Update interaction notebook introduction text

Author: erikvansebille

docs/user_guide/examples_v3/tutorial_interaction.ipynb

@@ -6,7 +6,7 @@
    "id": "0",
    "metadata": {},
    "source": [
-    "# Particle-Particle interaction\n"
+    "# 🎓 Particle-Particle interaction\n"
    ]
   },
   {
@@ -15,24 +15,7 @@
    "id": "1",
    "metadata": {},
    "source": [
-    "In this notebook, we show an example of the new 'particle-particle-interaction' functionality in Parcels. Note that this functionality is still in development, and the implementation is fairly rudimentary for now. Importantly:\n",
-    "\n",
-    "- The type of interactions that are supported is still limited\n",
-    "\n",
-    "Interactions are implemented through `InteractionKernels`, which are similar to normal `Kernels`. The `InteractionKernels` are applied between particles that are located closer to each other than a specified `interaction_distance`. In general, the code structure needs three adaptations to apply particle-particle interaction:\n",
-    "\n",
-    "1. The `ParticleSet` requires an `interaction_distance` argument upon creation, to define the `interaction_distance`.\n",
-    "2. `ParticleSet.execute()` requires the `pyfunc_inter` argument, which contains the `InteractionKernels` that will be executed, similarly to the `pyfunc` argument for normal `Kernels`.\n",
-    "3. `InteractionKernels` have two additional arguments compared to normal `Kernels`:\n",
-    "\n",
-    "```python\n",
-    "def InteractionKernel(particle, fieldset, time, neighbors, mutator)\n",
-    "```\n",
-    "\n",
-    "The `neighbors` argument provides a list of the particles that are within a neighborhood (i.e. closer than the `interaction_distance` argument in `ParticleSet` creation).\n",
-    "\n",
-    "The `mutator` argument is an initially empty list with all the mutations that need to be performed on particles at the end of running all `InteractionKernels` on all particles.\n",
-    "This `mutator` argument is required, because otherwise the order at which interactions are applied has implications for the simulation. As a consequence, the simulation will likely be dependent on the order of the particle list if no mutator list is used.\n"
+    "In this tutorial, we show an example of the 'particle-particle-interaction' functionality in Parcels. Note that this functionality is still fairly rudimentary for now. Importantly, as particle-interaction is a many-body problem it scales as $N^2$ and can thus become very slow for large ParticleSets. There is currently **no advanced optimisation** (such as using techniques from [Smoothed Particle Hydrodynamics](https://en.wikipedia.org/wiki/Smoothed-particle_hydrodynamics)) build-in to Parcels. "
    ]
   },
   {
@@ -43,7 +26,7 @@
    "source": [
     "## Pulling particles\n",
     "\n",
-    "Below is an example of what can be done with particle-particle interaction. We create a square grid of $N\\times N$ particles, which are all subject to Brownian Motion (via the built-in `DiffusionUniformKh` Kernel). Furthermore, some of the particles also 'attract' other particles that are within the interaction distance: these attracted particles move with a constant velocity to the attracting particles.\n"
+    "Below is an example of what can be done with particle-particle interaction. We create a square grid of $N\\times N$ particles, which are all subject to Brownian Motion (via the built-in `DiffusionUniformKh` Kernel). Furthermore, two of the particles also 'attract' other particles that are within the interaction distance: these attracted particles move with a constant velocity to the attracting particles.\n"
    ]
   },
   {
@@ -72,7 +55,7 @@
    "outputs": [],
    "source": [
     "def Pull(particles, fieldset):\n",
-    "    \"\"\"InterActionKernel that \"pulls\" all neighbor particles\n",
+    "    \"\"\"Kernel that \"pulls\" all neighbor particles\n",
     "    toward the attracting particle with a constant velocity\"\"\"\n",
     "    interaction_distance = 0.5\n",
     "    velocity = -0.04  # predefined attracting velocity\n",