`ak_F=-0.9`$. In the calculation, we assumed translation symmetry along z direction and `st-wslda-2d` was used. In the computation, `double` arithmetic is utilized.
+The solution of cold atomic gas in an external potential in the form of a tube. Gas with is in BCS regime with $`ak_F=-0.9`$. In the calculation, we assumed translation symmetry along the z direction, and `st-wslda-2d` was used. In the computation, `double` arithmetic is utilized.
 * [predefines.h](uploads/b0f9c475f5dbd44640310b713ecb5ea5/tube_predefines.h)
 * [problem-definition.h](uploads/cd9da4754c87bf4eabe4977246ba534b/tube_problem-definition.h)
 * [input.txt](uploads/df292f7036ca8ffd86d4986cb40c1449/tube_input.txt)
 * [output](uploads/799f6e104160a09fe4bf542d989cedcf/tube.out)
 
-The graph below shows density distribution (left) and the absolute value of delta (right) for the converged solution. 
+The graph below shows the density distribution (left) and the absolute value of delta (right) for the converged solution. 
 
 ![example-st-1](uploads/b8a8ec63f10ec99c2573207580e7ad32/example-st-1.png)
 
 # Example 2: vortex solution within BdG
-The solution representing a vortex confined in a tube. The conditions are the same as for *Example 1*. To speed up the convergence process we start from the state provided by *Example 1*. In the computation, `double complex` arithmetic is utilized.
+The solution represents a vortex confined in a tube. The conditions are the same as for *Example 1*. To speed up convergence, we start from the state provided in *Example 1*. In the computation, `double complex` arithmetic is utilized.
 * [predefines.h](uploads/0a1ad93743c8f9544e59338ba8220563/vortex_predefines.h)
 * [problem-definition.h](uploads/215195b78623a61bc1f4df47c27e5d7a/vortex_problem-definition.h)
 * [input.txt](uploads/1e340d91f45dc57900152866a9a956ef/vortex_input.txt)
 * [output](uploads/633a07650caee1345b0a1fbdd9513d51/vortex.out)
 
-The graph below shows density distribution (left) and the absolute value of delta (right) for the converged solution. By arrows currents are plotted. 
+The graph below shows the density distribution (left) and the absolute value of delta (right) for the converged solution. By arrows, currents are plotted. 
 ![example-st-2](uploads/f896b92eeaa489872600109615ef066b/example-st-2.png)
 
 # Example 3: mass imbalanced gas in a harmonic trap  
 This example is motivated by work [arXiv:1909.03424](https://arxiv.org/abs/1909.03424).
-Namely, let us consider gas of:  
+Namely, let us consider a gas of:  
 * component *a*: $`{}^{161}\textrm{Dy}`$,
 * component *b*: $`{}^{40}\textrm{K}`$,  
 
-confined in harmonic trap:  
+confined in a harmonic trap:  
 ```math
 V_{a,b}(x)=\dfrac{m_a \omega_a^2 x^2}{2}
 ```
-where traping frequencies of both components are different (in the example we use according to [arXiv:1909.03424](https://arxiv.org/abs/1909.03424) $`\omega_a/\omega_b=120/430`$). In addition $`N_{\textrm{Dy}} / N_{\textrm{K}} = 20000/8000`$.  In the calculations BdG functional is used, with the scattering length exceeding other length scales (in the example $`a=100`$). In the calculation `st-wslda-1d` was used. 
+where trapping frequencies of both components are different (in the example we use, according to [arXiv:1909.03424](https://arxiv.org/abs/1909.03424) $`\omega_a/\omega_b=120/430`$). In addition $`N_{\textrm{Dy}} / N_{\textrm{K}} = 20000/8000`$.  In the calculations BdG functional is used, with the scattering length exceeding other length scales (in the example $`a=100`$). In the calculation, `st-wslda-1d` was used. 
 * [predefines.h](uploads/8bed3548acc9dd04a2ccf54a35687ac7/DyK_predefines.h) 
 * [problem-definition.h](uploads/475df575833b5d4e92acd77b30992930/DyK_problem-definition.h)
 * [logger.h](uploads/8ac2b1262a442fa45092727564919f94/DyK_logger.h)