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Martínez-Calvo A, Biviano MD, Christensen AH, Katifori E, Jensen KH, Ruiz-García M. The fluidic memristor as a collective phenomenon in elastohydrodynamic networks. Nat Commun 2024; 15:3121. [PMID: 38600060 PMCID: PMC11006656 DOI: 10.1038/s41467-024-47110-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Accepted: 03/19/2024] [Indexed: 04/12/2024] Open
Abstract
Fluid flow networks are ubiquitous and can be found in a broad range of contexts, from human-made systems such as water supply networks to living systems like animal and plant vasculature. In many cases, the elements forming these networks exhibit a highly non-linear pressure-flow relationship. Although we understand how these elements work individually, their collective behavior remains poorly understood. In this work, we combine experiments, theory, and numerical simulations to understand the main mechanisms underlying the collective behavior of soft flow networks with elements that exhibit negative differential resistance. Strikingly, our theoretical analysis and experiments reveal that a minimal network of nonlinear resistors, which we have termed a 'fluidic memristor', displays history-dependent resistance. This new class of element can be understood as a collection of hysteresis loops that allows this fluidic system to store information, and it can be directly used as a tunable resistor in fluidic setups. Our results provide insights that can inform other applications of fluid flow networks in soft materials science, biomedical settings, and soft robotics, and may also motivate new understanding of the flow networks involved in animal and plant physiology.
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Affiliation(s)
- Alejandro Martínez-Calvo
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, 08544, USA
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ, USA
| | - Matthew D Biviano
- Department of Physics, Technical University of Denmark, DK 2800, Kgs. Lyngby, Denmark
| | | | - Eleni Katifori
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 19104, USA
- Center for Computational Biology, Flatiron Institute, New York, NY, 10010, USA
| | - Kaare H Jensen
- Department of Physics, Technical University of Denmark, DK 2800, Kgs. Lyngby, Denmark
| | - Miguel Ruiz-García
- Departamento de Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense Madrid, 28040, Madrid, Spain.
- GISC - Grupo Interdisciplinar de Sistemas Complejos, Universidad Complutense Madrid, 28040, Madrid, Spain.
- Department of Mathematics, Universidad Carlos III de Madrid, 28911, Leganés, Spain.
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Bhowmik BP, Moshe M, Procaccia I. Direct measurement of dipoles in anomalous elasticity of amorphous solids. Phys Rev E 2022; 105:L043001. [PMID: 35590659 DOI: 10.1103/physreve.105.l043001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Accepted: 03/16/2022] [Indexed: 06/15/2023]
Abstract
Recent progress in studying the physics of amorphous solids has revealed that mechanical strains can be strongly screened by the formation of plastic events that are typically quadrupolar in nature. The theory stipulates that gradients in the density of the quadrupoles act as emergent dipole sources, leading to strong screening and to qualitative changes in the mechanical response, as seen, for example, in the displacement field. In this Letter we first offer direct measurements of the dipole field, independently of any theoretical assumptions, and second we demonstrate detailed agreement with the recently proposed theory. These two goals are achieved by using data from both simulations and experiments. Finally, we show how measurements of the dipole fields pinpoint the theory parameters that determine the profile of the displacement field.
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Affiliation(s)
- Bhanu Prasad Bhowmik
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Michael Moshe
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 9190, Israel
| | - Itamar Procaccia
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
- Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an 710072, China
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Lemaître A, Mondal C, Moshe M, Procaccia I, Roy S, Screiber-Re'em K. Anomalous elasticity and plastic screening in amorphous solids. Phys Rev E 2021; 104:024904. [PMID: 34525578 DOI: 10.1103/physreve.104.024904] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2021] [Accepted: 08/04/2021] [Indexed: 11/07/2022]
Abstract
Amorphous solids appear to react elastically to small external strains, but in contrast to ideal elastic media, plastic responses abound immediately at any value of the strain. Such plastic responses are quasilocalized in nature, with the "cheapest" one being a quadrupolar source. The existence of such plastic responses results in screened elasticity in which strains and stresses can either quantitatively or qualitatively differ from the unscreened theory, depending on the specific screening mechanism. Here we offer a theory of such screening effects by plastic quadrupoles, dipoles, and monopoles, explain their natural appearance, and point out the analogy to electrostatic screening by electric charges and dipoles. For low density of quadrupoles the effect is to normalize the elastic moduli without a qualitative change compared to pure elasticity theory; for higher density of quadrupoles the screening effects result in qualitative changes. Predictions for the spatial dependence of displacement fields caused by local sources of strains are provided and compared to numerical simulations. We find that anomalous elasticity is richer than electrostatics in having a screening mode that does not appear in the electrostatic analog.
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Affiliation(s)
- Anaël Lemaître
- NAVIER, UMR 8205, École des Ponts ParisTech, IFSTTAR, CNRS, UPE, Champs-sur-Marne, France
| | - Chandana Mondal
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Michael Moshe
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, 9190 Israel
| | - Itamar Procaccia
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, 710072 China
| | - Saikat Roy
- Department of Chemical Engineering, Indian Institute of Technology Ropar, Punjab 140001, India
| | - Keren Screiber-Re'em
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, 9190 Israel
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Sarkar S, Čebron M, Brojan M, Košmrlj A. Method of image charges for describing deformation of bounded two-dimensional solids with circular inclusions. Phys Rev E 2021; 103:053004. [PMID: 34134231 DOI: 10.1103/physreve.103.053004] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Accepted: 03/17/2021] [Indexed: 02/04/2023]
Abstract
We present a method for predicting the linear response deformation of finite and semi-infinite 2D solid structures with circular holes and inclusions by employing the analogies with image charges and induction in electrostatics. Charges in electrostatics induce image charges near conductive boundaries and an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects. Similarly, charges in elasticity induce image charges near boundaries and external stress induces polarization (quadrupoles and other multipoles) inside holes and inclusions. Stresses generated by these induced elastic multipoles as well as stresses generated by their images near boundaries then lead to interactions between holes and inclusions and with their images, which induce additional polarization and thus additional deformation of holes and inclusions. We present a method that expands induced polarization in a series of elastic multipoles, which systematically takes into account the interactions of inclusions and holes with the external field, between them, and with their images. The results of our method for linear deformation of circular holes and inclusions near straight and curved boundaries show good agreement with both linear finite element simulations and experiments.
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Affiliation(s)
- Siddhartha Sarkar
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Matjaž Čebron
- Faculty of Mechanical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Miha Brojan
- Faculty of Mechanical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Andrej Košmrlj
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA.,Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
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