Geodesic flow

"A movement that flows over time in the 'most natural way' within space."

「空間の形そのものが、運動の運命を決める現象」

“都市の流れの増幅器”

Navier-Stokes equations

Navier-Stokes equations

[\rho\left(\frac{\partial \mathbf{u}}{\partial t}+\mathbf{u}\cdot\nabla\mathbf{u}\right)

-\nabla p+\mu\nabla^2\mathbf{u}+\mathbf{f}]

• (\rho)：Fluid density

• (\mathbf{u}): Velocity field

• (p): pressure

• (μ): viscosity coefficient

• (\mathbf{f}): External force

This equation is,

• water flow

• air

• vortex

• turbulence

• Thermal convection

These are fundamental equations that describe the motion of fluids.

In a hydrodynamic city, the flow of people, traffic, information, and the diffusion of economic activity are applied to urban space as fluid behaviors.

Mathematical Architecture

space