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Marchenko IG, Aksenova V, Marchenko II, Łuczka J, Spiechowicz J. Temperature anomalies of oscillating diffusion in ac-driven periodic systems. Phys Rev E 2023; 107:064116. [PMID: 37464623 DOI: 10.1103/physreve.107.064116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 06/02/2023] [Indexed: 07/20/2023]
Abstract
We analyze the impact of temperature on the diffusion coefficient of an inertial Brownian particle moving in a symmetric periodic potential and driven by a symmetric time-periodic force. Recent studies have revealed the low-friction regime in which the diffusion coefficient shows giant damped quasiperiodic oscillations as a function of the amplitude of the time-periodic force [I. G. Marchenko et al., Chaos 32, 113106 (2022)1054-150010.1063/5.0117902]. We find out that when temperature grows the diffusion coefficient increases at its minima; however, it decreases at the maxima within a finite temperature window. This curious behavior is explained in terms of the deterministic dynamics perturbed by thermal fluctuations and mean residence time of the particle in the locked and running trajectories. We demonstrate that temperature dependence of the diffusion coefficient can be accurately reconstructed from the stationary probability to occupy the running trajectories.
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Affiliation(s)
- I G Marchenko
- NSC Kharkiv Institute of Physics and Technology, Kharkiv 61108, Ukraine
- Karazin Kharkiv National University, Kharkiv 61022, Ukraine
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - V Aksenova
- NSC Kharkiv Institute of Physics and Technology, Kharkiv 61108, Ukraine
- Karazin Kharkiv National University, Kharkiv 61022, Ukraine
| | - I I Marchenko
- NTU Kharkiv Polytechnic Institute, Kharkiv 61002, Ukraine
| | - J Łuczka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Spiechowicz
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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2
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Spiechowicz J, Marchenko IG, Hänggi P, Łuczka J. Diffusion Coefficient of a Brownian Particle in Equilibrium and Nonequilibrium: Einstein Model and Beyond. ENTROPY (BASEL, SWITZERLAND) 2022; 25:42. [PMID: 36673183 PMCID: PMC9857877 DOI: 10.3390/e25010042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Revised: 12/21/2022] [Accepted: 12/21/2022] [Indexed: 06/17/2023]
Abstract
The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow our survey to the case of the diffusion coefficient for a Brownian particle that can be modeled in the framework of Langevin dynamics. Our main focus centers on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds, we consider a number of physical situations outside of free Brownian motion and end by surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature.
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Affiliation(s)
- Jakub Spiechowicz
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
| | - Ivan G. Marchenko
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
- Kharkiv Institute of Physics and Technology, 61108 Kharkiv, Ukraine
- Education and Research Institute of Computer Physics and Energy, Karazin Kharkiv National University, 61022 Kharkiv, Ukraine
| | - Peter Hänggi
- Institute of Physics, University of Augsburg, 86135 Augsburg, Germany
- Max-Planck Institute for Physics of Complex Systems, 01187 Dresden, Germany
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
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3
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G R A, Barik D. Roughness in the periodic potential induces absolute negative mobility in a driven Brownian ratchet. Phys Rev E 2022; 106:044129. [PMID: 36397596 DOI: 10.1103/physreve.106.044129] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Accepted: 10/03/2022] [Indexed: 06/16/2023]
Abstract
Absolute negative mobility, where particles move opposite to the direction as governed by the external load, is an anomalous transport property of a Brownian ratchet and has technological implications in mass separation and bioanalytical applications. We numerically investigated here the effect of roughness in symmetric periodic potential on the negative mobility of a driven inertial Brownian ratchet in the presence of an external load. We show that the microscopic spatial heterogeneity of the potential can generate negative mobility which would not otherwise be possible under smooth potential in the concerned parameter space. We determined the optimal condition in terms of parameter space for such anomalous behavior. Our calculations indicate that the shift of balance towards the negative velocity phase in the temporal oscillations of velocity and weakly chaotic dynamics are responsible factors for roughness-induced negative mobility. These calculations highlight a constructive role of roughness in the anomalous transport properties of Brownian ratchet.
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Affiliation(s)
- Archana G R
- School of Chemistry, University of Hyderabad, Gachibowli, 500046 Hyderabad, India
| | - Debashis Barik
- School of Chemistry, University of Hyderabad, Gachibowli, 500046 Hyderabad, India
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4
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Spiechowicz J, Łuczka J. Conundrum of weak-noise limit for diffusion in a tilted periodic potential. Phys Rev E 2021; 104:034104. [PMID: 34654194 DOI: 10.1103/physreve.104.034104] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2021] [Accepted: 08/20/2021] [Indexed: 11/07/2022]
Abstract
The weak-noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity, frequently hidden in deterministic systems, to give rise to phenomena that are absent for both noiseless and strong fluctuations regimes. Unfortunately, this limit is also notoriously hard to approach analytically or numerically. We reinvestigate in this context the paradigmatic model of nonequilibrium statistical physics consisting of inertial Brownian particles diffusing in a tilted periodic potential by exploiting state-of-the-art computer simulations of an extremely long timescale. In contrast to previous results on this longstanding problem, we draw an inference that in the parameter regime for which the particle velocity is bistable the lifetime of ballistic diffusion diverges to infinity when the thermal noise intensity tends to zero, i.e., an everlasting ballistic diffusion emerges. As a consequence, the diffusion coefficient does not reach its stationary constant value.
