Update path

Author: sabaronett

_research/05-code-comparison.md _research/05-code-comparisons.md_research/05-code-comparison.md renamed to _research/05-code-comparisons.md

@@ -1,6 +1,6 @@
 ---
-title: "Code Comparison"
-permalink: /research/code-comparison/
+title: "Code Comparisons"
+permalink: /research/code-comparisons/
 ---
 ## Streaming Instability
 
@@ -10,9 +10,9 @@ However, the non-trivial differences between numerical techniques (e.g., finite
 In an effort to address these issues, we are leading a comprehensive comparison of various multipurpose codes across some of the key models and problems previously studied in investigations into the streaming instability.
 
 
-### [<i class='fa-solid fa-file-pdf'></i>](/assets/docs/research/code-comparison/si/sicc_problem_set.pdf){:target="_blank"} [Problem Set](/assets/docs/research/code-comparison/si/sicc_problem_set.pdf){:target="_blank"}
+### [<i class='fa-solid fa-file-pdf'></i>](/assets/docs/research/code-comparisons/si/sicc_problem_set.pdf){:target="_blank"} [Problem Set](/assets/docs/research/code-comparisons/si/sicc_problem_set.pdf){:target="_blank"}
 
-We invite users and developers of hydrodynamics codes who wish to contribute to this project to review the Streaming Instability Code Comparison Problem Set ([PDF](/assets/docs/research/code-comparison/si/sicc_problem_set.pdf){:target="_blank"}).
+We invite users and developers of hydrodynamics codes who wish to contribute to this project to review the Streaming Instability Code Comparison Problem Set ([PDF](/assets/docs/research/code-comparisons/si/sicc_problem_set.pdf){:target="_blank"}).
 As this document continues to be developed, including the addition of new problems in future revisions, please contact [Stanley A. Baronett](/team/baronett-stanley/) with any questions or feedback that may be helpful toward future revisions.
 
 
@@ -35,20 +35,20 @@ From Baronett et al. (in preparation)
 
 #### Fiducial Grid Resolution
 
-{% include figure image_path='/assets/images/research/code-comparison/si/BA-512_snapshots.png' caption='**Figure 1.1.** Dust density snapshots for Problem BA at a grid resolution of 512².
+{% include figure image_path='/assets/images/research/code-comparisons/si/BA-512_snapshots.png' caption='**Figure 1.1.** Dust density snapshots for Problem BA at a grid resolution of 512².
 Each row shows the code labeled along the left margin.
 In alphabetical order from top to bottom, the upper group implements an average of one (1) Lagrangian particle per grid cell, and the lower group implements a pressureless dust fluid.
 Each column shows the simulation time in local orbital periods $$T$$ labeled along the top margin.
 The color scale at the bottom right shows the dust density $$\rho_\mathrm{d}$$ relative to the initially uniform gas density $$\rho_\mathrm{g,0}$$ and applies to all snapshots.
 Radial $$x$$ and vertical $$z$$ coordinates are in units of the vertical gas scale height $$H_\mathrm{g}$$.' %}
 
-{% include figure image_path='/assets/images/research/code-comparison/si/BA-512_time_series.png' caption='**Figure 1.2.** Maximum dust densities $$\max(\rho_\mathrm{d})$$ as a function of time for Problem BA at a grid resolution of 512².
+{% include figure image_path='/assets/images/research/code-comparisons/si/BA-512_time_series.png' caption='**Figure 1.2.** Maximum dust densities $$\max(\rho_\mathrm{d})$$ as a function of time for Problem BA at a grid resolution of 512².
 The units for density and time are the initially uniform gas density $$\rho_\mathrm{g,0}$$ and the local orbital period $$T$$, respectively.
 The top panel uses a similar cadence for each time series.
 The bottom panel shows the simple moving average $$\mathrm{SMA}$$ with a sampling window of $$10T$$.
 Dotted lines show codes that implement an average of $$n_\mathrm{p} = 1$$ Lagrangian particle per grid cell, solid lines show codes with pressureless dust fluids, and line colors show different codes.' %}
 
