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Spera G, Duclut C, Durand M, Tailleur J. Nematic Torques in Scalar Active Matter: When Fluctuations Favor Polar Order and Persistence. PHYSICAL REVIEW LETTERS 2024; 132:078301. [PMID: 38427854 DOI: 10.1103/physrevlett.132.078301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Revised: 07/12/2023] [Accepted: 01/08/2024] [Indexed: 03/03/2024]
Abstract
We study the impact of nematic alignment on scalar active matter in the disordered phase. We show that nematic torques control the emergent physics of particles interacting via pairwise forces and can either induce or prevent phase separation. The underlying mechanism is a fluctuation-induced renormalization of the mass of the polar field that generically arises from nematic torques. The correlations between the fluctuations of the polar and nematic fields indeed conspire to increase the particle persistence length, contrary to what phenomenological computations predict. This effect is generic and our theory also quantitatively accounts for how nematic torques enhance particle accumulation along confining boundaries and opposes demixing in mixtures of active and passive particles.
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Affiliation(s)
- Gianmarco Spera
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Charlie Duclut
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
- Laboratoire Physique des Cellules et Cancer (PCC), CNRS UMR 168, Institut Curie, Université PSL, Sorbonne Université, 75005 Paris, France
| | - Marc Durand
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Julien Tailleur
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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2
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Noguchi H. Membrane domain formation induced by binding/unbinding of curvature-inducing molecules on both membrane surfaces. SOFT MATTER 2023; 19:679-688. [PMID: 36597888 DOI: 10.1039/d2sm01536f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The domain formation of curvature-inducing molecules, such as peripheral or transmembrane proteins and conical surfactants, is studied in thermal equilibrium and nonequilibrium steady states using meshless membrane simulations. These molecules can bind to both surfaces of a bilayer membrane and also move to the opposite leaflet by a flip-flop. Under symmetric conditions for the two leaflets, the membrane domains form checkerboard patterns in addition to striped and spot patterns. The unbound membrane stabilizes the vertices of the checkerboard. Under asymmetric conditions, the domains form kagome-lattice and thread-like patterns. In the nonequilibrium steady states, a flow of the binding molecules between the upper and lower solutions can occur via flip-flop.
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Affiliation(s)
- Hiroshi Noguchi
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan.
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3
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Venturelli D, Gambassi A. Inducing oscillations of trapped particles in a near-critical Gaussian field. Phys Rev E 2022; 106:044112. [PMID: 36397516 DOI: 10.1103/physreve.106.044112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 09/09/2022] [Indexed: 06/16/2023]
Abstract
We study the nonequilibrium dynamics of two particles confined in two spatially separated harmonic potentials and linearly coupled to the same thermally fluctuating scalar field, a cartoon for optically trapped colloids in contact with a medium close to a continuous phase transition. When an external periodic driving is applied to one of these particles, a nonequilibrium periodic state is eventually reached in which their motion synchronizes thanks to the field-mediated effective interaction, a phenomenon already observed in experiments. We fully characterize the nonlinear response of the second particle as a function of the driving frequency, in particular far from the adiabatic regime in which the field can be assumed to relax instantaneously. We compare the perturbative, analytic solution to its adiabatic approximation, thus determining the limits of validity of the latter, and we qualitatively test our predictions against numerical simulations.
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Affiliation(s)
- Davide Venturelli
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy
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4
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Alston H, Parry AO, Voituriez R, Bertrand T. Intermittent attractive interactions lead to microphase separation in nonmotile active matter. Phys Rev E 2022; 106:034603. [PMID: 36266896 DOI: 10.1103/physreve.106.034603] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Accepted: 07/26/2022] [Indexed: 06/16/2023]
Abstract
Nonmotile active matter exhibits a wide range of nonequilibrium collective phenomena yet examples are crucially lacking in the literature. We present a microscopic model inspired by the bacteria Neisseria meningitidis in which diffusive agents feel intermittent attractive forces. Through a formal coarse-graining procedure, we show that this truly scalar model of active matter exhibits the time-reversal-symmetry breaking terms defining the Active Model B+ class. In particular, we confirm the presence of microphase separation by solving the kinetic equations numerically. We show that the switching rate controlling the interactions provides a regulation mechanism tuning the typical cluster size, e.g., in populations of bacteria interacting via type IV pili.
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Affiliation(s)
- Henry Alston
- Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2BZ, United Kingdom
| | - Andrew O Parry
- Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2BZ, United Kingdom
| | - Raphaël Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
- Laboratoire Jean Perrin, UMR 8237 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
| | - Thibault Bertrand
- Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2BZ, United Kingdom
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5
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Venturelli D, Ferraro F, Gambassi A. Nonequilibrium relaxation of a trapped particle in a near-critical Gaussian field. Phys Rev E 2022; 105:054125. [PMID: 35706305 DOI: 10.1103/physreve.105.054125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 04/22/2022] [Indexed: 06/15/2023]
Abstract
We study the nonequilibrium relaxational dynamics of a probe particle linearly coupled to a thermally fluctuating scalar field and subject to a harmonic potential, which provides a cartoon for an optically trapped colloid immersed in a fluid close to its bulk critical point. The average position of the particle initially displaced from the position of mechanical equilibrium is shown to feature long-time algebraic tails as the critical point of the field is approached, the universal exponents of which are determined in arbitrary spatial dimensions. As expected, this behavior cannot be captured by adiabatic approaches which assumes fast field relaxation. The predictions of the analytic, perturbative approach are qualitatively confirmed by numerical simulations.
