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Devauchelle O, Szymczak P, Nowakowski P. Dislike of general opinion makes for tight elections. Phys Rev E 2024; 109:044106. [PMID: 38755890 DOI: 10.1103/physreve.109.044106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Accepted: 02/19/2024] [Indexed: 05/18/2024]
Abstract
In modern democracies, the outcome of elections and referendums is often remarkably tight. The repetition of these divisive events are the hallmark of a split society; to the physicist, however, it is an astonishing feat for such large collections of diverse individuals. Many sociophysics models reproduce the emergence of collective human behavior with interacting agents, which respond to their environment according to simple rules, modulated by random fluctuations. A paragon of this class is the Ising model which, when interactions are strong, predicts that order can emerge from a chaotic initial state. In contrast with many elections, however, this model favors a strong majority. Here we introduce a new element to this classical theory, which accounts for the influence of opinion polls on the electorate. This brings about a new phase in which two groups divide the opinion equally. These political camps are spatially segregated, and the sharp boundary that separates them makes the system size dependent, even in the limit of a large electorate. Election data show that, since the early 1990s, countries with more than about a million voters often found themselves in this state, whereas elections in smaller countries yielded more consensual results. We suggest that this transition hinges on the electorate's awareness of the general opinion.
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Affiliation(s)
- O Devauchelle
- Université Paris Cité, Institut de Physique du Globe de Paris, CNRS, 1 rue Jussieu, 75238 Paris, France
| | - P Szymczak
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - P Nowakowski
- Group for Computational Life Sciences, Division of Physical Chemistry, Ruđer Bošković Institute, Bijenička cesta 54, 10000 Zagreb, Croatia and Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany
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Abramian A, Devauchelle O, Lajeunesse E. Laboratory rivers adjust their shape to sediment transport. Phys Rev E 2020; 102:053101. [PMID: 33327102 DOI: 10.1103/physreve.102.053101] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Accepted: 10/10/2020] [Indexed: 11/07/2022]
Abstract
An alluvial river builds its own bed with the sediment it transports; its shape thus depends not only on its water discharge but also on the sediment supply. Here we investigate the influence of the latter in laboratory experiments. We find that, as their natural counterpart, laboratory rivers widen to accommodate an increase of sediment supply. By tracking individual particles as they travel downstream, we show that, at equilibrium, the river shapes its channel so that the intensity of sediment transport follows a Boltzmann distribution. This mechanism selects a well-defined width over which the river transports sediment, while the sediment remains virtually idle on its banks. For lack of a comprehensive theory, we represent this behavior with a single-parameter empirical model which accords with our observations.
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Affiliation(s)
- A Abramian
- Université de Paris, Institut de physique du globe de Paris, CNRS, F-75005 Paris, France.,Sorbonne Université, Institut Jean Le Rond d'Alembert, CNRS, F-75005 Paris, France
| | - O Devauchelle
- Université de Paris, Institut de physique du globe de Paris, CNRS, F-75005 Paris, France
| | - E Lajeunesse
- Université de Paris, Institut de physique du globe de Paris, CNRS, F-75005 Paris, France
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Abstract
The coupling of sediment transport with the flow that drives it allows rivers to shape their own bed. Cross-stream fluxes of sediment play a crucial, yet poorly understood, role in this process. Here, we track particles in a laboratory flume to relate their statistical behavior to the self-organization of the granular bed they make up. As they travel downstream, the transported grains wander randomly across the bed's surface, thus inducing cross-stream diffusion. The balance of diffusion and gravity results in a peculiar Boltzmann distribution, in which the bed's roughness plays the role of thermal fluctuations, while its surface forms the potential well that confines the sediment flux.
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Affiliation(s)
- A Abramian
- Institut de Physique du Globe de Paris, 1 rue Jussieu, 75238 Paris, France
| | - O Devauchelle
- Institut de Physique du Globe de Paris, 1 rue Jussieu, 75238 Paris, France
| | - G Seizilles
- Institut de Physique du Globe de Paris, 1 rue Jussieu, 75238 Paris, France
| | - E Lajeunesse
- Institut de Physique du Globe de Paris, 1 rue Jussieu, 75238 Paris, France
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Abstract
Using laboratory experiments, we investigate the influence of water and sediment discharges on the morphology of an alluvial fan. In our flume, a single-thread laminar river deposits corundum sand into a conical fan. We record the fan progradation with top-view images and measure its shape using the deformation of a Moiré pattern. The fan remains virtually self-affine as it grows, with a nearly constant slope. We find that, when the sediment discharge is small, the longitudinal slope of the fan remains close to that of a river at the threshold for sediment transport. Consequently the slope depends on the water discharge only. A higher sediment discharge causes the fan's slope to depart from the threshold value. Due to the downstream decrease of the sediment load, this slope gets shallower towards the fan's toe. This mechanism generates a concave fan profile. This suggests that we could infer the sediment flux that feeds a fan based on its proximal slope.
