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Chakraborty T, Pradhan P. Time-dependent properties of run-and-tumble particles. II. Current fluctuations. Phys Rev E 2024; 109:044135. [PMID: 38755901 DOI: 10.1103/physreve.109.044135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 03/19/2024] [Indexed: 05/18/2024]
Abstract
We investigate steady-state current fluctuations in two models of hardcore run-and-tumble particles (RTPs) on a periodic one-dimensional lattice of L sites, for arbitrary tumbling rate γ=τ_{p}^{-1} and density ρ; model I consists of standard hardcore RTPs, while model II is an analytically tractable variant of model I, called a long-ranged lattice gas (LLG). We show that, in the limit of L large, the fluctuation of cumulative current Q_{i}(T,L) across the ith bond in a time interval T≫1/D grows first subdiffusively and then diffusively (linearly) with T: 〈Q_{i}^{2}〉∼T^{α} with α=1/2 for 1/D≪T≪L^{2}/D and α=1 for T≫L^{2}/D, where D(ρ,γ) is the collective- or bulk-diffusion coefficient; at small times T≪1/D, exponent α depends on the details. Remarkably, regardless of the model details, the scaled bond-current fluctuations D〈Q_{i}^{2}(T,L)〉/2χL≡W(y) as a function of scaled variable y=DT/L^{2} collapse onto a universal scaling curve W(y), where χ(ρ,γ) is the collective particle mobility. In the limit of small density and tumbling rate, ρ,γ→0, with ψ=ρ/γ fixed, there exists a scaling law: The scaled mobility γ^{a}χ(ρ,γ)/χ^{(0)}≡H(ψ) as a function of ψ collapses onto a scaling curve H(ψ), where a=1 and 2 in models I and II, respectively, and χ^{(0)} is the mobility in the limiting case of a symmetric simple exclusion process; notably, the scaling function H(ψ) is model dependent. For model II (LLG), we calculate exactly, within a truncation scheme, both the scaling functions, W(y) and H(ψ). We also calculate spatial correlation functions for the current and compare our theory with simulation results of model I; for both models, the correlation functions decay exponentially, with correlation length ξ∼τ_{p}^{1/2} diverging with persistence time τ_{p}≫1. Overall, our theory is in excellent agreement with simulations and complements the prior findings [T. Chakraborty and P. Pradhan, Phys. Rev. E 109, 024124 (2024)1539-375510.1103/PhysRevE.109.024124].
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Affiliation(s)
- Tanmoy Chakraborty
- Department of Physics of Complex Systems, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Punyabrata Pradhan
- Department of Physics of Complex Systems, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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2
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Chakraborty T, Pradhan P. Time-dependent properties of run-and-tumble particles: Density relaxation. Phys Rev E 2024; 109:024124. [PMID: 38491605 DOI: 10.1103/physreve.109.024124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Accepted: 01/03/2024] [Indexed: 03/18/2024]
Abstract
We characterize collective diffusion of hardcore run-and-tumble particles (RTPs) by explicitly calculating the bulk-diffusion coefficient D(ρ,γ) for arbitrary density ρ and tumbling rate γ, in systems on a d-dimensional periodic lattice. We study two minimal models of RTPs: Model I is the standard version of hardcore RTPs introduced in [Phys. Rev. E 89, 012706 (2014)10.1103/PhysRevE.89.012706], whereas model II is a long-ranged lattice gas (LLG) with hardcore exclusion, an analytically tractable variant of model I. We calculate the bulk-diffusion coefficient analytically for model II and numerically for model I through an efficient Monte Carlo algorithm; notably, both models have qualitatively similar features. In the strong-persistence limit γ→0 (i.e., dimensionless ratio r_{0}γ/v→0), with v and r_{0} being the self-propulsion speed and particle diameter, respectively, the fascinating interplay between persistence and interaction is quantified in terms of two length scales: (i) persistence length l_{p}=v/γ and (ii) a "mean free path," being a measure of the average empty stretch or gap size in the hopping direction. We find that the bulk-diffusion coefficient varies as a power law in a wide range of density: D∝ρ^{-α}, with exponent α gradually crossing over from α=2 at high densities to α=0 at low densities. As a result, the density relaxation is governed by a nonlinear diffusion equation with anomalous spatiotemporal scaling. In the thermodynamic limit, we show that the bulk-diffusion coefficient-for ρ,γ→0 with ρ/γ fixed-has a scaling form D(ρ,γ)=D^{(0)}F(ρav/γ), where a∼r_{0}^{d-1} is particle cross section and D^{(0)} is proportional to the diffusion coefficient of noninteracting particles; the scaling function F(ψ) is calculated analytically for model II (LLG) and numerically for model I. Our arguments are independent of dimensions and microscopic details.