-{% include figure image_path='/assets/images/research/code-comparison/si/BA-512_CDF.png' caption='**Figure 1.3.** Cumulative distribution functions of the dust density for Problem BA at a grid resolution of 512².
+{% include figure image_path='/assets/images/research/code-comparisons/si/BA-512_CDF.png' caption='**Figure 1.3.** Cumulative distribution functions of the dust density for Problem BA at a grid resolution of 512².
 In the upper panel, lines show densities time-averaged over the saturation state $$\overline{\rho_\mathrm{d}}$$, line colors different codes, and shaded areas the $$1\sigma$$ time variability.
 In the lower panel, lines and shaded areas show the meta-average $$\overline{\overline{\rho_\mathrm{d}}}$$ and standard deviation, respectively, of $$\overline{\rho_\mathrm{d}}$$ in the upper panel for each dust implementation.
 Dust densities are relative to the initially uniform gas density $$\rho_\mathrm{g,0}$$.
@@ -57,26 +57,26 @@ Dotted lines show codes that implement an average of $$n_\mathrm{p} = 1$$ Lagran
 
 ##### Additional Particles
 
-{% include figure image_path='/assets/images/research/code-comparison/si/BA-512-np9_snapshots.png' caption='**Figure 1.4.** Similar to Figure [1.1](#higher-particle-resolution:~:text=Permalink-,Figure%201.1.,-Dust%20density%20snapshots) except for only codes that implement an average of $$n_\mathrm{p} = 9$$ Lagrangian particles per grid cell.' %}
+{% include figure image_path='/assets/images/research/code-comparisons/si/BA-512-np9_snapshots.png' caption='**Figure 1.4.** Similar to Figure [1.1](#higher-particle-resolution:~:text=Permalink-,Figure%201.1.,-Dust%20density%20snapshots) except for only codes that implement an average of $$n_\mathrm{p} = 9$$ Lagrangian particles per grid cell.' %}
 
-{% include figure image_path='/assets/images/research/code-comparison/si/BA-512-np9_time_series.png' caption='**Figure 1.5.** Similar to Figure [1.2](#higher-particle-resolution:~:text=.-,Figure%201.2.,-Maximum%20dust%20densities) except comparing only Lagrangian-particle implementations with dashed lines showing an average of $$n_\mathrm{p} = 9$$ particles per grid cell.' %}
+{% include figure image_path='/assets/images/research/code-comparisons/si/BA-512-np9_time_series.png' caption='**Figure 1.5.** Similar to Figure [1.2](#higher-particle-resolution:~:text=.-,Figure%201.2.,-Maximum%20dust%20densities) except comparing only Lagrangian-particle implementations with dashed lines showing an average of $$n_\mathrm{p} = 9$$ particles per grid cell.' %}
 
-{% include figure image_path='/assets/images/research/code-comparison/si/BA-512-np9_CDF.png' caption='**Figure 1.6.** Similar to Figure [1.3](#higher-particle-resolution:~:text=show%20different%20codes.-,Figure%201.3.,-Cumulative%20distribution%20functions) except comparing only Lagrangian-particle implementations with dashed lines showing an average of $$n_\mathrm{p} = 9$$ particles per grid cell.' %}
+{% include figure image_path='/assets/images/research/code-comparisons/si/BA-512-np9_CDF.png' caption='**Figure 1.6.** Similar to Figure [1.3](#higher-particle-resolution:~:text=show%20different%20codes.-,Figure%201.3.,-Cumulative%20distribution%20functions) except comparing only Lagrangian-particle implementations with dashed lines showing an average of $$n_\mathrm{p} = 9$$ particles per grid cell.' %}
 
