Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organized criticality

2020 ◽  
pp. 2150029
Author(s):  
Marius Neuss
Keyword(s):  
Porous Media ◽  
Energy Functional ◽  
Physical Models ◽  
Well Posedness ◽  
Initial Value ◽  
Lipschitz Continuous ◽  
Self Organized ◽  
Porous Media Equations ◽  
Self Organized Criticality ◽  
Continuous Noise

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 criticality. We show that these SPDEs have unique SVI solutions which depend continuously on the initial value. In order to formulate this notion of solution and to prove uniqueness in the case of a slowly growing nonlinearity, the arising energy functional is analyzed in detail.

scholarly journals Stochastic Porous Media Equations and Self-Organized Criticality

2008 ◽  
Vol 285 (3) ◽  
pp. 901-923 ◽  
Author(s):  
Viorel Barbu ◽  
Giuseppe Da Prato ◽  
Michael Röckner
Keyword(s):  
Porous Media ◽  
Self Organized ◽  
Porous Media Equations ◽  
Self Organized Criticality

scholarly journals Ergodicity for Singular-Degenerate Stochastic Porous Media Equations

2021 ◽  
Author(s):  
Marius Neuß
Keyword(s):  
Porous Media ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Time Behaviour ◽  
Self Organized ◽  
Long Time Behaviour ◽  
Degenerate Form ◽  
Long Time ◽  
Porous Media Equations ◽  
Self Organized Criticality

AbstractThe long time behaviour of solutions to generalized stochastic porous media equations on bounded intervals with zero Dirichlet boundary conditions is studied. We focus on a degenerate form of nonlinearity arising in self-organized criticality. Based on the so-called lower bound technique, the existence and uniqueness of an invariant measure is proved.

scholarly journals A Self-Critique of Self-Organized Criticality in Astrophysics

2015 ◽  
Vol 11 (A29B) ◽  
pp. 735-736
Author(s):  
Markus J. Aschwanden
Keyword(s):  
Scaling Laws ◽  
Branching Processes ◽  
Physical Models ◽  
Asteroid Belt ◽  
Magnetospheric Substorms ◽  
Scale Free ◽  
Self Organized ◽  
Stellar Flares ◽  
Self Organized Criticality ◽  
Novel Applications

AbstractThe concept of “self-organized criticality” (SOC) was originally proposed as an explanation of 1/f-noise by Bak, Tang, and Wiesenfeld (1987), but turned out to have a far broader significance for scale-free nonlinear energy dissipation processes occurring in the entire universe. Over the last 30 years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into numerical SOC toy models. The novel applications stimulated also vigorous debates about the discrimination between SOC-related and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC models applied to astrophysical observations, attempt to describe what physics can be captured by SOC models, and offer a critique of weaknesses and strengths in existing SOC models.

scholarly journals STRONG SOLUTIONS FOR STOCHASTIC POROUS MEDIA EQUATIONS WITH JUMPS

2009 ◽  
Vol 12 (03) ◽  
pp. 413-426 ◽  
Author(s):  
VIOREL BARBU ◽  
CARLO MARINELLI
Keyword(s):  
Porous Media ◽  
Strong Solutions ◽  
Strong Sense ◽  
Well Posedness ◽  
Independent Increments ◽  
Integrable Martingale ◽  
Porous Media Equations

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by a square integrable martingale with stationary independent increments.

Problem behavior in autism spectrum disorders: A paradigmatic self-organized perspective of network structures

2019 ◽  
Vol 42 ◽  
Author(s):  
Lucio Tonello ◽  
Luca Giacobbi ◽  
Alberto Pettenon ◽  
Alessandro Scuotto ◽  
Massimo Cocchi ◽  
...  
Keyword(s):  
Autism Spectrum Disorder ◽  
Problem Behaviors ◽  
Autism Spectrum ◽  
The Self ◽  
Network Structures ◽  
Self Organized ◽  
Critical Equilibrium ◽  
Self Organized Criticality ◽  
Acute Agitation ◽  
Spectrum Disorders

AbstractAutism spectrum disorder (ASD) subjects can present temporary behaviors of acute agitation and aggressiveness, named problem behaviors. They have been shown to be consistent with the self-organized criticality (SOC), a model wherein occasionally occurring “catastrophic events” are necessary in order to maintain a self-organized “critical equilibrium.” The SOC can represent the psychopathology network structures and additionally suggests that they can be considered as self-organized systems.

Self-Organized Criticality in the Autowave Model of Speciation

2020 ◽  
Vol 75 (5) ◽  
pp. 398-408
Author(s):  
A. Y. Garaeva ◽  
A. E. Sidorova ◽  
N. T. Levashova ◽  
V. A. Tverdislov
Keyword(s):  
Self Organized ◽  
Self Organized Criticality

Modeling Extinction

2003 ◽  
Author(s):  
M. E. J. Newman ◽  
R. G. Palmer
Keyword(s):  
Evolutionary Biology ◽  
Large Scale ◽  
Competitive Exclusion ◽  
Applied Mathematics ◽  
Santa Fe ◽  
New Approach ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Extinction Events ◽  
Mass Extinction Events

Developed after a meeting at the Santa Fe Institute on extinction modeling, this book comments critically on the various modeling approaches. In the last decade or so, scientists have started to examine a new approach to the patterns of evolution and extinction in the fossil record. This approach may be called "statistical paleontology," since it looks at large-scale patterns in the record and attempts to understand and model their average statistical features, rather than their detailed structure. Examples of the patterns these studies examine are the distribution of the sizes of mass extinction events over time, the distribution of species lifetimes, or the apparent increase in the number of species alive over the last half a billion years. In attempting to model these patterns, researchers have drawn on ideas not only from paleontology, but from evolutionary biology, ecology, physics, and applied mathematics, including fitness landscapes, competitive exclusion, interaction matrices, and self-organized criticality. A self-contained review of work in this field.

Fractals, self-organized-criticality and the fixed scale transformation

1995 ◽  
Vol 6 ◽  
pp. 471-480 ◽  
Author(s):  
L. Pietronero ◽  
A. Vespignani
Keyword(s):  
Scale Transformation ◽  
Self Organized ◽  
Self Organized Criticality
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