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Affiliation(s)
- Tanmoy Chakraborty
- Department of Physics of Complex Systems, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Punyabrata Pradhan
- Department of Physics of Complex Systems, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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3
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Goswami K, Metzler R. Trapped tracer in a non-equilibrium bath: dynamics and energetics. SOFT MATTER 2023; 19:8802-8819. [PMID: 37946588 DOI: 10.1039/d3sm01177a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2023]
Abstract
We study the dynamics of a tracer that is elastically coupled to active particles being kept at two different temperatures, as a prototype of tracer dynamics in a non-equilibrium bath. Employing analytical techniques, we find the exact solution of the probability density function for the effective motion of the tracer. The analytical results are supported by numerical simulations. By combining the experimentally accessible quantities such as the response function and the power spectrum, we measure the non-equilibrium fluctuations in terms of the effective temperature. In addition, we compute the energy dissipation rate to find the precise effects of activity. Our study is relevant in understanding athermal fluctuations arising in cytoskeletal networks or inside a chromosome.
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Affiliation(s)
- Koushik Goswami
- Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.
| | - Ralf Metzler
- Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.
- Asia Pacific Centre for Theoretical Physics, Pohang 37673, Republic of Korea.
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4
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Wiese R, Kroy K, Levis D. Fluid-Glass-Jamming Rheology of Soft Active Brownian Particles. PHYSICAL REVIEW LETTERS 2023; 131:178302. [PMID: 37955492 DOI: 10.1103/physrevlett.131.178302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Revised: 09/13/2023] [Accepted: 10/03/2023] [Indexed: 11/14/2023]
Abstract
We numerically study the shear rheology of a binary mixture of soft active Brownian particles, from the fluid to the disordered solid regime. At low shear rates, we find a Newtonian regime, where a Green-Kubo relation with an effective temperature provides the linear viscosity. It is followed by a shear-thinning regime at high shear rates. At high densities, solidification is signaled by the emergence of a finite yield stress. We construct a "fluid-glass-jamming" phase diagram with activity replacing temperature. While both parameters gauge fluctuations, activity also changes the exponent characterizing the decay of the diffusivity close to the glass transition and the shape of the yield stress surface. The dense disordered active solid appears to be mostly dominated by athermal jamming rather than glass rheology.
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Affiliation(s)
- Roland Wiese
- Institute for Theoretical Physics, Leipzig University, 04103 Leipzig, Germany
| | - Klaus Kroy
- Institute for Theoretical Physics, Leipzig University, 04103 Leipzig, Germany
| | - Demian Levis
- Departement de Física de la Materia Condensada, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
- University of Barcelona Institute of Complex Systems (UBICS), Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
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5
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Hoang Ngoc Minh T, Rotenberg B, Marbach S. Ionic fluctuations in finite volumes: fractional noise and hyperuniformity. Faraday Discuss 2023; 246:225-250. [PMID: 37565454 DOI: 10.1039/d3fd00031a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/12/2023]
Abstract
Observing finite regions of a bigger system is a common aim, from microscopy to molecular simulations. In the latter especially, there is ongoing interest in predicting thermodynamic properties from tracking fluctuations in finite observation volumes. However, kinetic properties have received little attention, especially not in ionic solutions, where electrostatic interactions play a decisive role. Here, we probe ionic fluctuations in finite volumes with Brownian dynamics and build an analytical framework that reproduces our simulation results and is broadly applicable to other systems with pairwise interactions. Particle number and charge correlations exhibit a rich phenomenology with time, characterized by a diversity of timescales. The noise spectrum of both quantities decays as 1/f3/2, where f is the frequency. This signature of fractional noise shows the universality of 1/f3/2 scalings when observing diffusing particles in finite domains. The hyperuniform behaviour of charge fluctuations, namely that correlations scale with the area of the observation volume, is preserved in time. Correlations even become proportional to the box perimeter at sufficiently long times. Our results pave the way to understand fluctuations in more complex systems, from nanopores to single-particle electrochemistry.
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Affiliation(s)
- Thê Hoang Ngoc Minh
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
- Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens Cedex, France
| | - Sophie Marbach
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
- Courant Institute of Mathematical Sciences, New York University, NY, 10012, USA.
