## Project Details

### Description

Project Summary This three-year proposal on Algorithms for self-organizing particle systems is submitted to the NSF CCF-AF program, by Andrea W. Richa, Arizona State University. The goal of the proposed research is to lay the foundations for algorithmic research on self-organizing particle systems. Particle systems are physical systems of simple computational particles that can bond to other particles and that can use these bonds in order to communicate with neighboring particles and to move from one spot to another (non-occupied) spot. These particle systems are supposed to be able to self-organize in order to adapt to a desired shape without any central control. Self-organizing particle systems have many interesting applications like coating objects for monitoring and repair purposes and the formation of nano-scale devices for surgery and molecular-scale electronic structures. While there has been quite a lot of systems work in this area, especially in the context of modular self-reconfigurable robotic systems, only very little theoretical work has been done in this area so far. Our goal will be to prepare the ground for rigorous algorithmic research on self-organizing particle systems by proposing some basic models and solving some basic algorithmic problems in this area. More specifically, our research objective is to investigate distributed algorithms for self-organizing particle systems that can form a desired shape. Concretely, we are interested in finding algorithms for the following types of problems. Smart paint problems: Here, the problem is to cover the surface of a 2D- or 3D-object with a connected particle structure. Shape formation problems: Here, we will investigate ways of arranging particles so that they form a desired shape. Bridging and covering problems: Here, we will investigate ways of covering or bridging gaps. While we have already developed a model for 2D-particle structures (which is presented below), part of the research will also be to develop suitable models for 3D-structures, which are more complex as certain issues like gravity cannot be ignored in some cases. Our main analytical goal will be to show that our algorithms are correct, i.e., the particles eventually reach the given goal from any initial shape as long as they are well-initialized. Besides that, we will also study the efficiency and robustness of our strategies. A major issue for efficiency will be that we use methods that allow a high degree of parallelism so that they also work effectively for huge amounts of particles. Robustness is a key property for these systems as the particles might be simple and therefore error prone and the particle structures need to persist in noisy environments. Our basic strategy in this context will be to pursue the design of self-stabilizing algorithms. For all of these aspects, theoretical research is basically non-existent, so groundwork is need here to set up a solid base. Intellectual Merit This project will aim at bridging the gap between applied and theoretical research in selforganizing particle systems, and to significantly advance the field of self-organizing particle systems from an algorithmic/ computational point-of-view. It will provide the basic theoretical foundation that will allow for rigorous algorithmic research on self-organizing particle systems, by proposing basic models for 2D- and 3D particle structures and by developing robust and efficient algorithms for self-organizing particle systems that can form a desired shape. Broader Impact We anticipate that the proposed research will have an impact in several respects, such as: (i) bridging the large gap between theory and practice in the area of self-organizing particle systems, with impact on many application areas such as microfabrication and cellular engineering; (ii) international collaboration, since we will further foster the successful collaboration with Prof. Scheideler and the U. of Paderborn, Germany; (iii) multidisciplinary activities, since the topics in this proposal will foster collaboration with researchers in transdisciplinary areas such as nano-scale microfabrication, cellular engineering, nano-scale medical applications, biochemistry, etc.; (iv) advancing education and enhancing diversity at ASU. Keywords: Particle systems; self-organization; nano-structures; nano-computing.

Status | Finished |
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Effective start/end date | 8/1/14 → 7/31/19 |

### Funding

- National Science Foundation (NSF): $490,000.00

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