Feedback-Induced Phase Transitions in Active Heterogeneous Conductors
An active conducting medium is one where the resistance (conductance) of the medium is modified by the current (flow) and in turn modifies the flow, so that the classical linear laws relating current and resistance, e.g., Ohm’s law or Darcy’s law, are modified over time as the system itself evolves....
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| Format: | Article |
| Language: | English |
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American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/96370 https://orcid.org/0000-0002-1069-008X |
| _version_ | 1826189944834490368 |
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| author | Mahadevan, L. Ocko, Samuel Alan |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Mahadevan, L. Ocko, Samuel Alan |
| author_sort | Mahadevan, L. |
| collection | MIT |
| description | An active conducting medium is one where the resistance (conductance) of the medium is modified by the current (flow) and in turn modifies the flow, so that the classical linear laws relating current and resistance, e.g., Ohm’s law or Darcy’s law, are modified over time as the system itself evolves. We consider a minimal model for this feedback coupling in terms of two parameters that characterize the way in which addition or removal of matter follows a simple local (or nonlocal) feedback rule corresponding to either flow-seeking or flow-avoiding behavior. Using numerical simulations and a continuum mean field theory, we show that flow-avoiding feedback causes an initially uniform system to become strongly heterogeneous via a tunneling (channel-building) phase separation; flow-seeking feedback leads to an immuring (wall-building) phase separation. Our results provide a qualitative explanation for the patterning of active conducting media in natural systems, while suggesting ways to realize complex architectures using simple rules in engineered systems. |
| first_indexed | 2024-09-23T08:31:32Z |
| format | Article |
| id | mit-1721.1/96370 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:31:32Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/963702022-09-30T09:25:39Z Feedback-Induced Phase Transitions in Active Heterogeneous Conductors Mahadevan, L. Ocko, Samuel Alan Massachusetts Institute of Technology. Department of Physics Ocko, Samuel Alan An active conducting medium is one where the resistance (conductance) of the medium is modified by the current (flow) and in turn modifies the flow, so that the classical linear laws relating current and resistance, e.g., Ohm’s law or Darcy’s law, are modified over time as the system itself evolves. We consider a minimal model for this feedback coupling in terms of two parameters that characterize the way in which addition or removal of matter follows a simple local (or nonlocal) feedback rule corresponding to either flow-seeking or flow-avoiding behavior. Using numerical simulations and a continuum mean field theory, we show that flow-avoiding feedback causes an initially uniform system to become strongly heterogeneous via a tunneling (channel-building) phase separation; flow-seeking feedback leads to an immuring (wall-building) phase separation. Our results provide a qualitative explanation for the patterning of active conducting media in natural systems, while suggesting ways to realize complex architectures using simple rules in engineered systems. Henry W. Kendall Physics Fellowship Human Frontier Science Program (Strasbourg, France) (Grant RGP0066/2012-TURNER) 2015-04-03T16:04:38Z 2015-04-03T16:04:38Z 2015-04 2014-02 2015-04-02T22:00:07Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/96370 Ocko, Samuel A., and L. Mahadevan. "Feedback-Induced Phase Transitions in Active Heterogeneous Conductors" Phys. Rev. Lett. 114, 134501 (April 2015). © 2015 American Physical Society https://orcid.org/0000-0002-1069-008X en http://dx.doi.org/10.1103/PhysRevLett.114.134501 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Mahadevan, L. Ocko, Samuel Alan Feedback-Induced Phase Transitions in Active Heterogeneous Conductors |
| title | Feedback-Induced Phase Transitions in Active Heterogeneous Conductors |
| title_full | Feedback-Induced Phase Transitions in Active Heterogeneous Conductors |
| title_fullStr | Feedback-Induced Phase Transitions in Active Heterogeneous Conductors |
| title_full_unstemmed | Feedback-Induced Phase Transitions in Active Heterogeneous Conductors |
| title_short | Feedback-Induced Phase Transitions in Active Heterogeneous Conductors |
| title_sort | feedback induced phase transitions in active heterogeneous conductors |
| url | http://hdl.handle.net/1721.1/96370 https://orcid.org/0000-0002-1069-008X |
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