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6
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Daddi-Moussa-Ider A, Golestanian R, Vilfan A. Minimum entropy production by microswimmers with internal dissipation. Nat Commun 2023; 14:6060. [PMID: 37770449 PMCID: PMC10539332 DOI: 10.1038/s41467-023-41280-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Accepted: 08/29/2023] [Indexed: 09/30/2023] Open
Abstract
The energy dissipation and entropy production by self-propelled microswimmers differ profoundly from passive particles pulled by external forces. The difference extends both to the shape of the flow around the swimmer, as well as to the internal dissipation of the propulsion mechanism. Here we derive a general theorem that provides an exact lower bound on the total, external and internal, dissipation by a microswimmer. The problems that can be solved include an active surface-propelled droplet, swimmers with an extended propulsive layer and swimmers with an effective internal dissipation. We apply the theorem to determine the swimmer shapes that minimize the total dissipation while keeping the volume constant. Our results show that the entropy production by active microswimmers is subject to different fundamental limits than the entropy production by externally driven particles.
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Affiliation(s)
| | - Ramin Golestanian
- Max Planck Institute for Dynamics and Self-Organization (MPI-DS), 37077, Göttingen, Germany
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3PU, UK
| | - Andrej Vilfan
- Max Planck Institute for Dynamics and Self-Organization (MPI-DS), 37077, Göttingen, Germany.
- Jožef Stefan Institute, 1000, Ljubljana, Slovenia.
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7
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Chun HM, Horowitz JM. Trade-offs between number fluctuations and response in nonequilibrium chemical reaction networks. J Chem Phys 2023; 158:2888610. [PMID: 37144710 DOI: 10.1063/5.0148662] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 04/17/2023] [Indexed: 05/06/2023] Open
Abstract
We study the response of chemical reaction networks driven far from equilibrium to logarithmic perturbations of reaction rates. The response of the mean number of a chemical species is observed to be quantitively limited by number fluctuations and the maximum thermodynamic driving force. We prove these trade-offs for linear chemical reaction networks and a class of nonlinear chemical reaction networks with a single chemical species. Numerical results for several model systems support the conclusion that these trade-offs continue to hold for a broad class of chemical reaction networks, though their precise form appears to sensitively depend on the deficiency of the network.
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Affiliation(s)
- Hyun-Myung Chun
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, South Korea
| | - Jordan M Horowitz
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48104, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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8
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Crisanti A, Paoluzzi M. Most probable path of active Ornstein-Uhlenbeck particles. Phys Rev E 2023; 107:034110. [PMID: 37072947 DOI: 10.1103/physreve.107.034110] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 02/17/2023] [Indexed: 04/20/2023]
Abstract
Using the path integral representation of the nonequilibrium dynamics, we compute the most probable path between arbitrary starting and final points that is followed by an active particle driven by persistent noise. We focus our attention on the case of active particles immersed in harmonic potentials, where the trajectory can be computed analytically. Once we consider the extended Markovian dynamics where the self-propulsive drive evolves according to an Ornstein-Uhlenbeck process, we can compute the trajectory analytically with arbitrary conditions on position and self-propulsion velocity. We test the analytical predictions against numerical simulations and we compare the analytical results with those obtained within approximated equilibriumlike dynamics.
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Affiliation(s)
- Andrea Crisanti
- Dipartimento di Fisica, Sapienza Università di Roma Piazzale A. Moro 2, I-00185 Rome, Italy
| | - Matteo Paoluzzi
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, C. Martí Franquès 1, 08028 Barcelona, Spain
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9
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The Relationship between Structure and Performance of Different Polyimides Based on Molecular Simulations. Polymers (Basel) 2023; 15:polym15030646. [PMID: 36771947 PMCID: PMC9921807 DOI: 10.3390/polym15030646] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Revised: 01/21/2023] [Accepted: 01/23/2023] [Indexed: 01/28/2023] Open
Abstract
A polyimide (PI) molecular model was successfully constructed to compare the performance of PIs with different structures. In detail, the structure of the cross-linked PI resin, the prepolymer melt viscosity, and the glass-transition temperature (Tg) were investigated using molecular simulations. The results indicate that benzene ring and polyene-type cross-linked structures dominate the properties of the PIs. Moreover, the prepolymer melt viscosity simulations show that the 6FDA-APB and the ODPA-APB systems have a low viscosity. The results for the Tg and the distribution dihedral angle reveal that the key factor affecting bond flexibility may be the formation of a new dihedral angle after cross-linking, which affects the Tg. The above results provide an important reference for the design of PIs and have important value from the perspective of improving the efficiency of new product development.
