Related Experiment Video
Updated: Oct 25, 2025

3D Modeling of Dendritic Spines with Synaptic Plasticity
Published on: May 18, 2020
Dendrite tips as elliptical paraboloids
D V Alexandrov1, E A Titova2, P K Galenko1,3
1Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Ekaterinburg 620000, Russia.
Abstract:
This review article summarizes current theories of the steady-state growth mode of dendrites in the form of elliptical paraboloids. The shape of dendrite tips is analyzed, temperature and solute concentration distributions are described in its vicinity, and a solution of the hydrodynamic problem of a viscous incompressible fluid flowing against a dendrite tip is developed. A significant difference in analytical solutions describing a dendrite tip as an elliptic paraboloid as compared to an axisymmetric morphology is shown. The system of nonlinear equations for determining the stationary velocity of dendrite growth and the radii of curvature of the dendrite tip along the major and minor axis of the ellipse, respectively, is derived. The developed theory is compared with experimental data on the growth of ice crystals consisting of D2O or H2O.
Related Concept Videos
Centroid for the Paraboloid of Revolution
The centroid for the paraboloid of revolution is the point where all the mass of the paraboloid is concentrated. This centroid is important for engineering applications, as it determines how forces are...
Reflective Property of Parabolas
Parabolas
Neurons: The Cell Body and the Dendrites
Ellipses
Hyperbolas

