Hyperuniformity in phase ordering: the roles of activity, noise, and non-constant mobility
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2024
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| _version_ | 1866929493698936832 |
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| author | De Luca, Filippo Ma, Xiao Nardini, Cesare Cates, Michael E. |
| author_facet | De Luca, Filippo Ma, Xiao Nardini, Cesare Cates, Michael E. |
| contents | Hyperuniformity emerges generically in the coarsening regime of phase-separating fluids. Numerical studies of active and passive systems have shown that the structure factor $S(q)$ behaves as $q^ς$ for $q\to 0$, with hyperuniformity exponent $ς= 4$. For passive systems, this result was explained in 1991 by a qualitative scaling analysis of Tomita, exploiting isotropy at scales much larger than the coarsening length $\ell$. Here we reconsider and extend Tomita's argument to address cases of active phase separation and of non-constant mobility, again finding $ς=4$. We further show that dynamical noise of variance $D$ creates a transient $ς= 2$ regime for $\hat q\ll \hat{q}_\ast \sim \sqrt{D} t^{[1-(d+2)ν]/2}$, crossing over to $ς= 4$ at larger $\hat{q}$. Here, $ν$ is the coarsening exponent, with $\ell\sim t^ν$, and $\hat{q} \propto q \ell$ is the rescaled wavenumber. In diffusive coarsening, $ν=1/3$, so the rescaled crossover wavevector $\hat{q}_\ast$ vanishes at large times when $d\geq 2$. The slowness of this decay suggests a natural explanation for experiments that observe a long-lived $ς= 2$ scaling in phase-separating active fluids (where noise is typically large). Conversely, in $d=1$, we demonstrate that with noise the $ς= 2$ regime survives as $t\to\infty$, with $\hat{q}_\ast\sim D^{5/6}$. (The structure factor is not then determined by the zero-temperature fixed point.) We confirm our analytical predictions by numerical simulations of active and passive continuum theories in the deterministic case and of Model B for the stochastic case. We also compare them with related findings for a system near an absorbing-state transition rather than undergoing phase separation. A central role is played throughout by the presence or absence of a conservation law for the centre of mass position of the order parameter field. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_00508 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperuniformity in phase ordering: the roles of activity, noise, and non-constant mobility De Luca, Filippo Ma, Xiao Nardini, Cesare Cates, Michael E. Soft Condensed Matter Statistical Mechanics Hyperuniformity emerges generically in the coarsening regime of phase-separating fluids. Numerical studies of active and passive systems have shown that the structure factor $S(q)$ behaves as $q^ς$ for $q\to 0$, with hyperuniformity exponent $ς= 4$. For passive systems, this result was explained in 1991 by a qualitative scaling analysis of Tomita, exploiting isotropy at scales much larger than the coarsening length $\ell$. Here we reconsider and extend Tomita's argument to address cases of active phase separation and of non-constant mobility, again finding $ς=4$. We further show that dynamical noise of variance $D$ creates a transient $ς= 2$ regime for $\hat q\ll \hat{q}_\ast \sim \sqrt{D} t^{[1-(d+2)ν]/2}$, crossing over to $ς= 4$ at larger $\hat{q}$. Here, $ν$ is the coarsening exponent, with $\ell\sim t^ν$, and $\hat{q} \propto q \ell$ is the rescaled wavenumber. In diffusive coarsening, $ν=1/3$, so the rescaled crossover wavevector $\hat{q}_\ast$ vanishes at large times when $d\geq 2$. The slowness of this decay suggests a natural explanation for experiments that observe a long-lived $ς= 2$ scaling in phase-separating active fluids (where noise is typically large). Conversely, in $d=1$, we demonstrate that with noise the $ς= 2$ regime survives as $t\to\infty$, with $\hat{q}_\ast\sim D^{5/6}$. (The structure factor is not then determined by the zero-temperature fixed point.) We confirm our analytical predictions by numerical simulations of active and passive continuum theories in the deterministic case and of Model B for the stochastic case. We also compare them with related findings for a system near an absorbing-state transition rather than undergoing phase separation. A central role is played throughout by the presence or absence of a conservation law for the centre of mass position of the order parameter field. |
| title | Hyperuniformity in phase ordering: the roles of activity, noise, and non-constant mobility |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2405.00508 |