Related Experiment Video
Updated: Jun 26, 2025
09:53
Micropatterning Transmission Electron Microscopy Grids to Direct Cell Positioning within Whole-Cell Cryo-Electron Tomography Workflows
Published on: September 13, 2021
6.7K
Percolation of straight slots on a square grid.
Alexander S Balankin1, M A Martinez-Cruz1, F J Dorantes Benavidez1
1ESIME-Zacatenco, Instituto Politécnico Nacional, Ciudad de México 07738, Mexico.
Physical Review. E
|May 17, 2024
Summary
This study explores slot percolation on square grids, finding that longer slots significantly decrease the percolation threshold. Slot percolation bridges site percolation and continuous stick percolation models.
Area of Science:
- Statistical Physics
- Network Science
- Materials Science
Background:
- Percolation theory studies the formation of connected networks.
- Understanding network formation is crucial in various scientific fields.
Purpose of the Study:
- Investigate the site percolation of straight slots on a square grid.
- Analyze the impact of slot length on the percolation threshold.
- Characterize the slot percolation model's relationship to other percolation models.
Main Methods:
- Extensive Monte Carlo simulations.
- Finite-size scaling analysis.
- Studied slot lengths (l) from 1 to L-2 on square grids (L=50 to 1000).
Main Results:
- Percolation threshold (pC) strongly decreases as slot length (l) increases.
- pC shows minimal variation with changes in the ratio l/L.
- Derived functional dependencies for critical filling factor and percolation strength on slot length.
- Slot percolation interpolates between site percolation (l=1) and continuous stick percolation (l→∞).
Conclusions:
- Slot percolation belongs to the same universality class as standard Bernoulli percolation.
- Critical number of orthogonal widthless sticks per unit area is higher than for randomly oriented sticks.
Related Concept Videos
01:23Plane Potential Flows
379
Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, ϕ, representing the flow speed in a given direction, and a stream function, ψ, that visualizes the flow path, both governed by Laplace's equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
Uniform...
Uniform...
379
01:30Underflow Gates
48
Underflow gates are vital for controlling water flow in irrigation canals. The three main types of underflow gates — vertical, radial, and drum gates — serve different purposes while ensuring effective flow management. Vertical gates move up and down, generating a free-flowing water jet; radial gates pivot to regulate the flow; and drum gates rotate for precise adjustments. The flow through these gates is influenced by downstream conditions, resulting in free or drowned outflow.Free and...
48
01:21Boundary Conditions: Lossless Lines
91
Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
91
01:12Bewley Lattice Diagram
628
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
628
01:19Rectangular and Triangular Pulse Function
674
The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
674
01:18Streamlines, Streaklines, and Pathlines
1.3K
A streamline represents the trajectory that is always tangent to the fluid's velocity vector at any given point. The velocity of a fluid particle is always directed along the streamline, ensuring the particle continuously follows the streamline's path. Streamlines are particularly useful for visualizing the overall direction of flow in a fluid system, and they provide an instantaneous representation of the flow's velocity field. In steady flow, where conditions do not change over...
1.3K