1
|
Mukherjee A, Pradhan P. Dynamic correlations in the conserved Manna sandpile. Phys Rev E 2023; 107:024109. [PMID: 36932496 DOI: 10.1103/physreve.107.024109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Accepted: 01/20/2023] [Indexed: 02/11/2023]
Abstract
We study dynamic correlations for current and mass, as well as the associated power spectra, in the one-dimensional conserved Manna sandpile. We show that, in the thermodynamic limit, the variance of cumulative bond current up to time T grows subdiffusively as T^{1/2-μ} with the exponent μ≥0 depending on the density regimes considered and, likewise, the power spectra of current and mass at low frequency f varies as f^{1/2+μ} and f^{-3/2+μ}, respectively. Our theory predicts that, far from criticality, μ=0 and, near criticality, μ=(β+1)/2ν_{⊥}z>0 with β, ν_{⊥}, and z being the order parameter, correlation length, and dynamic exponents, respectively. The anomalous suppression of fluctuations near criticality signifies a "dynamic hyperuniformity," characterized by a set of fluctuation relations, in which current, mass, and tagged-particle displacement fluctuations are shown to have a precise quantitative relationship with the density-dependent activity (or its derivative). In particular, the relation, D_{s}(ρ[over ¯])=a(ρ[over ¯])/ρ[over ¯], between the self-diffusion coefficient D_{s}(ρ[over ¯]), activity a(ρ[over ¯]) and density ρ[over ¯] explains a previous simulation observation [Eur. Phys. J. B 72, 441 (2009)10.1140/epjb/e2009-00367-0] that, near criticality, the self-diffusion coefficient in the Manna sandpile has the same scaling behavior as the activity.
Collapse
Affiliation(s)
- Anirban Mukherjee
- 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
| |
Collapse
|
2
|
Chakraborti S, Chakraborty T, Das A, Dandekar R, Pradhan P. Transport and fluctuations in mass aggregation processes: Mobility-driven clustering. Phys Rev E 2021; 103:042133. [PMID: 34005942 DOI: 10.1103/physreve.103.042133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 03/31/2021] [Indexed: 11/07/2022]
Abstract
We calculate the bulk-diffusion coefficient and the conductivity in nonequilibrium conserved-mass aggregation processes on a ring. These processes involve chipping and fragmentation of masses, which diffuse on a lattice and aggregate with their neighboring masses on contact, and, under certain conditions, they exhibit a condensation transition. We find that, even in the absence of microscopic time reversibility, the systems satisfy an Einstein relation, which connects the ratio of the conductivity and the bulk-diffusion coefficient to mass fluctuation. Interestingly, when aggregation dominates over chipping, the conductivity or, equivalently, the mobility of masses, is greatly enhanced. The enhancement in the conductivity, in accordance with the Einstein relation, results in large mass fluctuations and can induce a mobility-driven clustering in the systems. Indeed, in a certain parameter regime, we show that the conductivity, along with the mass fluctuation, diverges beyond a critical density, thus characterizing the previously observed nonequilibrium condensation transition [Phys. Rev. Lett. 81, 3691 (1998)10.1103/PhysRevLett.81.3691] in terms of an instability in the conductivity. Notably, the bulk-diffusion coefficient remains finite in all cases. We find our analytic results in quite good agreement with simulations.
Collapse
Affiliation(s)
- Subhadip Chakraborti
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India.,International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Tanmoy Chakraborty
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Arghya Das
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Rahul Dandekar
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India.,Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| |
Collapse
|
3
|
Tapader D, Pradhan P, Dhar D. Density relaxation in conserved Manna sandpiles. Phys Rev E 2021; 103:032122. [PMID: 33862746 DOI: 10.1103/physreve.103.032122] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2020] [Accepted: 02/18/2021] [Indexed: 11/07/2022]
Abstract
We study relaxation of long-wavelength density perturbations in a one-dimensional conserved Manna sandpile. Far from criticality where correlation length ξ is finite, relaxation of density profiles having wave numbers k→0 is diffusive, with relaxation time τ_{R}∼k^{-2}/D with D being the density-dependent bulk-diffusion coefficient. Near criticality with kξ≳1, the bulk diffusivity diverges and the transport becomes anomalous; accordingly, the relaxation time varies as τ_{R}∼k^{-z}, with the dynamical exponent z=2-(1-β)/ν_{⊥}<2, where β is the critical order-parameter exponent and ν_{⊥} is the critical correlation-length exponent. Relaxation of initially localized density profiles on an infinite critical background exhibits a self-similar structure. In this case, the asymptotic scaling form of the time-dependent density profile is analytically calculated: we find that, at long times t, the width σ of the density perturbation grows anomalously, σ∼t^{w}, with the growth exponent ω=1/(1+β)>1/2. In all cases, theoretical predictions are in reasonably good agreement with simulations.
