Equilibrium to off-equilibrium crossover in homogeneous active matter

Cavagna, Andrea; Carlo, Luca Di; Giardina, Irene; Grigera, Tomás S.; Pisegna, Giulia

doi:10.1103/physrevresearch.3.013210

Cited by 13 publications

(18 citation statements)

References 34 publications

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“…One may worry that incompressibility introduces some non-local interactions in the system, then potentially changing the critical exponents with respect to the compressible case. However, numerical simulations of the standard compressible theory have found the dynamic scaling exponent to be in perfect agreement with theoretical RG results for incompressible theory [14], thus indicating that the effects of activity on the dynamical critical exponent are independent from whether incompressibility is enforced or not. This is very useful indeed, as it means that incompressibility can be used as a simplifying tool, without changing critical dynamics.…”

Section: Incompressible Flow and Fixed Network Assumptionsmentioning

confidence: 58%

“…Moreover, requiring incompressibility, hence imposing a solenoidal constraint on the velocity field, generates long-range interactions that could change the properties of a system; while this is indeed the case for the static behaviour of our theory, the longrange interactions are not sufficient to modify its dynamic universality class. Theoretical evidences of this fact have already been discussed in homogeneous active systems [14], therefore suggesting that the solenoidal constraint does not significantly affect the critical dynamic behaviour in the presence of neither activity nor mode-coupling terms. This result is very encouraging, as it allows to study the homogeneous phase of the off-equilibrium Inertial Spin Model under a incompressible hypothesis, where the absence of the density field leads to a great simplification of the calculation.…”

Section: Discussionmentioning

confidence: 75%

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Dynamical Renormalization Group for Mode-Coupling Field Theories with Solenoidal Constraint

et al. 2021

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The recent inflow of empirical data about the collective behaviour of strongly correlated biological systems has brought field theory and the renormalization group into the biophysical arena. Experiments on bird flocks and insect swarms show that social forces act on the particles’ velocity through the generator of its rotations, namely the spin, indicating that mode-coupling field theories are necessary to reproduce the correct dynamical behaviour. Unfortunately, a theory for three coupled fields—density, velocity and spin—has a prohibitive degree of intricacy. A simplifying path consists in getting rid of density fluctuations by studying incompressible systems. This requires imposing a solenoidal constraint on the primary field, an unsolved problem even for equilibrium mode-coupling theories. Here, we perform an equilibrium dynamic renormalization group analysis of a mode-coupling field theory subject to a solenoidal constraint; using the classification of Halperin and Hohenberg, we can dub this case as a solenoidal Model G. We demonstrate that the constraint produces a new vertex that mixes static and dynamical coupling constants, and that this vertex is essential to grant the closure of the renormalization group structure and the consistency of dynamics with statics. Interestingly, although the solenoidal constraint leads to a modification of the static universality class, we find that it does not change the dynamical universality class, a result that seems to represent an exception to the general rule that dynamical universality classes are narrower than static ones. Our results constitute a solid stepping stone in the admittedly large chasm towards developing an off-equilibrium mode-coupling theory of biological groups.

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Section: Incompressible Flow and Fixed Network Assumptionsmentioning

confidence: 58%

Section: Discussionmentioning

confidence: 75%

Dynamical Renormalization Group for Mode-Coupling Field Theories with Solenoidal Constraint

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…One may worry that incompressibility introduces some non-local interactions in the system, then potentially changing the critical exponents with respect to the compressible case. However, numerical simulations of the standard compressible theory have found the dynamic scaling exponent to be in perfect agreement with theoretical RG results for incompressible theory [35], thus indicating that the effects of activity on the dynamical critical exponent are independent from whether incompressibility is enforced or not. This is very useful indeed, as it means that incompressibility can be used as a simplifying tool, without changing critical dynamics.…”

Section: Incompressible Flow and Fixed Network Assumptionsmentioning

confidence: 58%

Dynamical renormalization group for mode-coupling field theories with solenoidal constraint

Cavagna,

di Carlo,

Giardina

et al. 2021

Preprint

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“…Disordered and ordered states are studied in terms of the spatial connected correlation function, C c (r) [56][57][58] , that provides the information about the spatial correlation between observables at separation r. To capture the effective one-dimensional aspect of the system, we study the spatial correlation of the velocity component tangent to the ring. We first introduce the correlation, C(r) as:…”

Section: B Spatial Velocity Correlations and Correlation Lengthmentioning

confidence: 99%

“…The argument of both correlations cannot exceed the maximal distance along with the ring, ∼ π R. We remark that using the connected velocity correlation function one can define the correlation length even in the case of non-ergodic systems and, in particular, when the spatial average, V (t), over the whole system does not vanish 56 (as found for the larger values of τ ). To include these possibilities, the correlation length λ is defined as 56 :…”

Section: B Spatial Velocity Correlations and Correlation Lengthmentioning

confidence: 99%

Collective effects in confined Active Brownian Particles

Caprini,

Maggi,

Marconi

2021

Preprint

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We investigate a two-dimensional system of active particles confined to a narrow annular domain. Despite the absence of explicit interactions among the velocities or the active forces of different particles, the system displays a transition from a disordered and stuck state to an ordered state of global collective motion where the particles rotate persistently clockwise or anticlockwise. We describe this behavior by introducing a suitable order parameter, the velocity polarization, measuring the global alignment of the particles' velocities along the tangential direction of the ring. We also measure the spatial velocity correlation function and its correlation length to characterize the two states. In the rotating phase, the velocity correlation displays an algebraic decay that is analytically predicted together with its correlation length while in the stuck regime the velocity correlation decays exponentially with a correlation length that increases with the persistence time. In the first case, the correlation (and, in particular, its correlation length) does not depend on the active force but the system size only. The global collective motion, an effect caused by the interplay between finite-size, periodicity, and persistent active forces, disappears as the size of the ring becomes infinite, suggesting that this phenomenon does not correspond to a phase transition in the usual thermodynamic sense.

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Equilibrium to off-equilibrium crossover in homogeneous active matter

Cited by 13 publications

References 34 publications

Dynamical Renormalization Group for Mode-Coupling Field Theories with Solenoidal Constraint

Dynamical Renormalization Group for Mode-Coupling Field Theories with Solenoidal Constraint

Dynamical renormalization group for mode-coupling field theories with solenoidal constraint

Collective effects in confined Active Brownian Particles

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