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Affiliation(s)
- J Spiechowicz
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Łuczka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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5
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G R A, Barik D. Roughness in the periodic potential enhances transport in a driven inertial ratchet. Phys Rev E 2021; 104:024103. [PMID: 34525624 DOI: 10.1103/physreve.104.024103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Accepted: 07/14/2021] [Indexed: 11/07/2022]
Abstract
We study the effects of roughness in the asymmetric periodic potential on the transport and diffusion of an inertial Brownian particle driven by a time-periodic force in a Gaussian environment. We find that moderate roughness leads to the loss of transient anomalous diffusion, and it helps to establish normal diffusion in the weak noise limit. We uncover a contrasting effect of roughness on the transport of particles in the weak and moderate to large noise limit. In the weak noise limit, small amplitude roughness results in the increase of directed transport, whereas in the moderate to large noise limit, roughness hinders transport. The deterministic dynamics of the system reveals that the purely periodic system under smooth potential transits into a chaotic system due to the moderate roughness in the potential. Therefore our calculations demonstrate the constructive role of roughness in the transport of particles in the inertial regime.
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Affiliation(s)
- Archana G R
- School of Chemistry, University of Hyderabad, Gachibowli, 500046, Hyderabad, India
| | - Debashis Barik
- School of Chemistry, University of Hyderabad, Gachibowli, 500046, Hyderabad, India
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Sun ZY, Yu X. Anomalous diffusion of discrete solitons driven by evolving disorder. Phys Rev E 2020; 101:062211. [PMID: 32688546 DOI: 10.1103/physreve.101.062211] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Accepted: 06/02/2020] [Indexed: 06/11/2023]
Abstract
Anomalous diffusion is simulated in this paper by studying the transport of discrete solitons in a lattice with evolving disorder. We find a Richardson-type diffusion for the small solitons and a regime of transient diffusion for larger solitons within the ensemble-averaged description. As a comparison, the time-averaged observables present a ballistic scaling for both cases. However, distribution of these observables changes remarkably with the soliton size. Our results suggest violation of ergodicity for the solitons' diffusive processes, which are expected to shed light on further understanding of the discreteness-disorder-nonlinearity interaction.
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Affiliation(s)
- Zhi-Yuan Sun
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
- International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China
| | - Xin Yu
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
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Spiechowicz J, Łuczka J. Diffusion in a biased washboard potential revisited. Phys Rev E 2020; 101:032123. [PMID: 32289947 DOI: 10.1103/physreve.101.032123] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Accepted: 03/03/2020] [Indexed: 06/11/2023]
Abstract
The celebrated Sutherland-Einstein relation for systems at thermal equilibrium states that spread of trajectories of Brownian particles is an increasing function of temperature. Here, we scrutinize the diffusion of underdamped Brownian motion in a biased periodic potential and analyze regimes in which a diffusion coefficient decreases with increasing temperature within a finite temperature window. Comprehensive numerical simulations of the corresponding Langevin equation performed with unprecedented resolution allow us to construct a phase diagram for the occurrence of the nonmonotonic temperature dependence of the diffusion coefficient. We discuss the relation of the later effect with the phenomenon of giant diffusion.
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Affiliation(s)
- J Spiechowicz
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Łuczka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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Marchenko IG, Marchenko II, Zhiglo AV. Enhanced diffusion with abnormal temperature dependence in underdamped space-periodic systems subject to time-periodic driving. Phys Rev E 2018; 97:012121. [PMID: 29448473 DOI: 10.1103/physreve.97.012121] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2016] [Indexed: 11/07/2022]
Abstract
We present a study of the diffusion enhancement of underdamped Brownian particles in a one-dimensional symmetric space-periodic potential due to external symmetric time-periodic driving with zero mean. We show that the diffusivity can be enhanced by many orders of magnitude at an appropriate choice of the driving amplitude and frequency. The diffusivity demonstrates abnormal (decreasing) temperature dependence at the driving amplitudes exceeding a certain value. At any fixed driving frequency Ω normal temperature dependence of the diffusivity is restored at low enough temperatures, T<T_{TAD}(Ω)-in contrast with the problem with constant external driving. At fixed temperature at small driving frequency the diffusivity either slowly decreases with Ω, or (at stronger driving) goes through a maximum near Ω_{2}, the reciprocal superdiffusion regime termination time. At high frequencies, between Ω_{2} and a fraction of the oscillation frequency at the potential minimum, the diffusivity is shown to decrease with Ω according to a power law, with the exponent related to the transient superdiffusion exponent. This behavior is found similar for the cases of sinusoidal in time and piecewise constant periodic ("square") driving.