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10
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Gnan N, Maggi C. Critical behavior of quorum-sensing active particles. SOFT MATTER 2022; 18:7654-7661. [PMID: 36169619 DOI: 10.1039/d2sm00654e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
It is still a debated issue whether all critical active particles belong to the same universality class. Here we numerically study the critical behavior of quorum sensing active particles that represents the archetypal model for interpreting motility-induced phase separation. Mean-field theory predicts that this model should undergo a full phase separation if particles slow-down enough when sensing the presence of their neighbors and that the coexistence line terminates in a critical point. By performing large-scale numerical simulations, we confirm this scenario, locate the critical point and use finite-size scaling analysis to show that the static and dynamic critical exponents of this active system substantially agree with those of the Ising universality class.
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Affiliation(s)
- Nicoletta Gnan
- ISC-CNR, Institute for Complex Systems, Piazzale A. Moro 2, I-00185, Roma, Italy.
- Dipartimento di Fisica, Università di Roma "Sapienza", I-00185, Roma, Italy
| | - Claudio Maggi
- Dipartimento di Fisica, Università di Roma "Sapienza", I-00185, Roma, Italy
- NANOTEC-CNR, Institute of Nanotechnology, Soft and Living Matter Laboratory-Piazzale A. Moro 2, I-00185, Roma, Italy.
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11
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Ferretti F, Grosse-Holz S, Holmes C, Shivers JL, Giardina I, Mora T, Walczak AM. Signatures of irreversibility in microscopic models of flocking. Phys Rev E 2022; 106:034608. [PMID: 36266796 DOI: 10.1103/physreve.106.034608] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2022] [Accepted: 08/17/2022] [Indexed: 06/16/2023]
Abstract
Flocking in d=2 is a genuine nonequilibrium phenomenon for which irreversibility is an essential ingredient. We study a class of minimal flocking models whose only source of irreversibility is self-propulsion and use the entropy production rate (EPR) to quantify the departure from equilibrium across their phase diagrams. The EPR is maximal in the vicinity of the order-disorder transition, where reshuffling of the interaction network is fast. We show that signatures of irreversibility come in the form of asymmetries in the steady-state distribution of the flock's microstates. These asymmetries occur as consequences of the time-reversal symmetry breaking in the considered self-propelled systems, independently of the interaction details. In the case of metric pairwise forces, they reduce to local asymmetries in the distribution of pairs of particles. This study suggests a possible use of pair asymmetries both to quantify the departure from equilibrium and to learn relevant information about aligning interaction potentials from data.
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Affiliation(s)
- Federica Ferretti
- Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy
- Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy
| | - Simon Grosse-Holz
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Institut Curie, Paris 75005, France
| | - Caroline Holmes
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Jordan L Shivers
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA
| | - Irene Giardina
- Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy
- Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy
- INFN, Unità di Roma 1, 00185 Rome, Italy
| | - Thierry Mora
- Laboratoire de Physique de l'École Normale Supérieure (PSL University), CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Aleksandra M Walczak
- Laboratoire de Physique de l'École Normale Supérieure (PSL University), CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
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12
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De Corato M, Pagonabarraga I. Onsager reciprocal relations and chemo-mechanical coupling for chemically active colloids. J Chem Phys 2022; 157:084901. [DOI: 10.1063/5.0098425] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Similar to cells, bacteria, and other micro-organisms, synthetic chemically active colloids can harness the energy from their environment through a surface chemical reaction and use the energy to self-propel in fluidic environments. In this paper, we study the chemo-mechanical coupling that leads to the self-propulsion of chemically active colloids. The coupling between chemical reactions and momentum transport is a consequence of Onsager reciprocal relations. They state that the velocity and the surface reaction rate are related to mechanical and chemical affinities through a symmetric matrix. A consequence of Onsager reciprocal relations is that if a chemical reaction drives the motion of the colloid, then an external force generates a reaction rate. Here, we investigate Onsager reciprocal relations for a spherical active colloid that catalyzes a reversible surface chemical reaction between two species. We solve the relevant transport equations using a perturbation expansion and numerical simulations to demonstrate the validity of reciprocal relations around the equilibrium. Our results are consistent with previous studies and highlight the key role of solute advection in preserving the symmetry of the Onsager matrix. Finally, we show that Onsager reciprocal relations break down around a nonequilibrium steady state, which has implications for the thermal fluctuations of the active colloids used in experiments.
