• Corpus ID: 233407593

Stochastic partial differential equations arising in self-organized criticality

@article{Baas2021StochasticPD,
  title={Stochastic partial differential equations arising in self-organized criticality},
  author={Lubom{\'i}r Ba{\~n}as and Benjamin Gess and Marius Neu{\ss}},
  journal={ArXiv},
  year={2021},
  volume={abs/2104.13336}
}
Scaling limits for the weakly driven Zhang and the Bak-Tang-Wiesenfeld (BTW) model for self-organized criticality are considered. It is shown that the weakly driven Zhang model converges to a stochastic PDE with singular-degenerate diffusion. In addition, the deterministic BTW model is proved to converge to a singular-degenerate PDE. Alternatively, the proof of convergence can be understood as a proof of convergence of a finite-difference discretization for singular-degenerate stochastic PDE… 
Self-Organised Critical Dynamics as a Key to Fundamental Features of Complexity in Physical, Biological, and Social Networks
Studies of many complex systems have revealed new collective behaviours that emerge through the mechanisms of self-organised critical fluctuations. Subject to the external and endogenous driving

References

SHOWING 1-10 OF 90 REFERENCES
Self-organized criticality via stochastic partial differential equations
Models of self-organized criticality, which can be described as singular diffusions with or without (multiplicative) Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models), are
Singular-Degenerate Multivalued Stochastic Fast Diffusion Equations
TLDR
A well-posedness framework based on Stochastic variational inequalities (SVI) is developed, characterizing solutions to the stochastic sign fast diffusion equation, previously obtained in a limiting sense only.
Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organized criticality
We consider a class of generalized stochastic porous media equations with multiplicative Lipschitz continuous noise. These equations can be related to physical models exhibiting self-organized
Self-organized criticality and convergence to equilibrium of solutions to nonlinear diffusion equations
  • V. Barbu
  • Mathematics
    Annu. Rev. Control.
  • 2010
Stochastic Porous Media Equations and Self-Organized Criticality
The existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and Wiener forcing term is proven. The finite time
Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise
We prove the existence of non-negative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal
Existence of Positive Solutions to Stochastic Thin-Film Equations
TLDR
Having established Holder regularity of approximate solutions, the convergence proof is based on compactness arguments---in particular on Jakubowski's generalization of Skorokhod's theorem---weak convergence methods, and recent tools on martingale convergence.
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