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Affiliation(s)
- I G Marchenko
- NSC "Kharkov Institute of Physics and Technology", 1 Akademicheskaya street, Kharkov 61108, Ukraine and Kharkov National University, 4 Svobody Square, Kharkov 61077, Ukraine
| | - I I Marchenko
- NTU "Kharkov Polytechnic Institute", 21 Frunze street, Kharkov 61145, Ukraine
| | - A V Zhiglo
- NSC "Kharkov Institute of Physics and Technology", 1 Akademicheskaya street, Kharkov 61108, Ukraine and Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
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9
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Subdiffusion via dynamical localization induced by thermal equilibrium fluctuations. Sci Rep 2017; 7:16451. [PMID: 29184075 PMCID: PMC5705761 DOI: 10.1038/s41598-017-16601-0] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2017] [Accepted: 11/15/2017] [Indexed: 12/03/2022] Open
Abstract
We reveal the mechanism of subdiffusion which emerges in a straightforward, one dimensional classical nonequilibrium dynamics of a Brownian ratchet driven by both a time-periodic force and Gaussian white noise. In a tailored parameter set for which the deterministic counterpart is in a non-chaotic regime, subdiffusion is a long-living transient whose lifetime can be many, many orders of magnitude larger than characteristic time scales of the setup thus being amenable to experimental observations. As a reason for this subdiffusive behaviour in the coordinate space we identify thermal noise induced dynamical localization in the velocity (momentum) space. This novel idea is distinct from existing knowledge and has never been reported for any classical or quantum system. It suggests reconsideration of generally accepted opinion that subdiffusion is due to broad distributions or strong correlations which reflect disorder, trapping, viscoelasticity of the medium or geometrical constraints.
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Spiechowicz J, Kostur M, Łuczka J. Brownian ratchets: How stronger thermal noise can reduce diffusion. CHAOS (WOODBURY, N.Y.) 2017; 27:023111. [PMID: 28249406 DOI: 10.1063/1.4976586] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e., a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force that takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as the temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum, and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by the thermal noise, and we explain this effect in terms of transition rates of a three-state stochastic model.
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Affiliation(s)
- Jakub Spiechowicz
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
| | - Marcin Kostur
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
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11
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Menditto R, Sickinger H, Weides M, Kohlstedt H, Koelle D, Kleiner R, Goldobin E. Tunable φ Josephson junction ratchet. Phys Rev E 2016; 94:042202. [PMID: 27841459 DOI: 10.1103/physreve.94.042202] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2016] [Indexed: 06/06/2023]
Abstract
We demonstrate experimentally the operation of a deterministic Josephson ratchet with tunable asymmetry. The ratchet is based on a φ Josephson junction with a ferromagnetic barrier operating in the underdamped regime. The system is probed also under the action of an additional dc current, which acts as a counterforce trying to stop the ratchet. Under these conditions the ratchet works against the counterforce, thus producing a nonzero output power. Finally, we estimate the efficiency of the φ Josephson junction ratchet.
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Affiliation(s)
- R Menditto
- Physikalisches Institut and Center for Quantum Science in LISA+, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany
| | - H Sickinger
- Physikalisches Institut and Center for Quantum Science in LISA+, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany
| | - M Weides
- Physikalisches Institut, Karlsruher Institut für Technologie, D-76128 Karlsruhe, Germany
| | - H Kohlstedt
- Nanoelektronik, Technische Fakultät, Christian-Albrechts-Universität zu Kiel, D-24143 Kiel, Germany
| | - D Koelle
- Physikalisches Institut and Center for Quantum Science in LISA+, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany
| | - R Kleiner
- Physikalisches Institut and Center for Quantum Science in LISA+, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany
| | - E Goldobin
- Physikalisches Institut and Center for Quantum Science in LISA+, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany
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12
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Spiechowicz J, Łuczka J, Hänggi P. Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation. Sci Rep 2016; 6:30948. [PMID: 27492219 PMCID: PMC4974640 DOI: 10.1038/srep30948] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2016] [Accepted: 07/11/2016] [Indexed: 11/18/2022] Open
Abstract
We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases.
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Affiliation(s)
- Jakub Spiechowicz
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
- Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
- Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland
| | - Peter Hänggi
- Institute of Physics, University of Augsburg, 86135 Augsburg, Germany
- Nanosystems Initiative Munich, Schellingstr, 4, D-80799 Műnchen, Germany
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Das M, Das D, Barik D, Ray DS. Landauer's blowtorch effect as a thermodynamic cross process: Brownian cooling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052102. [PMID: 26651642 DOI: 10.1103/physreve.92.052102] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Indexed: 06/05/2023]
Abstract
The local heating of a selected region in a double-well potential alters the relative stability of the two wells and gives rise to an enhancement of population transfer to the cold well. We show that this Landauer's blowtorch effect may be considered in the spirit of a thermodynamic cross process linearly connecting the flux of particles and the thermodynamic force associated with the temperature difference and consequently ensuring the existence of a reverse cross effect. This reverse effect is realized by directing the thermalized particles in a double-well potential by application of an external bias from one well to the other, which suffers cooling.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Debojyoti Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Debashis Barik
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Deb Shankar Ray
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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