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Affiliation(s)
- Marco De Corato
- Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
| | - Ignacio Pagonabarraga
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, C. Martí Franquès 1, 08028 Barcelona, Spain
- University of Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
- CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lasuanne (EPFL), Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
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13
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Ghosh A, Spakowitz AJ. Statistical behavior of nonequilibrium and living biological systems subjected to active and thermal fluctuations. Phys Rev E 2022; 105:014415. [PMID: 35193230 DOI: 10.1103/physreve.105.014415] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2021] [Accepted: 12/24/2021] [Indexed: 06/14/2023]
Abstract
We present a path-integral formulation of the motion of a particle subjected to fluctuating active and thermal forces. This general framework predicts the statistical behavior associated with the stochastic trajectories of the particle, accounting for all possible realizations of Brownian and active forces, over an arbitrary potential landscape. Temporal correlations in the active forces result in non-Markovian statistics, necessitating the inclusion of a fixed active-force value at specified times within the statistical treatment. We specialize our theory to that of exponentially correlated active forces for a particle in a harmonic potential. We find the exact results for the statistical distributions for the initial position of the particle, accounting for the impact of the correlated active forces at all times prior to the initial time. Our theory is then used to find the two-point distribution for the active Brownian particle, which governs the joint probability that a particle begins and ends at specified locations. Analyses of the active Brownian statistics demonstrate that the impact of active forces can be interpreted through a time-dependent temperature whose influence depends on the competition of timescales of the active-force correlation and the relaxation time of the particle in the harmonic potential. The general results presented in this work are transferable to a broad range of nonequilibrium systems with active and Brownian motion, and the time-dependent temperature serves as a governing principle to describe the competition of timescales associated with active forces and internal relaxation processes.
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Affiliation(s)
- Ashesh Ghosh
- Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA
| | - Andrew J Spakowitz
- Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA
- Department of Materials Science, Stanford University, Stanford, California 94305, USA
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
- Biophysics Program, Stanford University, Stanford, California 94305, USA
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14
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Linear response theory in stock markets. Sci Rep 2021; 11:23076. [PMID: 34845245 PMCID: PMC8630003 DOI: 10.1038/s41598-021-02263-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2021] [Accepted: 11/12/2021] [Indexed: 11/08/2022] Open
Abstract
Linear response theory relates the response of a system to a weak external force with its dynamics in equilibrium, subjected to fluctuations. Here, this framework is applied to financial markets; in particular we study the dynamics of a set of stocks from the NASDAQ during the last 20 years. Because unambiguous identification of external forces is not possible, critical events are identified in the series of stock prices as sudden changes, and the stock dynamics following an event is taken as the response to the external force. Linear response theory is applied with the log-return as the conjugate variable of the force, providing predictions for the average response of the price and return, which agree with observations, but fails to describe the volatility because this is expected to be beyond linear response. The identification of the conjugate variable allows us to define the perturbation energy for a system of stocks, and observe its relaxation after an event.
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15
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Knežević M, Avilés Podgurski LE, Stark H. Oscillatory active microrheology of active suspensions. Sci Rep 2021; 11:22706. [PMID: 34811417 PMCID: PMC8608831 DOI: 10.1038/s41598-021-02103-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Accepted: 11/09/2021] [Indexed: 11/09/2022] Open
Abstract
Using the method of Brownian dynamics, we investigate the dynamic properties of a 2d suspension of active disks at high Péclet numbers using active microrheology. In our simulations the tracer particle is driven either by a constant or an oscillatory external force. In the first case, we find that the mobility of the tracer initially appreciably decreases with the external force and then becomes approximately constant for larger forces. For an oscillatory driving force we find that the dynamic mobility shows a quite complex behavior-it displays a highly nonlinear behavior on both the amplitude and frequency of the driving force. In the range of forces studied, we do not observe a linear regime. This result is important because it reveals that a phenomenological description of tracer motion in active media in terms of a simple linear stochastic equation even with a memory-mobility kernel is not appropriate, in the general case.
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Affiliation(s)
- Miloš Knežević
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany.
| | - Luisa E Avilés Podgurski
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany
| | - Holger Stark
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany
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16
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Jerez MJY, Bonachita MA, Confesor MNP. Reversibility in nonequilibrium steady states as a measure of distance from equilibrium. Phys Rev E 2021; 104:044609. [PMID: 34781472 DOI: 10.1103/physreve.104.044609] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2021] [Accepted: 09/29/2021] [Indexed: 11/07/2022]
Abstract
From the detailed balance-like relation, we propose a measure, K^{*}, of a nonequilibrium steady-state (NESS) distance from equilibrium. We investigate in particular the NESS of a particle confined in a time-dependent harmonic potential of constant stiffness but with an ON-OFF state following a telegraph process. Experimental results coupled with simulations show that K^{*} increases at slow switching rates (far from equilibrium) and approaches to zero at equilibrium conditions. Thus, the steady-state distribution together with K^{*} fully characterizes a NESS.
