# In your field The same kernel language, five fields. A *lane* is one run of the kernel body, and a *sample* is one independent element of work. Each card links two ways in: **write the kernel** in hawk, or **compose the flow** around it in eagle (graphs, loops, copies, early stop). Every example runs on a CPU at a small size and on a GPU at a larger one. The pictures here are from those notebooks; nothing on this page is a timing. ```{raw} html
A triangle mesh of the unit square shaded by the source field recovered from the assembled load

Finite elements

Each triangle hands a share of its load to its three corners, and a node shared by several triangles collects them all.

Write the kernel Compose the flow

A square plate whose heat spreads out from a hot patch, animated

Heat diffusion

A grid of cells, each stepped from its four neighbours; the animation is the plate cooling.

Write the kernel Compose the flow

Waves on a shallow pool spreading and reflecting, animated

Fluids

Shallow water on a 2-D grid, with the total water checked at the end.

Write the kernel Compose the flow

Projectile paths ending one by one, with a count of the paths still running falling beside them, animated

Monte Carlo

An ensemble of projectiles, each stopping at its own impact; finished ones leave the launch.

Write the kernel Compose the flow

Two histograms of particle count and mass per bin, matching the expected curve

Particle binning

Add each particle's weight into its cell; if the particles are already sorted by cell, each run of the same cell is added in one go.

Write the kernel Compose the flow

``` Not your field? These are the same few words: a grid of lanes, a read of a neighbour, a sum or a scatter across lanes. [Batched small matrices](https://amasat01.github.io/hawk/content/vocabulary/11_batched_contraction.html) shows the plainest use of them, checked against `einsum`.