scholarly journals Clustering and assembly dynamics of a one-dimensional microphase former

Soft Matter ◽  
2018 ◽  
Vol 14 (20) ◽  
pp. 4101-4109 ◽  
Author(s):  
Yi Hu ◽  
Patrick Charbonneau
Keyword(s):  
Detailed Analysis ◽  
Long Range ◽  
Short Range ◽  
Dimensional Model ◽  
One Dimensional

We consider a one-dimensional model of short range attraction and long range repulsion interactions whose simplicity enables detailed analysis.

Nanoscale Pattern Formation in Polyelectrolyte Gels

2009 ◽  
Vol 1234 ◽  
Author(s):  
Prateek K. Jha ◽  
Francisco J. Solis ◽  
Juan J. de Pablo ◽  
Monica Olvera de la Cruz
Keyword(s):  
Pattern Formation ◽  
Phase Behavior ◽  
Long Range ◽  
Short Range ◽  
Physical Parameters ◽  
Finite Range ◽  
Complex Phase ◽  
One Dimensional ◽  
Polyelectrolyte Gels ◽  
Poor Solvent

AbstractPolyelectrolyte (PE) gels exhibit complex phase behavior that includes the existence of nanostructures in poor-solvent conditions. The formation of these inhomogeneous structures is made possible by the competition between the short-range hydrophobic, elastic, and entropic interactions and the long-range electrostatic forces. We develop a theoretical framework that describes the effect of monomer and charge inhomogeneities in PE gels. Numerical calculations performed on a salt-free PE gel with one-dimensional heterogeneities demonstrate the presence of nanophases for a finite range of physical parameters.

scholarly journals How many particles make up a chaotic many-body quantum system?

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Guy Zisling ◽  
Lea Santos ◽  
Yevgeny Bar Lev
Keyword(s):  
Long Range ◽  
Quantum Chaos ◽  
Short Range ◽  
Many Body ◽  
Interacting Particles ◽  
One Dimensional ◽  
Long Range Interactions ◽  
Minimum Number ◽  
Many Particles ◽  
Number Of Particles

We numerically investigate the minimum number of interacting particles, which is required for the onset of strong chaos in quantum systems on a one-dimensional lattice with short-range and long-range interactions. We consider multiple system sizes which are at least three times larger than the number of particles and find that robust signatures of quantum chaos emerge for as few as 4 particles in the case of short-range interactions and as few as 3 particles for long-range interactions, and without any apparent dependence on the size of the system.

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