Here is the list of experiments performed recently:

`patch_virus_1`: 64x64 points, dt=0.025, Ps=1 everywhere, V=0.1 inside a patch, no diffusion, no advection, no zooplankton (Figs. 1a, b and c)`patch_virus_6`:**100x100 points**, dt=0.025, Ps=1 everywhere, V=0.1 inside a patch, diffusion**diffk=0.1**, no advection, no zooplankton (Fig. 2)`patch_virus_4`: 100x100 points, dt=0.025, Ps=1 everywhere, V=0.1 inside a patch, diffusion**diffk=19.**, no advection, no zooplankton (Fig. 3)`patch_virus_7`: 100x100 points, dt=0.025, Ps=1 everywhere, V=0.1 inside a patch, diffusion**diffk=38.**, no advection, no zooplankton (Fig. 4)`patch_virus_8`:**256x256**points,**dt=0.0125**, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=38., no advection, no zooplankton (Fig. 5)`patch_virus_9`: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion**diffk=100.**, no advection, no zooplankton (Fig. 6)`patch_virus_10`: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion**diffk=0.1.**, no advection, no zooplankton (Fig. 7)`patch_virus_11`: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=0.1, no zooplankton but**chaotic advection**(Figs. 8a and b)`patch_virus_12`: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion**diffk=0.01**, no zooplankton but chaotic advection`patch_virus_13`: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion**diffk=1.0**, no zooplankton but chaotic advection.`patch_virus_14`: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion**diffk=10**, no zooplankton but chaotic advection.

We start with a low resolution (64x64 points) simulation with no diffusion and advection (`patch_virus_1`). The initial conditions are Ps=1 everywhere and there is a patch of virus V=0.1 in the center of the domain. The system oscillates until it reaches an equilibrium with Ps=1 outside the patch and equilivrated values of Ps and V inside the patch (Figs. 1a, b and c).

We then increase the diffusion (`diffk``=0.1, 19 and 38) with a simulation with 128x128 points (``patch_virus_6`, `patch_virus_4`, `patch_virus_7`): the front of the inside patch propagates outward, with the speed increasing with the diffusivity coefficient, but not proportionally (Figs. 2, 3 and 4).

Using 256x256 points and `diffk``=38 (``patch_virus_8`), we find that the front propagates slower than with 128x128 points (`patch_virus_7`) (Fig. 5). Why? The diffusion in the present case acts at the grid scale. With 256x256 points, the gradient would be sharper and that should correspond to a lower-resolution case with *higher* diffusivity coefficient and thus faster front. What is wrong with this reasoning?

We then increase the diffusion, `diffk=100` (`patch_virus_9`) or decrease it, `diffk=0.1` (`patch_virus_10`) with the same resolution. The front does not propagate faster in the former case but it does propagate slower in the latter case. Using 100x100 points, I have also noticed that after some threshold value for the diffusivity coefficient, the front does not propagate faster. I did not find any reason why the code would produce such threshold so I still do not understand why this is happening.

We then introduce chaotic advection (`coef=0.7*Lbox`) for different values of `diffk` (0.1, 0.01, 1 and 10 for `patch_virus_11`, `patch_virus_12`, `patch_virus_13` and `patch_virus_14`, respectively). The spatially-averaged Ps for these simulations is plotted in Fig. 9. There is no change and I do not understand why. If we take the simple example of a one-dimensional front, the stronger the diffusivity, the faster the front should flatten, is not it?). Maybe, this is indicative that all of the diffusion that is occurring is **numerical** diffusion and we would need a much stronger diffusion to see an effect of the explicit diffusion.

- Look at characteristics of a Fisher’s wave. Does it match what I see in the numerical simulations?

Snapshots and histograms are plotted with `plot_snapshot_current_run.py` and `plot_diag_num_diff_3.py` in `RESEARCH/MODELISATION/marine_viruses/current_version/runs/run_002/analysis/` on `ipu1`.