Related Experiment Video
Updated: Sep 4, 2025
09:32
Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
Published on: April 12, 2019
6.5K
Random adsorption process of linear k-mers on square lattices under the Achlioptas process
Fuxing Chen1, Ping Fang1, Liangsheng Li2
1School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Physical Review. E
|July 20, 2022
Summary
We investigated explosive percolation using k-mer random sequential adsorption. The Achlioptas process showed changing universality classes with k-mer size, while the inverse Achlioptas process remained consistent, differing from standard RSA.
Area of Science:
- Statistical Physics
- Complex Systems
- Network Science
Background:
- Percolation theory describes phase transitions in random systems.
- Explosive percolation exhibits abrupt transitions, unlike standard percolation.
- K-mer processes introduce sequence-dependent adsorption dynamics.
Purpose of the Study:
- To analyze explosive percolation using k-mer random sequential adsorption (RSA).
- To investigate the impact of the Achlioptas process (AP) and inverse Achlioptas process (IAP) on k-mer percolation.
- To determine the universality class and critical exponents of these transitions.
Main Methods:
- Finite-size scaling analysis was employed.
- Numerical simulations of k-mer RSA with AP and IAP were conducted.
- Percolation threshold and critical exponents were calculated.
Main Results:
- Percolation transitions were confirmed as continuous.
- The universality class for k-mer explosive percolation with AP varied with k-mer size.
- The universality class for k-mer explosive percolation with IAP was independent of k but distinct from standard RSA.
Conclusions:
- K-mer size significantly influences the universality class in AP-driven explosive percolation.
- IAP provides a robust universality class for k-mer explosive percolation, distinct from standard RSA.
- The study elucidates the complex interplay between adsorption processes and percolation dynamics.
Related Concept Videos
01:10α-Alkylation of Ketones via Enolate Ions
3.3K
Ketones with α protons are deprotonated by strong bases like lithium diisopropylamide (LDA) to form enolate ions. The anion is stabilized by resonance, and its hybrid structure exhibits negative charges on the carbonyl oxygen and the α carbon. This ambident nucleophile can attack an electrophile via two possible sites: the carbonyl oxygen, known as O-attack, or the α carbon, known as C-attack. The nucleophilic attack via the carbanionic site is preferred. This is due to the...
3.3K
01:17Ziegler–Natta Chain-Growth Polymerization: Overview
3.4K
Ziegler–Natta polymerization is another form of addition or chain‐growth polymerization used for synthesizing linear polymers over branched polymers. The catalyst used for polymerization is the Ziegler–Natta catalyst, named after Karl Ziegler and Giulio Natta, who developed it in 1953. This catalyst is an organometallic complex of titanium tetrachloride and triethyl aluminum, with the active form of the catalyst being an alkyl titanium compound. Using the Ziegler–Natta...
3.4K
01:10Factors Affecting α-Alkylation of Ketones: Choice of Base
3.3K
α-Alkylation of ketones is achieved in the presence of alkyl halides and a base. The reaction proceeds via the formation of an enolate ion followed by nucleophilic substitution. The choice of base employed is essential as it is the key factor in determining the reaction outcome.
The reaction involving bases like EtO− whose conjugate acid EtOH (pKa = 15.9) is stronger than the ketone (pKa = 19.2) results in an equilibrium mixture with higher ketone concentration. As a consequence,...
The reaction involving bases like EtO− whose conjugate acid EtOH (pKa = 15.9) is stronger than the ketone (pKa = 19.2) results in an equilibrium mixture with higher ketone concentration. As a consequence,...
3.3K