#vectorfields — Public Fediverse posts

Divergence and curl of vector fields are complementary concepts from vector calculus.

Divergence quantifies the rate at which a field flows outward from a point, and curl represents rotation.

\(\nabla\cdot\mathbf{F}\) denotes divergence (expansion/contraction)

\(\nabla\times\mathbf{F}\) denotes curl (rotation)

Left: A radial source field with pure divergence and no curl.

Centre: A rotational field with pure curl and no divergence.

Right: A spiral source field with both divergence and curl.

Credit: Alec Helbling

#Divergence #Curl #Vector #VectorFields #VectorCalculus

🧠 New preprint by Behrad et al. introducing #fastDSA, a much faster way to compare neural systems at the level of their dynamics, not just geometry or task performance.

What’s cool here: similarity is defined by shared #VectorFields, i.e. by the computational mechanism itself. This provides the first tool for mechanistic comparison of neural computations (to my knowledge).

🌍 https://arxiv.org/abs/2511.22828
💻 https://github.com/CMC-lab/fastDSA

#Neuroscience #CompNeuro #NeuralDynamics #Manifolds #DynamicalSystems

#PhysicsFactlet
Field lines are a convenient way to visualize vector fields, and are defined to be tangent to them at each point.
Due to inertia, field lines do not represent the trajectory that a test mass would follow in a force field.
#VectorFields #DifferentialGeometry #Visualization