# Collective Dynamics of Interacting Particles in Unsteady Flows

@article{Abedi2014CollectiveDO,
title={Collective Dynamics of Interacting Particles in Unsteady Flows},
author={Maryam Abedi and Mir Abbas Jalali},
journal={SIAM J. Appl. Dyn. Syst.},
year={2014},
volume={13},
pages={194-209}
}
• Published 11 February 2014
• Physics
• SIAM J. Appl. Dyn. Syst.
We use the Fokker--Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive potential field known as Morse potential. We assume Stokesian drag force between particles and their carrier fluid and find analytic single-peaked traveling solutions for the spatial density of particles in the catastrophic phase. In steady flow conditions the…

## References

SHOWING 1-10 OF 36 REFERENCES

### Asymptotic Dynamics of Attractive-Repulsive Swarms

• Mathematics
SIAM J. Appl. Dyn. Syst.
• 2009
An analytical upper bound is derived for the finite blow-up time after which the solution forms one or more $\delta$-functions of the conservation equation.

### Numerical Simulations of the Fourier-Transformed Vlasov-Maxwell System in Higher Dimensions—Theory and Applications

We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for

### Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling.

• Mathematics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2012
The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations.

### Unstable Disk Galaxies. I. Modal Properties

I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first-order

### Self-organization in systems of self-propelled particles.

• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2001
A continuum version of the discrete model consisting of self-propelled particles that obey simple interaction rules is developed and it is demonstrated that the agreement between the discrete and the continuum model is excellent.

### Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach

• Mathematics
Journal of Fluid Mechanics
• 2012
Abstract Aquatic bacteria like Bacillus subtilis are heavier than water yet they are able to swim up an oxygen gradient and concentrate in a layer below the water surface, which will undergo