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Affiliation(s)
- Davide Venturelli
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy
| | - Francesco Ferraro
- Alumnus, Physics Department, University of Trento, via Sommarive, 14 I-38123 Trento, Italy
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy
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Fournier JB. Field-mediated interactions of passive and conformation-active particles: multibody and retardation effects. SOFT MATTER 2022; 18:2634-2645. [PMID: 35302131 DOI: 10.1039/d1sm01823j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Particles in soft matter interact through the deformation field they create, as in the "cheerios" effect or the curvature-mediated interactions of membrane proteins. Using a simple model for field-mediated interactions between passive particles, or active particles that switch conformation randomly or synchronously, we derive generic results concerning multibody interactions, activity driven patterns, and retardation effects.
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Affiliation(s)
- Jean-Baptiste Fournier
- Université Paris Cité, CNRS, Laboratoire Matière et Systèmes Complexes (MSC), F-75013 Paris, France.
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Cagnetta F, Škultéty V, Evans MR, Marenduzzo D. Universal properties of active membranes. Phys Rev E 2022; 105:L012604. [PMID: 35193286 DOI: 10.1103/physreve.105.l012604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Accepted: 11/24/2021] [Indexed: 06/14/2023]
Abstract
We put forward a general field theory for nearly flat fluid membranes with embedded activators and analyze their critical properties using renormalization group techniques. Depending on the membrane-activator coupling, we find a crossover between acoustic and diffusive scaling regimes, with mean-field dynamical critical exponents z=1 and 2, respectively. We argue that the acoustic scaling, which is exact in all spatial dimensions, leads to an early-time behavior, which is representative of the spatiotemporal patterns observed at the leading edge of motile cells, such as oscillations superposed on the growth of the membrane width. In the case of mean-field diffusive scaling, one-loop corrections to the mean-field exponents reveal universal behavior distinct from the Kardar-Parisi-Zhang scaling of passive interfaces and signs of strong-coupling behavior.
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Affiliation(s)
- Francesco Cagnetta
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdom
| | - Viktor Škultéty
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdom
| | - Martin R Evans
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdom
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdom
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Cagnetta F, Škultéty V, Evans MR, Marenduzzo D. Renormalization group study of the dynamics of active membranes: Universality classes and scaling laws. Phys Rev E 2022; 105:014610. [PMID: 35193300 DOI: 10.1103/physreve.105.014610] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2020] [Accepted: 11/24/2021] [Indexed: 06/14/2023]
Abstract
Motivated by experimental observations of patterning at the leading edge of motile eukaryotic cells, we introduce a general model for the dynamics of nearly-flat fluid membranes driven from within by an ensemble of activators. We include, in particular, a kinematic coupling between activator density and membrane slope which generically arises whenever the membrane has a nonvanishing normal speed. We unveil the phase diagram of the model by means of a perturbative field-theoretical renormalization group analysis. Due to the aforementioned kinematic coupling the natural early-time dynamical scaling is acoustic, that is the dynamical critical exponent is 1. However, as soon as the the normal velocity of the membrane is tuned to zero, the system crosses over to diffusive dynamic scaling in mean field. Distinct critical points can be reached depending on how the limit of vanishing velocity is realized: in each of them corrections to scaling due to nonlinear coupling terms must be taken into account. The detailed analysis of these critical points reveals novel scaling regimes which can be accessed with perturbative methods, together with signs of strong coupling behavior, which establishes a promising ground for further nonperturbative calculations. Our results unify several previous studies on the dynamics of active membrane, while also identifying nontrivial scaling regimes which cannot be captured by passive theories of fluctuating interfaces and are relevant for the physics of living membranes.
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Affiliation(s)
- Francesco Cagnetta
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD Scotland, United Kingdom
| | - Viktor Škultéty
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD Scotland, United Kingdom
| | - Martin R Evans
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD Scotland, United Kingdom
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD Scotland, United Kingdom
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9
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Goutaland Q, van Wijland F, Fournier JB, Noguchi H. Binding of thermalized and active membrane curvature-inducing proteins. SOFT MATTER 2021; 17:5560-5573. [PMID: 33978669 DOI: 10.1039/d1sm00027f] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The phase behavior of a membrane induced by the binding of curvature-inducing proteins is studied by a combination of analytical and numerical approaches. In thermal equilibrium under the detailed balance between binding and unbinding, the membrane exhibits three phases: an unbound uniform flat phase (U), a bound uniform flat phase (B), and a separated/corrugated phase (SC). In the SC phase, the bound proteins form hexagonally-ordered bowl-shaped domains. The transitions between the U and SC phases and between the B and SC phases are second order and first order, respectively. At a small spontaneous curvature of the protein or high surface tension, the transition between B and SC phases becomes continuous. Moreover, a first-order transition between the U and B phases is found at zero spontaneous curvature driven by the Casimir-like interactions between rigid proteins. Furthermore, nonequilibrium dynamics is investigated by the addition of active binding and unbinding at a constant rate. The active binding and unbinding processes alter the stability of the SC phase.
