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Collaborative Research: Universal models of self-organized criticality
NSF
About This Grant
Fractals and power-law tails are ubiquitous in nature and are also the hallmarks of statistical physics systems at criticality. Theoretical physicists in the late 1980s proposed that this could be explained by natural systems spontaneously converging to critical states. This theory of self-organized criticality is widely accepted by physicists based on their simulations of simple mathematical sandpile models, which appear to self-organize. But these models are poorly understood mathematically and in some cases have been proven to behave contrary to physicists' expectations. This project aims to establish that activated random walk serves as a suitable mathematical model for self-organized criticality with the universality expected by physicists, and to investigate its behavior. The results of this project will be important not just to mathematicians but to physicists as well. This project involves graduate and undergraduate students. Activated random walk and the stochastic sandpile model are two of the mathematical models thought to exhibit self-organized criticality. One concrete goal of the project is to prove the density conjecture for activated random walk in dimensions two and higher. We will do this by establishing that the driven-dissipative version of activated random walk converges to the critical density of the fixed-energy version. We will also study the mixing time of the driven-dissipative activated random walk in all dimensions and determine critical exponents of activated random walk. Finally we will establish similar results for the stochastic sandpile model. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
Grant Summary
Collaborative Research: Universal models of self-organized criticality is a NSF grant providing up to $100K for university, nonprofit, small business. Applications are due 2026-08-31 (open). Check eligibility and apply with FindGrants.
Focus Areas
Eligibility
How to Apply
Up to $100K
2026-08-31
- 1Confirm your organization is eligible for Collaborative Research: Universal models of self-organized criticality from NSF, checking organization type, location, and any population or project requirements.
- 2Gather the required documents and information, including your organization details, project plan, and budget figures.
- 3Draft your application narrative and budget addressing the funder's priorities and review criteria. FindGrants can draft each section for you to review and edit.
- 4Review every section against the requirements checklist, then export a submission-ready application pack and submit it to NSF before the deadline.
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Collaborative Research: Universal models of self-organized criticality: Frequently Asked Questions
Who is eligible for the Collaborative Research: Universal models of self-organized criticality?
Collaborative Research: Universal models of self-organized criticality is offered by NSF and is generally open to university, nonprofit, small business. It is open to organizations nationwide unless the funder specifies otherwise. Review the specific eligibility terms before applying, since funders set their own requirements around organization type, location, and the population or project being served.
How much funding does the Collaborative Research: Universal models of self-organized criticality provide?
Collaborative Research: Universal models of self-organized criticality provides up to $100K per award from NSF. Actual award sizes depend on the scope of your project, available program funds, and the number of applicants, so build a budget that reflects realistic, allowable costs rather than the maximum figure.
When is the Collaborative Research: Universal models of self-organized criticality deadline?
Applications for Collaborative Research: Universal models of self-organized criticality are due 2026-08-31 (open). Because deadlines can change, verify the date with the funder, NSF, and give yourself enough time to prepare a complete, competitive application before the close date.
How do you apply for the Collaborative Research: Universal models of self-organized criticality?
To apply for Collaborative Research: Universal models of self-organized criticality, confirm your eligibility, gather the required documents, and prepare a narrative and budget that address the funder's priorities. FindGrants guides you step by step and can draft each section, then exports a submission-ready application pack for this grant from NSF.