# Small-scale behaviour in deterministic reaction models

@article{Politi2010SmallscaleBI, title={Small-scale behaviour in deterministic reaction models}, author={Paolo Politi and Daniel ben-Avraham}, journal={Journal of Physics A}, year={2010}, volume={43}, pages={405002} }

In a recent paper published in this journal (2009 J. Phys. A: Math. Theor. 42 495004) we studied a one-dimensional particles system where nearest particles attract with a force inversely proportional to a power ? of their distance and coalesce upon encounter. Numerics yielded a distribution function h(z) for the gap between neighbouring particles, with h(z) ~ z?(?) for small z and ?(?) > ?. We can now prove analytically that in the strict limit of z ? 0, ? = ? for ? > 0, corresponding to the…

## References

SHOWING 1-10 OF 13 REFERENCES

Deterministic reaction models with power-law forces

- Mathematics, Physics
- 2009

We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power α of their distance and coalesce upon encounter.…

From the conserved Kuramoto-Sivashinsky equation to a coalescing particles model

- Mathematics, Physics
- 2009

Abstract The conserved Kuramoto–Sivashinsky (CKS) equation, ∂ t u = − ∂ x x ( u + u x x + u x 2 ) , has recently been derived in the context of crystal growth, and it is also strictly related to a…

A particle model for the Kuramoto-Sivashinsky equation

- Physics
- 1995

Abstract We present a model of a gas of interacting particles on the line which exhibits spatiotemporal chaos. It possesses the symmetries and elementary microscopic properties of the one-dimensional…

Annihilation of charged particles.

- Physics, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

The kinetics of irreversible annihilation of charged particles performing overdamped motion induced by long-range interaction force, $F(r))\sim r^{-\lambda}$, is investigated and the asymptotic behavior is shown to be dependent on system size.

Universal Scaling in the Motion of Random Interfaces

- Physics
- 1982

The dynamics of interfaces where the normal component of an interface velocity is proportional to the curvature is studied. The dynamic structure function due to the motion of random interfaces is…

Phase-ordering kinetics of one-dimensional nonconserved scalar systems.

- Physics, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1994

The short-range solution also applies to systems with long-range interactions when \ensureMath{\sigma}\ensuremath{\rightarrow}\ensurmath{\infty}, and in that limit the amplitude of the growth law is exactly calculated.

Phys

- Rev. E 53, 3154
- 1996

Physica D 88

- 1
- 1995

Phys

- Rev. E 50, 1900
- 1994