Transport and fluctuations in mass aggregation processes: Mobility-driven clustering

Subhadip Chakraborti, Tanmoy Chakraborty, Arghya Das, Rahul Dandekar, and Punyabrata Pradhan
Phys. Rev. E 103, 042133 – Published 26 April 2021

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)] 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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  • Received 2 October 2020
  • Revised 1 February 2021
  • Accepted 31 March 2021

DOI:https://doi.org/10.1103/PhysRevE.103.042133

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Subhadip Chakraborti1,2,*, Tanmoy Chakraborty1,†, Arghya Das2,‡, Rahul Dandekar3,4, and Punyabrata Pradhan1

  • 1Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
  • 2International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
  • 3The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
  • 4Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India

  • *subhadip.chakraborti@icts.res.in
  • tanmoy.chakraborty@bose.res.in
  • arghya.das@icts.res.in

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Issue

Vol. 103, Iss. 4 — April 2021

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