# Lattice gases with a point source

@article{Krapivsky2014LatticeGW, title={Lattice gases with a point source}, author={Paul L. Krapivsky and Darko Stefanovic}, journal={arXiv: Statistical Mechanics}, year={2014} }

We study diffusive lattice gases with local injection of particles, namely we assume that whenever the origin becomes empty, a new particle is immediately injected into the origin. We consider two lattice gases: a symmetric simple exclusion process and random walkers. The interplay between the injection events and the positions of the particles already present implies an effective collective interaction even for the ostensibly non-interacting random walkers. We determine the average total…

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## References

SHOWING 1-10 OF 59 REFERENCES

Symmetric exclusion process with a localized source.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

The growth of the total number of particles in a symmetric exclusion process driven by a localized source grows with time as √t in one dimension, t/lnt in two dimensions, and linearly in higher dimensions.

Territory covered by N diffusing particles

- MathematicsNature
- 1992

THE number of distinct sites visited by a random walker after t steps is of great interest1–21, as it provides a direct measure of the territory covered by a diffusing particle. Thus, this quantity…

Diffusion-driven spreading phenomena: the structure of the hull of the visited territory.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

The hull of the territory visited by N random walkers after t time steps is studied and it is found that for all of them, the structure of the hull is self-similar and described by a fractal dimension d(H) that slowly approaches, with an increasing number of time steps, the value d( H)=4/3.

Exact time-dependent correlation functions for the symmetric exclusion process with open boundary.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

The symmetric exclusion model provides a rare example where such behavior can be proved rigorously on the level of equal-time two-point correlation functions.

Universal cumulants of the current in diffusive systems on a ring.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

This work calculates exactly the first cumulants of the integrated current and of the activity of the symmetric simple exclusion process on a ring with periodic boundary conditions and indicates that for large system sizes the large deviation functions of the current and the activity take a universal scaling form.

Universal fluctuations in the support of the random walk

- Mathematics, Physics
- 1997

A random walk starts from the origin of ad-dimensional lattice. The occupation numbern(x,t) equals unity if aftert steps site x has been visited by the walk, and zero otherwise. We study…

Statistical properties of the set of sites visited by the two-dimensional random walk

- Mathematics
- 1997

We study the support (i.e. the set of visited sites) of a t-step random walk on a two-dimensional square lattice in the large t limit. A broad class of global properties, M(t), of the support is…

Sorting single events: mean arrival times of N random walkers.

- Mathematics, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1999

This work investigates the first passage time for the first out of N identical independently diffusing particles in ordered and disordered structures and proposes a scaling behavior for the related quantity S(N)(t), the number of distinct sites visited by N particles.

Territory covered by N random walkers.

- Mathematics, PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1999

The problem of evaluating the number of distinct sites S(N)(t) covered up to time t by N random walkers is revisited and the asymptotic behavior is shown and the main and first two corrective terms are calculated.

Scaling Limits of Interacting Particle Systems

- Mathematics
- 1998

1. An Introductory Example: Independent Random Walks.- 2. Some Interacting Particle Systems.- 3. Weak Formulations of Local Equilibrium.- 4. Hydrodynamic Equation of Symmetric Simple Exclusion…