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Affiliation(s)
- Michael Jade Y Jerez
- Department of Physics and Complex Systems Group-PRISM, MSU-Iligan Institute of Technology, Andres Bonifacio Ave., Tibanga, Iligan City 9200, Philippines
| | - Mike A Bonachita
- Department of Physics and Complex Systems Group-PRISM, MSU-Iligan Institute of Technology, Andres Bonifacio Ave., Tibanga, Iligan City 9200, Philippines
| | - Mark Nolan P Confesor
- Department of Physics and Complex Systems Group-PRISM, MSU-Iligan Institute of Technology, Andres Bonifacio Ave., Tibanga, Iligan City 9200, Philippines
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17
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Hargus C, Epstein JM, Mandadapu KK. Odd Diffusivity of Chiral Random Motion. PHYSICAL REVIEW LETTERS 2021; 127:178001. [PMID: 34739294 DOI: 10.1103/physrevlett.127.178001] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2021] [Revised: 06/30/2021] [Accepted: 09/23/2021] [Indexed: 06/13/2023]
Abstract
Diffusive transport is characterized by a diffusivity tensor which may, in general, contain both a symmetric and an antisymmetric component. Although the latter is often neglected, we derive Green-Kubo relations showing it to be a general characteristic of random motion breaking time-reversal and parity symmetries, as encountered in chiral active matter. In analogy with the odd viscosity appearing in chiral active fluids, we term this component the odd diffusivity. We show how odd diffusivity emerges in a chiral random walk model, and demonstrate the applicability of the Green-Kubo relations through molecular dynamics simulations of a passive tracer particle diffusing in a chiral active bath.
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Affiliation(s)
- Cory Hargus
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
| | - Jeffrey M Epstein
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Kranthi K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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18
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Baldovin M, Caprini L, Vulpiani A. Handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics. Phys Rev E 2021; 104:L032101. [PMID: 34654124 DOI: 10.1103/physreve.104.l032101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2021] [Accepted: 07/17/2021] [Indexed: 11/07/2022]
Abstract
We introduce a general formulation of the fluctuation-dissipation relations (FDRs) holding also in far-from-equilibrium stochastic dynamics. A great advantage of this version of the FDR is that it does not require explicit knowledge of the stationary probability density function. Our formula applies to Markov stochastic systems with generic noise distributions: When the noise is additive and Gaussian, the relation reduces to those known in the literature; for multiplicative and non-Gaussian distributions (e.g., Cauchy noise) it provides exact results in agreement with numerical simulations. Our formula allows us to reproduce, in a suitable small-noise limit, the response functions of deterministic, strongly nonlinear dynamical models, even in the presence of chaotic behavior: This could have important practical applications in several contexts, including geophysics and climate. As a case of study, we consider the Lorenz '63 model, which is paradigmatic for the chaotic properties of deterministic dynamical systems.
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Affiliation(s)
- M Baldovin
- Dipartimento di Fisica, Università di Roma Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - L Caprini
- Scuola di Scienze e Tecnologie, Università di Camerino, via Madonna delle Carceri, 62032 Camerino, Italy
| | - A Vulpiani
- Dipartimento di Fisica, Università di Roma Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy
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19
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Asheichyk K, Fuchs M, Krüger M. Brownian systems perturbed by mild shear: comparing response relations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:405101. [PMID: 34139676 DOI: 10.1088/1361-648x/ac0c3c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2021] [Accepted: 06/17/2021] [Indexed: 06/12/2023]
Abstract
We present a comprehensive study of the linear response of interacting underdamped Brownian particles to simple shear flow. We collect six different routes for computing the response, two of which are based on the symmetry of the considered system and observable with respect to the shear axes. We include the extension of the Green-Kubo relation to underdamped cases, which shows two unexpected additional terms. These six computational methods are applied to investigate the relaxation of the response towards the steady state for different observables, where interesting effects due to interactions and a finite particle mass are observed. Moreover, we compare the different response relations in terms of their statistical efficiency, identifying their relative demand on experimental measurement time or computational resources in computer simulations. Finally, several measures of breakdown of linear response theory for larger shear rates are discussed.