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Affiliation(s)
- P Delorme
- Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris Diderot, CNRS, UMR7154, 1 rue Jussieu, 75238 Paris Cedex 05, France
| | - O Devauchelle
- Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris Diderot, CNRS, UMR7154, 1 rue Jussieu, 75238 Paris Cedex 05, France
| | - L Barrier
- Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris Diderot, CNRS, UMR7154, 1 rue Jussieu, 75238 Paris Cedex 05, France
| | - F Métivier
- Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris Diderot, CNRS, UMR7154, 1 rue Jussieu, 75238 Paris Cedex 05, France
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Devauchelle O, Szymczak P, Pecelerowicz M, Cohen Y, Seybold HJ, Rothman DH. Laplacian networks: Growth, local symmetry, and shape optimization. Phys Rev E 2017; 95:033113. [PMID: 28415309 DOI: 10.1103/physreve.95.033113] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2016] [Indexed: 06/07/2023]
Abstract
Inspired by river networks and other structures formed by Laplacian growth, we use the Loewner equation to investigate the growth of a network of thin fingers in a diffusion field. We first review previous contributions to illustrate how this formalism reduces the network's expansion to three rules, which respectively govern the velocity, the direction, and the nucleation of its growing branches. This framework allows us to establish the mathematical equivalence between three formulations of the direction rule, namely geodesic growth, growth that maintains local symmetry, and growth that maximizes flux into tips for a given amount of growth. Surprisingly, we find that this growth rule may result in a network different from the static configuration that optimizes flux into tips.
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Affiliation(s)
- O Devauchelle
- Institut de Physique du Globe de Paris, 1 rue Jussieu, 75238 Paris, France
| | - P Szymczak
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland
| | - M Pecelerowicz
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland
| | - Y Cohen
- Lorenz Center, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - H J Seybold
- Institute of Terrestrial Ecosystems, Department of Environmental Systems Science, ETH Zurich, Universitätstrasse 16, 8092 Zürich, Switzerland
| | - D H Rothman
- Lorenz Center, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Guerit L, Métivier F, Devauchelle O, Lajeunesse E, Barrier L. Laboratory alluvial fans in one dimension. Phys Rev E Stat Nonlin Soft Matter Phys 2014; 90:022203. [PMID: 25215729 DOI: 10.1103/physreve.90.022203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2014] [Indexed: 06/03/2023]
Abstract
When they reach a flat plain, rivers often deposit their sediment load into a cone-shaped structure called alluvial fan. We present a simplified experimental setup that reproduces, in one dimension, basic features of alluvial fans. A mixture of water and glycerol transports and deposits glass beads between two transparent panels separated by a narrow gap. As the beads, which mimic natural sediments, get deposited in this gap, they form an almost one-dimensional fan. At a moderate sediment discharge, the fan grows quasistatically and maintains its slope just above the threshold for sediment transport. The water discharge determines this critical slope. At leading order, the sediment discharge only controls the velocity at which the fan grows. A more detailed analysis reveals a slight curvature of the fan profile, which relates directly to the rate at which sediments are transported.
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Affiliation(s)
- L Guerit
- Institut de Physique du Globe de Paris -Sorbonne Paris Cité, Université Paris Diderot, CNRS, UMR7154, 1 rue Jussieu, 75238 Paris Cedex 05, France
| | - F Métivier
- Institut de Physique du Globe de Paris -Sorbonne Paris Cité, Université Paris Diderot, CNRS, UMR7154, 1 rue Jussieu, 75238 Paris Cedex 05, France
| | - O Devauchelle
- Institut de Physique du Globe de Paris -Sorbonne Paris Cité, Université Paris Diderot, CNRS, UMR7154, 1 rue Jussieu, 75238 Paris Cedex 05, France
| | - E Lajeunesse
- Institut de Physique du Globe de Paris -Sorbonne Paris Cité, Université Paris Diderot, CNRS, UMR7154, 1 rue Jussieu, 75238 Paris Cedex 05, France
| | - L Barrier
- Institut de Physique du Globe de Paris -Sorbonne Paris Cité, Université Paris Diderot, CNRS, UMR7154, 1 rue Jussieu, 75238 Paris Cedex 05, France
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Seizilles G, Devauchelle O, Lajeunesse E, Métivier F. Width of laminar laboratory rivers. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 87:052204. [PMID: 23767527 DOI: 10.1103/physreve.87.052204] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2013] [Indexed: 06/02/2023]
Abstract
A viscous fluid flowing over plastic grains spontaneously generates single-thread channels. With time, these laminar analogues of alluvial rivers reach a reproducible steady state, showing a well-defined width and cross section. In the absence of sediment transport, their shape conforms with the threshold hypothesis which states that, at equilibrium, the combined effects of gravity and flow-induced stress maintain the bed surface at the threshold of motion. This theory explains how the channel selects its size and slope for a given discharge. In this light, laboratory rivers illustrate the similarity between the avalanche angle of granular materials and Shields's criterion for sediment transport.
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Affiliation(s)
- G Seizilles
- Institut de Physique du Globe de Paris, 1 rue Jussieu, 75238 Paris cedex 05, France
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Affiliation(s)
- O. Devauchelle
- Laboratoire de Dynamique des Fluides Géologiques; Institut de Physique du Globe de Paris; Paris France
| | - L. Malverti
- Laboratoire de Dynamique des Fluides Géologiques; Institut de Physique du Globe de Paris; Paris France
| | - É. Lajeunesse
- Laboratoire de Dynamique des Fluides Géologiques; Institut de Physique du Globe de Paris; Paris France
| | - C. Josserand
- Institut Jean Le Rond d'Alembert; Université Pierre et Marie Curie, CNRS; Paris France
| | - P.-Y. Lagrée
- Institut Jean Le Rond d'Alembert; Université Pierre et Marie Curie, CNRS; Paris France
| | - F. Métivier
- Laboratoire de Dynamique des Fluides Géologiques; Institut de Physique du Globe de Paris; Paris France
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