Order-parameter scaling in fluctuation-dominated phase ordering

Kapri, Rajeev; Bandyopadhyay, Malay; Barma, Mustansir

doi:10.1103/physreve.93.012117

Cited by 10 publications

(21 citation statements)

References 21 publications

(38 reference statements)

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“…1) imply that H-particles tend to collect in local valleys. This reduces to the passive scalar problem studied earlier, in which particles exhibit FDPO, characterized by singularities of the 2-point correlations and giant fluctuations of the density [16,17]. Interestingly, this phase boundary can be identified exactly by looking for the onset of complex eigenvalues in a linear stability analysis of the coupled hydrodynamic equations for the landscape and the particles [14].…”

Section: Strong Phase Separation (Sps)mentioning

confidence: 99%

Large compact clusters and fast dynamics in coupled nonequilibrium systems

et al. 2016

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We demonstrate particle clustering on macroscopic scales in a coupled nonequilibrium system where two species of particles are advected by a fluctuating landscape and modify the landscape in the process. The phase diagram generated by varying the particle-landscape coupling, valid for all particle density and in both one and two dimensions, shows novel nonequilibrium phases. While particle species are completely phase separated, the landscape develops macroscopically ordered regions coexisting with a disordered region, resulting in coarsening and steady state dynamics on time scales which grow algebraically with size, not seen earlier in systems with pure domains.PACS numbers: 64.75.Gh, 68.43.Jk Particle clustering is important in many natural physical and biological phenomena, for instance, the formation of sediments [1] and protein clustering on a biological membrane [2]. Evidently, it is important to understand processes that cause clustering in different physical contexts, and how these processes influence the properties of the cluster and the time taken to form it. Often, large-scale clustering is driven by interactions with an external medium which itself has correlations in space and time [3][4][5]. An important physical effect in such systems is the back-influence of the particles on the medium. This interaction can aid clustering, or destroy it. If a cluster does form, it may be compact and robust, or a dynamic object that undergoes constant reorganization. The formation time may grow exponentially with the size, or as a power law. Given this wealth of possibilities, it is important to look for an understanding, within simple models, of the circumstances under which different sorts of macroscopically clustered states occur.In this letter, we derive the phase diagram of a simple model system as we vary the interaction between the environment and particles. In the process, we unmask a novel non-equilibrium phase of particles with compact clustering and rich and rapid dynamics coexisting with a macroscopically organized landscape. The model has partial overlap with the lattice gas model of Lahiri and Ramaswamy (LR) for sedimenting colloidal crystals [6,7], but the new phases manifest themselves outside the LR regime. Our results hold in both one and two dimensions.The model consists of two sets of particles moving stochastically in a fluctuating potential energy landscape. Particles try to minimize their energy by (a) moving along the local potential gradient of the landscape and (b) modifying the landscape around them in such a way as to lower the energy further. The model is generic but we discuss it in the language of particles confined to move on a fluctuating surface in the presence of gravity, where the particles can locally distort the surface shape to further lower the energy (see Fig. 1). One of the particle species is considered lighter and the other is heavier; we use the name LH (Light-heavy) model to describe the system. Process (b) affects the landscape dynamics quite differently in parts...

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Section: Strong Phase Separation (Sps)mentioning

confidence: 99%

Large compact clusters and fast dynamics in coupled nonequilibrium systems

et al. 2016

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“…In [13,14] we discussed the static and dynamic properties of the ordered phases in detail. The b = −b line acts as the boundary between the ordered and disordered phase and on this line fluctuation dominated phase ordering is observed, where landscape is completely disordered but the H particles show a tendency to form large clusters of fluctuating lengths [19][20][21][22]. In the disordered phase, neither the particles nor the landscape show any long ranged order.…”

Section: Model and The Phase Diagrammentioning

confidence: 99%

Dynamics of coupled modes for sliding particles on a fluctuating landscape

2019

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The recently developed formalism of nonlinear fluctuating hydrodynamics (NLFH) has been instrumental in unraveling many new dynamical universality classes in coupled driven systems with multiple conserved quantities. In principle, this formalism requires knowledge of the exact expression of locally conserved current in terms of local density of the conserved components. However, for most nonequilibrium systems an exact expression is not available and it is important to know what happens to the predictions of NLFH in these cases. We address this question for the first time here in a system with coupled time evolution of sliding particles on a fluctuating energy landscape. In the disordered phase this system shows short-ranged correlations, this system shows short-ranged correlations, the exact form of which is not known, and so the exact expression for current cannot be obtained. We use approximate expressions based on mean-field theory and corrections to it, to test the prediction of NLFH using numerical simulations. In this process we also discover important finite size effects and show how they affect the predictions of NLFH. We find that our system is rich enough to show a large variety of universality classes. From our analytics and simulations we have been able to find parameter values which lead to diffusive, Kardar-Parisi-Zhang (KPZ), 5/3 Lévy and modified KPZ universality classes. Interestingly, the scaling function in the modified KPZ case turns out to be close to the Prähofer-Spohn function which is known to describe usual KPZ scaling. Our analytics also predict the golden mean and the 3/2 Lévy universality classes within our model but our simulations could not verify this, perhaps due to strong finite size effects.

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“…The behavior of long-wavelength Fourier components of the density profile in this case resemble that of the Fourier modes of the LSC system under discussion here. In both cases, the fall of the dominant long-wavelength Fourier mode in time is accompanied by a rise of the amplitude of the next few modes [6,12,13,[53][54][55], with an amplitude that decreases with increasing mode number. This signifies that both for LSC and FDPO, the system evolves within the subset of states with macroscopic structures, never reaching completely disordered states.…”

Section: Structure Functions and Intermittencymentioning

confidence: 99%

“…The analogy with FDPO suggests some further directions. In their study of the passive particle system, Kapri et al [55] utilized the temporal structure functions to study the intermittency of the dominant Fourier mode, characterized by temporal second and fourth order structure functions. Therefore, we plot the second and fourth order structure functions in Fig.…”

Section: Structure Functions and Intermittencymentioning

confidence: 99%

Reversals in infinite-Prandtl-number Rayleigh-Bénard convection

2018

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Using direct numerical simulations, we study the statistical properties of reversals in two-dimensional Rayleigh-Bénard convection for infinite Prandtl number. We find that the large-scale circulation reverses irregularly, with the waiting time between two consecutive genuine reversals exhibiting a Poisson distribution on long timescales, while the interval between successive crossings on short timescales shows a power-law distribution. We observe that the vertical velocities near the sidewall and at the center show different statistical properties. The velocity near the sidewall shows a longer autocorrelation and 1/f^{2} power spectrum for a wide range of frequencies, compared to shorter autocorrelation and a narrower scaling range for the velocity at the center. The probability distribution of the velocity near the sidewall is bimodal, indicating a reversing velocity field. We also find that the dominant Fourier modes capture the dynamics at the sidewall and at the center very well. Moreover, we show a signature of weak intermittency in the fluctuations of velocity near the sidewall by computing temporal structure functions.

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Order-parameter scaling in fluctuation-dominated phase ordering

Cited by 10 publications

References 21 publications

Large compact clusters and fast dynamics in coupled nonequilibrium systems

Large compact clusters and fast dynamics in coupled nonequilibrium systems

Dynamics of coupled modes for sliding particles on a fluctuating landscape

Reversals in infinite-Prandtl-number Rayleigh-Bénard convection

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