PhysSandbox
Classical MechanicsWaves & SoundElectricity & MagnetismOptics & LightGravity & OrbitsLabs
🌙Astronomy & The Sky🌡️Thermodynamics🌍Biophysics, Fluids & Geoscience📐Math Visualization🔧Engineering🧪Chemistry

More from Biophysics, Fluids & Geoscience

Other simulators in this category — or see all 44.

View category →
NewSchool

Coupled FitzHugh–Nagumo Neurons

Launch Simulator

Two excitable FHN units with diffusive coupling: phase plots, time traces, and synchronization vs coupling strength.

NewSchool

Nernst Potentials & Membrane

Launch Simulator

Nernst E for K⁺ and Na⁺ from inside/outside concentrations; optional Goldman–Hodgkin–Katz resting estimate.

NewUniversity / research

Kelvin–Helmholtz Shear Instability

Launch Simulator

Two parallel flows with slip U: Fourier-mode growth rate sketch and animated interface billows (linear toy model).

NewUniversity / research

Taylor–Couette Flow (Criterion)

Launch Simulator

Gap d, cylinders Ω_i, Ω_o, kinematic ν: Taylor number Ta and critical Ta_c for toroidal rolls — cartoon + formula.

NewSchool

Darcy Flow & Penetration Depth

Launch Simulator

1D head h(z,t): ∂h/∂t = K ∂²h/∂z²; recharge at surface, fixed head at depth — relaxation time and diffusion length.

NewSchool

Groundwater Well Drawdown (Theis)

Launch Simulator

Confined-aquifer Theis solution: cone of depression s(r,t) = (Q/(4πT)) W(u), u = r²S/(4Tt); transmissivity, storativity, observation well.

PhysSandbox

Interactive physics, chemistry, and engineering simulators for students, teachers, and curious minds.

Physics

  • Classical Mechanics
  • Waves & Sound
  • Electricity & Magnetism

Science

  • Optics & Light
  • Gravity & Orbits
  • Astronomy & The Sky

More

  • Thermodynamics
  • Biophysics, Fluids & Geoscience
  • Math Visualization
  • Engineering
  • Chemistry

© 2026 PhysSandbox. Free interactive science simulators.

PrivacyTermsContact
Home/Biophysics, Fluids & Geoscience/Cable Equation on an Axon

Cable Equation on an Axon

1D passive cable ∂V/∂t = D∂²V/∂x² − (V−V_r)/τ + I; compare uniform fiber vs myelinated (higher D in internodes).

Cable parameters

0.35
2.8
12
8
1.2

Discrete passive cable: ∂V/∂t = ∂/∂x(D(x)∂V/∂x) − V/τ + I. Higher D in yellow “internode” bands mimics faster effective propagation along myelinated axons (qualitative, not cable equation with lumped nodes).

Measured values

V at far end0.0000

About this model

The passive cable equation linearizes membrane dynamics near rest: ∂V/∂t = ∂/∂x(D(x)∂V/∂x) − V/τ + I, where D bundles axial resistance and membrane capacitance in these teaching units. Piecewise larger D mimics lower loss in myelinated internodes, giving faster apparent propagation than a uniform fiber at the same mean parameters.

Who it's for: Students linking compartment models to saltatory conduction phenomenology.

Key terms

  • Cable equation
  • Myelin
  • Diffusion
  • Leak time constant

How it works

Finite-difference cable with piecewise diffusion coefficient: saltatory conduction cartoon by alternating low-D “node” and high-D myelinated stretches.

Frequently asked questions

Is this a full myelinated cable with explicit nodes of Ranvier?
No. It is a coarse finite-difference cartoon: periodically elevated D stands in for reduced leakage per unit length between excitable nodes.