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Affiliation(s)
- Kiryl Asheichyk
- 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
- Department of Theoretical Physics and Astrophysics, Belarusian State University, 5 Babruiskaya St., 220006 Minsk, Belarus
| | - Matthias Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
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20
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Maggi C, Paoluzzi M, Crisanti A, Zaccarelli E, Gnan N. Universality class of the motility-induced critical point in large scale off-lattice simulations of active particles. SOFT MATTER 2021; 17:3807-3812. [PMID: 33645615 DOI: 10.1039/d0sm02162h] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We perform large-scale computer simulations of an off-lattice two-dimensional model of active particles undergoing a motility-induced phase separation (MIPS) to investigate the system's critical behaviour close to the critical point of the MIPS curve. By sampling steady-state configurations for large system sizes and performing finite size scaling analysis we provide exhaustive evidence that the critical behaviour of this active system belongs to the Ising universality class. In addition to the scaling observables that are also typical of passive systems, we study the critical behaviour of the kinetic temperature difference between the two active phases. This quantity, which is always zero in equilibrium, displays instead a critical behavior in the active system which is well described by the same exponent of the order parameter in agreement with mean-field theory.
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Affiliation(s)
- Claudio Maggi
- NANOTEC-CNR, Institute of Nanotechnology, Soft and Living Matter Laboratory -Piazzale A. Moro 2, I-00185, Roma, Italy. and Dipartimento di Fisica, Università di Roma "Sapienza", I-00185, Roma, Italy
| | - Matteo Paoluzzi
- Departamento de Fìsica de la Matèria Condensada, Universitat de Barcelona, C. MartìFranquès 1, 08028 Barcelona, Spain
| | - Andrea Crisanti
- Dipartimento di Fisica, Università di Roma "Sapienza", I-00185, Roma, Italy and CNR-ISC, Institute of Complex Systems, Roma, Italy.
| | - Emanuela Zaccarelli
- Dipartimento di Fisica, Università di Roma "Sapienza", I-00185, Roma, Italy and CNR-ISC, Institute of Complex Systems, Roma, Italy.
| | - Nicoletta Gnan
- Dipartimento di Fisica, Università di Roma "Sapienza", I-00185, Roma, Italy and CNR-ISC, Institute of Complex Systems, Roma, Italy.
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21
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Martin D, O'Byrne J, Cates ME, Fodor É, Nardini C, Tailleur J, van Wijland F. Statistical mechanics of active Ornstein-Uhlenbeck particles. Phys Rev E 2021; 103:032607. [PMID: 33862678 DOI: 10.1103/physreve.103.032607] [Citation(s) in RCA: 68] [Impact Index Per Article: 22.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2020] [Accepted: 12/23/2020] [Indexed: 06/12/2023]
Abstract
We study the statistical properties of active Ornstein-Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffices to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We study in detail the steady-state distribution of AOUPs in the small persistence time limit and for spatially varying activity. At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. We characterize both the instability mechanism leading to phase separation and the resulting phase coexistence. We probe how, in the stationary state, AOUPs depart from their thermal equilibrium limit by investigating the emergence of ratchet currents and entropy production. In the small persistence time limit, we show how fluctuation-dissipation relations are recovered. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes.
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Affiliation(s)
- David Martin
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Jérémy O'Byrne
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Étienne Fodor
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Cesare Nardini
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Service de Physique de l'État Condensé, CNRS UMR 3680, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - Julien Tailleur
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Frédéric van Wijland
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
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22
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GrandPre T, Klymko K, Mandadapu KK, Limmer DT. Entropy production fluctuations encode collective behavior in active matter. Phys Rev E 2021; 103:012613. [PMID: 33601608 DOI: 10.1103/physreve.103.012613] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Accepted: 12/22/2020] [Indexed: 11/07/2022]
Abstract
We derive a general lower bound on distributions of entropy production in interacting active matter systems. The bound is tight in the limit that interparticle correlations are small and short-ranged, which we explore in four canonical active matter models. In all models studied, the bound is weak where collective fluctuations result in long-ranged correlations, which subsequently links the locations of phase transitions to enhanced entropy production fluctuations. We develop a theory for the onset of enhanced fluctuations and relate it to specific phase transitions in active Brownian particles. We also derive optimal control forces that realize the dynamics necessary to tune dissipation and manipulate the system between phases. In so doing, we uncover a general relationship between entropy production and pattern formation in active matter, as well as ways of controlling it.