Collapse
Affiliation(s)
- Dhiraj Tapader
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Deepak Dhar
- Department of Physics, Indian Institute of Science Education and Research, Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
| |
Collapse
|
4
|
Antonov NV, Gulitskiy NM, Kakin PI, Serov VD. Effects of turbulent environment and random noise on self-organized critical behavior: Universality versus nonuniversality. Phys Rev E 2021; 103:042106. [PMID: 34005875 DOI: 10.1103/physreve.103.042106] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2020] [Accepted: 03/08/2021] [Indexed: 11/07/2022]
Abstract
Self-organized criticality in the Hwa-Kardar model of a "running sandpile" [Phys. Rev. Lett. 62, 1813 (1989)10.1103/PhysRevLett.62.1813; Phys. Rev. A 45, 7002 (1992)10.1103/PhysRevA.45.7002] with a turbulent motion of the environment taken into account is studied with the field theoretic renormalization group (RG). The turbulent flow is modeled by the synthetic d-dimensional generalization of the anisotropic Gaussian velocity ensemble with finite correlation time, introduced by Avellaneda and Majda [Commun. Math. Phys. 131, 381 (1990)10.1007/BF02161420; Commun. Math. Phys. 146, 139 (1992)10.1007/BF02099212]. The Hwa-Kardar model with time-independent (spatially quenched) random noise is considered alongside the original model with white noise. The aim of the present paper is to explore fixed points of the RG equations which determine the possible types of universality classes (regimes of critical behavior of the system) and critical dimensions of the measurable quantities. Our calculations demonstrate that influence of the type of random noise is extremely large: in contrast to the case of white noise where the system possesses three fixed points, the case of spatially quenched noise involves four fixed points with overlapping stability regions. This means that in the latter case the critical behavior of the system depends not only on the global parameters of the system, which is the usual case, but also on the initial values of the charges (coupling constants) of the system. These initial conditions determine the specific fixed point which will be reached by the RG flow. Since now the critical properties of the system are not defined strictly by its parameters, the situation may be interpreted as a universality violation. Such systems are not forbidden, but they are rather rare. It is especially interesting that the same model without turbulent motion of the environment does not predict this nonuniversal behavior and demonstrates the usual one with prescribed universality classes instead [J. Stat. Phys. 178, 392 (2020)10.1007/s10955-019-02436-8].
Collapse
Affiliation(s)
- N V Antonov
- Department of Physics, Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russian Federation
| | - N M Gulitskiy
- Department of Physics, Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russian Federation
| | - P I Kakin
- Department of Physics, Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russian Federation
| | - V D Serov
- Department of Physics, Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russian Federation.,Department of Theoretical Physics, Peter the Great Saint Petersburg Polytechnic University, 29 Polytechnicheskaya st., Saint Petersburg 195251, Russian Federation
| |
Collapse
|
5
|
Effects of Turbulent Environment on Self-Organized Critical Behavior: Isotropy vs. Anisotropy. UNIVERSE 2020. [DOI: 10.3390/universe6090145] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
We study a self-organized critical system under the influence of turbulent motion of the environment. The system is described by the anisotropic continuous stochastic equation proposed by Hwa and Kardar [Phys. Rev. Lett.62: 1813 (1989)]. The motion of the environment is modelled by the isotropic Kazantsev–Kraichnan “rapid-change” ensemble for an incompressible fluid: it is Gaussian with vanishing correlation time and the pair correlation function of the form ∝δ(t−t′)/kd+ξ, where k is the wave number and ξ is an arbitrary exponent with the most realistic values ξ=4/3 (Kolmogorov turbulence) and ξ→2 (Batchelor’s limit). Using the field-theoretic renormalization group, we find infrared attractive fixed points of the renormalization group equation associated with universality classes, i.e., with regimes of critical behavior. The most realistic values of the spatial dimension d=2 and the exponent ξ=4/3 correspond to the universality class of pure turbulent advection where the nonlinearity of the Hwa–Kardar (HK) equation is irrelevant. Nevertheless, the universality class where both the (anisotropic) nonlinearity of the HK equation and the (isotropic) advecting velocity field are relevant also exists for some values of the parameters ε=4−d and ξ. Depending on what terms (anisotropic, isotropic, or both) are relevant in specific universality class, different types of scaling behavior (ordinary one or generalized) are established.
Collapse
|