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}
}
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… 

Figures from this paper

References

SHOWING 1-10 OF 36 REFERENCES

Asymptotic Dynamics of Attractive-Repulsive Swarms

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.

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.

High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids

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.

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

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