Related Experiment Video
Updated: Nov 6, 2025
07:15
Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure
Published on: April 25, 2025
702
A minimalist model for coevolving supply and drainage networks.
Shashank Kumar Anand1, Milad Hooshyar2, Jan Martin Nordbotten3
1Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA.
Royal Society Open Science
|May 11, 2021
Summary
We developed a minimalist model for coevolving supply and drainage networks, applicable to natural and artificial systems. This model reveals how network patterns emerge based on material flow and landscape properties.
Area of Science:
- Complex Systems Science
- Network Theory
- Mathematical Modeling
Background:
- Many natural and artificial systems feature intricate supply and/or drainage networks.
- Understanding the coevolution of these networks is crucial for various scientific disciplines.
Purpose of the Study:
- To present a minimalist model for coevolving supply and drainage networks in a continuous domain.
- To analyze network formation based on material flow and mediating scalar fields.
Main Methods:
- Developed a model using three coupled, nonlinear partial differential equations.
- Simulated spatial density patterns of input and output materials.
- Analyzed steady-state solutions as a function of non-dimensional channelization indices.
Main Results:
- The model generates networks interpretable as counter-flowing drainage or co-flowing supply and drainage mechanisms.
- In 2D, networks form on a landscape's ridges (supply) and valleys (drainage).
- In 3D, networks vascularize based on a chemical signal and 'erosion' strength, forming branched or congested patterns.
Conclusions:
- The minimalist model effectively captures the emergence of complex supply and drainage networks.
- Network spatial patterns can be classified and characterized by non-dimensional indices, offering insights into system organization.
Related Concept Videos
01:27Design Example: Design of an Irrigation Channel
351
Trapezoidal channels are widely used in irrigation systems due to their cost-effectiveness and efficiency in conveying water. Trapezoidal channels feature a flat bottom and sloping sides, making them stable and easier to construct compared to other shapes. The bottom width and side slope ratio are determined based on the required flow capacity and site conditions. The side slope is kept gentle for unlined channels to prevent soil erosion.Hydraulic parameters in channel design include the flow...
351
00:57Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models
187
Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
187
02:03Xylem and Transpiration-driven Transport of Resources
25.2K
The xylem of vascular plants distributes water and dissolved minerals that are taken up by the roots to the rest of the plant. The cells that transport xylem sap are dead upon maturity, and the movement of xylem sap is a passive process.
25.2K
01:21Design Example: Creating a Hydraulic Model of a Dam Spillway
444
Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.
444
01:30Typical Model Studies
502
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
502
02:12Short-distance Transport of Resources
16.9K
Short-distance transport refers to transport that occurs over a distance of just 2-3 cells, crossing the plasma membrane in the process. Small uncharged molecules, such as oxygen, carbon dioxide, and water, can diffuse across the plasma membrane on their own. In contrast, ions and larger molecules require the assistance of transport proteins due to their charge or size. Transport across membranes also occurs within individual cells, playing a variety of essential roles for the plant as a whole.
16.9K