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Affiliation(s)
- Quentin Goutaland
- Laboratoire Matière et Systèmes Complexes (MSC), Université de Paris & CNRS, 75013 Paris, France
| | - Frédéric van Wijland
- Laboratoire Matière et Systèmes Complexes (MSC), Université de Paris & CNRS, 75013 Paris, France
| | - Jean-Baptiste Fournier
- Laboratoire Matière et Systèmes Complexes (MSC), Université de Paris & CNRS, 75013 Paris, France
| | - Hiroshi Noguchi
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan. and Institut Lumière Matière, UMR 5306 CNRS, Université Lyon 1, F-69622 Villeurbanne, France
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10
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Wang G, Phan TV, Li S, Wombacher M, Qu J, Peng Y, Chen G, Goldman DI, Levin SA, Austin RH, Liu L. Emergent Field-Driven Robot Swarm States. PHYSICAL REVIEW LETTERS 2021; 126:108002. [PMID: 33784150 DOI: 10.1103/physrevlett.126.108002] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2020] [Revised: 12/22/2020] [Accepted: 02/15/2021] [Indexed: 06/12/2023]
Abstract
We present an ecology-inspired form of active matter consisting of a robot swarm. Each robot moves over a planar dynamic resource environment represented by a large light-emitting diode array in search of maximum light intensity; the robots deplete (dim) locally by their presence the local light intensity and seek maximum light intensity. Their movement is directed along the steepest local light intensity gradient; we call this emergent symmetry breaking motion "field drive." We show there emerge dynamic and spatial transitions similar to gas, crystalline, liquid, glass, and jammed states as a function of robot density, resource consumption rates, and resource recovery rates. Paradoxically the nongas states emerge from smooth, flat resource landscapes, not rough ones, and each state can directly move to a glassy state if the resource recovery rate is slow enough, at any robot density.
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Affiliation(s)
- Gao Wang
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, 400044 China
| | - Trung V Phan
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Shengkai Li
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Michael Wombacher
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, 400044 China
| | - Junle Qu
- Key Laboratory of Optoelectronics Devices and Systems of Ministry of Education/Guangdong Province, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060 China
| | - Yan Peng
- Research Institute of USV Engineering, Shanghai University, Shanghai, 200444 China
| | - Guo Chen
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, 400044 China
| | - Daniel I Goldman
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Simon A Levin
- Department of Environmental and Evolutionary Biology, Princeton University, Princeton New Jersey 08544, USA
| | - Robert H Austin
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Liyu Liu
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, 400044 China
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11
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Zakine R, Fournier JB, van Wijland F. Spatial organization of active particles with field-mediated interactions. Phys Rev E 2020; 101:022105. [PMID: 32168677 DOI: 10.1103/physreve.101.022105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2019] [Accepted: 01/14/2020] [Indexed: 11/07/2022]
Abstract
We consider a system of independent pointlike particles performing a Brownian motion while interacting with a Gaussian fluctuating background. These particles are in addition endowed with a discrete two-state internal degree of freedom that is subjected to a nonequilibrium source of noise, which affects their coupling with the background field. We explore the phase diagram of the system and pinpoint the role of the nonequilibrium drive in producing a nontrivial patterned spatial organization. We are able, by means of a weakly nonlinear analysis, to account for the parameter-dependence of the boundaries of the phase and pattern diagram in the stationary state.
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Affiliation(s)
- Ruben Zakine
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Jean-Baptiste Fournier
- 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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12
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Tarama S, Egelhaaf SU, Löwen H. Traveling band formation in feedback-driven colloids. Phys Rev E 2019; 100:022609. [PMID: 31574772 DOI: 10.1103/physreve.100.022609] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2019] [Indexed: 06/10/2023]
Abstract
Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an additional potential that is a superposition of repulsive potential energies centered around the positions of all the particles a delay time ago. Here we show that such a feedback leads to self-organization of the particles into traveling bands. The width of the bands and their propagation speed can be tuned by the delay time and the range of the imposed repulsive potential. The emerging traveling band behavior is observed in Brownian dynamics computer simulations as well as microscopic dynamic density functional theory. Traveling band formation also persists in systems of finite size leading to rotating traveling waves in the case of circularly confined systems.
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Affiliation(s)
- Sonja Tarama
- Institute for Theoretical Physics II: Soft Matter, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Stefan U Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institute for Theoretical Physics II: Soft Matter, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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