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Affiliation(s)
- Trevor GrandPre
- Department of Physics, University of California, Berkeley, California 94609, USA
| | - Katherine Klymko
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA
| | - Kranthi K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94609, USA.,Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA
| | - David T Limmer
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA.,Department of Chemistry, University of California, Berkeley, California 94609, USA.,Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA.,Kavli Energy NanoScience Institute, Berkeley, California 94609, USA
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23
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Abstract
We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein–Uhlenbeck particle (AOUP) model. We express the linear response in terms of correlations computed in the absence of perturbations, proposing a particularly compact and readable fluctuation–dissipation relation (FDR): such an expression explicitly separates equilibrium and non-equilibrium contributions due to self-propulsion. As a case study, we consider non-interacting AOUP confined in single-well and double-well potentials. In the former case, we also unveil the effect of dimensionality, studying one-, two-, and three-dimensional dynamics. We show that information about the distance from equilibrium can be deduced from the FDR, putting in evidence the roles of position and velocity variables in the non-equilibrium relaxation.
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24
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Caprini L, Marini Bettolo Marconi U. Active matter at high density: Velocity distribution and kinetic temperature. J Chem Phys 2020; 153:184901. [DOI: 10.1063/5.0029710] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Lorenzo Caprini
- Dipartimento di Fisica, Universitá di Camerino, Via Madonna delle Carceri, I-62032 Camerino, Italy
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25
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Javadi A, Arrieta J, Tuval I, Polin M. Photo-bioconvection: towards light control of flows in active suspensions. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190523. [PMID: 32762429 PMCID: PMC7422871 DOI: 10.1098/rsta.2019.0523] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
The persistent motility of individual constituents in microbial suspensions represents a prime example of the so-called active matter systems. Cells consume energy, exert forces and move, overall releasing the constraints of equilibrium statistical mechanics of passive elements and allowing for complex spatio-temporal patterns to emerge. Moreover, when subject to physico-chemical stimuli their collective behaviour often drives large-scale instabilities of a hydrodynamic nature, with implications for biomixing in natural environments and incipient industrial applications. In turn, our ability to exert external control of these driving stimuli could be used to govern the emerging patterns. Light, being easily manipulable and, at the same time, an important stimulus for a wide variety of microorganisms, is particularly well suited to this end. In this paper, we will discuss the current state, developments and some of the emerging advances in the fundamentals and applications of light-induced bioconvection with a focus on recent experimental realizations and modelling efforts. This article is part of the theme issue 'Stokes at 200 (part 2)'.
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Affiliation(s)
- A. Javadi
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
- e-mail:
| | - J. Arrieta
- Instituto Mediterráneo de Estudios Avanzados, IMEDEA, UIB-CSIC, 07190 Esporles, Spain
| | - I. Tuval
- Instituto Mediterráneo de Estudios Avanzados, IMEDEA, UIB-CSIC, 07190 Esporles, Spain
- Departamento de Física, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain
| | - M. Polin
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
- Centre for Mechanochemical Cell Biology, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
- e-mail:
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26
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Petrelli I, Cugliandolo LF, Gonnella G, Suma A. Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems. Phys Rev E 2020; 102:012609. [PMID: 32794963 DOI: 10.1103/physreve.102.012609] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2020] [Accepted: 06/25/2020] [Indexed: 05/15/2023]
Abstract
We study the stationary dynamics of an active interacting Brownian particle system. We measure the violations of the fluctuation dissipation theorem, and the corresponding effective temperature, in a locally resolved way. Quite naturally, in the homogeneous phases the diffusive properties and effective temperature are also homogeneous. Instead, in the inhomogeneous phases (close to equilibrium and within the MIPS sector) the particles can be separated in two groups with different diffusion properties and effective temperatures. Notably, at fixed activity strength the effective temperatures in the two phases remain distinct and approximately constant within the MIPS region, with values corresponding to the ones of the whole system at the boundaries of this sector of the phase diagram. We complement the study of the globally averaged properties with the theoretical and numerical characterization of the fluctuation distributions of the single-particle diffusion, linear response, and effective temperature in the homogeneous and inhomogeneous phases. We also distinguish the behavior of the (time-delayed) effective temperature from the (instantaneous) kinetic temperature, showing that the former is independent of the friction coefficient.
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Affiliation(s)
- Isabella Petrelli
- Dipartimento di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari, I-70126, Italy
| | - Leticia F Cugliandolo
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
- Institut Universitaire de France, 1 rue Descartes, 75005 Paris, France
| | - Giuseppe Gonnella
- Dipartimento di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari, I-70126, Italy
| | - Antonio Suma
- Dipartimento di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari, I-70126, Italy
- Institute for Computational Molecular Science, College of Science and Technology, Temple University, Philadelphia, Pennsylvania 19122, USA
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