 
 #### Higher Grid Resolution
 
-{% include figure image_path='/assets/images/research/code-comparison/si/BA-1024_snapshots.png' caption='**Figure 1.7.** Similar to Figure [1.1](#higher-particle-resolution:~:text=Permalink-,Figure%201.1.,-Dust%20density%20snapshots) except at a grid resolution of 1024².' %}
+{% include figure image_path='/assets/images/research/code-comparisons/si/BA-1024_snapshots.png' caption='**Figure 1.7.** Similar to Figure [1.1](#higher-particle-resolution:~:text=Permalink-,Figure%201.1.,-Dust%20density%20snapshots) except at a grid resolution of 1024².' %}
 
-{% include figure image_path='/assets/images/research/code-comparison/si/BA-1024_time_series.png' caption='**Figure 1.8.** Similar to Figure [1.2](#higher-particle-resolution:~:text=.-,Figure%201.2.,-Maximum%20dust%20densities) except with dashed lines showing grid resolutions of 1024².' %}
+{% include figure image_path='/assets/images/research/code-comparisons/si/BA-1024_time_series.png' caption='**Figure 1.8.** Similar to Figure [1.2](#higher-particle-resolution:~:text=.-,Figure%201.2.,-Maximum%20dust%20densities) except with dashed lines showing grid resolutions of 1024².' %}
 
-{% include figure image_path='/assets/images/research/code-comparison/si/BA-1024_CDF.png' caption='**Figure 1.9.** Similar to Figure [1.3](#higher-particle-resolution:~:text=show%20different%20codes.-,Figure%201.3.,-Cumulative%20distribution%20functions), except grid resolutions at 1024² appear as dashed and darker lines in the upper and lower panels, respectively.' %}
+{% include figure image_path='/assets/images/research/code-comparisons/si/BA-1024_CDF.png' caption='**Figure 1.9.** Similar to Figure [1.3](#higher-particle-resolution:~:text=show%20different%20codes.-,Figure%201.3.,-Cumulative%20distribution%20functions), except grid resolutions at 1024² appear as dashed and darker lines in the upper and lower panels, respectively.' %}
 
 
 ### Problem AB
 
-{% include figure image_path='/assets/images/research/code-comparison/si/AB-1024_snapshots.png' caption='**Figure 2.1.** Similar to Figure [1.1](#higher-particle-resolution:~:text=Permalink-,Figure%201.1.,-Dust%20density%20snapshots) except for Problem AB at a grid resolution of 1024².' %}
+{% include figure image_path='/assets/images/research/code-comparisons/si/AB-1024_snapshots.png' caption='**Figure 2.1.** Similar to Figure [1.1](#higher-particle-resolution:~:text=Permalink-,Figure%201.1.,-Dust%20density%20snapshots) except for Problem AB at a grid resolution of 1024².' %}
 
-{% include figure image_path='/assets/images/research/code-comparison/si/AB-1024_time_series.png' caption='**Figure 2.2.** Similar to Figure [1.2](#higher-particle-resolution:~:text=.-,Figure%201.2.,-Maximum%20dust%20densities) except for Problem AB at a grid resolutions of 1024².' %}
+{% include figure image_path='/assets/images/research/code-comparisons/si/AB-1024_time_series.png' caption='**Figure 2.2.** Similar to Figure [1.2](#higher-particle-resolution:~:text=.-,Figure%201.2.,-Maximum%20dust%20densities) except for Problem AB at a grid resolutions of 1024².' %}
 
-{% include figure image_path='/assets/images/research/code-comparison/si/AB-1024_CDF.png' caption='**Figure 2.3.** Similar to Figure [1.3](#higher-particle-resolution:~:text=show%20different%20codes.-,Figure%201.3.,-Cumulative%20distribution%20functions), except for Problem AB at a grid resolutions of 1024².' %}
+{% include figure image_path='/assets/images/research/code-comparisons/si/AB-1024_CDF.png' caption='**Figure 2.3.** Similar to Figure [1.3](#higher-particle-resolution:~:text=show%20different%20codes.-,Figure%201.3.,-Cumulative%20distribution%20functions), except for Problem AB at a grid resolutions of 1024².' %}