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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.
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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
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Dandekar R, Chakraborti S, Rajesh R. Hard core run and tumble particles on a one-dimensional lattice. Phys Rev E 2021; 102:062111. [PMID: 33466079 DOI: 10.1103/physreve.102.062111] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Accepted: 11/16/2020] [Indexed: 11/07/2022]
Abstract
We study the large scale behavior of a collection of hard core run and tumble particles on a one-dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin variable until the direction of spin is reversed. We map the run and tumble model to a mass transfer model with fluctuating directed bonds. We calculate the steady-state single-site mass distribution in the mass model within a mean field approximation for larger spin-flip rates and by analyzing an appropriate coalescence-fragmentation model for small spin-flip rates. We also calculate the hydrodynamic coefficients of diffusivity and conductivity for both large and small spin-flip rates and show that the Einstein relation is violated in both regimes. We also show how the nongradient nature of the process can be taken into account in a systematic manner to calculate the hydrodynamic coefficients.
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Affiliation(s)
- 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
| | | | - R Rajesh
- 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
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Chakraborty T, Chakraborti S, Das A, Pradhan P. Hydrodynamics, superfluidity, and giant number fluctuations in a model of self-propelled particles. Phys Rev E 2020; 101:052611. [PMID: 32575180 DOI: 10.1103/physreve.101.052611] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2019] [Accepted: 04/15/2020] [Indexed: 11/07/2022]
Abstract
We derive hydrodynamics of a prototypical one-dimensional model, having variable-range hopping, which mimics passive diffusion and ballistic motion of active, or self-propelled, particles. The model has two main ingredients-the hardcore interaction and the competing mechanisms of short- and long-range hopping. We calculate two density-dependent transport coefficients-the bulk-diffusion coefficient and the conductivity, the ratio of which, despite violation of detailed balance, is connected to particle-number fluctuation by an Einstein relation. In the limit of infinite-range hopping, the model exhibits, upon tuning density ρ (or activity), a "superfluidlike" transition from a finitely conducting fluid phase to an infinitely conducting "superfluid" phase, characterized by a divergence in conductivity χ(ρ)∼(ρ-ρ_{c})^{-1} with ρ_{c} being the critical density. The diverging conductivity greatly increases particle (or vacancy) mobility and thus induces "giant" number fluctuations in the system.
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Affiliation(s)
- Tanmoy Chakraborty
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - 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
| | - Arghya Das
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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Das A, Kundu A, Pradhan P. Einstein relation and hydrodynamics of nonequilibrium mass transport processes. Phys Rev E 2017; 95:062128. [PMID: 28709216 DOI: 10.1103/physreve.95.062128] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2017] [Indexed: 06/07/2023]
Abstract
We derive hydrodynamics of paradigmatic conserved-mass transport processes on a ring. The systems, governed by chipping, diffusion, and coalescence of masses, eventually reach a nonequilibrium steady state, having nontrivial correlations, with steady-state measures in most cases not known. In these processes, we analytically calculate two transport coefficients, bulk-diffusion coefficient and conductivity. Remarkably, the two transport coefficients obey an equilibrium-like Einstein relation even when the microscopic dynamics violates detailed balance and systems are far from equilibrium. Moreover, we show, using a macroscopic fluctuation theory, that the probability of large deviation in density, obtained from the above hydrodynamics, is in complete agreement with the same derived earlier by Das et al. [Phys. Rev. E 93, 062135 (2016)2470-004510.1103/PhysRevE.93.062135] using an additivity property.
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Affiliation(s)
- Arghya Das
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Anupam Kundu
- International Centre for Theoretical Sciences, TIFR, Bangalore 560012, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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Khan N, Sarkar P, Midya A, Mandal P, Mohanty PK. Continuously Varying Critical Exponents Beyond Weak Universality. Sci Rep 2017; 7:45004. [PMID: 28327622 PMCID: PMC5361157 DOI: 10.1038/srep45004] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Accepted: 02/14/2017] [Indexed: 11/09/2022] Open
Abstract
Renormalization group theory does not restrict the form of continuous variation of critical exponents which occurs in presence of a marginal operator. However, the continuous variation of critical exponents, observed in different contexts, usually follows a weak universality scenario where some of the exponents (e.g., β, γ, ν) vary keeping others (e.g., δ, η) fixed. Here we report ferromagnetic phase transition in (Sm1−yNdy)0.52Sr0.48MnO3 (0.5 ≤ y ≤ 1) single crystals where all three exponents β, γ, δ vary with Nd concentration y. Such a variation clearly violates both universality and weak universality hypothesis. We propose a new scaling theory that explains the present experimental results, reduces to the weak universality as a special case, and provides a generic route leading to continuous variation of critical exponents and multi-criticality.
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Affiliation(s)
- N Khan
- CMP Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhan Nagar, Kolkata 700064, India
| | - P Sarkar
- Department of Physics, Serampore College, Serampore 712201, India
| | - A Midya
- CMP Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhan Nagar, Kolkata 700064, India
| | - P Mandal
- CMP Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhan Nagar, Kolkata 700064, India
| | - P K Mohanty
- CMP Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhan Nagar, Kolkata 700064, India
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Das A, Chatterjee S, Pradhan P. Spatial correlations, additivity, and fluctuations in conserved-mass transport processes. Phys Rev E 2016; 93:062135. [PMID: 27415236 DOI: 10.1103/physreve.93.062135] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2016] [Indexed: 11/07/2022]
Abstract
We exactly calculate two-point spatial correlation functions in steady state in a broad class of conserved-mass transport processes, which are governed by chipping, diffusion, and coalescence of masses. We find that the spatial correlations are in general short-ranged and, consequently, on a large scale, these transport processes possess a remarkable thermodynamic structure in the steady state. That is, the processes have an equilibrium-like additivity property and, consequently, a fluctuation-response relation, which help us to obtain subsystem mass distributions in the limit of subsystem size large.
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Affiliation(s)
- Arghya Das
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Sayani Chatterjee
- 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
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Chakraborti S, Mishra S, Pradhan P. Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles. Phys Rev E 2016; 93:052606. [PMID: 27300950 DOI: 10.1103/physreve.93.052606] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Indexed: 06/06/2023]
Abstract
Using an additivity property, we study particle-number fluctuations in a system of interacting self-propelled particles, called active Brownian particles (ABPs), which consists of repulsive disks with random self-propulsion velocities. From a fluctuation-response relation, a direct consequence of additivity, we formulate a thermodynamic theory which captures the previously observed features of nonequilibrium phase transition in the ABPs from a homogeneous fluid phase to an inhomogeneous phase of coexisting gas and liquid. We substantiate the predictions of additivity by analytically calculating the subsystem particle-number distributions in the homogeneous fluid phase away from criticality where analytically obtained distributions are compatible with simulations in the ABPs.
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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
| | - Shradha Mishra
- 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
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